From 4a7f2e462d34892aecad650093d577e7a270f15b Mon Sep 17 00:00:00 2001 From: Anthony Scemama Date: Thu, 18 May 2023 19:42:46 +0200 Subject: [PATCH] Added org-mode file --- stochastic_triples.tex | 1 + triples.org | 4639 ++++++++++++++++++++++++++++++++++++++++ 2 files changed, 4640 insertions(+) create mode 100644 triples.org diff --git a/stochastic_triples.tex b/stochastic_triples.tex index 97ad2d1..c82e07c 100644 --- a/stochastic_triples.tex +++ b/stochastic_triples.tex @@ -137,6 +137,7 @@ In the following sections of this paper, we will provide a brief introduction to %a. Explanation of the algorithm's main principles and methodology % - Rewriting with nV in outer-most loops % - Implies summing all permutations of (a,b,c) to avoid extra dgemms +% - Comparison in number of Gflops to theory %b. Description of the stochastic sampling procedure % - Memoization % - Importance function diff --git a/triples.org b/triples.org new file mode 100644 index 0000000..381e5df --- /dev/null +++ b/triples.org @@ -0,0 +1,4639 @@ +#+TITLE: Stochastic perturbative triples + +* Stochastic formulation + +The perturbative correction is expressed as: + + \[ +E_{(T)} = \sum_{ijkabc} E_{ijk}^{abc} = \sum_{ijkabc} \frac{(4 W_{ijk}^{abc} + + W_{ijk}^{bca} + + W_{ijk}^{cab}) + (V_{ijk}^{abc} - V_{ijk}^{cba})}{\epsilon_i + \epsilon_j + \epsilon_k - +\epsilon_a - \epsilon_b - \epsilon_c} + \] + + +If $E_{(T)}$ is computed as + \[ +E_{(T)} = \sum_{ijkabc} \frac{1}{N} \left( E_{ijk}^{abc} \times N \right) + \] +where $N$ is the total number of terms, it can be computed by drawing +uniformly samples $E_{ijk}^{abc}$ and computing the statistical +average. + +The stochastic calculation is unbiased, but the rate of convergence of +the statistical error is be governed by the variance of the +samples. Moreover, the total computational time is proportional to +the number of computed samples. The objective of this work is to +propose a stochastic algorithm which gives an estimate of $E_{(T)}$ +with a small enough statistical error in less time than what is +required for the exact computation. + +* Memoization + +The perturbative correction can be re-expressed as the sum of +corrections indexed only by virtual orbitals: + + \[ +E_{(T)} = \sum_{a,b,c} E_{abc} + \] + +where + +\[ +E_{abc} = \sum_{ijk} E_{ijk}^{abc} + \] + +The Monte Carlo sampling can be made by drawing samples $E_{abc}$. +The great advantage of this re-expression is that the number of +triplets $(a,b,c)$ is $N_v^3$, which is expected to be small enough so +that all contributions $E_{abc}$ can be stored in memory. Therefore, +the first time a triplet $(a,b,c)$ is drawn, it is computed and +stored. Every next time the same triplet is drawn, the value is +fetched from memory. In this way, the $N_o^3 \times N_v$ cost of +computing the sample is paid only once, and all other evaluations are +negligible. + +Hence, using an number of Monte Carlo samples large enough such that each +contribution has been drawn at least once will have a computational +cost larger only by a negligible amount than the cost of making the +exact computation. + +* Importance sampling + +To reduce the variance of the samples, the samples are drawn using the +probability + +\[ +P(a,b,c) = \frac{1}{\mathcal{N}} \frac{1}{\epsilon_{\text{occ}} - \epsilon_a - \epsilon_b - \epsilon_c} +\] + +where $\mathcal{N}$ is such that $\sum P(a,b,c) = 1$, and $\epsilon_{\text{occ}}$ is the average of the energy +contributions of the occupied orbitals: +\[ \epsilon_{\text{occ}} = \frac{3}{N_o} \sum_i \epsilon_i. +\] + +The perturbative contribution is computed as + +\[ + \[ +E_{(T)} = \mathcal{N} \sum_{abc} P(a,b,c) \, E_{abc} \, + (\epsilon_{\text{occ}} - \epsilon_a - \epsilon_b - \epsilon_c) \, + \] + +This modification reduces the statistical error bars by a factor of two +for the same computational cost for two reasons: +1. The estimator has less fluctuations +2. Some triplets are more likely to be drawn than others, so + memoization is even more effective + +* Multiple buckets + +We use the inverse transform sampling technique to draw the +samples, so an array of pairs $( P(a,b,c), (a,b,c) )$ is stored. +To reduce even more the variance of the samples, this array is sorted +in decreasing order of $P(a,b,c)$, and the array is divided into +buckets $B$ where the sum of $P(a,b,c)$ in the same in each bucket. +As all buckets are equiprobable, one can safely generate samples which +are averages of samples drawn from each bucket. If the values of +$E_{abc}$ are skewed, this latest improvement reduces significantly +the variance. + +* Semi-stochastic algorithm + + The total perturbative contribution is the sum of contributions in +the buckets: + +\[ + E_{(T)} = \sum_B E_B = \sum_B\sum_{(a,b,c) \in B} E_{abc} +\] + +When all the triplets of a bucket $B$ have been drawn at least once, the +contribution $E_B$ can be computed. Then, there is no need to evaluate +$E_B$ stochastically and we can separate the buckets into stochastic +($\mathcal{S}$) and deterministic ($\mathcal{D}$) buckets: + +\[ +E_{(T)} = \sum_{B \in \mathcal{D}} E_B + \frac{1}{|\mathcal{S}|} \sum_{B \in \mathcal{S}} +\left \langle E^B_{abc} \times \frac{\epsilon_{\text{occ}} - +\epsilon_a - \epsilon_b - \epsilon_c}{\mathcal{N}} \right \rangle_{P(a,b,c), (a,b,c) \in B} +\] + +All the buckets don't have the same size: the number of triplets per +bucket is decreasing with the index of the bucket. So the first +buckets enter into the deterministic set first, and the stochastic +contribution becomes smaller and smaller. When all the triplets have +been drawn, the exact value is obtained without any statistical error. + +To accelerate the filling of the buckets, at every Monte Carlo +iteration we trigger the computation of the first non-computed +triplet. Hence, after $N$ drawings we are sure to have computed the +exact contribution. + +* Test code + + #+begin_src python :results output :session +import numpy as np +import gzip +import time + +ev_to_h = 0.03674930813664888 + #+end_src + + #+RESULTS: + + The gzipped input file ~h2o_qz.gz~ contains data for the computation + of the valence perturbative triples correction of the water molecule + in the cc-pVQZ basis set. + Each line is composed of $a$, $b$, $c$, $(\epsilon_a + \epsilon_b + \epsilon_c)$ and $3\times E_{abc}$. + + #+begin_src python :session +#TODO +#filetype=0 +#filename = "h2o_qz.gz" + +filetype=1 +#filename = "UEG/nelec-14-norb-147.out.gz" +#filename = "UEG/nelec-38-norb-341.out.gz" +filename = "HBN/hbn.out.gz" +#filename = "HBN/hbn-36-176.out.gz" + +denom = [] +eabc = [] +triplets = [] + +with gzip.open(filename, 'r') as f: + if filetype == 0: + for line in f: + a, b, c, d, e = line.split() + triplets.append( [int(a),int(b),int(c)] ) + denom.append(float(d)) + eabc.append(float(e)/3.) + + else: + for line in f: + a, b, c, d, e = line.split() + triplets.append( [int(a),int(b),int(c)] ) + denom.append(float(d)*ev_to_h) + eabc.append(-float(e)*ev_to_h) + +triplets = np.array(triplets) +denom = np.array(denom) +eabc = np.array(eabc) + #+end_src + + #+RESULTS: + + The exact contribution is the sum of all $E_{abc}$: + + #+NAME: e_ref + #+begin_src python :session +Nabc = int(len(eabc)) +sum(eabc) + #+end_src + + #+RESULTS: e_ref + : -0.03022743231272565 + +** Orbital energies + +*** Occupied + + The energies of the occupied orbitals are required to compute + $\epsilon_{\text{occ}}$: + + #+NAME:orb_energies-h2o + | 1 | -1.3495166001 | + | 2 | -0.7144028522 | + | 3 | -0.5819477116 | + | 4 | -0.5081442470 | + + #+NAME:orb_energies-14 + | 1 | -0.40729666 | + | 2 | -0.18688829 | + | 3 | -0.18688829 | + | 4 | -0.18688829 | + | 5 | -0.18688829 | + | 6 | -0.18688829 | + | 7 | -0.18688829 | + + #+NAME:orb_energies-38 + | 1 | -0.40945392 | + | 2 | -0.28354874 | + | 3 | -0.28354874 | + | 4 | -0.28354874 | + | 5 | -0.28354874 | + | 6 | -0.28354874 | + | 7 | -0.28354874 | + | 8 | -0.15943825 | + | 9 | -0.15943825 | + | 10 | -0.15943825 | + | 11 | -0.15943825 | + | 12 | -0.15943825 | + | 13 | -0.15943825 | + | 14 | -0.15943825 | + | 15 | -0.15943825 | + | 16 | -0.15943825 | + | 17 | -0.15943825 | + | 18 | -0.15943825 | + | 19 | -0.15943825 | + + #+NAME:orb_energies-hbn + | 1 | -0.93953654 | + | 2 | -0.92121891 | + | 3 | -0.78505256 | + | 4 | -0.77976882 | + | 5 | -0.48653647 | + | 6 | -0.47973909 | + | 7 | -0.33857221 | + | 8 | -0.30326521 | + | 9 | -0.30034533 | + | 10 | -0.22859891 | + | 11 | -0.18754927 | + | 12 | -0.18606588 | + | 13 | -0.15297849 | + | 14 | -0.15148893 | + | 15 | -0.12146057 | + | 16 | -0.084733892 | + + #+NAME:orb_energies-hbn-36 + | 1 | -0.93323231 | + | 2 | -0.91493460 | + | 3 | -0.77878864 | + | 4 | -0.77351063 | + | 5 | -0.48043513 | + | 6 | -0.47364310 | + | 7 | -0.33220283 | + | 8 | -0.29719087 | + | 9 | -0.29425309 | + | 10 | -0.22234047 | + | 11 | -0.18186670 | + | 12 | -0.18043512 | + | 13 | -0.14726115 | + | 14 | -0.14582101 | + | 15 | -0.11539548 | + | 16 | -0.078697018 | + + #+TBLFM: $3=$2*0.03674930813664888 + #+TBLFM: $1=@# + +*** Virtual + + The energies of the virtual orbitals are required for the importance + sampling function $\epsilon_{\text{vir}}$: + + #+NAME:vir_energies-h2o + | 1 | 0.1170780927 | + | 2 | 0.1710190904 | + | 3 | 0.4494673807 | + | 4 | 0.4621202460 | + | 5 | 0.5016951241 | + | 6 | 0.5836694028 | + | 7 | 0.6051947963 | + | 8 | 0.6146697086 | + | 9 | 0.6565051177 | + | 10 | 0.7182063878 | + | 11 | 0.8516191972 | + | 12 | 0.9198243228 | + | 13 | 1.1120958387 | + | 14 | 1.1574553944 | + | 15 | 1.3462327164 | + | 16 | 1.4165525262 | + | 17 | 1.4800979932 | + | 18 | 1.4849525169 | + | 19 | 1.5786053722 | + | 20 | 1.6868289625 | + | 21 | 1.9114339643 | + | 22 | 2.0688122674 | + | 23 | 2.1955484330 | + | 24 | 2.2920067741 | + | 25 | 2.3622513733 | + | 26 | 2.4242696557 | + | 27 | 2.4882741718 | + | 28 | 2.5209123081 | + | 29 | 2.5830337542 | + | 30 | 2.5867616694 | + | 31 | 2.6542316478 | + | 32 | 2.6703494422 | + | 33 | 2.8415133159 | + | 34 | 2.8617578839 | + | 35 | 3.0383168770 | + | 36 | 3.1276003251 | + | 37 | 3.2948068036 | + | 38 | 3.3464975106 | + | 39 | 3.4589491034 | + | 40 | 3.6284221842 | + | 41 | 3.8256509147 | + | 42 | 4.0020447839 | + | 43 | 4.1256277268 | + | 44 | 4.1867673535 | + | 45 | 4.2141487650 | + | 46 | 4.4362998361 | + | 47 | 4.4947291066 | + | 48 | 4.7060661936 | + | 49 | 4.7521034075 | + | 50 | 4.7996510056 | + | 51 | 4.9280320715 | + | 52 | 5.3624272963 | + | 53 | 5.4026006683 | + | 54 | 5.9752399036 | + | 55 | 6.1056730507 | + | 56 | 6.2495153622 | + | 57 | 6.3165406593 | + | 58 | 6.7312795276 | + | 59 | 6.7921966285 | + | 60 | 7.0753837689 | + | 61 | 7.2750220790 | + | 62 | 7.3155097230 | + | 63 | 7.3689101210 | + | 64 | 7.4373090211 | + | 65 | 7.5364710135 | + | 66 | 7.5557420909 | + | 67 | 7.5687553410 | + | 68 | 7.9995654839 | + | 69 | 8.0806018979 | + | 70 | 8.0989771117 | + | 71 | 8.1437725027 | + | 72 | 8.1500310933 | + | 73 | 8.2750489171 | + | 74 | 8.3193045638 | + | 75 | 8.3573477176 | + | 76 | 8.4311162300 | + | 77 | 8.6177564754 | + | 78 | 8.8437328029 | + | 79 | 8.9093818035 | + | 80 | 8.9656095271 | + | 81 | 9.2370137178 | + | 82 | 9.3925685769 | + | 83 | 9.4140146116 | + | 84 | 9.9230302951 | + | 85 | 10.0156977150 | + | 86 | 10.2889761593 | + | 87 | 10.4424540894 | + | 88 | 10.6589001318 | + | 89 | 10.7573224755 | + | 90 | 10.8181869588 | + | 91 | 11.2934414670 | + | 92 | 11.4080819018 | + | 93 | 11.6045421043 | + | 94 | 11.6427826465 | + | 95 | 11.7038554829 | + | 96 | 11.8458216549 | + | 97 | 12.1936857310 | + | 98 | 12.3399716139 | + | 99 | 12.4248976056 | + | 100 | 12.4326416584 | + | 101 | 12.4615374955 | + | 102 | 13.6268899965 | + | 103 | 13.8184890674 | + | 104 | 14.2866145595 | + | 105 | 14.6487775661 | + | 106 | 14.6790346791 | + | 107 | 14.8758761065 | + | 108 | 16.4564806016 | + | 109 | 16.8432677225 | + | 110 | 44.3828489701 | + + + #+NAME:vir_energies-14 + | 1 | 0.19320282 | + | 2 | 0.19320282 | + | 3 | 0.19320282 | + | 4 | 0.19320282 | + | 5 | 0.19320282 | + | 6 | 0.19320282 | + | 7 | 0.19320282 | + | 8 | 0.19320282 | + | 9 | 0.19320282 | + | 10 | 0.19320282 | + | 11 | 0.19320282 | + | 12 | 0.19320282 | + | 13 | 0.37219048 | + | 14 | 0.37219048 | + | 15 | 0.37219048 | + | 16 | 0.37219048 | + | 17 | 0.37219048 | + | 18 | 0.37219048 | + | 19 | 0.37219048 | + | 20 | 0.37219048 | + | 21 | 0.52219882 | + | 22 | 0.52219882 | + | 23 | 0.52219882 | + | 24 | 0.52219882 | + | 25 | 0.52219882 | + | 26 | 0.52219882 | + | 27 | 0.68533129 | + | 28 | 0.68533129 | + | 29 | 0.68533129 | + | 30 | 0.68533129 | + | 31 | 0.68533129 | + | 32 | 0.68533129 | + | 33 | 0.68533129 | + | 34 | 0.68533129 | + | 35 | 0.68533129 | + | 36 | 0.68533129 | + | 37 | 0.68533129 | + | 38 | 0.68533129 | + | 39 | 0.68533129 | + | 40 | 0.68533129 | + | 41 | 0.68533129 | + | 42 | 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| 128 | 0.70752745 | + | 129 | 0.78589516 | + | 130 | 0.78589516 | + | 131 | 0.78589516 | + | 132 | 0.78589516 | + | 133 | 0.78589516 | + | 134 | 0.78589516 | + | 135 | 0.78589516 | + | 136 | 0.78589516 | + | 137 | 0.78589516 | + | 138 | 0.78589516 | + | 139 | 0.78589516 | + | 140 | 0.78589516 | + | 141 | 0.78589516 | + | 142 | 0.78589516 | + | 143 | 0.78589516 | + | 144 | 0.78589516 | + | 145 | 0.78589516 | + | 146 | 0.78589516 | + | 147 | 0.78589516 | + | 148 | 0.78589516 | + | 149 | 0.78589516 | + | 150 | 0.78589516 | + | 151 | 0.78589516 | + | 152 | 0.78589516 | + | 153 | 0.86364035 | + | 154 | 0.86364035 | + | 155 | 0.86364035 | + | 156 | 0.86364035 | + | 157 | 0.86364035 | + | 158 | 0.86364035 | + | 159 | 0.86364035 | + | 160 | 0.86364035 | + | 161 | 0.94081079 | + | 162 | 0.94081079 | + | 163 | 0.94081079 | + | 164 | 0.94081079 | + | 165 | 0.94081079 | + | 166 | 0.94081079 | + | 167 | 0.94081079 | + | 168 | 0.94081079 | + | 169 | 0.94081079 | + | 170 | 0.94081079 | + | 171 | 0.94081079 | + | 172 | 0.94081079 | + | 173 | 0.94081079 | + | 174 | 0.94081079 | + | 175 | 0.94081079 | + | 176 | 0.94081079 | + | 177 | 0.94081079 | + | 178 | 0.94081079 | + | 179 | 0.94081079 | + | 180 | 0.94081079 | + | 181 | 0.94081079 | + | 182 | 0.94081079 | + | 183 | 0.94081079 | + | 184 | 0.94081079 | + | 185 | 1.0177694 | + | 186 | 1.0177694 | + | 187 | 1.0177694 | + | 188 | 1.0177694 | + | 189 | 1.0177694 | + | 190 | 1.0177694 | + | 191 | 1.0177694 | + | 192 | 1.0177694 | + | 193 | 1.0177694 | + | 194 | 1.0177694 | + | 195 | 1.0177694 | + | 196 | 1.0177694 | + | 197 | 1.0177694 | + | 198 | 1.0177694 | + | 199 | 1.0177694 | + | 200 | 1.0177694 | + | 201 | 1.0177694 | + | 202 | 1.0177694 | + | 203 | 1.0177694 | + | 204 | 1.0177694 | + | 205 | 1.0177694 | + | 206 | 1.0177694 | + | 207 | 1.0177694 | + | 208 | 1.0177694 | + | 209 | 1.0177694 | + | 210 | 1.0177694 | + | 211 | 1.0177694 | + | 212 | 1.0177694 | + | 213 | 1.0177694 | + | 214 | 1.0177694 | + | 215 | 1.0177694 | + | 216 | 1.0177694 | + | 217 | 1.0177694 | + | 218 | 1.0177694 | + | 219 | 1.0177694 | + | 220 | 1.0177694 | + | 221 | 1.0177694 | + | 222 | 1.0177694 | + | 223 | 1.0177694 | + | 224 | 1.0177694 | + | 225 | 1.0177694 | + | 226 | 1.0177694 | + | 227 | 1.0177694 | + | 228 | 1.0177694 | + | 229 | 1.0177694 | + | 230 | 1.0177694 | + | 231 | 1.0177694 | + | 232 | 1.0177694 | + | 233 | 1.1708206 | + | 234 | 1.1708206 | + | 235 | 1.1708206 | + | 236 | 1.1708206 | + | 237 | 1.1708206 | + | 238 | 1.1708206 | + | 239 | 1.2468683 | + | 240 | 1.2468683 | + | 241 | 1.2468683 | + | 242 | 1.2468683 | + | 243 | 1.2468683 | + | 244 | 1.2468683 | + | 245 | 1.2468683 | + | 246 | 1.2468683 | + | 247 | 1.2468683 | + | 248 | 1.2468683 | + | 249 | 1.2468683 | + | 250 | 1.2468683 | + | 251 | 1.2468683 | + | 252 | 1.2468683 | + | 253 | 1.2468683 | + | 254 | 1.2468683 | + | 255 | 1.2468683 | + | 256 | 1.2468683 | + | 257 | 1.2468683 | + | 258 | 1.2468683 | + | 259 | 1.2468683 | + | 260 | 1.2468683 | + | 261 | 1.2468683 | + | 262 | 1.2468683 | + | 263 | 1.2469208 | + | 264 | 1.2469208 | + | 265 | 1.2469208 | + | 266 | 1.2469208 | + | 267 | 1.2469208 | + | 268 | 1.2469208 | + | 269 | 1.2469208 | + | 270 | 1.2469208 | + | 271 | 1.2469208 | + | 272 | 1.2469208 | + | 273 | 1.2469208 | + | 274 | 1.2469208 | + | 275 | 