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f95ce56d94
@ -85,24 +85,12 @@
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\affiliation{\LCPQ}
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\affiliation{\LCPQ}
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\begin{abstract}
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\begin{abstract}
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We introduce a novel algorithm that leverages stochastic sampling
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We introduce a novel algorithm that leverages stochastic sampling techniques to approximate perturbative triples in the coupled-cluster (CC) framework.
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techniques to approximate perturbative triples correction in the
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By combining elements of randomness and determinism, our algorithm achieves a favorable balance between accuracy and computational cost.
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coupled-cluster (CC) framework.
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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.
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By combining elements of randomness and determinism, our algorithm
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We provide evidence that our semi-stochastic algorithm achieves substantial computational savings compared to traditional deterministic methods.
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achieves a favorable balance between accuracy and computational cost.
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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.
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The main advantage of this algorithm is that it allows for
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This work opens up new avenues for efficient and accurate computations, enabling investigations of complex molecular systems that were previously computationally prohibitive.
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calculations to be stopped at any time, providing an unbiased
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estimate, with a statistical error that goes to zero as the exact
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calculation is approached.
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We provide evidence that our semi-stochastic algorithm achieves
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substantial computational savings compared to traditional
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deterministic methods.
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Specifically, we demonstrate that a precision of 0.5 milliHartree can
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be attained with only 10\% of the computational effort required by the
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full calculation.
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This work opens up new avenues for efficient and accurate
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computations, enabling investigations of complex molecular systems
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that were previously computationally prohibitive.
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\bigskip
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\bigskip
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\begin{center}
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\begin{center}
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% \boxed{\includegraphics[width=0.5\linewidth]{TOC}}
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% \boxed{\includegraphics[width=0.5\linewidth]{TOC}}
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@ -203,42 +191,13 @@ accelerators.\cite{ma_2011,haidar_2015,dinapoli_2014,springer_2018}
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% - Benzene TZ
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% - Benzene TZ
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% - Streptocyanine QZ: Small molecule in a large basis set
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% - Streptocyanine QZ: Small molecule in a large basis set
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% - Caffeine def2-svp: Large molecule in a small basis set
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% - Caffeine def2-svp: Large molecule in a small basis set
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% - Vibrational frequency of F2/cc-pvqz
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%b. Discussion of the obtained results, comparing against other methods
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%b. Discussion of the obtained results, comparing against other methods
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% - Measure flops and compare to the peak
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% - Measure flops and compare to the peak
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%c. Analysis of the algorithm's accuracy, efficiency, and scalability
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%c. Analysis of the algorithm's accuracy, efficiency, and scalability
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%d. Discussion of any observed limitations or challenges
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%d. Discussion of any observed limitations or challenges
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\subsection{Vibrational frequency of \ce{F2}}
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In this example, we compute the vibrational frequency of \ce{F2} by
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computing the potential energy curve, and fitting it with a Morse
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potential
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\begin{equation}
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E(r) = D_e \left( 1 - e^{-a (r - r_e)} \right)^2 + E(r_e)
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\end{equation}
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where $E(r)$ is the energy at distance $r$, $D_e$ is the well depth,
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$r_e$ is the equilibrium bond distance, and $a$ is a parameter
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controlling the width of the potential well.
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The vibrational frequency $\nu$ is calculated as
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\begin{equation}
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\nu = \frac{1}{2 \pi c} \sqrt{\frac{2D_e a^2}{\mu}
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\end{equation}
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where $\mu$ is the mass of the Fluorine atom, and $c$ is the speed of
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light in cm/s.
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% CCSD
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%a = 2.2936 +/- 0.006318 (0.2755%)
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%De = 0.125888 +/- 0.0005213 (0.4141%)
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%re = 1.3893 +/- 0.0003428 (0.02468%)
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%E0 = -199.338 +/- 6.422e-05 (3.222e-05%)
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% CCSD(T) exact
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%a = 2.65592 +/- 0.0403 (1.518%)
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%De = 0.0718253 +/- 0.001879 (2.617%)
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%re = 1.4105 +/- 0.00215 (0.1524%)
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%E0 = -199.358 +/- 0.0003179 (0.0001595%)
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%=================================================================%
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\section{Conclusion}
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\section{Conclusion}
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\label{sec:conclusion}
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\label{sec:conclusion}
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434
triples.org
434
triples.org
@ -7362,440 +7362,6 @@ plot data using :1:2 w errorlines notitle, -678.026179485578 notitle
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#+RESULTS:
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#+RESULTS:
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[[file:caffeine_svp.png]]
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[[file:caffeine_svp.png]]
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* Vibration F2
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** Script to compute frequencies in cm-1
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#+begin_src bash :output raw
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tail -20 fit.log
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#+end_src
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#+NAME:freq_
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#+begin_src python :var a=1.2526 :var De=0.7 :results output :output drawer
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#!/usr/bin/env python
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"""Converts vibrational frequencies from atomic units to cm-1 for diatomics."""
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import sys
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from math import sqrt, pi
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# Atomic masses obtained using
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# import periodictable as pt
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# for el in pt.elements:
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# mass[el.symbol] = sorted([ (el[x].abundance,el[x].mass) for x in el.isotopes ])[-1][1]
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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}
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def convert(e1,e2,f):
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# Conversion factors
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hartree = 4.3597447222071e-18 # joules
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bohr = 1./18897161646.321 # m
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amu = 1.6605402e-27 # kg
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c = 299792458.0 # m/s
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mole = 6.02214076e23
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# Reduced mass in kg
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mu = mass[e1]*mass[e2] / (mass[e1]+mass[e2]) * amu
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# Frequency in reduced coordinates
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lam = (f * hartree / (bohr*bohr) ) / mu
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# Convert to wave numbers
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nu = sqrt(lam)/(2.*pi*c) * 0.01
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return nu
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#print("Frequency (in hartree/bohr^2) ? "),
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a = float(a)
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f = De*2.*a*a
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print( convert('F','F',f) )
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#+end_src
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#+RESULTS: freq_
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: 2471.921716627526
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** CCSD
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NIST Computational Chemistry Comparison and Benchmark Database,
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NIST Standard Reference Database Number 101
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Release 22, May 2022, Editor: Russell D. Johnson III
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http://cccbdb.nist.gov/
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Reference: 1016 cm^-1
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#+name:f2_ccsd
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| 1.20 | -199.300901502767 |
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| 1.25 | -199.320245823796 |
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| 1.30 | -199.331634513014 |
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| 1.35 | -199.337115250478 |
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| 1.40 | -199.338256839462 |
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| 1.45 | -199.336266825958 |
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| 1.50 | -199.332076468455 |
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#+begin_src gnuplot :var data=f2_ccsd :results file :file f2_ccsd.png
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reset
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a0 = 1.8897161646321
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E(r) = De * (1-exp(-a*(r-re)))**2 + E0
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a = 1.40546
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re = 2.66544
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De = 0.0718256
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E0 = -199.358
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set xrange [2:5]
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fit E(x) data using ($1*a0):2 via a, re, De, E0
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plot E(x), data using ($1*a0):2 w p
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#+end_src
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#+RESULTS:
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[[file:f2_ccsd.png]]
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#+begin_example
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a = 1.18566 +/- 0.001801 (0.1519%)
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re = 2.62779 +/- 4.734e-05 (0.001801%)
