On the Accuracy of the Algebraic Approximation in Molecular Electronic Structure Studies: VII. Matrix Valence Bond Calculations for the Hydrogen Molecule Ground State

Int J of Quantum Chemistry

2004

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ABSTRACT:The development of robust many-body methods for the molecular electronic structure problem with respect to multireference functions has attracted much attention over the past two decades. In recent years, multireference methods based on the Brillouin-Wigner expansion have been shown to overcome the intruder state problems which have plagued similar approaches based on the Rayleigh-Schrö dinger series. However, there are some problems in molecular electronic structure theory, which may be handled by means of multireference methods, but can be treated by methods that avoid the use of multireference functions. We consider two examples of alternatives to multireference methods for the molecular electronic structure problem. The study of excited states having the same symmetry as the ground state or some lower lying excited state often involves the use of a multireference function. We describe an alternative procedure based on the generalized Rayleigh-Ritz variation principle. Gidopoulos, Glushkov, and Wilson have termed this the optimized trace method. The generalized Rayleigh-Ritz principle for the relativistic formulation of the molecular electronic structure problem is briefly also considered. Molecular dissociative processes are frequently described by quantum chemical methods based on multireference functions. Single-reference Hartree-Fock methods usually provide a qualitatively incorrect description of such processes even in the simplest of molecules, H 2 . However, approximate single configuration wave functions constructed from nonorthogonal orbitals can often afford a useful approximation to bond-breaking processes. Each occupied nonorthogonal orbital is then an eigenfunction of a different Fock-like operator. Each of these Fock-like operators supports a spectrum of M single particle states, where M is the size of the basis set, and only the lowest of these is occupied. We briefly consider the relativistic formulation of the molecular electronic structure problem based on approximations involving products of nonorthogonal functions within the Furry bound state interaction picture of quantum electrodynamics.

Section: Wave Function Of Coulson and Fischer And Its Extensionsmentioning

confidence: 95%

Alternatives to multireference methods for the molecular electronic structure problem

Int J of Quantum Chemistry

2004

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“…The present paper complements a series devoted to the accurate implementation of the algebraic approximation in molecular electronic structure studies [4][5][6][7][8][9][10]. Comparisons of finite-difference and finite basis set Hartree-Fock calculations for diatomic molecules have demonstrated that energies approaching the sub-µHartree level of accuracy can be obtained by exploiting standard quantum chemical procedures in a systematic fashion [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Systematic construction of basis subsets of higher angular momentum functions in electron correlation energy calculations

Moncrieff

J. Phys. B: At. Mol. Opt. Phys.

1999

High-precision many-body perturbation theory calculations are reported for the ground state of the neon atom within the algebraic approximation, i.e. by using a finite basis set expansion. The second-order many-body perturbation theory correlation energy component is calculated using an even-tempered universal basis set sequence of Gaussian-type functions of increasing angular quantum number. The basis subsets for each symmetry are systematically truncated so as to attempt to maintain an accuracy of ~1 µHartree. The resulting energy components are compared with other recent results, including those obtained by employing correlation-consistent basis sets and the recent finite-element study by Flores and Kolb. A sub-µHartree level of accuracy was achieved for the E2( = 1) energy component.

On the application of hierarchical orthogonality restrictions to spin-coupled wave functions

1999

Int. J. Quant. Chem.

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