1.2469208 | + | 276 | 1.2469208 | + | 277 | 1.2469208 | + | 278 | 1.2469208 | + | 279 | 1.2469208 | + | 280 | 1.2469208 | + | 281 | 1.2469208 | + | 282 | 1.2469208 | + | 283 | 1.2469208 | + | 284 | 1.2469208 | + | 285 | 1.2469208 | + | 286 | 1.2469208 | + | 287 | 1.3228043 | + | 288 | 1.3228043 | + | 289 | 1.3228043 | + | 290 | 1.3228043 | + | 291 | 1.3228043 | + | 292 | 1.3228043 | + | 293 | 1.3228043 | + | 294 | 1.3228043 | + | 295 | 1.3228043 | + | 296 | 1.3228043 | + | 297 | 1.3228043 | + | 298 | 1.3228043 | + | 299 | 1.3228723 | + | 300 | 1.3228723 | + | 301 | 1.3228723 | + | 302 | 1.3228723 | + | 303 | 1.3228723 | + | 304 | 1.3228723 | + | 305 | 1.3228723 | + | 306 | 1.3228723 | + | 307 | 1.3228723 | + | 308 | 1.3228723 | + | 309 | 1.3228723 | + | 310 | 1.3228723 | + | 311 | 1.3228723 | + | 312 | 1.3228723 | + | 313 | 1.3228723 | + | 314 | 1.3228723 | + | 315 | 1.3228723 | + | 316 | 1.3228723 | + | 317 | 1.3228723 | + | 318 | 1.3228723 | + | 319 | 1.3228723 | + | 320 | 1.3228723 | + | 321 | 1.3228723 | + | 322 | 1.3228723 | + + + #+NAME:vir_energies-hbn + | 1 | 0.46523374 | + | 2 | 0.47190413 | + | 3 | 0.52766278 | + | 4 | 0.75894665 | + | 5 | 0.79372894 | + | 6 | 0.81533720 | + | 7 | 0.85502910 | + | 8 | 0.85996841 | + | 9 | 0.86164099 | + | 10 | 0.87081777 | + | 11 | 0.92274576 | + | 12 | 0.93485125 | + | 13 | 0.98156862 | + | 14 | 0.98258918 | + | 15 | 0.98352706 | + | 16 | 1.0139348 | + | 17 | 1.1023545 | + | 18 | 1.1149920 | + | 19 | 1.2342007 | + | 20 | 1.2570760 | + | 21 | 1.2905259 | + | 22 | 1.3642916 | + | 23 | 1.3661178 | + | 24 | 1.4402250 | + | 25 | 1.5383045 | + | 26 | 1.5553226 | + | 27 | 1.6069830 | + | 28 | 1.6114899 | + | 29 | 1.6612452 | + | 30 | 1.6830711 | + | 31 | 1.7813984 | + | 32 | 1.8183162 | + | 33 | 1.8190747 | + | 34 | 1.8305486 | + | 35 | 1.8460614 | + | 36 | 1.8723801 | + | 37 | 2.0206319 | + | 38 | 2.0432636 | + | 39 | 2.0757063 | + | 40 | 2.1004740 | + | 41 | 2.1054700 | + | 42 | 2.1063651 | + | 43 | 2.2238620 | + | 44 | 2.2446128 | + | 45 | 2.3007112 | + | 46 | 2.3328563 | + | 47 | 2.4020334 | + | 48 | 2.4188139 | + | 49 | 2.4204084 | + | 50 | 2.4650720 | + | 51 | 2.5651099 | + | 52 | 2.7104512 | + | 53 | 2.7373724 | + | 54 | 2.7437489 | + | 55 | 2.8547023 | + | 56 | 2.8580549 | + | 57 | 2.8726837 | + | 58 | 2.9212925 | + | 59 | 2.9333791 | + | 60 | 2.9595462 | + | 61 | 2.9712978 | + | 62 | 2.9781069 | + | 63 | 2.9805534 | + | 64 | 3.0321222 | + | 65 | 3.0844009 | + | 66 | 3.0880791 | + | 67 | 3.1729389 | + | 68 | 3.1765382 | + | 69 | 3.2249290 | + | 70 | 3.2617942 | + | 71 | 3.2988499 | + | 72 | 3.5313407 | + | 73 | 3.5900472 | + | 74 | 3.5924177 | + | 75 | 3.7169678 | + | 76 | 3.7567167 | + | 77 | 3.8425762 | + | 78 | 3.8658065 | + | 79 | 3.8664628 | + | 80 | 3.9456514 | + + + #+NAME:vir_energies-hbn-36 + | 1 | 0.45821960 | + | 2 | 0.45955397 | + | 3 | 0.52417218 | + | 4 | 0.75814810 | + | 5 | 0.76944736 | + | 6 | 0.79918247 | + | 7 | 0.83833757 | + | 8 | 0.84234429 | + | 9 | 0.84624883 | + | 10 | 0.84773610 | + | 11 | 0.86555326 | + | 12 | 0.90752856 | + | 13 | 0.91381841 | + | 14 | 0.93078158 | + | 15 | 0.94927271 | + | 16 | 1.0019894 | + | 17 | 1.0516346 | + | 18 | 1.0603957 | + | 19 | 1.1622263 | + | 20 | 1.2124273 | + | 21 | 1.2251086 | + | 22 | 1.2669459 | + | 23 | 1.3119527 | + | 24 | 1.3236910 | + | 25 | 1.4020074 | + | 26 | 1.4180400 | + | 27 | 1.4247132 | + | 28 | 1.4252123 | + | 29 | 1.4343132 | + | 30 | 1.4943183 | + | 31 | 1.5538082 | + | 32 | 1.5739816 | + | 33 | 1.5797415 | + | 34 | 1.5878624 | + | 35 | 1.6135695 | + | 36 | 1.6136001 | + | 37 | 1.6199772 | + | 38 | 1.6589831 | + | 39 | 1.7186777 | + | 40 | 1.7815760 | + | 41 | 1.8076690 | + | 42 | 1.8148269 | + | 43 | 1.8396877 | + | 44 | 1.8671517 | + | 45 | 1.8879163 | + | 46 | 1.9024199 | + | 47 | 1.9776692 | + | 48 | 1.9806444 | + | 49 | 2.0328782 | + | 50 | 2.0402167 | + | 51 | 2.0535394 | + | 52 | 2.1583521 | + | 53 | 2.2173123 | + | 54 | 2.2298141 | + | 55 | 2.2445000 | + | 56 | 2.2944750 | + | 57 | 2.3297962 | + | 58 | 2.3424792 | + | 59 | 2.3443938 | + | 60 | 2.3605343 | + | 61 | 2.4364144 | + | 62 | 2.4587039 | + | 63 | 2.4595817 | + | 64 | 2.5735021 | + | 65 | 2.5857946 | + | 66 | 2.6315694 | + | 67 | 2.6660058 | + | 68 | 2.6670340 | + | 69 | 2.7380125 | + | 70 | 2.8020294 | + | 71 | 2.8441878 | + | 72 | 2.8727076 | + | 73 | 2.8830104 | + | 74 | 2.9157291 | + | 75 | 2.9276150 | + | 76 | 2.9350208 | + | 77 | 2.9790396 | + | 78 | 3.0588475 | + | 79 | 3.1333010 | + | 80 | 3.1380314 | + | 81 | 3.1675500 | + | 82 | 3.1780752 | + | 83 | 3.1878095 | + | 84 | 3.2247691 | + | 85 | 3.2446009 | + | 86 | 3.2626894 | + | 87 | 3.3304832 | + | 88 | 3.3478010 | + | 89 | 3.4550268 | + | 90 | 3.4889406 | + | 91 | 3.5369474 | + | 92 | 3.5465361 | + | 93 | 3.5513747 | + | 94 | 3.5521487 | + | 95 | 3.5986419 | + | 96 | 3.6403020 | + | 97 | 3.7330773 | + | 98 | 3.7426986 | + | 99 | 3.8073074 | + | 100 | 3.8372094 | + | 101 | 3.8411368 | + | 102 | 3.8413932 | + | 103 | 3.8451913 | + | 104 | 3.8725514 | + | 105 | 3.9332957 | + | 106 | 3.9460972 | + | 107 | 3.9506332 | + | 108 | 3.9697667 | + | 109 | 3.9830317 | + | 110 | 4.0843935 | + | 111 | 4.1546720 | + | 112 | 4.1606148 | + | 113 | 4.1872647 | + | 114 | 4.1948277 | + | 115 | 4.1983197 | + | 116 | 4.2076585 | + | 117 | 4.2141985 | + | 118 | 4.2384778 | + | 119 | 4.2905590 | + | 120 | 4.3597337 | + | 121 | 4.4268950 | + | 122 | 4.4429214 | + | 123 | 4.4447499 | + | 124 | 4.4831871 | + | 125 | 4.4875016 | + | 126 | 4.5399434 | + | 127 | 4.5508515 | + | 128 | 4.5755937 | + | 129 | 4.5866014 | + | 130 | 4.7271287 | + | 131 | 4.7297052 | + | 132 | 4.7502066 | + | 133 | 4.7600181 | + | 134 | 4.7745013 | + | 135 | 4.8402334 | + | 136 | 4.8438511 | + | 137 | 4.8754985 | + | 138 | 4.8769072 | + | 139 | 4.9093041 | + | 140 | 4.9869284 | + | 141 | 4.9905789 | + | 142 | 4.9981826 | + | 143 | 5.0028200 | + | 144 | 5.0579505 | + | 145 | 5.0811681 | + | 146 | 5.1274989 | + | 147 | 5.1731798 | + | 148 | 5.2753752 | + | 149 | 5.2894543 | + | 150 | 5.2915312 | + | 151 | 5.3884059 | + | 152 | 5.4042175 | + | 153 | 5.4225445 | + | 154 | 5.5326874 | + | 155 | 5.5802786 | + | 156 | 5.6484393 | + | 157 | 5.7163910 | + | 158 | 5.7426619 | + | 159 | 5.9004863 | + | 160 | 6.0031234 | + + #+TBLFM: $1=@# + #+TBLFM: $3=$2*0.03674930813664888 + +*** Code + + # TODO TODO + #+NAME: e_occ + #+begin_src python :var orb_energies=orb_energies-hbn :var vir_energies=vir_energies-hbn :session +epsilon = np.array(orb_energies)[:,1] +epsilon_v = np.array(vir_energies)[:,1] +e_occ = 3.*sum(epsilon)/len(epsilon) +e_occ + #+end_src + + #+RESULTS: e_occ + : -1.208795827875 + +** Uniform distribution + + Below is a simple code which computes the stochastic average with a + uniform sampling. Each unit of time corresponds to the computation + of a $E_{abc}$ contribution. The output is a table containing the + time, the running average and the statistical error. + + The maximum running time for the computation of the exact quantity + is $N_v^3$ = src_python[:session]{len(eabc)}. + + + #+begin_src python :session +date = 0 # Current time: increments when a new triplet is computed +ET = 0. # Accumulator +ET2 = 0. # Accumulator of E^2 for variance +computed = np.zeros(len(eabc)) # If true, the (a,b,c) triplet has already + # been computed +result = {} + +isample = 0 +time0 = time.time() +while date < Nabc*0.99: + if time.time() - time0 > 60.: break + isample += 1 + eta = np.random.uniform() # Random number between 0 and 1 + abc = int(eta * Nabc) # Triplet (a,b,c) drawn + s = eabc[abc] * Nabc + if computed[abc] == 0: + computed[abc] = 1 + date += 1 + ET += s + ET2 += s*s + if date % int(Nabc/100) == 0: + average = ET/isample + variance = ET2/isample - average*average + result[date/Nabc] = (average, np.sqrt(variance/(isample-1))) + +[ ("%.3f"%k, v1, v2) for (k, (v1, v2)) in result.items() ] + #+end_src + + #+NAME:data_uniform + #+RESULTS: + | 0.010 | -0.03437642645957338 | 0.0030753630637821525 | + | 0.020 | -0.03196781983908248 | 0.001837822949804852 | + | 0.030 | -0.03177580311852873 | 0.001720127332029026 | + | 0.040 | -0.032298975146952 | 0.001428537377973462 | + | 0.050 | -0.031126606689641206 | 0.001185117590763498 | + | 0.060 | -0.030516572686857285 | 0.001022406320141158 | + | 0.070 | -0.03031613476271244 | 0.0009134000426629288 | + | 0.080 | -0.030158573217771642 | 0.0008258298216325343 | + | 0.090 | -0.029933996997862877 | 0.0007575679186364425 | + | 0.100 | -0.029939102663094793 | 0.0007449215086748057 | + | 0.110 | -0.03027078211599003 | 0.0007190676006701886 | + | 0.120 | -0.030412162274688476 | 0.000685566251636473 | + | 0.130 | -0.030270750417570543 | 0.0006430858167234617 | + | 0.140 | -0.030498507348269383 | 0.0006158540830116521 | + | 0.150 | -0.030490507925363328 | 0.0005906102179915185 | + | 0.160 | -0.030518954198717314 | 0.0005703431837634973 | + | 0.170 | -0.030213640271687846 | 0.0005409517176894218 | + | 0.180 | -0.030258679245643547 | 0.0005253652905405611 | + | 0.190 | -0.030333274426206692 | 0.0005198998863964522 | + | 0.200 | -0.0302733911551464 | 0.0005005950671897297 | + | 0.210 | -0.03026559364033272 | 0.0004825220030277329 | + | 0.220 | -0.03025586551613391 | 0.0004697550023708562 | + | 0.230 | -0.030302109366235522 | 0.0004642042573853746 | + | 0.240 | -0.030334648269316054 | 0.0004512365616056368 | + | 0.250 | -0.030361980739061295 | 0.00043886764696707026 | + | 0.260 | -0.030283750363813 | 0.0004275759671604114 | + | 0.270 | -0.03019387833526731 | 0.00041502890927369997 | + | 0.280 | -0.030136619610862777 | 0.00040250878507234827 | + | 0.290 | -0.030268317789462457 | 0.0003982341164866337 | + | 0.300 | -0.030181731817639737 | 0.0003874278989981271 | + | 0.310 | -0.030301090062314424 | 0.0003846766981229691 | + | 0.320 | -0.030181632844130373 | 0.0003735298694478283 | + | 0.330 | -0.030346788080401393 | 0.00037055227897075124 | + | 0.340 | -0.030321083505389944 | 0.0003625084242273785 | + | 0.350 | -0.03031844120867735 | 0.000356806596366249 | + | 0.360 | -0.03035148716708672 | 0.0003506711400078661 | + | 0.370 | -0.030277830709765356 | 0.000342171531867949 | + | 0.380 | -0.030378816651894357 | 0.00033986289765587766 | + | 0.390 | -0.030365402689548193 | 0.00033692599619419145 | + | 0.400 | -0.030354069178420165 | 0.0003304829598541888 | + | 0.410 | -0.03035383639056811 | 0.0003244053095678985 | + | 0.420 | -0.030471269175802472 | 0.00032212755052154384 | + | 0.430 | -0.030418257107866987 | 0.00031449404856775384 | + | 0.440 | -0.030474283193158074 | 0.00030961993631343425 | + | 0.450 | -0.03040771869558633 | 0.0003028770206064099 | + | 0.460 | -0.03043384154552774 | 0.0002986987882455902 | + | 0.470 | -0.03039059595415329 | 0.0002931504370002957 | + | 0.480 | -0.030399559731904162 | 0.0002914390291029102 | + | 0.490 | -0.03040840624488255 | 0.0002871330399747792 | + | 0.500 | -0.030433618775920112 | 0.0002831855505470479 | + | 0.510 | -0.030391034199860004 | 0.0002784795162104784 | + | 0.520 | -0.030423899086325607 | 0.0002743308344880197 | + | 0.530 | -0.030444941603789376 | 0.00027245899521168617 | + | 0.540 | -0.03041330750788333 | 0.00026863589194129245 | + | 0.550 | -0.030443843453372817 | 0.0002647887384537327 | + | 0.559 | -0.030395222302231326 | 0.0002601415325019499 | + | 0.569 | -0.03038575991898126 | 0.0002560350009762799 | + | 0.579 | -0.030397495421124035 | 0.0002527936986919491 | + | 0.589 | -0.03035703357086474 | 0.00024921038282965305 | + | 0.599 | -0.030367073503388766 | 0.00024530800378388815 | + | 0.609 | -0.03034865292438221 | 0.00024057255779665634 | + | 0.619 | -0.030347539456847126 | 0.00023759795719966657 | + | 0.629 | -0.03036816530066652 | 0.00023386406758813552 | + | 0.639 | -0.030309451544814934 | 0.0002309476317856454 | + | 0.649 | -0.03028625725934087 | 0.0002285039730992457 | + | 0.659 | -0.030283171113352016 | 0.00022505030956627053 | + | 0.669 | -0.030216545004483557 | 0.00022075959106823286 | + | 0.679 | -0.03018791803686861 | 0.000216409617148716 | + | 0.689 | -0.030130871402653105 | 0.00021274698033747194 | + | 0.699 | -0.030153535988059074 | 0.00020996270408764868 | + | 0.709 | -0.030168044632427723 | 0.0002072153449956144 | + | 0.719 | -0.03015132154087348 | 0.00020371937659283525 | + | 0.729 | -0.03014144950971066 | 0.00020003627563828567 | + | 0.739 | -0.030186887963037024 | 0.00019794215640513352 | + | 0.749 | -0.030190200081583077 | 0.00019445302614139054 | + | 0.759 | -0.03018461151070908 | 0.00019183973114613275 | + | 0.769 | -0.03015529655509179 | 0.00018896773795239234 | + | 0.779 | -0.030134327355261274 | 0.00018637601547252417 | + | 0.789 | -0.03020981162451403 | 0.0001840077069555368 | + | 0.799 | -0.030186994680259767 | 0.0001818700167991961 | + | 0.809 | -0.030213376244598432 | 0.00018020714866842657 | + | 0.819 | -0.030183390128740703 | 0.00017697198221723528 | + | 0.829 | -0.030188624472397507 | 0.00017415838147679145 | + | 0.839 | -0.030213048689140157 | 0.0001718757355807843 | + | 0.849 | -0.030212269469307065 | 0.0001688540171202461 | + | 0.859 | -0.03023028482655304 | 0.00016658369092061525 | + | 0.869 | -0.03025162562379045 | 0.00016327923756701636 | + | 0.879 | -0.030271262286699296 | 0.00016065941240476654 | + | 0.889 | -0.03024066238325353 | 0.00015672825220353865 | + | 0.899 | -0.030180757283723773 | 0.00015292568557125476 | + | 0.909 | -0.030208761640158285 | 0.00015035198771780757 | + | 0.919 | -0.030197429406441458 | 0.0001473411347540838 | + | 0.929 | -0.03020283963451932 | 0.0001434342057913342 | + | 0.939 | -0.030210225556278718 | 0.0001389552464182351 | + | 0.949 | -0.030208953008535155 | 0.0001355572097081645 | + | 0.959 | -0.030234393661962507 | 0.00013108868970967383 | + | 0.969 | -0.03017826794775221 | 0.00012494937843904978 | + | 0.979 | -0.03019828956553072 | 0.00011867981991075709 | + | 0.989 | -0.03022660358379614 | 0.00010982186878635525 | + +** Importance sampling + +*** Preparation + + Sort the data according to $-1/\Delta \epsilon_o \times 1/\epsilon_a$: + + #+begin_src python :session +def importance_function(i): + ea, eb, ec = epsilon_v[triplets[i,:]-1] +# return -1./denom[i] +# return -1./denom[i]**2 +# return -1./denom[i] * 1./ea + return -1./denom[i] * 1./ea**2 +# return -1./(ea*eb*ec) +# return -1./(ea*eb*ec)**2 +# return -1./denom[i] * ( +# 1./((ea-eb)**2-e_occ) + 1./((ea-ec)**2-e_occ) + 1./((eb-ec)**2-e_occ)) +# return 1. + +to_sort = [] +for i in range(Nabc): + to_sort.append( (importance_function(i), eabc[i], denom[i]) ) +to_sort.sort() + +eabc_sorted = [] +denom_sorted = [] +for (_, y, z) in to_sort: + eabc_sorted.append(y) + denom_sorted.append(z) +denom_sorted = np.array(denom_sorted) +eabc_sorted = np.array(eabc_sorted) + #+end_src + + #+RESULTS: + + + We build the array ~waccu~ which contains $w(x) = \frac{\int_0^x + P(y)\,dy}{\int_0^1 P(y)\, dy}$ for the inverse transform sampling. + + #+begin_src python :session +w = [] +for (x, _, _) in to_sort: + w.append(-x) +w = np.array(w) +waccu = np.array(w) + +sum_w= 0. +for i in range(len(w)): + sum_w += w[i] + waccu[i] = sum_w +waccu = waccu / sum_w +w = w / sum_w +w + #+end_src + + #+RESULTS: + | 0.000162384392 | 0.000161615667 | 0.000156174841 | ... | 2.82313861e-07 | 2.80523353e-07 | 2.80412476e-07 | + + We will draw uniform random numbers and find their index in the + array ~waccu~: + + #+begin_src python :session +def find_sample(eta): + return np.searchsorted(waccu, eta, side='left', sorter=None) + #+end_src + + #+RESULTS: + +*** Sampling + + #+begin_src python :session +ET = 0. # Accumulator +ET2 = 0. # Accumulator of E^2 for variance +computed = np.zeros(Nabc) # If true, the (a,b,c) triplet has already + # been computed +date = 0. # Current time: increments when a new triplet is computed +dt = 1./Nabc +result = {} + +isample = 0 +prevdate = 0. +time0 = time.time() +while date < 0.99: + if time.time() - time0 > 60.: break + isample += 1 + eta = np.random.uniform() # Random number between 0 and 1 + abc = find_sample(eta) + s = eabc_sorted[abc] / w[abc] + if computed[abc] == 0: + computed[abc] = 1 + date += dt + ET += s + ET2 += s*s + if date - prevdate > 0.01: + prevdate = date + dtmp = 1./isample + average = ET*dtmp + variance = ET2*dtmp - average*average + result[date] = ( average, np.sqrt(variance/(isample-1)) ) + +[ ("%.3f"%k, v1, v2) for (k, (v1, v2)) in result.items() ] + #+end_src + + #+NAME:data_importance + #+RESULTS: + | 0.010 | -0.03027212822147209 | 0.0011742893979352206 | + | 0.020 | -0.0313009364341866 | 0.0009252120899929328 | + | 0.030 | -0.031057363530977423 | 0.0007281055373661676 | + | 0.040 | -0.031249853375632717 | 0.0006402801404234216 | + | 0.050 | -0.03122110948462111 | 0.0005750574146217905 | + | 0.060 | -0.03128348204672714 | 0.0005275262000247139 | + | 0.070 | -0.0308998979808618 | 0.0004726597407782536 | + | 0.080 | -0.03082342928319695 | 0.00044136523641729995 | + | 0.090 | -0.03061878595835833 | 0.00040625560663516984 | + | 0.100 | -0.03039442587808384 | 0.00037445927958614157 | + | 0.110 | -0.030414153392358843 | 0.0003555022536120971 | + | 0.120 | -0.030433890781777325 | 0.0003386617754861883 | + | 0.130 | -0.030412842186671795 | 0.00032521342707965395 | + | 0.140 | -0.030135851295907408 | 0.0003054031156376609 | + | 0.150 | -0.03017758373987041 | 0.00029160561167065966 | + | 0.160 | -0.030071710241627626 | 0.00028285433322913355 | + | 0.170 | -0.030187691754911785 | 0.00027362801402723217 | + | 0.180 | -0.03017792919745682 | 0.00026256836577371164 | + | 0.190 | -0.030066918230931893 | 0.0002520216317979708 | + | 0.200 | -0.03012732632783178 | 0.0002442961255034912 | + | 0.210 | -0.030138915946570068 | 0.00023654277814720348 | + | 0.220 | -0.030135951124831976 | 0.00022882972065217942 | + | 0.230 | -0.030189298295077573 | 0.00022288280644866787 | + | 0.240 | -0.030179114235883018 | 0.0002165756153934681 | + | 0.250 | -0.03020755367006979 | 0.00021062441315912225 | + | 0.260 | -0.030150949451180773 | 0.00020297280220009072 | + | 0.270 | -0.030113105404734098 | 0.0001968538782253076 | + | 0.280 | -0.03001178610814453 | 0.000190510244582427 | + | 0.290 | -0.030105460516270968 | 0.00018580175733023656 | + | 0.300 | -0.030206578515471226 | 0.0001820686148935213 | + | 0.310 | -0.030220596073402568 | 0.00017695300024148726 | + | 0.320 | -0.030253362198926707 | 0.000173110033483545 | + | 0.330 | -0.03025716666455987 | 0.00016884806376386556 | + | 0.340 | -0.03024767268207987 | 0.00016474215718864923 | + | 0.350 | -0.030245608121976592 | 0.0001610389817601625 | + | 0.360 | -0.030228130070767308 | 0.00015681822177276763 | + | 0.370 | -0.03019666434207847 | 0.00015286660948749957 | + | 0.380 | -0.0302247108757732 | 0.00014956619859720995 | + | 0.390 | -0.030277506060936692 | 0.0001473951646458563 | + | 0.400 | -0.030311036212474794 | 0.00014525747787829678 | + | 0.410 | -0.030319395740519034 | 0.0001423403120586929 | + | 0.420 | -0.030328754540608446 | 0.00013953020416052482 | + | 0.430 | -0.030335025610265645 | 0.00013717074592026099 | + | 0.440 | -0.03032536551327421 | 0.00013420580225141168 | + | 0.450 | -0.030317525082447477 | 0.00013090745868107453 | + | 0.460 | -0.030331154567198596 | 0.0001280412784818255 | + | 0.470 | -0.030346821228602428 | 0.0001254894342261729 | + | 0.480 | -0.030341062669058966 | 0.0001227585525308749 | + | 0.490 | -0.03032284123943016 | 0.0001199017169732116 | + | 0.500 | -0.030324593697131128 | 0.00011716907194040494 | + | 0.510 | -0.03036599520797054 | 0.0001149841429523499 | + | 0.520 | -0.030373500023963107 | 0.00011257695085119413 | + | 0.530 | -0.030398568034173238 | 0.00011033955037405243 | + | 0.540 | -0.030379771640186178 | 0.00010826945179330241 | + | 0.550 | -0.030392078925771775 | 0.00010591950473282571 | + | 0.560 | -0.0304026454971627 | 0.00010358492676711116 | + | 0.570 | -0.030389082287990102 | 0.0001011027020601961 | + | 0.580 | -0.03042023586750155 | 9.908928944756498e-05 | + | 0.590 | -0.03042662529206729 | 9.688702814501591e-05 | + | 0.600 | -0.03044723783359543 | 9.482918893094575e-05 | + | 0.610 | -0.03043219469351895 | 9.26971869085586e-05 | + | 0.620 | -0.03041964871512123 | 9.045177316867549e-05 | + | 0.630 | -0.03040801626098958 | 8.839118804599184e-05 | + | 0.640 | -0.030423340462181085 | 8.667968332871836e-05 | + | 0.650 | -0.03039653789830176 | 8.44014731598794e-05 | + | 0.660 | -0.03038052592884054 | 8.248031393751431e-05 | + | 0.670 | -0.030383047104467806 | 8.066997772997924e-05 | + | 0.680 | -0.03037101495895282 | 7.865737348265977e-05 | + | 0.690 | -0.030390109013467823 | 7.687785167133467e-05 | + | 0.700 | -0.03039164278824196 | 7.530409352036397e-05 | + | 0.710 | -0.030376353526121343 | 7.323158011397256e-05 | + | 0.720 | -0.030343481470340126 | 7.126805565409954e-05 | + | 0.730 | -0.03031777838164579 | 6.936365378349401e-05 | + | 0.740 | -0.030329363559433456 | 6.769454854815683e-05 | + | 0.750 | -0.030330011749874996 | 6.59686784438342e-05 | + | 0.760 | -0.030329426846525974 | 6.427621173496454e-05 | + | 0.770 | -0.030326548388485877 | 6.244765973081217e-05 | + | 0.780 | -0.030329650883986148 | 6.082490018420884e-05 | + | 0.790 | -0.030322073238055823 | 5.910514588411257e-05 | + | 0.800 | -0.030312381215268632 | 5.7421583243115227e-05 | + | 0.810 | -0.030299053653321258 | 5.5699918230207584e-05 | + | 0.820 | -0.030311512280480676 | 5.4102331646809365e-05 | + | 0.830 | -0.030325578671112484 | 5.2582898838102214e-05 | + | 0.840 | -0.030321914469912063 | 5.089177178614602e-05 | + | 0.850 | -0.030319285429001232 | 4.914371564960337e-05 | + | 0.860 | -0.030313500328097136 | 4.7470383207069204e-05 | + | 0.870 | -0.030305455309798633 | 4.582229909456817e-05 | + | 0.880 | -0.03029270937963236 | 4.401899624643128e-05 | + | 0.890 | -0.030287372422237557 | 4.221534263667604e-05 | + | 0.900 | -0.030273826343971428 | 4.0445160816126796e-05 | + | 0.910 | -0.030279937846679802 | 3.864802165815449e-05 | + | 0.920 | -0.03027407657538685 | 3.680080289715885e-05 | + | 0.930 | -0.030275647635292845 | 3.5030900270752445e-05 | + | 0.940 | -0.030275268108168343 | 3.30505449660589e-05 | + | 0.950 | -0.030255391500928076 | 3.1140646530112084e-05 | + | 0.960 | -0.030249858250144413 | 2.9083139511987113e-05 | + | 0.970 | -0.030243251806653753 | 2.6630322771430047e-05 | + | 0.980 | -0.030257401812890404 | 2.3870299829544822e-05 | + + #+RESULTS: + +** Semi-stochastic + +*** Preparation + + We split the contributions into 40 buckets: + + #+begin_src python :session +Nbuckets = 40 # Number of buckets + +bucket = [] +abc_old = 0 +idx0 = 0 +idx1 = 0 +bounds = [] +for i in range(Nbuckets): + accu = 0 + xi = (i+1)/Nbuckets + while idx1 < len(eabc) and waccu[idx1] <= xi: + accu += 1 + idx1 += 1 + bucket.append(accu) + bounds.append( (idx0, idx1) ) + idx0 = idx1 + #+end_src + + #+RESULTS: + + Contributions of each bucket: + + #+name:E_B +#+begin_src python :session +result = [] +for i in range(Nbuckets): + result.append( (i+1, sum(eabc_sorted[bounds[i][0]:bounds[i][1]])) ) +result +#+end_src + +#+RESULTS: E_B +| 1 | -0.0013677742901972176 | +| 2 | -0.0011041914108332854 | +| 3 | -0.0009275898609788052 | +| 4 | -0.0008073200317293237 | +| 5 | -0.0007790507659793898 | +| 6 | -0.0006121615146329108 | +| 7 | -0.0005770622533542697 | +| 8 | -0.0005142604992375494 | +| 9 | -0.00046382101884437956 | +| 10 | -0.0004039453565831979 | +| 11 | -0.000389650155472885 | +| 12 | -0.00029544073304587146 | +| 13 | -0.0003250768234388132 | +| 14 | -0.00028341936089169763 | +| 15 | -0.0002473003234040006 | +| 16 | -0.0003442889080859639 | +| 17 | -0.0003435619631738471 | +| 18 | -0.0004858997139826501 | +| 19 | -0.0009618635728221805 | +| 20 | -0.001429989465699455 | +| 21 | -0.0013470049374201519 | +| 22 | -0.001176633686853677 | +| 23 | -0.0009970812970662656 | +| 24 | -0.0009399212374881834 | +| 25 | -0.0009377932840110686 | +| 26 | -0.0008548897786545894 | +| 27 | -0.0007917116515238299 | +| 28 | -0.0008377443725186978 | +| 29 | -0.0008085988173851557 | +| 30 | -0.0007679194358436122 | +| 31 | -0.0006805914110088752 | +| 32 | -0.0006632464581929114 | +| 33 | -0.000653886276418067 | +| 34 | -0.0006694575639034294 | +| 35 | -0.0006153089357946734 | +| 36 | -0.0008010751950592366 | +| 37 | -0.0010914570803250902 | +| 38 | -0.0011707797198706584 | +| 39 | -0.0009276499869679824 | +| 40 | -0.0008310131640315182 | + + #+begin_src gnuplot :var data=E_B :results file :file E_B.png +reset +set grid +set xlabel "Bucket index" +set ylabel "E_B" +plot data u 1:2 w lp title "" + + #+end_src + + #+RESULTS: + [[file:E_B.png]] + +*** Sampling + #+begin_src python :session +ET = np.zeros(Nbuckets) # Energy of the bucket +ET2 = np.zeros(Nbuckets) +computed = np.zeros(Nabc) # If true, the (a,b,c) triplet has already + # been computed +bucket_comp = [ 0 ]*Nbuckets # Number of computed elements in the bucket +bucket_sampled = [ 0 ]*Nbuckets # Number of samples drawn in the bucket +imin = 0 # First non-computed contribution +date = 0 +dt = 1./Nabc +result = {} + +isample = 0 +prevdate = 0. +time0 = time.time() +while date < 0.99: + if time.time() - time0 > 60.: break + isample += 1 + # Force computation of 1st uncomputed triplet + while imin < Nabc and computed[imin] == 1: + imin += 1 + computed[imin] = 1 + date += dt + for i in range(Nbuckets): + if imin < bounds[i][1]: + bucket_comp[i] += 1 + break + + # Random sampling + eta = np.random.uniform(0.,1./Nbuckets) # Random number between + # 0 and 1/Nbuckets +# if True: +# i = np.random.randint(low=0,high=Nbuckets) + for i in range(Nbuckets): + eta_i = eta + i/Nbuckets + abc = find_sample(eta_i) + if computed[abc] == 0: + computed[abc] = 1 + date += dt + bucket_comp[i] += 1 + bucket_sampled[i] += 1 + s = eabc_sorted[abc] / w[abc] + ET[i] += s + ET2[i] += s*s + + if date - prevdate > 0.001: + prevdate = date + sum_det = 0. + average = 0. + variance = 0. + N = 0 + norm = 0. + for i in range(Nbuckets): + if bucket_comp[i] >= bucket[i]: + sum_det += sum(eabc_sorted[bounds[i][0]:bounds[i][1]]) + else: + average += ET [i] + variance += ET2[i] + N += bucket_sampled[i] + norm += sum(w[bounds[i][0]:bounds[i][1]]) + if N == 0: + break + average = average/N * norm + variance = variance/N * norm * norm - average*average + result[date] = ( sum_det + average, np.sqrt(variance/(N-1)) ) + +[ ("%.3f"%k, v1, v2) for (k, (v1, v2)) in result.items() ] + #+end_src + + #+NAME:data_semistoch + #+RESULTS: + | 0.001 | -0.03700252934055045 | 0.0039446587198956025 | + | 0.003 | -0.03816535382359609 | 0.0038208208777224563 | + | 0.004 | -0.03823708722776118 | 0.0028909427306171133 | + | 0.006 | -0.035477058071137275 | 0.002247199750908954 | + | 0.007 | -0.034245613400924205 | 0.001896709248931999 | + | 0.008 | -0.03364206951878407 | 0.0016639509024875523 | + | 0.010 | -0.03272048663758599 | 0.0014711824914169181 | + | 0.011 | -0.03204661390178344 | 0.001322421630968049 | + | 0.012 | -0.03247239543109624 | 0.0012886273407492139 | + | 0.014 | -0.03175941391454308 | 0.00118359399240578 | + | 0.015 | -0.03147754125129678 | 0.0011108993494206017 | + | 0.016 | -0.031017678239190105 | 0.0010391294918667723 | + | 0.018 | -0.031231735536857996 | 0.0009952425287539474 | + | 0.019 | -0.030918409685504133 | 0.0009434169449510998 | + | 0.020 | -0.03076948352418771 | 0.000903940058511309 | + | 0.021 | -0.030731805827973045 | 0.000870986845165927 | + | 0.023 | -0.030657131449181856 | 0.0008446635016691032 | + | 0.024 | -0.030418434317601425 | 0.0008236052557121908 | + | 0.026 | -0.030413475405211866 | 0.0008038247047447392 | + | 0.027 | -0.0302634458743812 | 0.00077726661752534 | + | 0.028 | -0.030099860020646314 | 0.0007493781343440913 | + | 0.030 | -0.030031414584741206 | 0.0007247571482425683 | + | 0.031 | -0.029861913390748302 | 0.0007034977703759773 | + | 0.032 | -0.030059889998951636 | 0.000683003955292924 | + | 0.034 | -0.029942110833037733 | 0.0006673144407280344 | + | 0.035 | 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0.848 | -0.030212914230549053 | 8.069731197354463e-06 | + | 0.849 | -0.030212953716411677 | 8.043986969019347e-06 | + | 0.850 | -0.03021337904791928 | 8.052526081092125e-06 | + | 0.851 | -0.03021253619709572 | 8.019288359006694e-06 | + | 0.852 | -0.03021216948387092 | 7.992129530728743e-06 | + | 0.853 | -0.030211891511483624 | 7.960756929300705e-06 | + | 0.854 | -0.03021142179201084 | 7.929445023496794e-06 | + | 0.855 | -0.030211836368956625 | 7.909213798763553e-06 | + | 0.856 | -0.03021157505453853 | 7.879422529059699e-06 | + | 0.857 | -0.03021193164627511 | 7.85791751968503e-06 | + | 0.858 | -0.03021132442692887 | 7.83470242959927e-06 | + | 0.859 | -0.030211287149203982 | 7.813621931912011e-06 | + | 0.860 | -0.030211584071993525 | 7.80397160335191e-06 | + | 0.861 | -0.030211285278577468 | 7.77654482554094e-06 | + | 0.862 | -0.03021070343028317 | 7.745932597042503e-06 | + | 0.863 | -0.030211016980507457 | 7.744047226813484e-06 | + | 0.864 | -0.03021071484125383 | 7.716390287305682e-06 | + | 0.865 | -0.030211632585633637 | 7.705545160475695e-06 | + | 0.866 | -0.030211663711614573 | 7.682790041511805e-06 | + | 0.867 | -0.030211254671414292 | 7.65550693394998e-06 | + | 0.868 | -0.03021092567597769 | 7.626054483899228e-06 | + | 0.869 | -0.030210264176316608 | 7.599758782715608e-06 | + | 0.870 | -0.03021000909210467 | 7.571923607063591e-06 | + | 0.872 | -0.030209337376001313 | 7.545823488032606e-06 | + | 0.873 | -0.030209832543496615 | 7.53232886321725e-06 | + | 0.874 | -0.030210172562503072 | 7.5195359229938765e-06 | + | 0.875 | -0.030209880607499167 | 7.491189136978581e-06 | + | 0.876 | -0.03021015086278947 | 7.4684975729141745e-06 | + | 0.877 | -0.03021062663656375 | 7.447351195738599e-06 | + | 0.878 | -0.030210761567348005 | 7.421476379596416e-06 | + | 0.879 | -0.030211788583739314 | 7.408919410352043e-06 | + | 0.880 | -0.030212088640987327 | 7.386235194380184e-06 | + | 0.881 | -0.030211786771356528 | 7.358734158329978e-06 | + | 0.882 | -0.03021107271687905 | 7.332152942587671e-06 | + | 0.883 | -0.030210820700011933 | 7.309760714878662e-06 | + | 0.884 | -0.03021032528245062 | 7.287552042071234e-06 | + | 0.885 | -0.030210667617637382 | 7.272619550731226e-06 | + | 0.886 | -0.030210534702831755 | 7.250939416238533e-06 | + | 0.887 | -0.030210946730824674 | 7.2793252349112675e-06 | + | 0.888 | -0.030211252139993497 | 7.2648090326639045e-06 | + | 0.889 | -0.030210665082162854 | 7.240579121463229e-06 | + | 0.890 | -0.03021087774424671 | 7.221960125950946e-06 | + | 0.891 | -0.030211452716676957 | 7.211951374554893e-06 | + | 0.892 | -0.030210694858355754 | 7.184074515170302e-06 | + | 0.893 | -0.030210083062529838 | 7.158333262367399e-06 | + | 0.894 | -0.030210977834800413 | 7.151539847082595e-06 | + | 0.895 | -0.030210669641171445 | 7.12454694261228e-06 | + | 0.896 | -0.030211331051111158 | 7.128299400843476e-06 | + | 0.897 | -0.03021120935321755 | 7.104054172134005e-06 | + | 0.898 | -0.03021140956618183 | 7.079676713170904e-06 | + | 0.899 | -0.03021129189126742 | 7.062917562447002e-06 | + | 0.900 | -0.0302117660429539 | 7.048190506182905e-06 | + | 0.901 | -0.030212107465792854 | 7.035624120166649e-06 | + | 0.902 | -0.030212355366550418 | 7.019206498291099e-06 | + | 0.903 | -0.03021337302594268 | 7.017319386632158e-06 | + | 0.904 | -0.03021369810945497 | 7.001908048869648e-06 | + | 0.905 | -0.030213185303807757 | 6.9751250094704174e-06 | + | 0.906 | -0.03021451380662918 | 7.03340512194063e-06 | + | 0.907 | -0.030213729788559407 | 7.003593200684789e-06 | + | 0.908 | -0.030213722778432706 | 6.98776083870591e-06 | + | 0.909 | -0.030213117850751096 | 6.962538580572595e-06 | + | 0.910 | -0.030213237683233737 | 6.939545272611981e-06 | + | 0.911 | -0.03021314737188534 | 6.918589578781604e-06 | + | 0.912 | -0.030213018975091734 | 6.893923822089388e-06 | + | 0.913 | -0.03021330245351052 | 6.892247712272672e-06 | + | 0.914 | -0.03021311587060586 | 6.866801502716889e-06 | + | 0.915 | -0.030212959227322575 | 6.84181437274924e-06 | + | 0.916 | -0.030212414092534588 | 6.816561394471185e-06 | + | 0.917 | -0.030212136360792487 | 6.7960736338012995e-06 | + | 0.918 | -0.030211732584037084 | 6.7747221438673855e-06 | + | 0.919 | -0.03021210585476781 | 6.7697727461243385e-06 | + | 0.920 | -0.0302116693858556 | 6.7435640414947464e-06 | + | 0.921 | -0.030211483225436563 | 6.722243439601207e-06 | + | 0.922 | -0.030211487960060443 | 6.697392227767628e-06 | + | 0.923 | -0.030211120762383147 | 6.675194193865902e-06 | + | 0.924 | -0.03021186881170036 | 6.663111583642154e-06 | + | 0.925 | -0.030211387204286975 | 6.639492381564352e-06 | + | 0.926 | -0.030211223994855024 | 6.616685809080732e-06 | + | 0.927 | -0.030211709678181403 | 6.609004532495233e-06 | + | 0.928 | -0.0302119772474608 | 6.588167128881656e-06 | + | 0.929 | -0.030211614701277516 | 6.564996041769278e-06 | + | 0.930 | -0.030212049809856197 | 6.547742505037693e-06 | + | 0.931 | -0.030211521488944102 | 6.528313624966542e-06 | + + + | System | (T) in mH | 1mH absolute error | 1% relative error | + |--------------+-----------+--------------------+-------------------| + | Water | -8.9892 | 0.1% | 6% | + | HBN | -30.2274 | 1.8% | 13% | + | UEG (14,147) | -37.8054 | 0.5% | 2% | + | UEG (38,341) | -138.2314 | x 2% | x 2% | + +** Final plot + +*** Water + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file convergence-h2o.png +reset +set grid +set style fill transparent solid 0.50 border +e_ref = e_ref + 0. +set ylabel "E_{(T)} (a.u.)" +set xlabel "Fraction of computed (a,b,c) triplets" +#set yrange [e_ref-.0005:e_ref+.0005] +plot data_uniform u ($1):($2+$3):($2-$3) w filledcurves ls 1 title "Uniform", \ + data_uniform u ($1):($2) w l ls 1 title "", \ + data_importance u ($1):($2+$3):($2-$3) w filledcurves ls 3 title "Importance sampling", \ + data_importance u ($1):($2) w l ls 3 title "", \ + data_semistoch u ($1):($2+$3):($2-$3) w filledcurves ls 4 title "Semi-stochastic", \ + data_semistoch u ($1):($2) w l ls 4 title "", \ + e_ref title "Exact" lc black + #+end_src + + #+RESULTS: + [[file:convergence-h2o.png]] + + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file error-h2o.png +reset +set grid +set log y +set style fill transparent solid 0.50 border +set ylabel "Error bar (a.u)" +set xlabel "Fraction of computed (a,b,c) triplets" +set format y "10^{%T}" +plot data_uniform u 1:3 w l ls 1 title "Uniform", \ + data_importance u 1:3 w l ls 3 title "Importance sampling", \ + data_semistoch u 1:3 w l ls 4 title "Semi-stochastic" + #+end_src + + #+RESULTS: + [[file:error-h2o.png]] + +*** 14 electrons + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file convergence-14.png +reset +set grid +set style fill transparent solid 0.50 border +e_ref = e_ref + 0. +set ylabel "E_{(T)} (a.u.)" +set xlabel "Fraction of computed (a,b,c) triplets" +#set yrange [e_ref-.0005:e_ref+.0005] +plot data_uniform u ($1):($2+$3):($2-$3) w filledcurves ls 1 title "Uniform", \ + data_uniform u ($1):($2) w l ls 1 title "", \ + data_importance u ($1):($2+$3):($2-$3) w filledcurves ls 3 title "Importance sampling", \ + data_importance u ($1):($2) w l ls 3 title "", \ + data_semistoch u ($1):($2+$3):($2-$3) w filledcurves ls 4 title "Semi-stochastic", \ + data_semistoch u ($1):($2) w l ls 4 title "", \ + e_ref title "Exact" lc black + #+end_src + + #+RESULTS: + [[file:convergence-14.png]] + + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file error-14.png +reset +set grid +set log y +set style fill transparent solid 0.50 border +set ylabel "Error bar (a.u)" +set xlabel "Fraction of computed (a,b,c) triplets" +set format y "10^{%T}" +plot data_uniform u 1:3 w l ls 1 title "Uniform", \ + data_importance u 1:3 w l ls 3 title "Importance sampling", \ + data_semistoch u 1:3 w l ls 4 title "Semi-stochastic" + #+end_src + + #+RESULTS: + [[file:error-14.png]] + +*** 38 electrons + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file convergence-38.png +reset +set grid +set style fill transparent solid 0.50 border +e_ref = e_ref + 0. +set ylabel "E_{(T)} (a.u.)" +set xlabel "Fraction of computed (a,b,c) triplets" +#set yrange [e_ref-.0005:e_ref+.0005] +plot data_uniform u ($1):($2+$3):($2-$3) w filledcurves ls 1 title "Uniform", \ + data_uniform u ($1):($2) w l ls 1 title "", \ + data_importance u ($1):($2+$3):($2-$3) w filledcurves ls 3 title "Importance sampling", \ + data_importance u ($1):($2) w l ls 3 title "", \ + data_semistoch u ($1):($2+$3):($2-$3) w filledcurves ls 4 title "Semi-stochastic", \ + data_semistoch u ($1):($2) w l ls 4 title "", \ + e_ref title "Exact" lc black + #+end_src + + #+RESULTS: + [[file:convergence-38.png]] + + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file error-38.png +reset +set grid +set log y +set style fill transparent solid 0.50 border +set ylabel "Error bar (a.u)" +set xlabel "Fraction of computed (a,b,c) triplets" +set format y "10^{%T}" +plot data_uniform u 1:3 w l ls 1 title "Uniform", \ + data_importance u 1:3 w l ls 3 title "Importance sampling", \ + data_semistoch u 1:3 w l ls 4 title "Semi-stochastic" + #+end_src + + #+RESULTS: + [[file:error-38.png]] + +*** HBN + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file convergence-hbn.png +reset +set grid +set style fill transparent solid 0.50 border +e_ref = e_ref + 0. +set ylabel "E_{(T)} (a.u.)" +set xlabel "Fraction of computed (a,b,c) triplets" +#set yrange [e_ref-.0005:e_ref+.0005] +plot data_uniform u ($1):($2+$3):($2-$3) w filledcurves ls 1 title "Uniform", \ + data_uniform u ($1):($2) w l ls 1 title "", \ + data_importance u ($1):($2+$3):($2-$3) w filledcurves ls 3 title "Importance sampling", \ + data_importance u ($1):($2) w l ls 3 title "", \ + data_semistoch u ($1):($2+$3):($2-$3) w filledcurves ls 4 title "Semi-stochastic", \ + data_semistoch u ($1):($2) w l ls 4 title "", \ + e_ref title "Exact" lc black + #+end_src + + #+RESULTS: + [[file:convergence-hbn.png]] + + #+begin_src gnuplot :var e_ref=e_ref :var data_semistoch=data_semistoch :var data_uniform=data_uniform :var data_importance=data_importance :results file :file error-hbn.png +reset +set grid +set log y +set style fill transparent solid 0.50 border +set ylabel "Error bar (a.u)" +set xlabel "Fraction of computed (a,b,c) triplets" +set format y "10^{%T}" +plot data_uniform u 1:3 w l ls 1 title "Uniform", \ + data_importance u 1:3 w l ls 3 title "Importance sampling", \ + data_semistoch u 1:3 w l ls 4 title "Semi-stochastic" + #+end_src + + #+RESULTS: + [[file:error-hbn.png]] + +* Appendix + +** Fortran code + +*** Naive expression + #+begin_src f90 :exports code + energy = 0d0 + do a = 1, nV + do b = 1, nV + do c = 1, nV + do k = 1, nO + do j = 1, nO + do i = 1, nO + energy = energy + (4.d0 * W(i,j,k,a,b,c) + & + W(i,j,k,b,c,a) + & + W(i,j,k,c,a,b)) * & + (V(i,j,k,a,b,c) - V(i,j,k,c,b,a)) / & + (f_o(i) + f_o(j) + f_o(k) - f_v(a) - f_v(b) - f_v(c)) + enddo + enddo + enddo + enddo + enddo + enddo + + energy = energy / 3.d0 + print*,"(T)", energy + #+end_src + + +*** Optimized functions + + Here, we compute in the inner-most loop all possible permutations + of $(a,b,c)$ with $a \ne b \ne c$. In the second loop, we compute + the contributions where two indices are the same. When $a=b=c$, the + contribution is zero. + + #+begin_src f90 + e = 0d0 + !$OMP DO SCHEDULE(dynamic) + do a = 1, nV + do b = a+1, nV + do c = b+1, nV + delta_abc = f_v(a) + f_v(b) + f_v(c) + call form_w_abc(nO,nV,a,b,c,T_voov,T_oovv,X_vovv,X_ooov,W_abc,W_cba,W_bca,W_cab,W_bac,W_acb) + call form_v_abc(nO,nV,a,b,c,t1,X_oovv,W_abc,V_abc,W_cba,V_cba,W_bca,V_bca,W_cab,V_cab,W_bac,V_bac,W_acb,V_acb) + do k = 1, nO + do j = 1, nO + do i = 1, nO + delta = 1.d0 / (f_o(i) + f_o(j) + f_o(k) - delta_abc) + e = e + delta * ( & + (4d0 * (W_abc(i,j,k) - W_cba(i,j,k)) + & + W_bca(i,j,k) - W_bac(i,j,k) + & + W_cab(i,j,k) - W_acb(i,j,k) ) * (V_abc(i,j,k) - V_cba(i,j,k)) + & + (4d0 * (W_acb(i,j,k) - W_bca(i,j,k)) + & + W_cba(i,j,k) - W_cab(i,j,k) + & + W_bac(i,j,k) - W_abc(i,j,k) ) * (V_acb(i,j,k) - V_bca(i,j,k)) + & + (4d0 * (W_bac(i,j,k) - W_cab(i,j,k)) + & + W_acb(i,j,k) - W_abc(i,j,k) + & + W_cba(i,j,k) - W_bca(i,j,k) ) * (V_bac(i,j,k) - V_cab(i,j,k)) ) + enddo + enddo + enddo + enddo + enddo + + c = a + do b = 1, nV + if (b == c) cycle + delta_abc = f_v(a) + f_v(b) + f_v(c) + call form_w_abc(nO,nV,a,b,c,T_voov,T_oovv,X_vovv,X_ooov,W_abc,W_cba,W_bca,W_cab,W_bac,W_acb) + call form_v_abc(nO,nV,a,b,c,t1,X_oovv,W_abc,V_abc,W_cba,V_cba,W_bca,V_bca,W_cab,V_cab,W_bac,V_bac,W_acb,V_acb) + do k = 1, nO + do j = 1, nO + do i = 1, nO + delta = 1.0d0 / (f_o(i) + f_o(j) + f_o(k) - delta_abc) + e = e + delta * ( & + (4d0 * W_abc(i,j,k) + W_bca(i,j,k) + W_cab(i,j,k)) * (V_abc(i,j,k) - V_cba(i,j,k)) + & + (4d0 * W_acb(i,j,k) + W_cba(i,j,k) + W_bac(i,j,k)) * (V_acb(i,j,k) - V_bca(i,j,k)) + & + (4d0 * W_bac(i,j,k) + W_acb(i,j,k) + W_cba(i,j,k)) * (V_bac(i,j,k) - V_cab(i,j,k)) ) + enddo + enddo + enddo + enddo + enddo + !$OMP END DO NOWAIT + + !$OMP CRITICAL + energy = energy + e + !$OMP END CRITICAL + + deallocate(W_abc, W_cab, W_bca, W_bac, W_cba, W_acb, & + V_abc, V_cab, V_bca, V_bac, V_cba, V_acb ) + + !$OMP END PARALLEL + #+end_src + +* Plots + #+begin_src gnuplot :results file :file tmp.png +reset +binwidth=1 +set boxwidth binwidth +bin(x,width)=width*floor(x/width) +plot 'data' using (bin($4,binwidth)):($7) smooth freq with boxes + #+end_src + + #+RESULTS: + [[file:tmp.png]] + + #+begin_src python :results output +import numpy as np +data = [] +with open('data','r') as f: + for line in f: + l = line.split() + a, b, c = int(l[0]), int(l[1]), int(l[2]) + ea, eb, ec = float(l[3]), float(l[4]), float(l[5]) + e = float(l[6]) +# data.append(e) +# data.append(e * (ea + eb + ec)) +# data.append(e * (ea + eb + ec) * ea) +# data.append(e * (ea + eb + ec) * eb) +# data.append(e * (ea + eb + ec) * ec) +# data.append(e * (ea + eb + ec) * ea*eb) +# data.append(e * (ea + eb + ec) * ea*eb*ec) +# data.append(e * (ea + eb + ec + 0.037)**2) + data.append(e * (ea * eb * ec)**1) + +data = np.array(data) +average = sum(data)/len(data) +variance = sum( (data-average)**3 ) /(len(data)-1) +error = np.sqrt(variance/len(data)) +print(average, '+/-', error) +print(error/average) + + #+end_src + + #+RESULTS: + : 0.0030955494327421676 +/- 4.131592930193792e-06 + : 0.0013346880804077012 + + 1/(ea*eb*ec) : 0.004730162427068331 + 1/(ea*eb) : 0.004730162427068331 + 1/ec : 0.006151067343303064 + 1/eb : 0.0056790423986561225 + 1/ea : 0.007281256366224999 + denom : 0.008468893789021222 + orig : 0.011634889545203767 + + #+begin_src gnuplot :results file :file tmp.png +reset +plot 'data' using :($7 * ($4*$5*$6)**1 ) w p + #+end_src + #+RESULTS: + [[file:tmp.png]] + + +** Test 2 + + #+begin_src python :session :results output +with open('data2','w') as f: + for i in range(Nabc): + f.write("%e %e\n"%(w[i], eabc_sorted[i])) + + #+end_src + + #+RESULTS: + + #+begin_src gnuplot :results file :file tmp.png +reset +plot 'data2' using :($7 * ($4*$5*$6)**1 ) w p + #+end_src + +* Results QP + + +** Benzene + + #+begin_example +12 +Benzene +C 0.000000 1.392503 0.000000 +C -1.205943 0.696252 0.000000 +C -1.205943 -0.696252 0.000000 +C 0.000000 -1.392503 0.000000 +C 1.205943 -0.696252 0.000000 +C 1.205943 0.696252 0.000000 +H -2.141717 1.236521 0.000000 +H -2.141717 -1.236521 0.000000 +H 0.000000 -2.473042 0.000000 +H 2.141717 -1.236521 0.000000 +H 2.141717 1.236521 0.000000 +H 0.000000 2.473042 0.000000 + #+end_example + +*** Benzene DZ + + Intel(R) Core(TM) i7-1165G7 @ 2.80GHz, 4 cores + +**** Gaussian16 + + CCSD(T,TWInCore) + + Wavefunction amplitudes converged. E(Corr)= -231.54403350 + CCSD(T)= -0.23157977364D+03 + 283.27 s + +**** Stochastic algorithm + + Time: 2.36414194107056 s + + E(CCSD) = -231.544034027686 Ha + Correlation = -0.821789081365 Ha + Conv = 9.18E-07 + + Computing (T) correction... + + |---------------+------------+-------| + | E(CCSD(T)) | Error | % | + |---------------+------------+-------| + | -231.58030122 | 0.4195E-03 | 19.66 | + | -231.58021542 | 0.2290E-03 | 39.16 | + | -231.57982156 | 0.1324E-03 | 58.61 | + | -231.57980529 | 0.6177E-04 | 78.09 | + | -231.57977003 | 0.6253E-05 | 97.53 | + |---------------+------------+-------| + + Time: 5.18708086013794 s + + E(CCSD(T)) = -231.579770030057 Ha + E(T) = -0.035736002371 Ha + Correlation = -0.857525083736 Ha + +*** Benzene TZ + + Intel(R) Xeon(R) Gold 6130 CPU @ 2.10GHz, 32 cores + +**** Gaussian16 + + Wavefunction amplitudes converged. E(Corr)= -231.75392219 + +**** Stochastic algorithm + + Time: 90.0595779418945 s + + Successful convergence after 9 iterations + + E(CCSD) = -231.753922932570 Ha + Correlation = -0.974220010793 Ha + Conv = 6.97E-07 + + #+NAME:benzene_tz + |---------------+------------+-------| + | E(CCSD(T)) | Error | % | + |---------------+------------+-------| + | -231.80582073 | 0.1702E-02 | 0.43 | + | -231.80568602 | 0.1182E-02 | 0.86 | + | -231.80638784 | 0.9730E-03 | 1.28 | + | -231.80583046 | 0.8243E-03 | 1.70 | + | -231.80564026 | 0.7246E-03 | 2.13 | + | -231.80549184 | 0.6546E-03 | 2.55 | + | -231.80528021 | 0.5917E-03 | 2.97 | + | -231.80533305 | 0.5513E-03 | 3.39 | + | -231.80552546 | 0.5262E-03 | 3.81 | + | -231.80531583 | 0.4945E-03 | 4.23 | + | -231.80535472 | 0.4705E-03 | 4.66 | + | -231.80557527 | 0.4565E-03 | 5.08 | + | -231.80557303 | 0.4355E-03 | 5.50 | + | -231.80548029 | 0.4202E-03 | 5.92 | + | -231.80556655 | 0.4050E-03 | 6.34 | + | -231.80563017 | 0.3936E-03 | 6.77 | + | -231.80566114 | 0.3827E-03 | 7.19 | + | -231.80558699 | 0.3701E-03 | 7.61 | + | -231.80567134 | 0.3635E-03 | 8.03 | + | -231.80560792 | 0.3524E-03 | 8.45 | + | -231.80599656 | 0.2819E-03 | 8.87 | + | -231.80600921 | 0.2748E-03 | 9.29 | + | -231.80602737 | 0.2682E-03 | 9.71 | + | -231.80602047 | 0.2619E-03 | 10.13 | + | -231.80600268 | 0.2562E-03 | 10.55 | + | -231.80605143 | 0.2532E-03 | 10.97 | + | -231.80603473 | 0.2490E-03 | 11.39 | + | -231.80606029 | 0.2452E-03 | 11.81 | + | -231.80608868 | 0.2406E-03 | 12.23 | + | -231.80608311 | 0.2367E-03 | 12.65 | + | -231.80603067 | 0.2316E-03 | 13.07 | + | -231.80602845 | 0.2276E-03 | 13.49 | + | -231.80598091 | 0.2235E-03 | 13.91 | + | -231.80592227 | 0.2203E-03 | 14.33 | + | -231.80586276 | 0.2164E-03 | 14.75 | + | -231.80585569 | 0.2125E-03 | 15.17 | + | -231.80588786 | 0.2088E-03 | 15.59 | + | -231.80580990 | 0.1836E-03 | 16.01 | + | -231.80575077 | 0.1801E-03 | 16.43 | + | -231.80575959 | 0.1777E-03 | 16.85 | + | -231.80577139 | 0.1757E-03 | 17.27 | + | -231.80573497 | 0.1730E-03 | 17.69 | + | -231.80571827 | 0.1703E-03 | 18.11 | + | -231.80570941 | 0.1679E-03 | 18.53 | + | -231.80568515 | 0.1654E-03 | 18.95 | + | -231.80565681 | 0.1628E-03 | 19.37 | + | -231.80563140 | 0.1606E-03 | 19.79 | + | -231.80564907 | 0.1587E-03 | 20.21 | + | -231.80561730 | 0.1562E-03 | 20.63 | + | -231.80558851 | 0.1539E-03 | 21.05 | + | -231.80559825 | 0.1525E-03 | 21.48 | + | -231.80563699 | 0.1512E-03 | 21.90 | + | -231.80562532 | 0.1326E-03 | 22.32 | + | -231.80558771 | 0.1310E-03 | 22.74 | + | -231.80558484 | 0.1299E-03 | 23.16 | + | -231.80559053 | 0.1284E-03 | 23.58 | + | -231.80560391 | 0.1271E-03 | 24.00 | + | -231.80561828 | 0.1261E-03 | 24.42 | + | -231.80562601 | 0.1249E-03 | 24.84 | + | -231.80562503 | 0.1235E-03 | 25.26 | + | -231.80561025 | 0.1221E-03 | 25.68 | + | -231.80561714 | 0.1209E-03 | 26.10 | + | -231.80561468 | 0.1197E-03 | 26.52 | + | -231.80562579 | 0.1185E-03 | 26.94 | + | -231.80561713 | 0.1103E-03 | 27.36 | + | -231.80560273 | 0.1091E-03 | 27.78 | + | -231.80563253 | 0.1084E-03 | 28.20 | + | -231.80564377 | 0.1075E-03 | 28.62 | + | -231.80564167 | 0.1064E-03 | 29.04 | + | -231.80563093 | 0.1054E-03 | 29.46 | + | -231.80563660 | 0.1049E-03 | 29.88 | + | -231.80563212 | 0.1040E-03 | 30.30 | + | -231.80563092 | 0.1030E-03 | 30.72 | + | -231.80563308 | 0.1021E-03 | 31.14 | + | -231.80563106 | 0.1011E-03 | 31.56 | + | -231.80567721 | 0.9500E-04 | 31.98 | + | -231.80566323 | 0.9423E-04 | 32.40 | + | -231.80565084 | 0.9338E-04 | 32.82 | + | -231.80564784 | 0.9250E-04 | 33.24 | + | -231.80565170 | 0.9174E-04 | 33.66 | + | -231.80566332 | 0.9103E-04 | 34.08 | + | -231.80566231 | 0.9026E-04 | 34.50 | + | -231.80567450 | 0.8967E-04 | 34.92 | + | -231.80567643 | 0.8886E-04 | 35.34 | + | -231.80567236 | 0.8800E-04 | 35.76 | + | -231.80570112 | 0.8340E-04 | 36.18 | + | -231.80569928 | 0.8278E-04 | 36.60 | + | -231.80570171 | 0.8228E-04 | 37.02 | + | -231.80568327 | 0.8151E-04 | 37.44 | + | -231.80568723 | 0.8078E-04 | 37.86 | + | -231.80568265 | 0.8013E-04 | 38.28 | + | -231.80569338 | 0.7963E-04 | 38.69 | + | -231.80567324 | 0.7899E-04 | 39.11 | + | -231.80563524 | 0.7452E-04 | 39.53 | + | -231.80564097 | 0.7398E-04 | 39.95 | + | -231.80565289 | 0.7357E-04 | 40.37 | + | -231.80564818 | 0.7296E-04 | 40.79 | + | -231.80565600 | 0.7251E-04 | 41.21 | + | -231.80565207 | 0.7194E-04 | 41.63 | + | -231.80566001 | 0.7143E-04 | 42.05 | + | -231.80566004 | 0.7083E-04 | 42.47 | + | -231.80564267 | 0.6744E-04 | 42.89 | + | -231.80563415 | 0.6689E-04 | 43.31 | + | -231.80563791 | 0.6641E-04 | 43.72 | + | -231.80563744 | 0.6596E-04 | 44.14 | + | -231.80563826 | 0.6551E-04 | 44.56 | + | -231.80563215 | 0.6500E-04 | 44.98 | + | -231.80563720 | 0.6456E-04 | 45.40 | + | -231.80563619 | 0.6246E-04 | 45.82 | + | -231.80563835 | 0.6198E-04 | 46.24 | + | -231.80564409 | 0.6157E-04 | 46.66 | + | -231.80563762 | 0.6119E-04 | 47.08 | + | -231.80563979 | 0.6080E-04 | 47.50 | + | -231.80565249 | 0.6042E-04 | 47.92 | + | -231.80565287 | 0.6003E-04 | 48.34 | + | -231.80566663 | 0.5788E-04 | 48.76 | + | -231.80567701 | 0.5766E-04 | 49.18 | + | -231.80567437 | 0.5721E-04 | 49.60 | + | -231.80567603 | 0.5686E-04 | 50.02 | + | -231.80567932 | 0.5655E-04 | 50.44 | + | -231.80568558 | 0.5616E-04 | 50.86 | + | -231.80568611 | 0.5583E-04 | 51.28 | + | -231.80568801 | 0.5329E-04 | 51.70 | + | -231.80569324 | 0.5295E-04 | 52.12 | + | -231.80569806 | 0.5258E-04 | 52.53 | + | -231.80569919 | 0.5219E-04 | 52.95 | + | -231.80569441 | 0.5179E-04 | 53.37 | + | -231.80569178 | 0.5145E-04 | 53.79 | + | -231.80570274 | 0.4828E-04 | 54.21 | + | -231.80571023 | 0.4804E-04 | 54.64 | + | -231.80570955 | 0.4772E-04 | 55.05 | + | -231.80571522 | 0.4742E-04 | 55.47 | + | -231.80571110 | 0.4711E-04 | 55.89 | + | -231.80569718 | 0.4400E-04 | 56.31 | + | -231.80570477 | 0.4381E-04 | 56.73 | + | -231.80569947 | 0.4350E-04 | 57.15 | + | -231.80569318 | 0.4321E-04 | 57.56 | + | -231.80569576 | 0.4290E-04 | 57.98 | + | -231.80570782 | 0.4050E-04 | 58.40 | + | -231.80570906 | 0.4027E-04 | 58.82 | + | -231.80570963 | 0.4000E-04 | 59.24 | + | -231.80570842 | 0.3974E-04 | 59.66 | + | -231.80570764 | 0.3947E-04 | 60.08 | + | -231.80571662 | 0.3712E-04 | 60.50 | + | -231.80571952 | 0.3690E-04 | 60.92 | + | -231.80572084 | 0.3668E-04 | 61.34 | + | -231.80571920 | 0.3644E-04 | 61.76 | + | -231.80572058 | 0.3620E-04 | 62.18 | + | -231.80572094 | 0.3389E-04 | 62.59 | + | -231.80572010 | 0.3366E-04 | 63.01 | + | -231.80572148 | 0.3347E-04 | 63.43 | + | -231.80572100 | 0.3327E-04 | 63.85 | + | -231.80571891 | 0.3128E-04 | 64.27 | + | -231.80571950 | 0.3106E-04 | 64.68 | + | -231.80571796 | 0.3086E-04 | 65.10 | + | -231.80571719 | 0.3064E-04 | 65.52 | + | -231.80570329 | 0.2833E-04 | 65.94 | + | -231.80570411 | 0.2819E-04 | 66.36 | + | -231.80570353 | 0.2802E-04 | 66.78 | + | -231.80570459 | 0.2786E-04 | 67.20 | + | -231.80570001 | 0.2628E-04 | 67.61 | + | -231.80570281 | 0.2612E-04 | 68.03 | + | -231.80570545 | 0.2596E-04 | 68.45 | + | -231.80570837 | 0.2583E-04 | 68.87 | + | -231.80571420 | 0.2446E-04 | 69.29 | + | -231.80571712 | 0.2430E-04 | 69.70 | + | -231.80571366 | 0.2411E-04 | 70.12 | + | -231.80572181 | 0.2295E-04 | 70.54 | + | -231.80572527 | 0.2282E-04 | 70.96 | + | -231.80572548 | 0.2266E-04 | 71.38 | + | -231.80572717 | 0.2159E-04 | 71.79 | + | -231.80572893 | 0.2147E-04 | 72.21 | + | -231.80573143 | 0.2133E-04 | 72.63 | + | -231.80573576 | 0.2039E-04 | 73.04 | + | -231.80573648 | 0.2025E-04 | 73.46 | + | -231.80573447 | 0.2010E-04 | 73.88 | + | -231.80573276 | 0.1929E-04 | 74.30 | + | -231.80573004 | 0.1914E-04 | 74.71 | + | -231.80572435 | 0.1824E-04 | 75.13 | + | -231.80572626 | 0.1812E-04 | 75.54 | + | -231.80572718 | 0.1800E-04 | 75.96 | + | -231.80573168 | 0.1727E-04 | 76.38 | + | -231.80573042 | 0.1717E-04 | 76.80 | + | -231.80572534 | 0.1637E-04 | 77.21 | + | -231.80572609 | 0.1626E-04 | 77.63 | + | -231.80572710 | 0.1562E-04 | 78.05 | + | -231.80572948 | 0.1551E-04 | 78.47 | + | -231.80572869 | 0.1540E-04 | 78.89 | + | -231.80573529 | 0.1483E-04 | 79.30 | + | -231.80573552 | 0.1473E-04 | 79.72 | + | -231.80573496 | 0.1396E-04 | 80.14 | + | -231.80573536 | 0.1339E-04 | 80.55 | + | -231.80573698 | 0.1330E-04 | 80.97 | + | -231.80573519 | 0.1268E-04 | 81.39 | + | -231.80573370 | 0.1258E-04 | 81.81 | + | -231.80573230 | 0.1201E-04 | 82.23 | + | -231.80573221 | 0.1192E-04 | 82.64 | + | -231.80572889 | 0.1129E-04 | 83.06 | + | -231.80573070 | 0.1087E-04 | 83.48 | + | -231.80573069 | 0.1079E-04 | 83.90 | + | -231.80572791 | 0.1030E-04 | 84.32 | + | -231.80572916 | 0.9864E-05 | 84.73 | + | -231.80573030 | 0.9504E-05 | 85.15 | + | -231.80573409 | 0.9133E-05 | 85.57 | + | -231.80573446 | 0.9056E-05 | 85.99 | + | -231.80573537 | 0.8694E-05 | 86.40 | + | -231.80573086 | 0.8322E-05 | 86.82 | + | -231.80573012 | 0.7984E-05 | 87.24 | + | -231.80572517 | 0.7645E-05 | 87.65 | + | -231.80572484 | 0.7265E-05 | 88.07 | + | -231.80572223 | 0.6877E-05 | 88.49 | + | -231.80572365 | 0.6538E-05 | 88.90 | + | -231.80572196 | 0.6240E-05 | 89.32 | + | -231.80572052 | 0.5931E-05 | 89.74 | + | -231.80572150 | 0.5322E-05 | 90.16 | + | -231.80572299 | 0.5070E-05 | 90.57 | + | -231.80572435 | 0.4825E-05 | 90.99 | + | -231.80572740 | 0.4575E-05 | 91.41 | + | -231.80572812 | 0.4136E-05 | 91.83 | + | -231.80572667 | 0.3904E-05 | 92.25 | + | -231.80572641 | 0.3526E-05 | 92.66 | + | -231.80572734 | 0.3352E-05 | 93.08 | + | -231.80572923 | 0.2997E-05 | 93.50 | + | -231.80572857 | 0.2716E-05 | 93.92 | + | -231.80572984 | 0.2452E-05 | 94.33 | + | -231.80572846 | 0.2219E-05 | 94.75 | + | -231.80572965 | 0.2026E-05 | 95.17 | + | -231.80572998 | 0.1864E-05 | 95.58 | + | -231.80573034 | 0.1634E-05 | 96.00 | + | -231.80573038 | 0.1455E-05 | 96.42 | + | -231.80572994 | 0.1339E-05 | 96.84 | + | -231.80573009 | 0.1191E-05 | 97.26 | + | -231.80573022 | 0.1077E-05 | 97.68 | + | -231.80573054 | 0.9794E-06 | 98.10 | + | -231.80573088 | 0.8814E-06 | 98.52 | + | -231.80573038 | 0.8139E-06 | 98.95 | + | -231.80573031 | 0.4206E-06 | 99.38 | + | -231.80572937 | 0.2185E-06 | 99.82 | + |---------------+------------+-------| + + Time: 239.890999078751 s + + E(CCSD(T)) = -231.805729365546 Ha + E(T) = -0.051806432976 Ha + Correlation = -1.026026443769 Ha + + #+begin_src gnuplot :var data=benzene_tz :results file :file benzene_tz.png +reset +set grid +set format y "%10.4f" +set ylabel "(T) (a.u)" +set xlabel "Wall clock time (s)" +plot data using :1:2 w errorlines notitle, -231.805729365546 notitle + #+end_src + + #+RESULTS: + [[file:benzene_tz.png]] + +** Streptocyanine QZ + +*** Geometry + + #+begin_example +8 +Streptocyanine-C1 +C 0.000000 0.000000 0.425929 +N 0.000000 1.161139 -0.177701 +N 0.000000 -1.161139 -0.177701 +H 0.000000 0.000000 1.505176 +H 0.000000 1.254035 -1.182034 +H 0.000000 -1.254035 -1.182034 +H 0.000000 2.007765 0.367245 +H 0.000000 -2.007765 0.367245 + #+end_example + + 315 MOs + HF: -149.5404341190290 + +*** Stochastic algorithm + Time: 127.198801040649 s + + Successful convergence after 10 iterations + + E(CCSD) = -150.162036576177 Ha + Correlation = -0.621602548836 Ha + Conv = 6.91E-07 + + #+NAME:strepto_qz + |---------------+------------+-------| + | E(CCSD(T)) | Error | % | + |---------------+------------+-------| + | -150.18755289 | 0.3236E-03 | 1.33 | + | -150.18749603 | 0.2240E-03 | 2.69 | + | -150.18753707 | 0.1571E-03 | 4.05 | + | -150.18764846 | 0.1373E-03 | 5.41 | + | -150.18760591 | 0.1214E-03 | 6.77 | + | -150.18754960 | 0.9845E-04 | 8.13 | + | -150.18754334 | 0.9176E-04 | 9.49 | + | -150.18755251 | 0.7994E-04 | 10.84 | + | -150.18754178 | 0.7515E-04 | 12.20 | + | -150.18754220 | 0.7023E-04 | 13.56 | + | -150.18754476 | 0.6258E-04 | 14.92 | + | -150.18755984 | 0.5938E-04 | 16.27 | + | -150.18757249 | 0.5661E-04 | 17.63 | + | -150.18756762 | 0.4951E-04 | 18.99 | + | -150.18756197 | 0.4759E-04 | 20.35 | + | -150.18757288 | 0.4598E-04 | 21.70 | + | -150.18758115 | 0.4099E-04 | 23.06 | + | -150.18758419 | 0.3965E-04 | 24.41 | + | -150.18757470 | 0.3824E-04 | 25.77 | + | -150.18757089 | 0.3491E-04 | 27.12 | + | -150.18757876 | 0.3382E-04 | 28.48 | + | -150.18760689 | 0.3078E-04 | 29.84 | + | -150.18759859 | 0.2991E-04 | 31.19 | + | -150.18760844 | 0.2776E-04 | 32.55 | + | -150.18761368 | 0.2702E-04 | 33.90 | + | -150.18762310 | 0.2486E-04 | 35.26 | + | -150.18762591 | 0.2429E-04 | 36.62 | + | -150.18762535 | 0.2228E-04 | 37.97 | + | -150.18762385 | 0.2176E-04 | 39.33 | + | -150.18763225 | 0.2007E-04 | 40.68 | + | -150.18763223 | 0.1958E-04 | 42.04 | + | -150.18763397 | 0.1798E-04 | 43.39 | + | -150.18763340 | 0.1757E-04 | 44.75 | + | -150.18764070 | 0.1621E-04 | 46.10 | + | -150.18763986 | 0.1498E-04 | 47.46 | + | -150.18763739 | 0.1464E-04 | 48.82 | + | -150.18763883 | 0.1346E-04 | 50.17 | + | -150.18764267 | 0.1255E-04 | 51.53 | + | -150.18764269 | 0.1229E-04 | 52.88 | + | -150.18764424 | 0.1142E-04 | 54.24 | + | -150.18765046 | 0.1058E-04 | 55.60 | + | -150.18765008 | 0.9804E-05 | 56.95 | + | -150.18765061 | 0.9602E-05 | 58.31 | + | -150.18764718 | 0.8941E-05 | 59.66 | + | -150.18765089 | 0.8398E-05 | 61.02 | + | -150.18764789 | 0.7875E-05 | 62.37 | + | -150.18764931 | 0.7430E-05 | 63.72 | + | -150.18764581 | 0.6968E-05 | 65.08 | + | -150.18764195 | 0.6562E-05 | 66.43 | + | -150.18764743 | 0.6188E-05 | 67.79 | + | -150.18764632 | 0.5825E-05 | 69.14 | + | -150.18764715 | 0.5539E-05 | 70.49 | + | -150.18765097 | 0.5292E-05 | 71.84 | + | -150.18765066 | 0.5036E-05 | 73.20 | + | -150.18764911 | 0.4698E-05 | 74.55 | + | -150.18765017 | 0.4478E-05 | 75.90 | + | -150.18764929 | 0.4274E-05 | 77.25 | + | -150.18764876 | 0.4021E-05 | 78.61 | + | -150.18764747 | 0.3796E-05 | 79.96 | + | -150.18764725 | 0.3571E-05 | 81.31 | + | -150.18764619 | 0.3359E-05 | 82.66 | + | -150.18764469 | 0.3151E-05 | 84.01 | + | -150.18764433 | 0.2899E-05 | 85.36 | + | -150.18764369 | 0.2633E-05 | 86.71 | + | -150.18764453 | 0.2399E-05 | 88.06 | + | -150.18764511 | 0.2151E-05 | 89.41 | + | -150.18764428 | 0.1906E-05 | 90.76 | + | -150.18764536 | 0.1634E-05 | 92.12 | + | -150.18764554 | 0.1442E-05 | 93.47 | + | -150.18764540 | 0.1139E-05 | 94.82 | + | -150.18764707 | 0.7326E-06 | 96.18 | + | -150.18764777 | 0.2304E-06 | 97.55 | + | -150.18764760 | NaN | 98.92 | + |---------------+------------+-------| + + Time: 74.8391861915588 s + + E(CCSD(T)) = -150.187647603273 Ha + E(T) = -0.025611027096 Ha + Correlation = -0.647213575932 Ha + + #+begin_src gnuplot :var data=strepto_qz :results file :file strepto qz.png +reset +set grid +set format y "%10.4f" +set ylabel "(T) (a.u)" +set xlabel "Wall clock time (s)" +plot data using :1:2 w errorlines notitle, -150.187647603273 notitle + #+end_src + + #+RESULTS: + [[file:strepto qz.png]] + +** Caffeine def2-svp +*** Geometry + + #+begin_example +H -3.380413 -1.127237 0.573304 +N 0.966830 -1.073743 -0.819823 +C 0.056729 0.852720 0.392316 +N -1.375174 -1.021224 -0.057055 +C -1.261502 0.259071 0.523414 +C -0.306834 -1.683633 -0.716934 +C 1.139424 0.187412 -0.270090 +N 0.560263 2.083910 0.825159 +O -0.492680 -2.818056 -1.209473 +C -2.632807 -1.730396 -0.006095 +O -2.230134 0.798862 1.089973 +H 2.549699 2.973498 0.622959 +C 2.052743 -1.736089 -1.493128 +H -2.480772 -2.726953 0.488263 +H -3.008904 -1.902526 -1.049802 +H 2.917610 -1.848152 -0.785787 +H 2.378786 -1.121192 -2.374366 +H 1.718988 -2.748992 -1.843921 +C -0.151845 3.097005 1.534835 +C 1.893410 2.118125 0.419319 +N 2.286125 0.996844 -0.244030 +H -0.168703 4.043656 0.930109 +H 0.353532 3.297906 2.517775 +H -1.207450 2.753759 1.720305 + #+end_example + HF: -675.7951033355195 + + Time: 125.921180963516 s + + E(CCSD) = -677.937618736963 Ha + Correlation = -2.142515403784 Ha + Conv = 5.18E-07 + + #+NAME:caffeine_svp + |---------------+------------+-------| + | E(CCSD(T)) | Error | % | + |---------------+------------+-------| + | -678.02853922 | 0.5258E-02 | 0.10 | + | -678.02976334 | 0.3787E-02 | 0.19 | + | -678.02906265 | 0.3220E-02 | 0.27 | + | -678.02888097 | 0.3069E-02 | 0.35 | + | -678.02579694 | 0.2578E-02 | 0.43 | + | -678.02539115 | 0.2311E-02 | 0.51 | + | -678.02621342 | 0.2161E-02 | 0.59 | + | -678.02699050 | 0.2054E-02 | 0.67 | + | -678.02692044 | 0.1975E-02 | 0.75 | + | -678.02637757 | 0.1821E-02 | 0.83 | + | -678.02647872 | 0.1720E-02 | 0.92 | + | -678.02562780 | 0.1627E-02 | 0.99 | + | -678.02619592 | 0.1579E-02 | 1.07 | + | -678.02595517 | 0.1507E-02 | 1.15 | + | -678.02586955 | 0.1442E-02 | 1.23 | + | -678.02637232 | 0.1414E-02 | 1.31 | + | -678.02664314 | 0.1399E-02 | 1.39 | + | -678.02689058 | 0.1373E-02 | 1.47 | + | -678.02685870 | 0.1328E-02 | 1.55 | + | -678.02652022 | 0.1284E-02 | 1.63 | + | -678.02684814 | 0.1283E-02 | 1.71 | + | -678.02660690 | 0.1240E-02 | 1.79 | + | -678.02661689 | 0.1230E-02 | 1.87 | + | -678.02656400 | 0.1202E-02 | 1.94 | + | -678.02649762 | 0.1174E-02 | 2.03 | + | -678.02622086 | 0.1144E-02 | 2.10 | + | -678.02622715 | 0.1114E-02 | 2.18 | + | -678.02626622 | 0.1091E-02 | 2.26 | + | -678.02636527 | 0.1078E-02 | 2.34 | + | -678.02631587 | 0.1058E-02 | 2.42 | + | -678.02657845 | 0.1043E-02 | 2.50 | + | -678.02687191 | 0.1048E-02 | 2.58 | + | -678.02655328 | 0.1025E-02 | 2.65 | + | -678.02667586 | 0.1013E-02 | 2.74 | + | -678.02662550 | 0.9936E-03 | 2.81 | + | -678.02673402 | 0.9801E-03 | 2.89 | + | -678.02671217 | 0.9668E-03 | 2.97 | + | -678.02654649 | 0.9498E-03 | 3.05 | + | -678.02641864 | 0.9325E-03 | 3.13 | + | -678.02619833 | 0.9146E-03 | 3.20 | + | -678.02635933 | 0.9117E-03 | 3.28 | + | -678.02638714 | 0.9020E-03 | 3.36 | + | -678.02638762 | 0.8877E-03 | 3.44 | + | -678.02620569 | 0.8725E-03 | 3.52 | + | -678.02632108 | 0.8752E-03 | 3.60 | + | -678.02624951 | 0.8666E-03 | 3.68 | + | -678.02634128 | 0.8553E-03 | 3.76 | + | -678.02629702 | 0.8438E-03 | 3.84 | + | -678.02620958 | 0.8327E-03 | 3.91 | + | -678.02601577 | 0.8197E-03 | 3.99 | + | -678.02593911 | 0.8071E-03 | 4.08 | + | -678.02593695 | 0.7985E-03 | 4.15 | + | -678.02585749 | 0.7913E-03 | 4.23 | + | -678.02574423 | 0.7805E-03 | 4.31 | + | -678.02573482 | 0.7751E-03 | 4.38 | + | -678.02592698 | 0.7814E-03 | 4.46 | + | -678.02594764 | 0.7810E-03 | 4.54 | + | -678.02615643 | 0.7901E-03 | 4.62 | + | -678.02619722 | 0.7823E-03 | 4.70 | + | -678.02614753 | 0.7742E-03 | 4.78 | + | -678.02606502 | 0.7656E-03 | 4.87 | + | -678.02599775 | 0.7571E-03 | 4.95 | + | -678.02589536 | 0.7476E-03 | 5.03 | + | -678.02574244 | 0.7389E-03 | 5.10 | + | -678.02565028 | 0.7315E-03 | 5.18 | + | -678.02548026 | 0.7217E-03 | 5.26 | + | -678.02540730 | 0.7144E-03 | 5.34 | + | -678.02550370 | 0.7120E-03 | 5.42 | + | -678.02574955 | 0.7153E-03 | 5.50 | + | -678.02576361 | 0.7083E-03 | 5.58 | + | -678.02572066 | 0.7007E-03 | 5.67 | + | -678.02577570 | 0.6947E-03 | 5.74 | + | -678.02573023 | 0.6878E-03 | 5.82 | + | -678.02577669 | 0.6918E-03 | 5.90 | + | -678.02570115 | 0.6847E-03 | 5.98 | + | -678.02568007 | 0.6793E-03 | 6.05 | + | -678.02573338 | 0.6747E-03 | 6.13 | + | -678.02578413 | 0.6720E-03 | 6.21 | + | -678.02589182 | 0.6733E-03 | 6.29 | + | -678.02592822 | 0.6699E-03 | 6.37 | + | -678.02596892 | 0.6636E-03 | 6.45 | + | -678.02595619 | 0.6592E-03 | 6.52 | + | -678.02599991 | 0.6573E-03 | 6.60 | + | -678.02598874 | 0.6537E-03 | 6.68 | + | -678.02599536 | 0.6488E-03 | 6.77 | + | -678.02594647 | 0.6429E-03 | 6.84 | + | -678.02606288 | 0.6408E-03 | 6.92 | + | -678.02614621 | 0.6408E-03 | 7.00 | + | -678.02627335 | 0.6429E-03 | 7.08 | + | -678.02628164 | 0.6393E-03 | 7.16 | + | -678.02622248 | 0.6342E-03 | 7.24 | + | -678.02618428 | 0.6292E-03 | 7.31 | + | -678.02616016 | 0.6250E-03 | 7.39 | + | -678.02614620 | 0.6205E-03 | 7.47 | + | -678.02610230 | 0.6156E-03 | 7.55 | + | -678.02611827 | 0.6128E-03 | 7.63 | + | -678.02611198 | 0.6100E-03 | 7.71 | + | -678.02618189 | 0.6111E-03 | 7.79 | + | -678.02615684 | 0.6065E-03 | 7.86 | + | -678.02613302 | 0.6021E-03 | 7.95 | + | -678.02608384 | 0.5969E-03 | 8.03 | + | -678.02608570 | 0.5940E-03 | 8.10 | + | -678.02615085 | 0.5903E-03 | 8.19 | + | -678.02609892 | 0.5860E-03 | 8.26 | + | -678.02608281 | 0.5829E-03 | 8.34 | + | -678.02607409 | 0.5786E-03 | 8.42 | + | -678.02608769 | 0.5759E-03 | 8.49 | + | -678.02607334 | 0.5722E-03 | 8.57 | + | -678.02604848 | 0.5678E-03 | 8.65 | + | -678.02598877 | 0.5641E-03 | 8.73 | + | -678.02598935 | 0.5636E-03 | 8.81 | + | -678.02599804 | 0.5605E-03 | 8.89 | + | -678.02599312 | 0.5575E-03 | 8.96 | + | -678.02601211 | 0.5556E-03 | 9.05 | + | -678.02597626 | 0.5519E-03 | 9.12 | + | -678.02597768 | 0.5484E-03 | 9.20 | + | -678.02596787 | 0.5447E-03 | 9.29 | + | -678.02603084 | 0.5425E-03 | 9.36 | + | -678.02603386 | 0.5399E-03 | 9.44 | + | -678.02601157 | 0.5366E-03 | 9.52 | + | -678.02616305 | 0.5370E-03 | 9.61 | + | -678.02625585 | 0.5358E-03 | 9.69 | + | -678.02622004 | 0.5332E-03 | 9.76 | + | -678.02621213 | 0.5308E-03 | 9.84 | + | -678.02620178 | 0.5281E-03 | 9.92 | + | -678.02620548 | 0.5258E-03 | 10.00 | + | -678.02625366 | 0.5265E-03 | 10.08 | + | -678.02617978 | 0.5231E-03 | 10.16 | + | -678.02610918 | 0.5193E-03 | 10.24 | + | -678.02609771 | 0.5162E-03 | 10.32 | + | -678.02613070 | 0.5139E-03 | 10.40 | + | -678.02613181 | 0.5125E-03 | 10.47 | + | -678.02609490 | 0.5096E-03 | 10.56 | + | -678.02601821 | 0.5068E-03 | 10.63 | + | -678.02602616 | 0.5048E-03 | 10.71 | + | -678.02600678 | 0.5018E-03 | 10.79 | + | -678.02603594 | 0.5006E-03 | 10.87 | + | -678.02599939 | 0.4983E-03 | 10.95 | + | -678.02597726 | 0.4961E-03 | 11.02 | + | -678.02603454 | 0.4945E-03 | 11.10 | + | -678.02600197 | 0.4914E-03 | 11.18 | + | -678.02604507 | 0.4917E-03 | 11.26 | + | -678.02609435 | 0.4901E-03 | 11.34 | + | -678.02639591 | 0.3986E-03 | 11.42 | + | -678.02644330 | 0.3984E-03 | 11.50 | + | -678.02645665 | 0.3971E-03 | 11.58 | + | -678.02640918 | 0.3947E-03 | 11.66 | + | -678.02640199 | 0.3930E-03 | 11.74 | + | -678.02640530 | 0.3911E-03 | 11.82 | + | -678.02634926 | 0.3890E-03 | 11.90 | + | -678.02638905 | 0.3876E-03 | 11.98 | + | -678.02640485 | 0.3888E-03 | 12.06 | + | -678.02636158 | 0.3869E-03 | 12.14 | + | -678.02642047 | 0.3860E-03 | 12.22 | + | -678.02637355 | 0.3843E-03 | 12.30 | + | -678.02633055 | 0.3823E-03 | 12.38 | + | -678.02634384 | 0.3811E-03 | 12.45 | + | -678.02638266 | 0.3797E-03 | 12.53 | + | -678.02639829 | 0.3780E-03 | 12.61 | + | -678.02638164 | 0.3762E-03 | 12.69 | + | -678.02638919 | 0.3748E-03 | 12.77 | + | -678.02632591 | 0.3728E-03 | 12.85 | + | -678.02632059 | 0.3714E-03 | 12.92 | + | -678.02630756 | 0.3695E-03 | 13.00 | + | -678.02630362 | 0.3688E-03 | 13.08 | + | -678.02632925 | 0.3676E-03 | 13.16 | + | -678.02633379 | 0.3661E-03 | 13.24 | + | -678.02631000 | 0.3646E-03 | 13.32 | + | -678.02628425 | 0.3629E-03 | 13.40 | + | -678.02625660 | 0.3616E-03 | 13.47 | + | -678.02624652 | 0.3616E-03 | 13.55 | + | -678.02626584 | 0.3607E-03 | 13.63 | + | -678.02629342 | 0.3597E-03 | 13.70 | + | -678.02630045 | 0.3592E-03 | 13.79 | + | -678.02629182 | 0.3579E-03 | 13.86 | + | -678.02634662 | 0.3572E-03 | 13.95 | + | -678.02633349 | 0.3558E-03 | 14.03 | + | -678.02631804 | 0.3543E-03 | 14.10 | + | -678.02629839 | 0.3532E-03 | 14.18 | + | -678.02629671 | 0.3517E-03 | 14.26 | + | -678.02632929 | 0.3508E-03 | 14.34 | + | -678.02633752 | 0.3501E-03 | 14.42 | + | -678.02634198 | 0.3490E-03 | 14.50 | + | -678.02640084 | 0.3499E-03 | 14.58 | + | -678.02637622 | 0.3486E-03 | 14.65 | + | -678.02638770 | 0.3475E-03 | 14.74 | + | -678.02636350 | 0.3466E-03 | 14.82 | + | -678.02637033 | 0.3457E-03 | 14.89 | + | -678.02636321 | 0.3443E-03 | 14.97 | + | -678.02635260 | 0.3432E-03 | 15.05 | + | -678.02632719 | 0.3418E-03 | 15.14 | + | -678.02633278 | 0.3407E-03 | 15.21 | + | -678.02629352 | 0.3390E-03 | 15.29 | + | -678.02632960 | 0.3384E-03 | 15.37 | + | -678.02632434 | 0.3372E-03 | 15.44 | + | -678.02630471 | 0.3357E-03 | 15.52 | + | -678.02638707 | 0.3374E-03 | 15.60 | + | -678.02640638 | 0.3368E-03 | 15.68 | + | -678.02640266 | 0.3357E-03 | 15.76 | + | -678.02637315 | 0.3343E-03 | 15.84 | + | -678.02637397 | 0.3334E-03 | 15.91 | + | -678.02635827 | 0.3319E-03 | 15.99 | + | -678.02636463 | 0.3305E-03 | 16.07 | + | -678.02637029 | 0.3299E-03 | 16.15 | + | -678.02636120 | 0.3290E-03 | 16.23 | + | -678.02633933 | 0.3278E-03 | 16.31 | + | -678.02632651 | 0.3266E-03 | 16.39 | + | -678.02630377 | 0.3255E-03 | 16.47 | + | -678.02627527 | 0.3242E-03 | 16.56 | + | -678.02624228 | 0.3230E-03 | 16.63 | + | -678.02621270 | 0.3218E-03 | 16.72 | + | -678.02619352 | 0.3205E-03 | 16.79 | + | -678.02618604 | 0.3197E-03 | 16.87 | + | -678.02618344 | 0.3189E-03 | 16.95 | + | -678.02615704 | 0.3175E-03 | 17.03 | + | -678.02618214 | 0.3176E-03 | 17.11 | + | -678.02617113 | 0.3166E-03 | 17.19 | + | -678.02615187 | 0.3157E-03 | 17.26 | + | -678.02612469 | 0.3147E-03 | 17.34 | + | -678.02611844 | 0.3138E-03 | 17.43 | + | -678.02613556 | 0.3130E-03 | 17.51 | + | -678.02614441 | 0.3126E-03 | 17.59 | + | -678.02613057 | 0.3116E-03 | 17.67 | + | -678.02613356 | 0.3111E-03 | 17.74 | + | -678.02611422 | 0.3101E-03 | 17.82 | + | -678.02610066 | 0.3094E-03 | 17.90 | + | -678.02615220 | 0.3100E-03 | 17.98 | + | -678.02616512 | 0.3095E-03 | 18.06 | + | -678.02617293 | 0.3090E-03 | 18.13 | + | -678.02618057 | 0.3081E-03 | 18.21 | + | -678.02618078 | 0.3074E-03 | 18.29 | + | -678.02618831 | 0.3066E-03 | 18.37 | + | -678.02620266 | 0.3062E-03 | 18.45 | + | -678.02624681 | 0.3059E-03 | 18.53 | + | -678.02621762 | 0.3049E-03 | 18.61 | + | -678.02620014 | 0.3038E-03 | 18.69 | + | -678.02620583 | 0.3031E-03 | 18.77 | + | -678.02623418 | 0.3031E-03 | 18.85 | + | -678.02621930 | 0.3022E-03 | 18.93 | + | -678.02619654 | 0.3012E-03 | 19.00 | + | -678.02619958 | 0.3005E-03 | 19.08 | + | -678.02620455 | 0.3000E-03 | 19.16 | + | -678.02621012 | 0.2994E-03 | 19.23 | + | -678.02620154 | 0.2985E-03 | 19.30 | + | -678.02619311 | 0.2981E-03 | 19.38 | + | -678.02616212 | 0.2970E-03 | 19.46 | + | -678.02616745 | 0.2962E-03 | 19.54 | + | -678.02613904 | 0.2950E-03 | 19.62 | + | -678.02612359 | 0.2940E-03 | 19.70 | + | -678.02612577 | 0.2935E-03 | 19.78 | + | -678.02612237 | 0.2927E-03 | 19.86 | + | -678.02612675 | 0.2921E-03 | 19.94 | + | -678.02611442 | 0.2912E-03 | 20.02 | + | -678.02610412 | 0.2905E-03 | 20.10 | + | -678.02611582 | 0.2900E-03 | 20.18 | + | -678.02613239 | 0.2892E-03 | 20.26 | + | -678.02614391 | 0.2886E-03 | 20.33 | + | -678.02612516 | 0.2878E-03 | 20.41 | + | -678.02612616 | 0.2870E-03 | 20.49 | + | -678.02613426 | 0.2863E-03 | 20.57 | + | -678.02612940 | 0.2853E-03 | 20.65 | + | -678.02610556 | 0.2470E-03 | 20.73 | + | -678.02610145 | 0.2464E-03 | 20.81 | + | -678.02607889 | 0.2457E-03 | 20.90 | + | -678.02606769 | 0.2449E-03 | 20.98 | + | -678.02608965 | 0.2444E-03 | 21.06 | + | -678.02608284 | 0.2435E-03 | 21.13 | + | -678.02607711 | 0.2427E-03 | 21.21 | + | -678.02609378 | 0.2421E-03 | 21.29 | + | -678.02607486 | 0.2414E-03 | 21.37 | + | -678.02607368 | 0.2408E-03 | 21.45 | + | -678.02608108 | 0.2402E-03 | 21.53 | + | -678.02608720 | 0.2397E-03 | 21.61 | + | -678.02608655 | 0.2396E-03 | 21.69 | + | -678.02610551 | 0.2392E-03 | 21.77 | + | -678.02607995 | 0.2383E-03 | 21.85 | + | -678.02605807 | 0.2375E-03 | 21.93 | + | -678.02602864 | 0.2369E-03 | 22.00 | + | -678.02603523 | 0.2365E-03 | 22.08 | + | -678.02604275 | 0.2359E-03 | 22.17 | + | -678.02606612 | 0.2360E-03 | 22.25 | + | -678.02605947 | 0.2354E-03 | 22.32 | + | -678.02603959 | 0.2347E-03 | 22.40 | + | -678.02603868 | 0.2340E-03 | 22.49 | + | -678.02604945 | 0.2337E-03 | 22.56 | + | -678.02601817 | 0.2330E-03 | 22.64 | + | -678.02603633 | 0.2329E-03 | 22.72 | + | -678.02605026 | 0.2324E-03 | 22.80 | + | -678.02603659 | 0.2317E-03 | 22.88 | + | -678.02603654 | 0.2311E-03 | 22.97 | + | -678.02603072 | 0.2305E-03 | 23.04 | + | -678.02603012 | 0.2301E-03 | 23.12 | + | -678.02604038 | 0.2298E-03 | 23.20 | + | -678.02604082 | 0.2294E-03 | 23.28 | + | -678.02607429 | 0.2293E-03 | 23.36 | + | -678.02606579 | 0.2289E-03 | 23.43 | + | -678.02607164 | 0.2286E-03 | 23.51 | + | -678.02608144 | 0.2282E-03 | 23.60 | + | -678.02607438 | 0.2276E-03 | 23.68 | + | -678.02606522 | 0.2272E-03 | 23.76 | + | -678.02607896 | 0.2267E-03 | 23.84 | + | -678.02608842 | 0.2262E-03 | 23.92 | + | -678.02607339 | 0.2257E-03 | 24.00 | + | -678.02605228 | 0.2252E-03 | 24.08 | + | -678.02606007 | 0.2247E-03 | 24.16 | + | -678.02606018 | 0.2242E-03 | 24.24 | + | -678.02606494 | 0.2238E-03 | 24.31 | + | -678.02609212 | 0.2236E-03 | 24.39 | + | -678.02609217 | 0.2232E-03 | 24.47 | + | -678.02608586 | 0.2227E-03 | 24.54 | + | -678.02608815 | 0.2222E-03 | 24.62 | + | -678.02610090 | 0.2219E-03 | 24.70 | + | -678.02609152 | 0.2214E-03 | 24.78 | + | -678.02610035 | 0.2211E-03 | 24.85 | + | -678.02609807 | 0.2207E-03 | 24.93 | + | -678.02608812 | 0.2203E-03 | 25.00 | + | -678.02607523 | 0.2197E-03 | 25.08 | + | -678.02609734 | 0.2195E-03 | 25.16 | + | -678.02607320 | 0.2188E-03 | 25.24 | + | -678.02606916 | 0.2184E-03 | 25.31 | + | -678.02605308 | 0.2179E-03 | 25.39 | + | -678.02606153 | 0.2176E-03 | 25.47 | + | -678.02605711 | 0.2170E-03 | 25.55 | + | -678.02606474 | 0.2166E-03 | 25.63 | + | -678.02605328 | 0.2161E-03 | 25.71 | + | -678.02604935 | 0.2156E-03 | 25.79 | + | -678.02605021 | 0.2153E-03 | 25.87 | + | -678.02605473 | 0.2147E-03 | 25.95 | + | -678.02606813 | 0.2144E-03 | 26.03 | + | -678.02606241 | 0.2140E-03 | 26.11 | + | -678.02605729 | 0.2136E-03 | 26.19 | + | -678.02606254 | 0.2131E-03 | 26.27 | + | -678.02608133 | 0.2127E-03 | 26.35 | + | -678.02607459 | 0.2123E-03 | 26.43 | + | -678.02604597 | 0.2117E-03 | 26.52 | + | -678.02604872 | 0.2115E-03 | 26.59 | + | -678.02605380 | 0.2111E-03 | 26.67 | + | -678.02604658 | 0.2106E-03 | 26.76 | + | -678.02605234 | 0.2102E-03 | 26.84 | + | -678.02603972 | 0.2099E-03 | 26.91 | + | -678.02602235 | 0.2093E-03 | 26.99 | + | -678.02602424 | 0.2088E-03 | 27.08 | + | -678.02599840 | 0.2082E-03 | 27.17 | + | -678.02599195 | 0.2077E-03 | 27.25 | + | -678.02599747 | 0.2073E-03 | 27.32 | + | -678.02597648 | 0.2067E-03 | 27.40 | + | -678.02597909 | 0.2064E-03 | 27.48 | + | -678.02599035 | 0.2060E-03 | 27.56 | + | -678.02600115 | 0.2055E-03 | 27.64 | + | -678.02600134 | 0.2052E-03 | 27.72 | + | -678.02608356 | 0.1905E-03 | 27.80 | + | -678.02607887 | 0.1901E-03 | 27.88 | + | -678.02608516 | 0.1899E-03 | 27.96 | + | -678.02607817 | 0.1895E-03 | 28.04 | + | -678.02606440 | 0.1891E-03 | 28.12 | + | -678.02607021 | 0.1888E-03 | 28.20 | + | -678.02607421 | 0.1885E-03 | 28.28 | + | -678.02606208 | 0.1881E-03 | 28.36 | + | -678.02607092 | 0.1879E-03 | 28.45 | + | -678.02608183 | 0.1876E-03 | 28.53 | + | -678.02609352 | 0.1874E-03 | 28.61 | + | -678.02609971 | 0.1871E-03 | 28.69 | + | -678.02609476 | 0.1867E-03 | 28.78 | + | -678.02608991 | 0.1863E-03 | 28.85 | + | -678.02608095 | 0.1860E-03 | 28.92 | + | -678.02608413 | 0.1857E-03 | 29.01 | + | -678.02608126 | 0.1853E-03 | 29.09 | + | -678.02608495 | 0.1850E-03 | 29.17 | + | -678.02606722 | 0.1846E-03 | 29.25 | + | -678.02607311 | 0.1843E-03 | 29.33 | + | -678.02608056 | 0.1840E-03 | 29.41 | + | -678.02608175 | 0.1838E-03 | 29.48 | + | -678.02609396 | 0.1838E-03 | 29.57 | + | -678.02609583 | 0.1835E-03 | 29.64 | + | -678.02609841 | 0.1833E-03 | 29.72 | + | -678.02607932 | 0.1828E-03 | 29.80 | + | -678.02608625 | 0.1825E-03 | 29.88 | + | -678.02608028 | 0.1822E-03 | 29.96 | + | -678.02608193 | 0.1819E-03 | 30.05 | + | -678.02607805 | 0.1816E-03 | 30.12 | + | -678.02606295 | 0.1813E-03 | 30.20 | + | -678.02605146 | 0.1808E-03 | 30.28 | + | -678.02605424 | 0.1805E-03 | 30.36 | + | -678.02604814 | 0.1802E-03 | 30.44 | + | -678.02604207 | 0.1798E-03 | 30.52 | + | -678.02604047 | 0.1794E-03 | 30.60 | + | -678.02603503 | 0.1791E-03 | 30.67 | + | -678.02603101 | 0.1787E-03 | 30.75 | + | -678.02602956 | 0.1784E-03 | 30.83 | + | -678.02602480 | 0.1781E-03 | 30.91 | + | -678.02603217 | 0.1780E-03 | 30.99 | + | -678.02603465 | 0.1777E-03 | 31.07 | + | -678.02604053 | 0.1775E-03 | 31.14 | + | -678.02602691 | 0.1771E-03 | 31.22 | + | -678.02604001 | 0.1769E-03 | 31.31 | + | -678.02604046 | 0.1766E-03 | 31.38 | + | -678.02603915 | 0.1764E-03 | 31.47 | + | -678.02603158 | 0.1761E-03 | 31.54 | + | -678.02604616 | 0.1758E-03 | 31.62 | + | -678.02604322 | 0.1755E-03 | 31.69 | + | -678.02603979 | 0.1752E-03 | 31.77 | + | -678.02604155 | 0.1749E-03 | 31.85 | + | -678.02603450 | 0.1746E-03 | 31.93 | + | -678.02602211 | 0.1743E-03 | 32.01 | + | -678.02601848 | 0.1741E-03 | 32.10 | + | -678.02601638 | 0.1737E-03 | 32.18 | + | -678.02600568 | 0.1734E-03 | 32.25 | + | -678.02599472 | 0.1731E-03 | 32.33 | + | -678.02599446 | 0.1729E-03 | 32.41 | + | -678.02598212 | 0.1725E-03 | 32.49 | + | -678.02598715 | 0.1724E-03 | 32.57 | + | -678.02597528 | 0.1720E-03 | 32.65 | + | -678.02596768 | 0.1716E-03 | 32.72 | + | -678.02595901 | 0.1713E-03 | 32.81 | + | -678.02595794 | 0.1711E-03 | 32.88 | + | -678.02595735 | 0.1708E-03 | 32.97 | + | -678.02595048 | 0.1705E-03 | 33.05 | + | -678.02594412 | 0.1701E-03 | 33.13 | + | -678.02593159 | 0.1698E-03 | 33.21 | + | -678.02592163 | 0.1695E-03 | 33.29 | + | -678.02591348 | 0.1693E-03 | 33.37 | + | -678.02592315 | 0.1692E-03 | 33.45 | + | -678.02591972 | 0.1689E-03 | 33.53 | + | -678.02590635 | 0.1684E-03 | 33.61 | + | -678.02588948 | 0.1580E-03 | 33.70 | + | -678.02588981 | 0.1577E-03 | 33.77 | + | -678.02588773 | 0.1574E-03 | 33.85 | + | -678.02588720 | 0.1572E-03 | 33.93 | + | -678.02588919 | 0.1570E-03 | 34.01 | + | -678.02590015 | 0.1568E-03 | 34.09 | + | -678.02589667 | 0.1566E-03 | 34.17 | + | -678.02588918 | 0.1563E-03 | 34.25 | + | -678.02588912 | 0.1560E-03 | 34.33 | + | -678.02589661 | 0.1558E-03 | 34.41 | + | -678.02590532 | 0.1557E-03 | 34.49 | + | -678.02590423 | 0.1554E-03 | 34.57 | + | -678.02591523 | 0.1552E-03 | 34.64 | + | -678.02591345 | 0.1550E-03 | 34.73 | + | -678.02590907 | 0.1547E-03 | 34.81 | + | -678.02590259 | 0.1544E-03 | 34.89 | + | -678.02590705 | 0.1542E-03 | 34.97 | + | -678.02590706 | 0.1540E-03 | 35.05 | + | -678.02591051 | 0.1538E-03 | 35.12 | + | -678.02590760 | 0.1535E-03 | 35.21 | + | -678.02589643 | 0.1533E-03 | 35.28 | + | -678.02590090 | 0.1530E-03 | 35.36 | + | -678.02590181 | 0.1528E-03 | 35.44 | + | -678.02589238 | 0.1524E-03 | 35.52 | + | -678.02588468 | 0.1522E-03 | 35.60 | + | -678.02588218 | 0.1519E-03 | 35.67 | + | -678.02589418 | 0.1519E-03 | 35.75 | + | -678.02589841 | 0.1516E-03 | 35.84 | + | -678.02589181 | 0.1513E-03 | 35.91 | + | -678.02589229 | 0.1511E-03 | 35.99 | + | -678.02588695 | 0.1509E-03 | 36.07 | + | -678.02590053 | 0.1508E-03 | 36.15 | + | -678.02590285 | 0.1505E-03 | 36.23 | + | -678.02589402 | 0.1502E-03 | 36.31 | + | -678.02588087 | 0.1499E-03 | 36.39 | + | -678.02586841 | 0.1495E-03 | 36.47 | + | -678.02586325 | 0.1493E-03 | 36.54 | + | -678.02586666 | 0.1491E-03 | 36.62 | + | -678.02585607 | 0.1489E-03 | 36.71 | + | -678.02585467 | 0.1487E-03 | 36.78 | + | -678.02585497 | 0.1485E-03 | 36.86 | + | -678.02585706 | 0.1482E-03 | 36.94 | + | -678.02584560 | 0.1479E-03 | 37.02 | + | -678.02584790 | 0.1477E-03 | 37.10 | + | -678.02583388 | 0.1475E-03 | 37.17 | + | -678.02584928 | 0.1473E-03 | 37.25 | + | -678.02584804 | 0.1471E-03 | 37.33 | + | -678.02584032 | 0.1469E-03 | 37.40 | + | -678.02583783 | 0.1466E-03 | 37.49 | + | -678.02583879 | 0.1464E-03 | 37.56 | + | -678.02584001 | 0.1462E-03 | 37.64 | + | -678.02584928 | 0.1460E-03 | 37.71 | + | -678.02583259 | 0.1458E-03 | 37.79 | + | -678.02583676 | 0.1456E-03 | 37.87 | + | -678.02584875 | 0.1456E-03 | 37.95 | + | -678.02585724 | 0.1456E-03 | 38.03 | + | -678.02585733 | 0.1454E-03 | 38.11 | + | -678.02584964 | 0.1452E-03 | 38.19 | + | -678.02584882 | 0.1451E-03 | 38.27 | + | -678.02586013 | 0.1450E-03 | 38.35 | + | -678.02587226 | 0.1448E-03 | 38.42 | + | -678.02586454 | 0.1446E-03 | 38.50 | + | -678.02586056 | 0.1445E-03 | 38.58 | + | -678.02586199 | 0.1443E-03 | 38.66 | + | -678.02599140 | 0.1389E-03 | 38.74 | + | -678.02598438 | 0.1387E-03 | 38.82 | + | -678.02598875 | 0.1385E-03 | 38.90 | + | -678.02598619 | 0.1384E-03 | 38.98 | + | -678.02598819 | 0.1382E-03 | 39.06 | + | -678.02598958 | 0.1380E-03 | 39.14 | + | -678.02599488 | 0.1379E-03 | 39.22 | + | -678.02598909 | 0.1377E-03 | 39.30 | + | -678.02598354 | 0.1375E-03 | 39.38 | + | -678.02599123 | 0.1374E-03 | 39.46 | + | -678.02599444 | 0.1372E-03 | 39.54 | + | -678.02598625 | 0.1370E-03 | 39.62 | + | -678.02598471 | 0.1367E-03 | 39.70 | + | -678.02600613 | 0.1368E-03 | 39.78 | + | -678.02600665 | 0.1365E-03 | 39.86 | + | -678.02600361 | 0.1363E-03 | 39.94 | + | -678.02601746 | 0.1361E-03 | 40.02 | + | -678.02601790 | 0.1359E-03 | 40.10 | + | -678.02602671 | 0.1357E-03 | 