Second quantization and exchange perturbation theory for intermolecular interactions. the basis set superposition error problem

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Abstract

The application of the second-quantized formalism to treat the antisymmetry problem in perturbation theory (PT) of intermolecular interactions is reviewed. It is emphasized that second quantization permits one to work exclusively in the space of fully antisymmetric wavefunctions and to develop a unique many-body PT with a well-defined order parameter λ. However, owing to intermolecular overlap, one has to work with non-hermitian operators. This non-hermitian formalism can also be used to decouple the finite basis correction terms, giving rise to a basis set superposition error (BSSE) when using the chemical hamiltonian approach (CHA). A formal non-linear Schrödinger equation is written down yielding the BSSE-free wavefunctions and the "CHA/CE energy" (i.e. conventional energy expectation value over the BSSE-free wave-function). A double PT is developed to treat pure interaction and the interference from BSSE separately. Numerical applications on the H2-H2 interaction are presented as an example to demonstrate the reliability of this scheme.

Original languageEnglish
Pages (from-to)51-63
Number of pages13
JournalJournal of Molecular Structure: THEOCHEM
Volume232
Issue numberC
DOIs
Publication statusPublished - Jul 26 1991

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Wave functions
perturbation theory
Hamiltonians
interactions
antisymmetry
formalism
Nonlinear equations
nonlinear equations
wave functions
interference
operators
energy

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Computational Theory and Mathematics
  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Second quantization and exchange perturbation theory for intermolecular interactions. the basis set superposition error problem",
abstract = "The application of the second-quantized formalism to treat the antisymmetry problem in perturbation theory (PT) of intermolecular interactions is reviewed. It is emphasized that second quantization permits one to work exclusively in the space of fully antisymmetric wavefunctions and to develop a unique many-body PT with a well-defined order parameter λ. However, owing to intermolecular overlap, one has to work with non-hermitian operators. This non-hermitian formalism can also be used to decouple the finite basis correction terms, giving rise to a basis set superposition error (BSSE) when using the chemical hamiltonian approach (CHA). A formal non-linear Schr{\"o}dinger equation is written down yielding the BSSE-free wavefunctions and the {"}CHA/CE energy{"} (i.e. conventional energy expectation value over the BSSE-free wave-function). A double PT is developed to treat pure interaction and the interference from BSSE separately. Numerical applications on the H2-H2 interaction are presented as an example to demonstrate the reliability of this scheme.",
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AU - Surján, P.

AU - Mayer, I.

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N2 - The application of the second-quantized formalism to treat the antisymmetry problem in perturbation theory (PT) of intermolecular interactions is reviewed. It is emphasized that second quantization permits one to work exclusively in the space of fully antisymmetric wavefunctions and to develop a unique many-body PT with a well-defined order parameter λ. However, owing to intermolecular overlap, one has to work with non-hermitian operators. This non-hermitian formalism can also be used to decouple the finite basis correction terms, giving rise to a basis set superposition error (BSSE) when using the chemical hamiltonian approach (CHA). A formal non-linear Schrödinger equation is written down yielding the BSSE-free wavefunctions and the "CHA/CE energy" (i.e. conventional energy expectation value over the BSSE-free wave-function). A double PT is developed to treat pure interaction and the interference from BSSE separately. Numerical applications on the H2-H2 interaction are presented as an example to demonstrate the reliability of this scheme.

AB - The application of the second-quantized formalism to treat the antisymmetry problem in perturbation theory (PT) of intermolecular interactions is reviewed. It is emphasized that second quantization permits one to work exclusively in the space of fully antisymmetric wavefunctions and to develop a unique many-body PT with a well-defined order parameter λ. However, owing to intermolecular overlap, one has to work with non-hermitian operators. This non-hermitian formalism can also be used to decouple the finite basis correction terms, giving rise to a basis set superposition error (BSSE) when using the chemical hamiltonian approach (CHA). A formal non-linear Schrödinger equation is written down yielding the BSSE-free wavefunctions and the "CHA/CE energy" (i.e. conventional energy expectation value over the BSSE-free wave-function). A double PT is developed to treat pure interaction and the interference from BSSE separately. Numerical applications on the H2-H2 interaction are presented as an example to demonstrate the reliability of this scheme.

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