diff --git a/Manuscript/stochastic_triples.tex b/Manuscript/stochastic_triples.tex index e3efb07..b2c69bf 100644 --- a/Manuscript/stochastic_triples.tex +++ b/Manuscript/stochastic_triples.tex @@ -85,12 +85,24 @@ \affiliation{\LCPQ} \begin{abstract} -We introduce a novel algorithm that leverages stochastic sampling techniques to approximate perturbative triples in the coupled-cluster (CC) framework. -By combining elements of randomness and determinism, our algorithm achieves a favorable balance between accuracy and computational cost. -The main advantage of this algorithm is that it allows for calculations to be stopped at any time, providing an unbiased estimate, with a statistical error that goes to zero as the exact calculation is approached. -We provide evidence that our semi-stochastic algorithm achieves substantial computational savings compared to traditional deterministic methods. -Specifically, we demonstrate that a precision of 0.5 milliHartree can be attained with only 10\% of the computational effort required by the full calculation. -This work opens up new avenues for efficient and accurate computations, enabling investigations of complex molecular systems that were previously computationally prohibitive. +We introduce a novel algorithm that leverages stochastic sampling +techniques to approximate perturbative triples correction in the +coupled-cluster (CC) framework. +By combining elements of randomness and determinism, our algorithm +achieves a favorable balance between accuracy and computational cost. +The main advantage of this algorithm is that it allows for +calculations to be stopped at any time, providing an unbiased +estimate, with a statistical error that goes to zero as the exact +calculation is approached. +We provide evidence that our semi-stochastic algorithm achieves +substantial computational savings compared to traditional +deterministic methods. +Specifically, we demonstrate that a precision of 0.5 milliHartree can +be attained with only 10\% of the computational effort required by the +full calculation. +This work opens up new avenues for efficient and accurate +computations, enabling investigations of complex molecular systems +that were previously computationally prohibitive. \bigskip \begin{center} % \boxed{\includegraphics[width=0.5\linewidth]{TOC}} @@ -191,13 +203,42 @@ accelerators.\cite{ma_2011,haidar_2015,dinapoli_2014,springer_2018} % - Benzene TZ % - Streptocyanine QZ: Small molecule in a large basis set % - Caffeine def2-svp: Large molecule in a small basis set +% - Vibrational frequency of F2/cc-pvqz %b. Discussion of the obtained results, comparing against other methods % - Measure flops and compare to the peak %c. Analysis of the algorithm's accuracy, efficiency, and scalability %d. Discussion of any observed limitations