40.18 | + | -678.02604156 | 0.1357E-03 | 40.26 | + | -678.02605502 | 0.1356E-03 | 40.33 | + | -678.02605056 | 0.1354E-03 | 40.41 | + | -678.02604965 | 0.1351E-03 | 40.49 | + | -678.02604934 | 0.1350E-03 | 40.57 | + | -678.02604617 | 0.1347E-03 | 40.65 | + | -678.02604133 | 0.1345E-03 | 40.73 | + | -678.02604307 | 0.1343E-03 | 40.81 | + | -678.02604828 | 0.1341E-03 | 40.89 | + | -678.02604418 | 0.1339E-03 | 40.97 | + | -678.02603323 | 0.1337E-03 | 41.05 | + | -678.02602898 | 0.1335E-03 | 41.13 | + | -678.02602949 | 0.1334E-03 | 41.20 | + | -678.02603016 | 0.1332E-03 | 41.28 | + | -678.02602357 | 0.1330E-03 | 41.36 | + | -678.02602551 | 0.1328E-03 | 41.44 | + | -678.02602111 | 0.1326E-03 | 41.52 | + | -678.02601433 | 0.1324E-03 | 41.59 | + | -678.02600852 | 0.1323E-03 | 41.67 | + | -678.02600552 | 0.1321E-03 | 41.75 | + | -678.02601446 | 0.1319E-03 | 41.84 | + | -678.02601142 | 0.1317E-03 | 41.92 | + | -678.02601636 | 0.1315E-03 | 42.00 | + | -678.02601731 | 0.1313E-03 | 42.08 | + | -678.02601411 | 0.1311E-03 | 42.16 | + | -678.02601572 | 0.1309E-03 | 42.24 | + | -678.02600744 | 0.1307E-03 | 42.32 | + | -678.02600033 | 0.1305E-03 | 42.39 | + | -678.02599810 | 0.1303E-03 | 42.48 | + | -678.02599407 | 0.1301E-03 | 42.56 | + | -678.02599358 | 0.1298E-03 | 42.64 | + | -678.02599416 | 0.1297E-03 | 42.72 | + | -678.02599208 | 0.1295E-03 | 42.79 | + | -678.02603344 | 0.1248E-03 | 42.86 | + | -678.02603292 | 0.1246E-03 | 42.94 | + | -678.02603003 | 0.1245E-03 | 43.02 | + | -678.02603056 | 0.1243E-03 | 43.10 | + | -678.02601823 | 0.1241E-03 | 43.18 | + | -678.02601604 | 0.1239E-03 | 43.26 | + | -678.02600631 | 0.1236E-03 | 43.34 | + | -678.02600427 | 0.1235E-03 | 43.42 | + | -678.02600104 | 0.1233E-03 | 43.50 | + | -678.02600550 | 0.1232E-03 | 43.58 | + | -678.02600605 | 0.1229E-03 | 43.66 | + | -678.02600075 | 0.1227E-03 | 43.74 | + | -678.02599404 | 0.1225E-03 | 43.82 | + | -678.02599525 | 0.1224E-03 | 43.89 | + | -678.02599414 | 0.1222E-03 | 43.97 | + | -678.02598445 | 0.1221E-03 | 44.05 | + | -678.02598032 | 0.1219E-03 | 44.13 | + | -678.02598256 | 0.1218E-03 | 44.21 | + | -678.02597560 | 0.1215E-03 | 44.29 | + | -678.02597470 | 0.1214E-03 | 44.38 | + | -678.02598395 | 0.1213E-03 | 44.45 | + | -678.02597854 | 0.1211E-03 | 44.54 | + | -678.02597162 | 0.1209E-03 | 44.61 | + | -678.02598139 | 0.1207E-03 | 44.69 | + | -678.02598402 | 0.1206E-03 | 44.77 | + | -678.02598362 | 0.1204E-03 | 44.85 | + | -678.02599266 | 0.1203E-03 | 44.92 | + | -678.02600672 | 0.1202E-03 | 45.01 | + | -678.02601505 | 0.1201E-03 | 45.09 | + | -678.02601176 | 0.1199E-03 | 45.16 | + | -678.02601205 | 0.1198E-03 | 45.25 | + | -678.02601859 | 0.1197E-03 | 45.31 | + | -678.02601913 | 0.1195E-03 | 45.40 | + | -678.02601287 | 0.1194E-03 | 45.48 | + | -678.02601496 | 0.1192E-03 | 45.56 | + | -678.02601540 | 0.1190E-03 | 45.64 | + | -678.02602270 | 0.1189E-03 | 45.72 | + | -678.02602604 | 0.1187E-03 | 45.79 | + | -678.02602490 | 0.1186E-03 | 45.87 | + | -678.02602870 | 0.1185E-03 | 45.94 | + | -678.02601119 | 0.1183E-03 | 46.03 | + | -678.02601741 | 0.1182E-03 | 46.10 | + | -678.02602543 | 0.1181E-03 | 46.18 | + | -678.02602807 | 0.1179E-03 | 46.26 | + | -678.02603589 | 0.1179E-03 | 46.34 | + | -678.02604040 | 0.1178E-03 | 46.42 | + | -678.02603563 | 0.1175E-03 | 46.50 | + | -678.02602512 | 0.1124E-03 | 46.58 | + | -678.02602355 | 0.1122E-03 | 46.66 | + | -678.02603462 | 0.1121E-03 | 46.74 | + | -678.02603469 | 0.1120E-03 | 46.82 | + | -678.02603957 | 0.1119E-03 | 46.90 | + | -678.02603430 | 0.1118E-03 | 46.98 | + | -678.02603522 | 0.1118E-03 | 47.06 | + | -678.02603096 | 0.1117E-03 | 47.14 | + | -678.02603560 | 0.1116E-03 | 47.22 | + | -678.02605447 | 0.1115E-03 | 47.29 | + | -678.02603730 | 0.1113E-03 | 47.37 | + | -678.02602994 | 0.1111E-03 | 47.46 | + | -678.02603521 | 0.1110E-03 | 47.54 | + | -678.02603871 | 0.1109E-03 | 47.61 | + | -678.02603798 | 0.1107E-03 | 47.69 | + | -678.02603231 | 0.1106E-03 | 47.77 | + | -678.02602907 | 0.1105E-03 | 47.85 | + | -678.02603386 | 0.1103E-03 | 47.94 | + | -678.02604570 | 0.1103E-03 | 48.01 | + | -678.02604884 | 0.1102E-03 | 48.09 | + | -678.02604765 | 0.1101E-03 | 48.17 | + | -678.02605171 | 0.1100E-03 | 48.25 | + | -678.02605584 | 0.1098E-03 | 48.33 | + | -678.02606009 | 0.1097E-03 | 48.40 | + | -678.02606089 | 0.1095E-03 | 48.48 | + | -678.02605553 | 0.1094E-03 | 48.56 | + | -678.02606031 | 0.1092E-03 | 48.63 | + | -678.02606332 | 0.1091E-03 | 48.71 | + | -678.02606253 | 0.1090E-03 | 48.80 | + | -678.02604995 | 0.1088E-03 | 48.87 | + | -678.02604696 | 0.1086E-03 | 48.95 | + | -678.02604123 | 0.1085E-03 | 49.03 | + | -678.02604783 | 0.1084E-03 | 49.11 | + | -678.02604398 | 0.1082E-03 | 49.19 | + | -678.02604972 | 0.1081E-03 | 49.26 | + | -678.02605030 | 0.1080E-03 | 49.34 | + | -678.02605443 | 0.1079E-03 | 49.42 | + | -678.02605070 | 0.1078E-03 | 49.50 | + | -678.02604567 | 0.1077E-03 | 49.58 | + | -678.02604612 | 0.1075E-03 | 49.66 | + | -678.02604356 | 0.1074E-03 | 49.74 | + | -678.02604745 | 0.1073E-03 | 49.82 | + | -678.02604707 | 0.1072E-03 | 49.90 | + | -678.02602112 | 0.1034E-03 | 49.98 | + | -678.02601414 | 0.1032E-03 | 50.06 | + | -678.02601121 | 0.1031E-03 | 50.14 | + | -678.02600930 | 0.1030E-03 | 50.21 | + | -678.02601216 | 0.1028E-03 | 50.29 | + | -678.02600504 | 0.1027E-03 | 50.37 | + | -678.02601312 | 0.1026E-03 | 50.45 | + | -678.02601391 | 0.1024E-03 | 50.53 | + | -678.02602187 | 0.1023E-03 | 50.61 | + | -678.02603247 | 0.1023E-03 | 50.69 | + | -678.02603325 | 0.1022E-03 | 50.77 | + | -678.02602994 | 0.1020E-03 | 50.85 | + | -678.02603217 | 0.1019E-03 | 50.93 | + | -678.02602441 | 0.1018E-03 | 51.01 | + | -678.02602835 | 0.1016E-03 | 51.09 | + | -678.02603359 | 0.1017E-03 | 51.17 | + | -678.02603841 | 0.1015E-03 | 51.25 | + | -678.02604111 | 0.1014E-03 | 51.33 | + | -678.02604196 | 0.1013E-03 | 51.41 | + | -678.02604056 | 0.1012E-03 | 51.49 | + | -678.02604459 | 0.1011E-03 | 51.57 | + | -678.02604726 | 0.1010E-03 | 51.64 | + | -678.02605482 | 0.1011E-03 | 51.72 | + | -678.02605492 | 0.1009E-03 | 51.80 | + | -678.02605385 | 0.1008E-03 | 51.88 | + | -678.02605244 | 0.1007E-03 | 51.96 | + | -678.02605607 | 0.1005E-03 | 52.04 | + | -678.02606070 | 0.1005E-03 | 52.12 | + | -678.02606156 | 0.1003E-03 | 52.20 | + | -678.02606117 | 0.1002E-03 | 52.28 | + | -678.02607098 | 0.1001E-03 | 52.36 | + | -678.02607446 | 0.9999E-04 | 52.44 | + | -678.02607853 | 0.9989E-04 | 52.52 | + | -678.02607837 | 0.9978E-04 | 52.60 | + | -678.02608416 | 0.9977E-04 | 52.68 | + | -678.02608811 | 0.9963E-04 | 52.76 | + | -678.02608681 | 0.9948E-04 | 52.84 | + | -678.02608637 | 0.9939E-04 | 52.92 | + | -678.02610909 | 0.9666E-04 | 53.00 | + | -678.02610364 | 0.9654E-04 | 53.08 | + | -678.02609431 | 0.9639E-04 | 53.16 | + | -678.02608645 | 0.9624E-04 | 53.24 | + | -678.02608870 | 0.9611E-04 | 53.32 | + | -678.02609322 | 0.9606E-04 | 53.40 | + | -678.02609073 | 0.9592E-04 | 53.48 | + | -678.02608964 | 0.9583E-04 | 53.56 | + | -678.02608892 | 0.9573E-04 | 53.64 | + | -678.02608565 | 0.9562E-04 | 53.72 | + | -678.02608067 | 0.9551E-04 | 53.80 | + | -678.02608119 | 0.9541E-04 | 53.88 | + | -678.02608262 | 0.9529E-04 | 53.96 | + | -678.02608573 | 0.9520E-04 | 54.04 | + | -678.02607942 | 0.9504E-04 | 54.12 | + | -678.02607861 | 0.9495E-04 | 54.20 | + | -678.02608093 | 0.9481E-04 | 54.28 | + | -678.02608453 | 0.9472E-04 | 54.36 | + | -678.02608451 | 0.9461E-04 | 54.43 | + | -678.02608166 | 0.9451E-04 | 54.51 | + | -678.02607711 | 0.9438E-04 | 54.59 | + | -678.02606876 | 0.9421E-04 | 54.67 | + | -678.02606783 | 0.9414E-04 | 54.75 | + | -678.02606277 | 0.9401E-04 | 54.83 | + | -678.02606100 | 0.9390E-04 | 54.91 | + | -678.02605168 | 0.9377E-04 | 54.99 | + | -678.02605168 | 0.9367E-04 | 55.06 | + | -678.02605275 | 0.9357E-04 | 55.14 | + | -678.02605329 | 0.9346E-04 | 55.23 | + | -678.02605046 | 0.9335E-04 | 55.31 | + | -678.02605001 | 0.9323E-04 | 55.39 | + | -678.02604532 | 0.9312E-04 | 55.46 | + | -678.02604726 | 0.9304E-04 | 55.54 | + | -678.02604903 | 0.9295E-04 | 55.62 | + | -678.02607499 | 0.9057E-04 | 55.70 | + | -678.02607742 | 0.9049E-04 | 55.78 | + | -678.02607711 | 0.9038E-04 | 55.85 | + | -678.02607665 | 0.9023E-04 | 55.93 | + | -678.02608483 | 0.9022E-04 | 56.01 | + | -678.02608306 | 0.9008E-04 | 56.09 | + | -678.02608767 | 0.8996E-04 | 56.18 | + | -678.02609654 | 0.8990E-04 | 56.26 | + | -678.02609887 | 0.8983E-04 | 56.34 | + | -678.02609802 | 0.8969E-04 | 56.42 | + | -678.02610361 | 0.8964E-04 | 56.50 | + | -678.02610513 | 0.8958E-04 | 56.57 | + | -678.02610753 | 0.8948E-04 | 56.65 | + | -678.02611311 | 0.8940E-04 | 56.73 | + | -678.02611604 | 0.8929E-04 | 56.81 | + | -678.02611571 | 0.8919E-04 | 56.88 | + | -678.02611614 | 0.8908E-04 | 56.96 | + | -678.02611780 | 0.8900E-04 | 57.04 | + | -678.02612055 | 0.8888E-04 | 57.12 | + | -678.02612332 | 0.8878E-04 | 57.20 | + | -678.02612648 | 0.8870E-04 | 57.29 | + | -678.02613128 | 0.8863E-04 | 57.37 | + | -678.02613127 | 0.8851E-04 | 57.44 | + | -678.02612823 | 0.8842E-04 | 57.52 | + | -678.02612467 | 0.8833E-04 | 57.60 | + | -678.02612532 | 0.8822E-04 | 57.67 | + | -678.02612712 | 0.8811E-04 | 57.75 | + | -678.02612511 | 0.8798E-04 | 57.83 | + | -678.02612820 | 0.8789E-04 | 57.92 | + | -678.02612883 | 0.8782E-04 | 58.00 | + | -678.02612416 | 0.8770E-04 | 58.08 | + | -678.02612529 | 0.8548E-04 | 58.16 | + | -678.02612959 | 0.8540E-04 | 58.23 | + | -678.02613329 | 0.8533E-04 | 58.32 | + | -678.02613068 | 0.8519E-04 | 58.39 | + | -678.02613173 | 0.8508E-04 | 58.47 | + | -678.02613212 | 0.8497E-04 | 58.54 | + | -678.02612654 | 0.8486E-04 | 58.62 | + | -678.02612698 | 0.8474E-04 | 58.70 | + | -678.02613068 | 0.8465E-04 | 58.78 | + | -678.02613040 | 0.8456E-04 | 58.86 | + | -678.02613090 | 0.8444E-04 | 58.94 | + | -678.02612615 | 0.8431E-04 | 59.01 | + | -678.02612672 | 0.8424E-04 | 59.09 | + | -678.02612319 | 0.8413E-04 | 59.18 | + | -678.02612610 | 0.8404E-04 | 59.25 | + | -678.02612200 | 0.8392E-04 | 59.33 | + | -678.02612096 | 0.8384E-04 | 59.41 | + | -678.02611778 | 0.8375E-04 | 59.49 | + | -678.02611148 | 0.8362E-04 | 59.56 | + | -678.02611128 | 0.8352E-04 | 59.64 | + | -678.02610700 | 0.8339E-04 | 59.73 | + | -678.02610704 | 0.8331E-04 | 59.81 | + | -678.02610469 | 0.8320E-04 | 59.89 | + | -678.02610729 | 0.8311E-04 | 59.97 | + | -678.02611304 | 0.8302E-04 | 60.05 | + | -678.02611085 | 0.8291E-04 | 60.13 | + | -678.02611007 | 0.8281E-04 | 60.20 | + | -678.02610913 | 0.8272E-04 | 60.29 | + | -678.02613259 | 0.8099E-04 | 60.36 | + | -678.02613365 | 0.8091E-04 | 60.44 | + | -678.02612834 | 0.8078E-04 | 60.52 | + | -678.02613015 | 0.8068E-04 | 60.59 | + | -678.02612425 | 0.8056E-04 | 60.67 | + | -678.02612707 | 0.8050E-04 | 60.75 | + | -678.02613435 | 0.8048E-04 | 60.83 | + | -678.02613261 | 0.8035E-04 | 60.91 | + | -678.02613791 | 0.8029E-04 | 60.99 | + | -678.02613782 | 0.8018E-04 | 61.06 | + | -678.02614440 | 0.8011E-04 | 61.14 | + | -678.02614152 | 0.7997E-04 | 61.22 | + | -678.02613671 | 0.7987E-04 | 61.30 | + | -678.02614081 | 0.7977E-04 | 61.38 | + | -678.02614360 | 0.7970E-04 | 61.46 | + | -678.02614543 | 0.7963E-04 | 61.54 | + | -678.02614583 | 0.7953E-04 | 61.62 | + | -678.02614492 | 0.7945E-04 | 61.70 | + | -678.02614383 | 0.7937E-04 | 61.79 | + | -678.02614208 | 0.7926E-04 | 61.86 | + | -678.02613812 | 0.7916E-04 | 61.94 | + | -678.02613509 | 0.7907E-04 | 62.02 | + | -678.02614012 | 0.7900E-04 | 62.09 | + | -678.02614218 | 0.7893E-04 | 62.17 | + | -678.02614524 | 0.7883E-04 | 62.25 | + | -678.02614790 | 0.7879E-04 | 62.32 | + | -678.02614769 | 0.7706E-04 | 62.40 | + | -678.02614298 | 0.7697E-04 | 62.48 | + | -678.02614378 | 0.7690E-04 | 62.57 | + | -678.02614695 | 0.7682E-04 | 62.65 | + | -678.02615049 | 0.7674E-04 | 62.72 | + | -678.02614953 | 0.7665E-04 | 62.80 | + | -678.02614289 | 0.7654E-04 | 62.88 | + | -678.02614126 | 0.7645E-04 | 62.96 | + | -678.02614507 | 0.7637E-04 | 63.04 | + | -678.02615221 | 0.7631E-04 | 63.12 | + | -678.02615425 | 0.7622E-04 | 63.20 | + | -678.02615148 | 0.7613E-04 | 63.28 | + | -678.02615014 | 0.7603E-04 | 63.36 | + | -678.02614930 | 0.7595E-04 | 63.44 | + | -678.02614815 | 0.7586E-04 | 63.52 | + | -678.02614755 | 0.7576E-04 | 63.60 | + | -678.02614572 | 0.7565E-04 | 63.68 | + | -678.02614638 | 0.7559E-04 | 63.75 | + | -678.02614804 | 0.7550E-04 | 63.83 | + | -678.02614548 | 0.7538E-04 | 63.92 | + | -678.02614769 | 0.7527E-04 | 64.00 | + | -678.02614257 | 0.7515E-04 | 64.08 | + | -678.02614199 | 0.7507E-04 | 64.15 | + | -678.02614457 | 0.7502E-04 | 64.23 | + | -678.02614497 | 0.7491E-04 | 64.31 | + | -678.02615673 | 0.7304E-04 | 64.39 | + | -678.02616114 | 0.7297E-04 | 64.47 | + | -678.02616393 | 0.7287E-04 | 64.55 | + | -678.02616691 | 0.7279E-04 | 64.63 | + | -678.02616509 | 0.7270E-04 | 64.70 | + | -678.02616502 | 0.7259E-04 | 64.79 | + | -678.02616332 | 0.7249E-04 | 64.87 | + | -678.02616664 | 0.7243E-04 | 64.95 | + | -678.02616260 | 0.7234E-04 | 65.02 | + | -678.02616584 | 0.7225E-04 | 65.11 | + | -678.02616689 | 0.7218E-04 | 65.19 | + | -678.02616737 | 0.7208E-04 | 65.27 | + | -678.02616900 | 0.7201E-04 | 65.34 | + | -678.02616938 | 0.7192E-04 | 65.42 | + | -678.02616588 | 0.7183E-04 | 65.50 | + | -678.02615905 | 0.7172E-04 | 65.58 | + | -678.02615858 | 0.7163E-04 | 65.66 | + | -678.02616091 | 0.7160E-04 | 65.73 | + | -678.02616386 | 0.7159E-04 | 65.81 | + | -678.02616872 | 0.7153E-04 | 65.89 | + | -678.02617184 | 0.7143E-04 | 65.97 | + | -678.02617026 | 0.7137E-04 | 66.05 | + | -678.02616803 | 0.7131E-04 | 66.13 | + | -678.02615498 | 0.6977E-04 | 66.21 | + | -678.02614988 | 0.6969E-04 | 66.29 | + | -678.02615327 | 0.6962E-04 | 66.37 | + | -678.02615325 | 0.6951E-04 | 66.45 | + | -678.02615307 | 0.6945E-04 | 66.52 | + | -678.02614981 | 0.6937E-04 | 66.60 | + | -678.02615050 | 0.6927E-04 | 66.68 | + | -678.02615353 | 0.6922E-04 | 66.76 | + | -678.02615320 | 0.6914E-04 | 66.84 | + | -678.02615292 | 0.6904E-04 | 66.91 | + | -678.02615665 | 0.6897E-04 | 67.00 | + | -678.02615314 | 0.6887E-04 | 67.08 | + | -678.02615128 | 0.6879E-04 | 67.15 | + | -678.02615881 | 0.6876E-04 | 67.23 | + | -678.02615914 | 0.6867E-04 | 67.31 | + | -678.02615734 | 0.6858E-04 | 67.39 | + | -678.02616194 | 0.6851E-04 | 67.47 | + | -678.02616217 | 0.6846E-04 | 67.55 | + | -678.02616043 | 0.6837E-04 | 67.63 | + | -678.02616498 | 0.6831E-04 | 67.71 | + | -678.02616184 | 0.6822E-04 | 67.79 | + | -678.02615572 | 0.6697E-04 | 67.86 | + | -678.02615555 | 0.6689E-04 | 67.94 | + | -678.02615857 | 0.6680E-04 | 68.02 | + | -678.02616015 | 0.6679E-04 | 68.10 | + | -678.02615869 | 0.6669E-04 | 68.18 | + | -678.02615401 | 0.6659E-04 | 68.26 | + | -678.02615500 | 0.6651E-04 | 68.34 | + | -678.02616008 | 0.6647E-04 | 68.42 | + | -678.02616447 | 0.6642E-04 | 68.49 | + | -678.02616333 | 0.6631E-04 | 68.57 | + | -678.02616264 | 0.6623E-04 | 68.65 | + | -678.02615841 | 0.6613E-04 | 68.73 | + | -678.02616216 | 0.6608E-04 | 68.81 | + | -678.02615913 | 0.6600E-04 | 68.89 | + | -678.02615470 | 0.6592E-04 | 68.97 | + | -678.02615738 | 0.6583E-04 | 69.05 | + | -678.02615730 | 0.6575E-04 | 69.13 | + | -678.02615268 | 0.6565E-04 | 69.21 | + | -678.02615087 | 0.6558E-04 | 69.29 | + | -678.02614102 | 0.6438E-04 | 69.36 | + | -678.02613779 | 0.6431E-04 | 69.44 | + | -678.02614005 | 0.6428E-04 | 69.52 | + | -678.02614450 | 0.6422E-04 | 69.60 | + | -678.02614276 | 0.6415E-04 | 69.68 | + | -678.02614195 | 0.6407E-04 | 69.76 | + | -678.02614750 | 0.6405E-04 | 69.84 | + | -678.02614497 | 0.6395E-04 | 69.91 | + | -678.02614303 | 0.6388E-04 | 70.00 | + | -678.02614084 | 0.6379E-04 | 70.07 | + | -678.02614102 | 0.6371E-04 | 70.15 | + | -678.02614069 | 0.6364E-04 | 70.23 | + | -678.02614325 | 0.6358E-04 | 70.31 | + | -678.02614419 | 0.6351E-04 | 70.39 | + | -678.02614910 | 0.6346E-04 | 70.47 | + | -678.02615538 | 0.6358E-04 | 70.55 | + | -678.02615457 | 0.6351E-04 | 70.62 | + | -678.02615899 | 0.6348E-04 | 70.70 | + | -678.02615985 | 0.6340E-04 | 70.78 | + | -678.02616131 | 0.6231E-04 | 70.86 | + | -678.02615829 | 0.6222E-04 | 70.94 | + | -678.02615688 | 0.6216E-04 | 71.02 | + | -678.02615490 | 0.6209E-04 | 71.09 | + | -678.02615363 | 0.6201E-04 | 71.17 | + | -678.02615489 | 0.6195E-04 | 71.25 | + | -678.02615807 | 0.6188E-04 | 71.33 | + | -678.02615679 | 0.6178E-04 | 71.40 | + | -678.02615464 | 0.6169E-04 | 71.49 | + | -678.02615643 | 0.6165E-04 | 71.56 | + | -678.02615842 | 0.6159E-04 | 71.65 | + | -678.02616022 | 0.6152E-04 | 71.72 | + | -678.02615852 | 0.6146E-04 | 71.80 | + | -678.02615878 | 0.6139E-04 | 71.88 | + | -678.02615792 | 0.6132E-04 | 71.96 | + | -678.02615826 | 0.6127E-04 | 72.04 | + | -678.02615491 | 0.6121E-04 | 72.11 | + | -678.02615734 | 0.6115E-04 | 72.19 | + | -678.02615297 | 0.6105E-04 | 72.27 | + | -678.02617035 | 0.6004E-04 | 72.35 | + | -678.02616798 | 0.5995E-04 | 72.43 | + | -678.02617029 | 0.5990E-04 | 72.50 | + | -678.02616904 | 0.5981E-04 | 72.58 | + | -678.02616735 | 0.5973E-04 | 72.66 | + | -678.02616537 | 0.5965E-04 | 72.74 | + | -678.02616394 | 0.5958E-04 | 72.81 | + | -678.02616598 | 0.5950E-04 | 72.89 | + | -678.02616716 | 0.5944E-04 | 72.98 | + | -678.02616611 | 0.5936E-04 | 73.05 | + | -678.02616336 | 0.5928E-04 | 73.13 | + | -678.02616636 | 0.5923E-04 | 73.20 | + | -678.02616889 | 0.5916E-04 | 73.28 | + | -678.02616900 | 0.5911E-04 | 73.36 | + | -678.02616696 | 0.5904E-04 | 73.44 | + | -678.02616583 | 0.5896E-04 | 73.52 | + | -678.02615914 | 0.5783E-04 | 73.60 | + | -678.02615795 | 0.5776E-04 | 73.68 | + | -678.02615490 | 0.5769E-04 | 73.76 | + | -678.02615644 | 0.5760E-04 | 73.85 | + | -678.02615450 | 0.5754E-04 | 73.92 | + | -678.02615217 | 0.5747E-04 | 74.00 | + | -678.02615314 | 0.5741E-04 | 74.08 | + | -678.02615433 | 0.5735E-04 | 74.16 | + | -678.02615389 | 0.5728E-04 | 74.24 | + | -678.02615164 | 0.5718E-04 | 74.31 | + | -678.02615352 | 0.5713E-04 | 74.39 | + | -678.02615113 | 0.5706E-04 | 74.46 | + | -678.02615077 | 0.5696E-04 | 74.55 | + | -678.02615409 | 0.5691E-04 | 74.62 | + | -678.02615055 | 0.5682E-04 | 74.70 | + | -678.02615794 | 0.5592E-04 | 74.78 | + | -678.02615776 | 0.5585E-04 | 74.85 | + | -678.02615667 | 0.5577E-04 | 74.94 | + | -678.02615319 | 0.5568E-04 | 75.02 | + | -678.02615379 | 0.5562E-04 | 75.10 | + | -678.02615464 | 0.5557E-04 | 75.18 | + | -678.02615203 | 0.5550E-04 | 75.27 | + | -678.02615243 | 0.5544E-04 | 75.34 | + | -678.02615116 | 0.5536E-04 | 75.42 | + | -678.02614639 | 0.5527E-04 | 75.50 | + | -678.02614791 | 0.5521E-04 | 75.58 | + | -678.02615026 | 0.5511E-04 | 75.65 | + | -678.02614942 | 0.5503E-04 | 75.73 | + | -678.02614673 | 0.5497E-04 | 75.81 | + | -678.02614232 | 0.5402E-04 | 75.89 | + | -678.02613952 | 0.5396E-04 | 75.97 | + | -678.02613960 | 0.5388E-04 | 76.04 | + | -678.02614138 | 0.5380E-04 | 76.12 | + | -678.02613691 | 0.5372E-04 | 76.20 | + | -678.02613509 | 0.5364E-04 | 76.27 | + | -678.02613559 | 0.5357E-04 | 76.35 | + | -678.02613508 | 0.5351E-04 | 76.43 | + | -678.02613130 | 0.5346E-04 | 76.51 | + | -678.02613221 | 0.5338E-04 | 76.59 | + | -678.02612745 | 0.5331E-04 | 76.67 | + | -678.02612716 | 0.5324E-04 | 76.75 | + | -678.02613130 | 0.5234E-04 | 76.83 | + | -678.02613110 | 0.5229E-04 | 76.91 | + | -678.02613012 | 0.5219E-04 | 76.99 | + | -678.02612791 | 0.5210E-04 | 77.07 | + | -678.02612558 | 0.5204E-04 | 77.15 | + | -678.02612552 | 0.5197E-04 | 77.23 | + | -678.02612447 | 0.5191E-04 | 77.30 | + | -678.02612108 | 0.5184E-04 | 77.38 | + | -678.02612098 | 0.5174E-04 | 77.46 | + | -678.02612094 | 0.5168E-04 | 77.54 | + | -678.02612232 | 0.5161E-04 | 77.62 | + | -678.02612355 | 0.5155E-04 | 77.71 | + | -678.02612059 | 0.5069E-04 | 77.79 | + | -678.02611880 | 0.5060E-04 | 77.86 | + | -678.02612063 | 0.5055E-04 | 77.94 | + | -678.02611786 | 0.5047E-04 | 78.02 | + | -678.02611466 | 0.5036E-04 | 78.10 | + | -678.02611630 | 0.5032E-04 | 78.19 | + | -678.02611470 | 0.5026E-04 | 78.26 | + | -678.02611478 | 0.5020E-04 | 78.34 | + | -678.02612004 | 0.5015E-04 | 78.42 | + | -678.02612418 | 0.5010E-04 | 78.49 | + | -678.02612357 | 0.5002E-04 | 78.57 | + | -678.02612293 | 0.4995E-04 | 78.65 | + | -678.02613445 | 0.4907E-04 | 78.73 | + | -678.02613221 | 0.4900E-04 | 78.81 | + | -678.02613527 | 0.4894E-04 | 78.89 | + | -678.02613702 | 0.4888E-04 | 78.97 | + | -678.02613896 | 0.4881E-04 | 79.05 | + | -678.02613684 | 0.4873E-04 | 79.13 | + | -678.02613470 | 0.4867E-04 | 79.21 | + | -678.02613781 | 0.4861E-04 | 79.28 | + | -678.02613974 | 0.4856E-04 | 79.36 | + | -678.02614119 | 0.4849E-04 | 79.44 | + | -678.02614307 | 0.4843E-04 | 79.52 | + | -678.02614297 | 0.4838E-04 | 79.59 | + | -678.02613973 | 0.4753E-04 | 79.67 | + | -678.02614170 | 0.4746E-04 | 79.75 | + | -678.02614230 | 0.4742E-04 | 79.83 | + | -678.02614456 | 0.4737E-04 | 79.90 | + | -678.02614842 | 0.4732E-04 | 79.98 | + | -678.02614726 | 0.4726E-04 | 80.06 | + | -678.02614741 | 0.4721E-04 | 80.14 | + | -678.02615364 | 0.4719E-04 | 80.22 | + | -678.02615748 | 0.4714E-04 | 80.30 | + | -678.02615762 | 0.4709E-04 | 80.38 | + | -678.02616047 | 0.4702E-04 | 80.45 | + | -678.02616411 | 0.4630E-04 | 80.53 | + | -678.02616417 | 0.4623E-04 | 80.61 | + | -678.02616231 | 0.4616E-04 | 80.69 | + | -678.02616318 | 0.4611E-04 | 80.77 | + | -678.02616480 | 0.4603E-04 | 80.84 | + | -678.02616143 | 0.4598E-04 | 80.92 | + | -678.02616482 | 0.4592E-04 | 81.00 | + | -678.02616304 | 0.4587E-04 | 81.08 | + | -678.02616319 | 0.4583E-04 | 81.15 | + | -678.02616463 | 0.4580E-04 | 81.23 | + | -678.02616151 | 0.4573E-04 | 81.31 | + | -678.02615473 | 0.4498E-04 | 81.39 | + | -678.02615426 | 0.4491E-04 | 81.46 | + | -678.02615121 | 0.4485E-04 | 81.54 | + | -678.02615338 | 0.4481E-04 | 81.62 | + | -678.02615470 | 0.4474E-04 | 81.70 | + | -678.02615448 | 0.4469E-04 | 81.78 | + | -678.02615370 | 0.4464E-04 | 81.86 | + | -678.02615460 | 0.4459E-04 | 81.94 | + | -678.02615394 | 0.4454E-04 | 82.01 | + | -678.02615664 | 0.4451E-04 | 82.09 | + | -678.02615046 | 0.4362E-04 | 82.17 | + | -678.02615045 | 0.4357E-04 | 82.25 | + | -678.02615281 | 0.4353E-04 | 82.33 | + | -678.02615124 | 0.4346E-04 | 82.41 | + | -678.02615002 | 0.4338E-04 | 82.49 | + | -678.02615271 | 0.4335E-04 | 82.57 | + | -678.02615277 | 0.4328E-04 | 82.65 | + | -678.02615360 | 0.4324E-04 | 82.72 | + | -678.02615376 | 0.4317E-04 | 82.80 | + | -678.02615303 | 0.4252E-04 | 82.88 | + | -678.02615138 | 0.4244E-04 | 82.96 | + | -678.02615067 | 0.4237E-04 | 83.04 | + | -678.02614987 | 0.4230E-04 | 83.12 | + | -678.02615401 | 0.4224E-04 | 83.20 | + | -678.02614989 | 0.4217E-04 | 83.28 | + | -678.02615106 | 0.4213E-04 | 83.36 | + | -678.02615319 | 0.4206E-04 | 83.44 | + | -678.02615486 | 0.4141E-04 | 83.51 | + | -678.02615419 | 0.4135E-04 | 83.60 | + | -678.02615386 | 0.4130E-04 | 83.67 | + | -678.02615093 | 0.4124E-04 | 83.75 | + | -678.02615199 | 0.4119E-04 | 83.84 | + | -678.02615223 | 0.4112E-04 | 83.91 | + | -678.02615326 | 0.4107E-04 | 83.99 | + | -678.02615615 | 0.4100E-04 | 84.07 | + | -678.02615165 | 0.4034E-04 | 84.15 | + | -678.02614927 | 0.4029E-04 | 84.23 | + | -678.02614987 | 0.4021E-04 | 84.31 | + | -678.02615164 | 0.4016E-04 | 84.39 | + | -678.02615207 | 0.4010E-04 | 84.46 | + | -678.02615418 | 0.4004E-04 | 84.54 | + | -678.02615092 | 0.3997E-04 | 84.62 | + | -678.02616582 | 0.3944E-04 | 84.70 | + | -678.02616775 | 0.3939E-04 | 84.77 | + | -678.02617019 | 0.3935E-04 | 84.85 | + | -678.02617126 | 0.3931E-04 | 84.93 | + | -678.02617128 | 0.3927E-04 | 85.01 | + | -678.02617002 | 0.3919E-04 | 85.09 | + | -678.02617075 | 0.3911E-04 | 85.17 | + | -678.02617422 | 0.3904E-04 | 85.25 | + | -678.02618247 | 0.3847E-04 | 85.33 | + | -678.02618352 | 0.3840E-04 | 85.40 | + | -678.02618190 | 0.3834E-04 | 85.48 | + | -678.02617939 | 0.3828E-04 | 85.56 | + | -678.02618154 | 0.3822E-04 | 85.64 | + | -678.02617862 | 0.3815E-04 | 85.72 | + | -678.02617777 | 0.3807E-04 | 85.80 | + | -678.02617404 | 0.3749E-04 | 85.87 | + | -678.02617603 | 0.3744E-04 | 85.95 | + | -678.02617808 | 0.3737E-04 | 86.03 | + | -678.02618080 | 0.3733E-04 | 86.11 | + | -678.02617940 | 0.3726E-04 | 86.19 | + | -678.02617986 | 0.3720E-04 | 86.27 | + | -678.02617795 | 0.3714E-04 | 86.34 | + | -678.02617908 | 0.3662E-04 | 86.42 | + | -678.02617793 | 0.3655E-04 | 86.50 | + | -678.02617915 | 0.3651E-04 | 86.58 | + | -678.02617719 | 0.3643E-04 | 86.66 | + | -678.02617724 | 0.3637E-04 | 86.74 | + | -678.02617452 | 0.3631E-04 | 86.82 | + | -678.02617518 | 0.3582E-04 | 86.90 | + | -678.02617712 | 0.3577E-04 | 86.97 | + | -678.02617633 | 0.3572E-04 | 87.05 | + | -678.02617535 | 0.3565E-04 | 87.13 | + | -678.02617734 | 0.3563E-04 | 87.21 | + | -678.02617815 | 0.3556E-04 | 87.29 | + | -678.02618018 | 0.3553E-04 | 87.37 | + | -678.02617850 | 0.3504E-04 | 87.45 | + | -678.02618020 | 0.3501E-04 | 87.52 | + | -678.02617940 | 0.3494E-04 | 87.61 | + | -678.02618233 | 0.3492E-04 | 87.68 | + | -678.02618474 | 0.3494E-04 | 87.76 | + | -678.02618518 | 0.3488E-04 | 87.84 | + | -678.02618727 | 0.3443E-04 | 87.92 | + | -678.02618547 | 0.3437E-04 | 88.00 | + | -678.02618445 | 0.3430E-04 | 88.08 | + | -678.02618127 | 0.3422E-04 | 88.16 | + | -678.02618363 | 0.3417E-04 | 88.24 | + | -678.02617928 | 0.3371E-04 | 88.32 | + | -678.02617870 | 0.3365E-04 | 88.39 | + | -678.02617628 | 0.3358E-04 | 88.47 | + | -678.02617627 | 0.3351E-04 | 88.55 | + | -678.02617889 | 0.3345E-04 | 88.63 | + | -678.02617785 | 0.3338E-04 | 88.71 | + | -678.02618560 | 0.3297E-04 | 88.78 | + | -678.02618771 | 0.3294E-04 | 88.86 | + | -678.02618681 | 0.3287E-04 | 88.94 | + | -678.02618672 | 0.3282E-04 | 89.02 | + | -678.02618357 | 0.3274E-04 | 89.10 | + | -678.02618492 | 0.3232E-04 | 89.18 | + | -678.02618371 | 0.3227E-04 | 89.26 | + | -678.02618050 | 0.3219E-04 | 89.33 | + | -678.02618041 | 0.3212E-04 | 89.41 | + | -678.02618180 | 0.3206E-04 | 89.49 | + | -678.02618088 | 0.3200E-04 | 89.57 | + | -678.02617848 | 0.3158E-04 | 89.65 | + | -678.02617863 | 0.3152E-04 | 89.73 | + | -678.02618032 | 0.3146E-04 | 89.80 | + | -678.02617879 | 0.3138E-04 | 89.88 | + | -678.02617776 | 0.3133E-04 | 89.96 | + | -678.02617076 | 0.3088E-04 | 90.04 | + | -678.02617168 | 0.3082E-04 | 90.11 | + | -678.02616965 | 0.3076E-04 | 90.19 | + | -678.02616714 | 0.3071E-04 | 90.27 | + | -678.02616596 | 0.3064E-04 | 90.35 | + | -678.02616625 | 0.3014E-04 | 90.43 | + | -678.02616327 | 0.3009E-04 | 90.50 | + | -678.02616232 | 0.3002E-04 | 90.58 | + | -678.02616184 | 0.2997E-04 | 90.66 | + | -678.02615604 | 0.2953E-04 | 90.74 | + | -678.02615556 | 0.2947E-04 | 90.82 | + | -678.02615670 | 0.2941E-04 | 90.89 | + | -678.02615649 | 0.2936E-04 | 90.97 | + | -678.02616310 | 0.2938E-04 | 91.05 | + | -678.02616245 | 0.2888E-04 | 91.13 | + | -678.02616312 | 0.2884E-04 | 91.20 | + | -678.02616365 | 0.2879E-04 | 91.28 | + | -678.02616312 | 0.2871E-04 | 91.36 | + | -678.02616086 | 0.2833E-04 | 91.44 | + | -678.02615771 | 0.2825E-04 | 91.51 | + | -678.02615626 | 0.2818E-04 | 91.59 | + | -678.02615931 | 0.2814E-04 | 91.66 | + | -678.02616887 | 0.2780E-04 | 91.74 | + | -678.02617029 | 0.2774E-04 | 91.82 | + | -678.02617612 | 0.2777E-04 | 91.90 | + | -678.02617396 | 0.2737E-04 | 91.97 | + | -678.02617399 | 0.2732E-04 | 92.05 | + | -678.02617014 | 0.2725E-04 | 92.13 | + | -678.02616998 | 0.2718E-04 | 92.21 | + | -678.02616179 | 0.2668E-04 | 92.29 | + | -678.02616234 | 0.2662E-04 | 92.37 | + | -678.02616124 | 0.2657E-04 | 92.45 | + | -678.02616000 | 0.2651E-04 | 92.53 | + | -678.02616198 | 0.2611E-04 | 92.60 | + | -678.02616136 | 0.2604E-04 | 92.68 | + | -678.02616130 | 0.2597E-04 | 92.76 | + | -678.02616185 | 0.2591E-04 | 92.84 | + | -678.02616177 | 0.2548E-04 | 92.91 | + | -678.02616136 | 0.2541E-04 | 92.99 | + | -678.02616314 | 0.2537E-04 | 93.07 | + | -678.02617021 | 0.2499E-04 | 93.14 | + | -678.02616943 | 0.2494E-04 | 93.22 | + | -678.02617273 | 0.2492E-04 | 93.30 | + | -678.02617500 | 0.2488E-04 | 93.38 | + | -678.02617300 | 0.2448E-04 | 93.46 | + | -678.02617302 | 0.2442E-04 | 93.54 | + | -678.02617209 | 0.2439E-04 | 93.61 | + | -678.02617414 | 0.2406E-04 | 93.69 | + | -678.02617676 | 0.2410E-04 | 93.77 | + | -678.02617562 | 0.2406E-04 | 93.85 | + | -678.02617938 | 0.2373E-04 | 93.93 | + | -678.02618064 | 0.2368E-04 | 94.01 | + | -678.02618173 | 0.2362E-04 | 94.08 | + | -678.02618058 | 0.2323E-04 | 94.16 | + | -678.02618107 | 0.2316E-04 | 94.24 | + | -678.02618296 | 0.2310E-04 | 94.32 | + | -678.02618398 | 0.2280E-04 | 94.39 | + | -678.02618232 | 0.2273E-04 | 94.47 | + | -678.02618422 | 0.2270E-04 | 94.55 | + | -678.02618516 | 0.2235E-04 | 94.63 | + | -678.02618629 | 0.2229E-04 | 94.71 | + | -678.02618629 | 0.2223E-04 | 94.79 | + | -678.02618365 | 0.2188E-04 | 94.87 | + | -678.02618400 | 0.2183E-04 | 94.95 | + | -678.02618779 | 0.2150E-04 | 95.03 | + | -678.02618830 | 0.2145E-04 | 95.11 | + | -678.02618978 | 0.2147E-04 | 95.18 | + | -678.02619583 | 0.2111E-04 | 95.26 | + | -678.02619640 | 0.2104E-04 | 95.34 | + | -678.02619921 | 0.2067E-04 | 95.42 | + | -678.02619815 | 0.2060E-04 | 95.49 | + | -678.02619776 | 0.2054E-04 | 95.57 | + | -678.02620404 | 0.2023E-04 | 95.65 | + | -678.02620317 | 0.2015E-04 | 95.73 | + | -678.02619689 | 0.1986E-04 | 95.81 | + | -678.02619689 | 0.1980E-04 | 95.89 | + | -678.02619850 | 0.1951E-04 | 95.97 | + | -678.02619782 | 0.1945E-04 | 96.05 | + | -678.02619230 | 0.1917E-04 | 96.13 | + | -678.02619228 | 0.1912E-04 | 96.21 | + | -678.02619382 | 0.1886E-04 | 96.28 | + | -678.02619348 | 0.1881E-04 | 96.36 | + | -678.02619157 | 0.1854E-04 | 96.44 | + | -678.02619041 | 0.1846E-04 | 96.51 | + | -678.02619367 | 0.1816E-04 | 96.59 | + | -678.02619373 | 0.1811E-04 | 96.67 | + | -678.02619115 | 0.1784E-04 | 96.74 | + | -678.02619245 | 0.1777E-04 | 96.82 | + | -678.02619253 | 0.1751E-04 | 96.90 | + | -678.02619672 | 0.1752E-04 | 96.98 | + | -678.02619439 | 0.1725E-04 | 97.06 | + | -678.02619572 | 0.1702E-04 | 97.14 | + | -678.02619563 | 0.1697E-04 | 97.22 | + | -678.02619526 | 0.1673E-04 | 97.29 | + | -678.02619687 | 0.1669E-04 | 97.37 | + | -678.02619812 | 0.1645E-04 | 97.45 | + | -678.02619809 | 0.1639E-04 | 97.52 | + | -678.02619166 | 0.1605E-04 | 97.60 | + | -678.02619434 | 0.1577E-04 | 97.68 | + | -678.02619324 | 0.1569E-04 | 97.76 | + | -678.02619365 | 0.1543E-04 | 97.84 | + | -678.02619607 | 0.1512E-04 | 97.92 | + | -678.02619644 | 0.1506E-04 | 97.99 | + | -678.02619676 | 0.1462E-04 | 98.07 | + | -678.02619464 | 0.1412E-04 | 98.15 | + | -678.02619330 | 0.1404E-04 | 98.22 | + | -678.02618564 | 0.1321E-04 | 98.30 | + | -678.02618389 | 0.1254E-04 | 98.38 | + | -678.02618403 | 0.1248E-04 | 98.45 | + | -678.02618872 | 0.1208E-04 | 98.53 | + | -678.02618541 | 0.1160E-04 | 98.61 | + | -678.02618790 | 0.1158E-04 | 98.69 | + | -678.02618850 | 0.1098E-04 | 98.76 | + | -678.02618992 | 0.1039E-04 | 98.84 | + | -678.02618425 | 0.9926E-05 | 98.92 | + | -678.02618449 | 0.9871E-05 | 99.00 | + | -678.02618196 | 0.9397E-05 | 99.07 | + | -678.02618322 | 0.8616E-05 | 99.15 | + | -678.02618705 | 0.8099E-05 | 99.23 | + | -678.02618758 | 0.8081E-05 | 99.31 | + | -678.02618891 | 0.7384E-05 | 99.39 | + | -678.02618188 | 0.5774E-05 | 99.46 | + | -678.02618004 | 0.4525E-05 | 99.54 | + | -678.02617763 | 0.3286E-05 | 99.62 | + | -678.02617839 | 0.3286E-05 | 99.69 | + | -678.02617826 | 0.1864E-05 | 99.77 | + | -678.02617811 | 0.1849E-05 | 99.85 | + | -678.02617949 | 0.1036E-05 | 99.92 | + |---------------+------------+-------| + + Time: 1328.17061614990 s + + E(CCSD(T)) = -678.026179485578 Ha + E(T) = -0.088560748615 Ha + Correlation = -2.231076152399 Ha + + + #+begin_src gnuplot :var data=caffeine_svp :results file :file caffeine_svp.png +reset +set grid +set format y "%10.4f" +set ylabel "(T) (a.u)" +set xlabel "Wall clock time (s)" +set yrange[-678.027:-678.025] +plot data using :1:2 w errorlines notitle, -678.026179485578 notitle + #+end_src + + #+RESULTS: + [[file:caffeine_svp.png]] + +* Export :noexport: + #+BEGIN_SRC elisp :output none +(setq org-latex-listings 'minted + org-latex-packages-alist '(("" "minted")) + org-latex-minted-options + '(("frame" "lines") + ("fontsize" "\\scriptsize")) + org-latex-to-pdf-process + '("pdflatex -interaction nonstopmode -shell-escape -output-directory %o %f" + "pdflatex -interaction nonstopmode -shell-escape -output-directory %o %f")) + +(org-latex-export-to-pdf) + #+END_SRC + + #+RESULTS: + : /home/scemama/TripleStoch/triples.pdf + +#+BEGIN_SRC bash :results output +pdflatex -interaction nonstopmode -shell-escape triples.tex +#+END_SRC + +#+RESULTS: