Journal ArticleDOI
Electron Correlation in Closed Shell Systems. I. Perturbation Theory Using Gaussian‐Type Geminals
Kee‐Chuan Pan,Harry F. King +1 more
TLDR
In this paper, the authors used Rayleigh-Schroedinger perturbation theory with the symmetric sum of Hartree-Fock operators for H 0.3428/a.Abstract:
The calculation of electron correlation energy in closed‐shell atoms and molecules is approached using Rayleigh‐Schroedinger perturbation theory with the symmetric sum of Hartree‐Fock operators for H0. The alleged advantages of using a VN−1 potential are questioned. Variational equations for first‐order pair correlation functions are computed for He, Be, B+ and Ne by expansion in linear combinations of correlated Gaussian‐type geminal basis functions containing r122 in the exponent. Such functions form mathematically complete sets, have convenient symmetry properties, and are integrable in closed form. An extensive search for optimum exponential parameters yielded trial functions for each of the ss orbital pairs giving better than 99% of the limiting second‐order pair energy using only five basis functions per pair. Similar but less thorough studies of sp and pp pairs in neon are also reported. Careful attention is paid to computational accuracy. An upper bound of −0.3428 a.u. is established on the second...read more
Citations
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Journal ArticleDOI
Explicitly correlated electrons in molecules.
TL;DR: Explicitly Correlated Electrons in Molecules Christof Hattig, Wim Klopper,* Andreas K€ohn, and David P. Tew Lehrstuhl.
Journal ArticleDOI
R12 methods in explicitly correlated molecular electronic structure theory
TL;DR: In this paper, it was shown that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear (r 12) to some suitably chosen short-range form (e.g., exp(−αr 12).
Journal ArticleDOI
Theory and application of explicitly correlated Gaussians
Jim Mitroy,Sergiy Bubin,Wataru Horiuchi,Yasuyuki Suzuki,Ludwik Adamowicz,Wojciech Cencek,Krzysztof Szalewicz,Jacek Komasa,D Blume,Kalman Varga +9 more
TL;DR: The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems as mentioned in this paper.
Journal ArticleDOI
Variation-perturbation treatment of the hydrogen bond between water molecules
TL;DR: In this paper, the authors calculated the hydrogen-bond energy of two water molecules as a sum of the electrostatic, exchange, induction and dispersion contributions, neglecting the electron correlation within the free monomers.
Journal ArticleDOI
Explicitly correlated second order perturbation theory: Introduction of a rational generator and numerical quadratures
TL;DR: A rational generator, which fulfills the cusp conditions for singlet and triplet electron pairs, is proposed and applied to explicitly correlated second order Møller-Plesset perturbation theory calculations.
References
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Journal ArticleDOI
Note on an Approximation Treatment for Many-Electron Systems
Chr. Møller,Milton S. Plesset +1 more
TL;DR: In this article, a perturbation theory for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation was developed, and it was shown by this development that the first order correction for the energy and the charge density of the system is zero.
Journal ArticleDOI
An efficient method for finding the minimum of a function of several variables without calculating derivatives
Journal ArticleDOI
Molecular Dynamics Study of Liquid Water
TL;DR: In this paper, a sample of water, consisting of 216 rigid molecules at mass density 1 gm/cm3, has been simulated by computer using the molecular dynamics technique, subject to an effective pair potential that incorporates the principal structural effects of manybody interactions in real water.
Book
The Many-body Problem
TL;DR: A survey with emphasis on physical considerations can be found in this article, with a focus on mathematical principles and techniques, and specific problems in the following areas: general formulationElectron GasInteracting Fermion SystemInteracting Boson SystemsSuperconductivity
Journal ArticleDOI
Criteria for the Construction of Good Self‐Consistent‐Field Molecular Orbital Wave Functions, and the Significance of LCAO‐MO Population Analysis
TL;DR: In this paper, the concept of induced configuration mixing is proposed as a helpful way of thinking of the higher-order interactions which carry the wave function from that of a groundstate atom pair over toward an SCF-MO form.
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