or challenges +\subsection{Vibrational frequency of \ce{F2}} + +In this example, we compute the vibrational frequency of \ce{F2} by +computing the potential energy curve, and fitting it with a Morse +potential +\begin{equation} + E(r) = D_e \left( 1 - e^{-a (r - r_e)} \right)^2 + E(r_e) +\end{equation} +where $E(r)$ is the energy at distance $r$, $D_e$ is the well depth, +$r_e$ is the equilibrium bond distance, and $a$ is a parameter +controlling the width of the potential well. +The vibrational frequency $\nu$ is calculated as +\begin{equation} + \nu = \frac{1}{2 \pi c} \sqrt{\frac{2D_e a^2}{\mu} +\end{equation} +where $\mu$ is the mass of the Fluorine atom, and $c$ is the speed of +light in cm/s. + +% CCSD +%a = 2.2936 +/- 0.006318 (0.2755%) +%De = 0.125888 +/- 0.0005213 (0.4141%) +%re = 1.3893 +/- 0.0003428 (0.02468%) +%E0 = -199.338 +/- 6.422e-05 (3.222e-05%) + +% CCSD(T) exact +%a = 2.65592 +/- 0.0403 (1.518%) +%De = 0.0718253 +/- 0.001879 (2.617%) +%re = 1.4105 +/- 0.00215 (0.1524%) +%E0 = -199.358 +/- 0.0003179 (0.0001595%) -%=================================================================% \section{Conclusion} \label{sec:conclusion} diff --git a/triples.org b/triples.org index 3491d4a..98f4dac 100644 --- a/triples.org +++ b/triples.org @@ -7362,6 +7362,440 @@ plot data using :1:2 w errorlines notitle, -678.026179485578 notitle #+RESULTS: [[file:caffeine_svp.png]] +* Vibration F2 +** Script to compute frequencies in cm-1 + + #+begin_src bash :output raw +tail -20 fit.log + #+end_src + + #+NAME:freq_ + #+begin_src python :var a=1.2526 :var De=0.7 :results output :output drawer +#!/usr/bin/env python +"""Converts vibrational frequencies from atomic units to cm-1 for diatomics.""" + +import sys +from math import sqrt, pi + +# Atomic masses obtained using +# import periodictable as pt +# for el in pt.elements: +# mass[el.symbol] = sorted([ (el[x].abundance,el[x].mass) for x in el.isotopes ])[-1][1] + +mass = {'H': 1.0078250321, 'He': 4.0026032497, 'Li': 7.016004, 'Be': 9.0121821, 'B': 11.0093055, 'C': 12.0, 'N': 14.0030740052, 'O': 15.9949146221, 'F': 18.9984032, 'Ne': 19.9924401759, 'Na': 22.98976967, 'Mg': 23.9850419, 'Al': 26.98153844, 'Si': 27.9769265327, 'P': 30.97376151, 'S': 31.97207069, 'Cl': 34.96885271, 'Ar': 39.962383123, 'K': 38.9637069, 'Ca': 39.9625912, 'Sc': 44.9559102, 'Ti': 47.9479471, 'V': 50.9439637, 'Cr': 51.9405119, 'Mn': 54.9380496, 'Fe': 55.9349421, 'Co': 58.9332002, 'Ni': 57.9353479, 'Cu': 62.9296011, 'Zn': 63.9291466, 'Ga': 68.925581, 'Ge': 73.9211782, 'As': 74.9215964, 'Se': 79.9165218, 'Br': 78.9183376, 'Kr': 83.911507, 'Rb': 84.9117893, 'Sr': 87.9056143, 'Y': 88.9058479, 'Zr': 89.9047037, 'Nb': 92.9063775, 'Mo': 97.9054078, 'Tc': 114.93828, 'Ru': 101.9043495, 'Rh': 102.905504, 'Pd': 105.903483, 'Ag': 106.905093, 'Cd': 113.9033581, 'In': 114.903878, 'Sn': 119.9021966, 'Sb': 120.903818, 'Te': 129.9062228, 'I': 126.904468, 'Xe': 131.9041545, 'Cs': 132.905447, 'Ba': 137.905241, 'La': 138.906348, 'Ce': 139.905434, 'Pr': 140.907648, 'Nd': 141.907719, 'Pm': 162.95352, 'Sm': 151.919728, 'Eu': 152.921226, 'Gd': 157.924101, 'Tb': 158.925343, 'Dy': 163.929171, 'Ho': 164.930319, 'Er': 165.93029, 'Tm': 168.934211, 'Yb': 173.9388581, 'Lu': 174.9407679, 'Hf': 179.9465488, 'Ta': 180.947996, 'W': 183.9509326, 'Re': 186.9557508, 'Os': 191.961479, 'Ir': 192.962924, 'Pt': 194.964774, 'Au': 196.966552, 'Hg': 201.970626, 'Tl': 204.974412, 'Pb': 207.976636, 'Bi': 208.980383, 'Po': 218.0089658, 'At': 223.02534, 'Rn': 228.03808, 'Fr': 232.04965, 'Ra': 234.05055, 'Ac': 236.05518, 'Th': 232.0380504, 'Pa': 231.0358789, 'U': 238.0507826, 'Np': 244.06785, 'Pu': 247.07407, 'Am': 249.07848, 'Cm': 252.08487, 'Bk': 254.0906, 'Cf': 256.09344, 'Es': 257.09598, 'Fm': 259.10059, 'Md': 260.10365, 'No': 262.10752, 'Lr': 263.11139, 'Rf': 264.11398, 'Db': 265.11866, 'Sg': 266.12193, 'Bh': 267.12774, 'Hs': 269.13411, 'Mt': 271.14123, 'Ds': 273.14925, 'Rg': 272.15348, 'Cn': 0, 'Nh': 0, 'Fl': 0, 'Mc': 0, 'Lv': 0, 'Ts': 0, 'Og': 0} + +def convert(e1,e2,f): + # Conversion factors + hartree = 4.3597447222071e-18 # joules + bohr = 1./18897161646.321 # m + amu = 1.6605402e-27 # kg + c = 299792458.0 # m/s + mole = 6.02214076e23 + + # Reduced mass in kg + mu = mass[e1]*mass[e2] / (mass[e1]+mass[e2]) * amu + + # Frequency in reduced coordinates + lam = (f * hartree / (bohr*bohr) ) / mu + + # Convert to wave numbers + nu = sqrt(lam)/(2.*pi*c) * 0.01 + + return nu + + +#print("Frequency (in hartree/bohr^2) ? "), +a = float(a) +f = De*2.*a*a + +print( convert('F','F',f) ) + #+end_src + + #+RESULTS: freq_ + : 2471.921716627526 + + +** CCSD + +NIST Computational Chemistry Comparison and Benchmark Database, +NIST Standard Reference Database Number 101 +Release 22, May 2022, Editor: Russell D. Johnson III +http://cccbdb.nist.gov/ + + Reference: 1016 cm^-1 + + #+name:f2_ccsd + | 1.20 | -199.300901502767 | + | 1.25 | -199.320245823796 | + | 1.30 | -199.331634513014 | + | 1.35 | -199.337115250478 | + | 1.40 | -199.338256839462 | + | 1.45 | -199.336266825958 | + | 1.50 | -199.332076468455 | + + #+begin_src gnuplot :var data=f2_ccsd :results file :file f2_ccsd.png +reset +a0 = 1.8897161646321 +E(r) = De * (1-exp(-a*(r-re)))**2 + E0 +a = 1.40546 +re = 2.66544 +De = 0.0718256 +E0 = -199.358 +set xrange [2:5] +fit E(x) data using ($1*a0):2 via a, re, De, E0 +plot E(x), data using ($1*a0):2 w p + #+end_src + + #+RESULTS: + [[file:f2_ccsd.png]] + + #+begin_example +a = 1.18566 +/- 0.001801 (0.1519%) +re = 2.62779 +/- 4.734e-05 (0.001801%) +De = 0.131861 +/- 0.0004739 (0.3594%) +E0 = -199.338 +/- 3.212e-06 (1.612e-06%) + #+end_example + + #+CALL:freq(1.18566,0.131861) + + #+RESULTS: + : 1015.5273789489723 + +** CCSD(T) exact + + Harmonic CCSD(T)/cc-pVQZ: 921 cm^-1 + Experimental: 894 cm^-1 + + + #+name:f2_ccsdt_ex + | 1.20 | -199.316930965941 | + | 1.25 | -199.337265800989 | + | 1.30 | -199.349733323061 | + | 1.35 | -199.356388989864 | + | 1.40 | -199.358812230238 | + | 1.45 | -199.358223196104 | + | 1.50 | -199.355566745188 | + + #+begin_src gnuplot :var data=f2_ccsdt_ex :results file :file f2_ccsdt_ex.png +reset +a0 = 1.8897161646321 +E(r) = De * (1-exp(-a*(r-re)))**2 + E0 +a = 1.40546 +re = 2.66544 +De = 0.0718256 +E0 = -199.358 +set xrange [2:4] +fit E(x) data using ($1*a0):2 via a, re, De, E0 +plot E(x), data using ($1*a0):2 w p + #+end_src + + #+RESULTS: + [[file:f2_ccsdt_ex.png]] + + #+begin_example +a = 1.26212 +/- 0.003274 (0.2594%) +re = 2.67046 +/- 9.555e-05 (0.003578%) +De = 0.0956201 +/- 0.0006465 (0.6761%) +E0 = -199.359 +/- 5.345e-06 (2.681e-06%) + #+end_example + + #+CALL:freq(1.26212,0.0956201) + + #+RESULTS: + : 920.5524350188175 + +* Vibration CuCl + 23 + 23 electrons = 46 electrons + 6 frozen orbitals (12 electrons) + 163 MOs total + + 34 electrons in 157 MOs + +** Script to compute frequencies in cm-1 + + #+begin_src bash :output raw +tail -20 fit.log + #+end_src + + #+RESULTS: + | final | sum | of | squares | of | residuals | : | 1.94178e-06 | | + | rel. | change | during | last | iteration | : | -3.41338e-13 | | | + | | | | | | | | | | + | degrees | of | freedom | (FIT_NDF) | : | 17 | | | | + | rms | of | residuals | (FIT_STDFIT) | = | sqrt(WSSR/ndf) | : | 0.000337968 | | + | variance | of | residuals | (reduced | chisquare) | = | WSSR/ndf | : | 1.14222e-07 | + | | | | | | | | | | + | Final | set | of | parameters | Asymptotic | Standard | Error | | | + | ======================= | ========================== | | | | | | | | + | a | = | 0.8637 | +/- | 0.005479 | (0.6344%) | | | | + | re | = | 3.948 | +/- | 0.001468 | (0.03719%) | | | | + | De | = | 0.0912735 | +/- | 0.001791 | (1.962%) | | | | + | E0 | = | -2099.73 | +/- | 0.0001235 | (5.883e-06%) | | | | + | | | | | | | | | | + | correlation | matrix | of | the | fit | parameters: | | | | + | a | re | De | E0 | | | | | | + | a | 1.0 | | | | | | | | + | re | -0.108 | 1.0 | | | | | | | + | De | -0.972 | -0.122 | 1.0 | | | | | | + | E0 | 0.677 | 0.055 | -0.711 | 1.0 | | | | | + + #+NAME:freq + #+begin_src python :var a=1.2526 :var De=0.7 :results output :output drawer +#!/usr/bin/env python +"""Converts vibrational frequencies from atomic units to cm-1 for diatomics.""" + +import sys +from math import sqrt, pi + +# Atomic masses obtained using +# import periodictable as pt +# for el in pt.elements: +# mass[el.symbol] = sorted([ (el[x].abundance,el[x].mass) for x in el.isotopes ])[-1][1] + +mass = {'H': 1.0078250321, 'He': 4.0026032497, 'Li': 7.016004, 'Be': 9.0121821, 'B': 11.0093055, 'C': 12.0, 'N': 14.0030740052, 'O': 15.9949146221, 'F': 18.9984032, 'Ne': 19.9924401759, 'Na': 22.98976967, 'Mg': 23.9850419, 'Al': 26.98153844, 'Si': 27.9769265327, 'P': 30.97376151, 'S': 31.97207069, 'Cl': 34.96885271, 'Ar': 39.962383123, 'K': 38.9637069, 'Ca': 39.9625912, 'Sc': 44.9559102, 'Ti': 47.9479471, 'V': 50.9439637, 'Cr': 51.9405119, 'Mn': 54.9380496, 'Fe': 55.9349421, 'Co': 58.9332002, 'Ni': 57.9353479, 'Cu': 62.9296011, 'Zn': 63.9291466, 'Ga': 68.925581, 'Ge': 73.9211782, 'As': 74.9215964, 'Se': 79.9165218, 'Br': 78.9183376, 'Kr': 83.911507, 'Rb': 84.9117893, 'Sr': 87.9056143, 'Y': 88.9058479, 'Zr': 89.9047037, 'Nb': 92.9063775, 'Mo': 97.9054078, 'Tc': 114.93828, 'Ru': 101.9043495, 'Rh': 102.905504, 'Pd': 105.903483, 'Ag': 106.905093, 'Cd': 113.9033581, 'In': 114.903878, 'Sn': 119.9021966, 'Sb': 120.903818, 'Te': 129.9062228, 'I': 126.904468, 'Xe': 131.9041545, 'Cs': 132.905447, 'Ba': 137.905241, 'La': 138.906348, 'Ce': 139.905434, 'Pr': 140.907648, 'Nd': 141.907719, 'Pm': 162.95352, 'Sm': 151.919728, 'Eu': 152.921226, 'Gd': 157.924101, 'Tb': 158.925343, 'Dy': 163.929171, 'Ho': 164.930319, 'Er': 165.93029, 'Tm': 168.934211, 'Yb': 173.9388581, 'Lu': 174.9407679, 'Hf': 179.9465488, 'Ta': 180.947996, 'W': 183.9509326, 'Re': 186.9557508, 'Os': 191.961479, 'Ir': 192.962924, 'Pt': 194.964774, 'Au': 196.966552, 'Hg': 201.970626, 'Tl': 204.974412, 'Pb': 207.976636, 'Bi': 208.980383, 'Po': 218.0089658, 'At': 223.02534, 'Rn': 228.03808, 'Fr': 232.04965, 'Ra': 234.05055, 'Ac': 236.05518, 'Th': 232.0380504, 'Pa': 231.0358789, 'U': 238.0507826, 'Np': 244.06785, 'Pu': 247.07407, 'Am': 249.07848, 'Cm': 252.08487, 'Bk': 254.0906, 'Cf': 256.09344, 'Es': 257.09598, 'Fm': 259.10059, 'Md': 260.10365, 'No': 262.10752, 'Lr': 263.11139, 'Rf': 264.11398, 'Db': 265.11866, 'Sg': 266.12193, 'Bh': 267.12774, 'Hs': 269.13411, 'Mt': 271.14123, 'Ds': 273.14925, 'Rg': 272.15348, 'Cn': 0, 'Nh': 0, 'Fl': 0, 'Mc': 0, 'Lv': 0, 'Ts': 0, 'Og': 0} + +def convert(e1,e2,f): + # Conversion factors + hartree = 4.3597447222071e-18 # joules + bohr = 1./18897161646.321 # m + amu = 1.6605402e-27 # kg + c = 299792458.0 # m/s + mole = 6.02214076e23 + + # Reduced mass in kg + mu = mass[e1]*mass[e2] / (mass[e1]+mass[e2]) * amu + + # Frequency in reduced coordinates + lam = (f * hartree / (bohr*bohr) ) / mu + + # Convert to wave numbers + nu = sqrt(lam)/(2.*pi*c) * 0.01 + + return nu + + +#print("Frequency (in hartree/bohr^2) ? "), +a = float(a) +f = De*2.*a*a + +print( convert('Cu','Cl',f) ) + #+end_src + + #+RESULTS: freq + : 1606.9338540276244 + +** CCSD + +NIST Computational Chemistry Comparison and Benchmark Database, +NIST Standard Reference Database Number 101 +Release 22, May 2022, Editor: Russell D. Johnson III +http://cccbdb.nist.gov/ + + Reference: 418 cm^-1 + + #+name:cucl_ccsd + | 1.50 | -2099.486410873280 | + | 1.55 | -2099.543699210125 | + | 1.60 | -2099.589314361086 | + | 1.65 | -2099.625339778701 | + | 1.70 | -2099.653512737443 | + | 1.75 | -2099.675272554191 | + | 1.80 | -2099.691805023191 | + | 1.85 | -2099.704090874785 | + | 1.90 | -2099.712929797538 | + | 1.95 | -2099.718979067095 | + | 2.00 | -2099.722774674517 | + | 2.05 | -2099.724755534740 | + | 2.10 | -2099.725278146519 | + | 2.15 | -2099.724633969314 | + | 2.20 | -2099.723061015635 | + | 2.25 | -2099.720753446736 | + | 2.30 | -2099.717868046847 | + | 2.35 | -2099.714536050722 | + | 2.40 | -2099.710862892300 | + | 2.45 | -2099.706934614773 | + | 2.50 | -2099.702822147426 | + | 2.55 | -2099.698584961555 | + | 2.60 | -2099.694269954830 | + | 2.65 | -2099.689916001502 | + + #+begin_src gnuplot :var data=cucl_ccsd :results file :file cucl_ccsd.png +reset +a0 = 1.8897161646321 +E(r) = De * (1-exp(-a*(r-re)))**2 + E0 +a = 1. +re = 3.9 +De = 0.1 +E0 = -2099.725 +set xrange [2.7:5] +fit E(x) data using ($1*a0):2 via a, re, De, E0 +plot E(x), data using ($1*a0):2 w p + #+end_src + + #+RESULTS: + [[file:cucl_ccsd.png]] + + #+begin_example +a = 0.850836 +/- 0.005939 (0.698%) +re = 3.94582 +/- 0.001786 (0.04526%) +De = 0.0961907 +/- 0.00189 (1.965%) +E0 = -2099.73 +/- 0.0001574 (7.496e-06%) + #+end_example + + #+CALL:freq(0.8637,0.0912735) + + #+RESULTS: + : 400.10303409950683 + +** CCSD(T) 1% + + | 1.50 | -2099.53432314 | 1.4370E-03 | + | 1.55 | -2099.58890791 | 1.3630E-03 | + | 1.60 | -2099.63464947 | 1.1896E-03 | + | 1.65 | -2099.67175286 | 1.5710E-03 | + | 1.70 | -2099.69974767 | 1.6166E-03 | + | 1.75 | -2099.71877319 | 1.3199E-03 | + | 1.80 | -2099.73774273 | 1.6649E-03 | + | 1.85 | -2099.74897746 | 1.4668E-03 | + | 1.90 | -2099.75550908 | 1.4868E-03 | + | 1.95 | -2099.76232971 | 1.6105E-03 | + | 2.00 | -2099.76550160 | 1.5386E-03 | + | 2.05 | -2099.76565267 | 1.5202E-03 | + | 2.10 | -2099.76718796 | 1.7046E-03 | + | 2.15 | -2099.76485609 | 1.7470E-03 | + | 2.20 | -2099.76331490 | 1.4802E-03 | + | 2.25 | -2099.76237391 | 1.7474E-03 | + | 2.30 | -2099.76090908 | 1.9686E-03 | + | 2.35 | -2099.75681975 | 1.9951E-03 | + | 2.40 | -2099.73868918 | 8.8739E-04 | + | 2.45 | -2099.74813718 | 2.4288E-03 | + | 2.50 | -2099.74125661 | 1.6437E-03 | + | 2.55 | -2099.74031232 | 2.4057E-03 | + | 2.60 | -2099.73104343 | 1.4544E-03 | + | 2.65 | -2099.72866832 | 1.6894E-03 | + + #+name:cucl_ccsdt + | 1.55 | -2099.58890791 | 1.3630E-03 | + | 1.65 | -2099.67175286 | 1.5710E-03 | + | 1.75 | -2099.71877319 | 1.3199E-03 | + | 1.85 | -2099.74897746 | 1.4668E-03 | + | 1.95 | -2099.76232971 | 1.6105E-03 | + | 2.05 | -2099.76565267 | 1.5202E-03 | + | 2.15 | -2099.76485609 | 1.7470E-03 | + | 2.25 | -2099.76237391 | 1.7474E-03 | + | 2.35 | -2099.75681975 | 1.9951E-03 | + | 2.45 | -2099.74813718 | 2.4288E-03 | + | 2.55 | -2099.74031232 | 2.4057E-03 | + | 2.65 | -2099.72866832 | 1.6894E-03 | + + #+begin_src gnuplot :var data=cucl_ccsdt :results file :file cucl_ccsdt.png +reset +a0 = 1.8897161646321 +E(r) = De * (1-exp(-a*(r-re)))**2 + E0 +a = 1. +re = 3.9 +De = 0.1 +E0 = -2099.767 +set xrange [2.7:5.2] +fit E(x) data using ($1*a0):2 via a, re, De, E0 +plot E(x), data using ($1*a0):2:3 w err + #+end_src + + #+RESULTS: + [[file:cucl_ccsdt.png]] + + + #+begin_example +a = 0.84615 +/- 0.03216 (3.8%) +re = 3.92539 +/- 0.01058 (0.2696%) +De = 0.101589 +/- 0.00932 (9.174%) +E0 = -2099.77 +/- 0.0008014 (3.817e-05%) + #+end_example + + #+CALL:freq(0.84615,0.101589) + + #+RESULTS: + : 413.5302408975902 + + #+CALL:freq(0.895573,0.0854261) + + #+RESULTS: + : 401.3588602143032 + +** CCSD(T) exact + + #+name:cucl_ccsdt_ex + | 1.50 | -2099.533616067071 | + | 1.55 | -2099.590506349950 | + | 1.60 | -2099.635662051331 | + | 1.65 | -2099.671184187604 | + | 1.70 | -2099.698826802514 | + | 1.75 | -2099.720045862965 | + | 1.80 | -2099.736043284873 | + | 1.85 | -2099.747811193906 | + | 1.90 | -2099.756159621832 | + | 1.95 | -2099.761752030920 | + | 2.00 | -2099.765128141854 | + | 2.05 | -2099.766727898670 | + | 2.10 | -2099.766907494029 | + | 2.15 | -2099.765956694308 | + | 2.20 | -2099.764111168127 | + | 2.25 | -2099.761562105614 | + | 2.30 | -2099.758464229658 | + | 2.35 | -2099.754944906474 | + | 2.40 | -2099.751100967299 | + | 2.45 | -2099.747028328725 | + | 2.50 | -2099.742790106242 | + | 2.55 | -2099.738443175793 | + | 2.60 | -2099.734033236772 | + | 2.65 | -2099.729597826175 | + + #+begin_src gnuplot :var data=cucl_ccsdt_ex :results file :file cucl_ccsdt_ex.png +reset +a0 = 1.8897161646321 +E(r) = De * (1-exp(-a*(r-re)))**2 + E0 +a = 1. +re = 3.9 +De = 0.1 +E0 = -2099.767 +set xrange [2.7:5.2] +fit E(x) data using ($1*a0):2 via a, re, De, E0 +plot E(x), data using ($1*a0):2 + #+end_src + + #+RESULTS: + [[file:cucl_ccsdt_ex.png]] + + #+begin_example +a = 0.853035 +/- 0.006204 (0.7273%) +re = 3.91994 +/- 0.002032 (0.05183%) +De = 0.100264 +/- 0.001906 (1.901%) +E0 = -2099.77 +/- 0.0001757 (8.367e-06%) + #+end_example + + #+CALL:freq(0.853035,0.100264) + + #+RESULTS: + : 414.16742408686565 + + + #+begin_src gnuplot :var data=cucl_ccsdt :var data2=cucl_ccsdt_ex :results file :file cucl_ccsdt2.png +reset +set grid +a0 = 1.8897161646321 +E(r) = De * (1-exp(-a*(r-re)))**2 + E0 +a = 1. +re = 3.9 +De = 0.1 +E0 = -2099.767 +set xrange [2.7:5.5] +fit E(x) data using ($1*a0):2 via a, re, De, E0 +set xrange [3.0:5.2] +plot data2 using ($1*a0-0.002):2 pointtype 2 lt 3 title "Full", data using ($1*a0+0.002):2:3 w err pt 0 lt 8 title "1%", E(x) title "" lt 5 + #+end_src + + #+RESULTS: + [[file:cucl_ccsdt2.png]] * Export :noexport: #+BEGIN_SRC elisp :output none