Approximate energy‐evaluating schemes for a system of weakly overlapping group functions

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Abstract

The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. © 1995 John Wiley & Sons, Inc.

Original languageEnglish
Pages (from-to)485-493
Number of pages9
JournalInternational Journal of Quantum Chemistry
Volume53
Issue number5
DOIs
Publication statusPublished - 1995

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projection
Bond length
energy
matrices
power series
inclusions

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

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title = "Approximate energy‐evaluating schemes for a system of weakly overlapping group functions",
abstract = "The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. {\circledC} 1995 John Wiley & Sons, Inc.",
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T1 - Approximate energy‐evaluating schemes for a system of weakly overlapping group functions

AU - Ferenczy, G.

PY - 1995

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N2 - The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. © 1995 John Wiley & Sons, Inc.

AB - The energy of weakly overlapping group functions can be written as a series according to the powers of the (σ – I) matrix, where σ is the molecular overlap matrix and I is the unit matrix [1,2]. This power series of the energy is studied by investigating the importance of different order terms to obtain accurate energies and to predict equilibrium bond lengths. It is found that the series is truncated advantageously at an even‐order term. Approximate formulas for the first‐ and second‐order terms are proposed in order to reduce computational work. Numerical examples are presented to illustrate the effect of these terms to the energy. The relation of the projection energy to the approximate first‐ and second‐order terms is also discussed. It is found that, by choosing appropriate projection factors, the projection energy corrects the zeroth‐order energy more efficiently than does the first‐order term. The inclusion of the approximate second‐order term represents a slight improvement with respect to the use of the projection energy at the expense of some extra computation. © 1995 John Wiley & Sons, Inc.

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