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De = 0.131861 +/- 0.0004739 (0.3594%)
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E0 = -199.338 +/- 3.212e-06 (1.612e-06%)
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#+end_example
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#+CALL:freq(1.18566,0.131861)
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#+RESULTS:
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: 1015.5273789489723
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** CCSD(T) exact
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Harmonic CCSD(T)/cc-pVQZ: 921 cm^-1
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Experimental: 894 cm^-1
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#+name:f2_ccsdt_ex
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| 1.20 | -199.316930965941 |
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| 1.25 | -199.337265800989 |
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| 1.30 | -199.349733323061 |
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| 1.35 | -199.356388989864 |
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| 1.40 | -199.358812230238 |
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| 1.45 | -199.358223196104 |
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| 1.50 | -199.355566745188 |
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#+begin_src gnuplot :var data=f2_ccsdt_ex :results file :file f2_ccsdt_ex.png
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reset
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a0 = 1.8897161646321
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E(r) = De * (1-exp(-a*(r-re)))**2 + E0
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a = 1.40546
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re = 2.66544
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De = 0.0718256
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E0 = -199.358
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set xrange [2:4]
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fit E(x) data using ($1*a0):2 via a, re, De, E0
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plot E(x), data using ($1*a0):2 w p
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#+end_src
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#+RESULTS:
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[[file:f2_ccsdt_ex.png]]
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#+begin_example
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a = 1.26212 +/- 0.003274 (0.2594%)
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re = 2.67046 +/- 9.555e-05 (0.003578%)
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De = 0.0956201 +/- 0.0006465 (0.6761%)
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E0 = -199.359 +/- 5.345e-06 (2.681e-06%)
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#+end_example
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#+CALL:freq(1.26212,0.0956201)
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#+RESULTS:
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: 920.5524350188175
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* Vibration CuCl
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23 + 23 electrons = 46 electrons
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6 frozen orbitals (12 electrons)
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163 MOs total
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34 electrons in 157 MOs
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** Script to compute frequencies in cm-1
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#+begin_src bash :output raw
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tail -20 fit.log
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#+end_src
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#+RESULTS:
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| final | sum | of | squares | of | residuals | : | 1.94178e-06 | |
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| rel. | change | during | last | iteration | : | -3.41338e-13 | | |
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| | | | | | | | | |
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| degrees | of | freedom | (FIT_NDF) | : | 17 | | | |
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| rms | of | residuals | (FIT_STDFIT) | = | sqrt(WSSR/ndf) | : | 0.000337968 | |
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| variance | of | residuals | (reduced | chisquare) | = | WSSR/ndf | : | 1.14222e-07 |
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| | | | | | | | | |
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| Final | set | of | parameters | Asymptotic | Standard | Error | | |
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| ======================= | ========================== | | | | | | | |
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| a | = | 0.8637 | +/- | 0.005479 | (0.6344%) | | | |
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| re | = | 3.948 | +/- | 0.001468 | (0.03719%) | | | |
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| De | = | 0.0912735 | +/- | 0.001791 | (1.962%) | | | |
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| E0 | = | -2099.73 | +/- | 0.0001235 | (5.883e-06%) | | | |
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| | | | | | | | | |
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| correlation | matrix | of | the | fit | parameters: | | | |
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| a | re | De | E0 | | | | | |
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| a | 1.0 | | | | | | | |
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| re | -0.108 | 1.0 | | | | | | |
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| De | -0.972 | -0.122 | 1.0 | | | | | |
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| E0 | 0.677 | 0.055 | -0.711 | 1.0 | | | | |
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#+NAME:freq
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#+begin_src python :var a=1.2526 :var De=0.7 :results output :output drawer
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#!/usr/bin/env python
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|
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"""Converts vibrational frequencies from atomic units to cm-1 for diatomics."""
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import sys
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from math import sqrt, pi
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# Atomic masses obtained using
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# import periodictable as pt
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# for el in pt.elements:
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# mass[el.symbol] = sorted([ (el[x].abundance,el[x].mass) for x in el.isotopes ])[-1][1]
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|
||||||
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:
|
* Export :noexport:
|
||||||
#+BEGIN_SRC elisp :output none
|
#+BEGIN_SRC elisp :output none
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user