Benchmark correlation energies for small molecules

O’Neill, Darragh P.; Gill, Peter M. W.

doi:10.1080/00268970512331339323

Cited by 52 publications

(31 citation statements)

References 27 publications

(35 reference statements)

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“…The error due to remaining basis-set incompleteness and residual correlation effects was estimated by the difference in the all-electron CCSDT-R12 correlation energy between aug-cc-pCVTZ and QZ plus the effect of the quadruples. Our best estimate of the correlation energy agrees perfectly with the value ͑−371 mE h ͒ derived from experimental data by O'Neill and Gill 78 and also with the CBS extrapolated value ͑−371.3 mE h ͒ of Harding et al 79 The total energy ͑eigenvalue͒ of the Schrödinger equation of H 2 O is obtained as the sum of the converged HF energy 19 79 as well as with the value derived from experimental data also by Bytautas and Ruedenberg. 84 Our error estimate of 3 mE h corresponds to 2 kcal/mol and, therefore, our composite method based on the CC-R12 and grid-based HF methods can almost achieve the chemical accuracy in the total energy ͑and even higher accuracy in relative energies͒ without extrapolations of the CBS limits.…”

Section: Resultssupporting

confidence: 89%

Higher-order explicitly correlated coupled-cluster methods

Shiozaki

Kamiya

Hirata

et al. 2009

The Journal of Chemical Physics

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Efficient computer codes for the explicitly correlated coupled-cluster (CC-R12 or F12) methods with up to triple (CCSDT-R12) and quadruple excitations (CCSDTQ-R12), which take account of the spin, Abelian point-group, and index-permutation symmetries and are based on complete diagrammatic equations, have been implemented with the aid of the computerized symbolic algebra SMITH. Together with the explicitly correlated coupled-cluster singles and doubles (CCSD-R12) method reported earlier [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], they form a hierarchy of systematic approximations (CCSD-R12

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Section: Resultssupporting

confidence: 89%

Higher-order explicitly correlated coupled-cluster methods

Shiozaki

Kamiya

Hirata

et al. 2009

The Journal of Chemical Physics

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“…[12], and M11 [30]. Considering that the five functionals are among the most cited works of all time [9], the results validate the accuracy of the correlation energy functional in Eq. (1).…”

Section: Resultssupporting

confidence: 58%

“…Since the original idea was conceived in the 1920s by Thomas and Fermi [6], progress has been made continuously in the field including the seminal work of Becke [7] in 1988 which brought the error of the exchange energy down to less than 1% (as compared to the exact Hartree-Fock exchange). The Becke-88 functional is also the key ingredient in constructing the B3 hybrid functional [8], the top 10 most cited paper of all time [9].…”

Section: Introductionmentioning

confidence: 99%

Understanding electron correlation energy through density functional theory

Chachiyo¹,

Chachiyo²

2020

Computational and Theoretical Chemistry

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A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation energies, the total energies, and the ionization energies of test atoms and molecules; and despite the unique simplicities, the functionals' accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11. Therefore, we propose that, as guided by the simplicities and supported by the accuracies, the correlation energy is the energy that locally tends to drive the system toward the uniform electron gas. Without Correlation Include Correlation ExactlyHarmonic Potential Coulomb Repulsion

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“…A combination of experimental and theoretical molecular geometries are used in this study [15][16][17][18]. The zero point energies and experimental atomization energies are from Feller et al [15,19].…”

Section: Computational Setupmentioning

confidence: 99%

Approaching chemical accuracy with quantum Monte Carlo

Petruzielo

Toulouse

Umrigar

2012

The Journal of Chemical Physics

111

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A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.

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Benchmark correlation energies for small molecules

Abstract: We present estimates of the exact correlation energies for 56 small molecules whose experimental atomization energies are known accurately. These should prove useful in the assessment and parameterization of new quantum chemical methods.

Cited by 52 publications

References 27 publications

Higher-order explicitly correlated coupled-cluster methods

Higher-order explicitly correlated coupled-cluster methods

Understanding electron correlation energy through density functional theory

Approaching chemical accuracy with quantum Monte Carlo

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