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Valence Bond Theory and Hybridized Orbitals02:38

Valence Bond Theory and Hybridized Orbitals

According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
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Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure around a central atom from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding...
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The perfect quadruples model for electron correlation in a valence active space.

John A Parkhill1, Keith Lawler, Martin Head-Gordon

  • 1Department of Chemistry, University of California, Berkeley, California 94720, USA.

The Journal of Chemical Physics
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

A new perfect quadruples (PQ) model offers a highly accurate, computationally efficient local approximation to the Schrodinger equation. This coupled cluster (CC) theory truncation improves electron correlation for studying molecular systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Coupled cluster (CC) theory provides accurate solutions to the Schrodinger equation.
  • Approximations are needed for computational efficiency in quantum chemistry.
  • Active space methods simplify calculations by focusing on relevant orbitals.

Purpose of the Study:

  • To introduce a novel local approximation to the Schrodinger equation within a valence active space.
  • To develop a computationally tractable method based on coupled cluster (CC) theory.
  • To improve the accuracy of electron correlation treatment in quantum chemical calculations.

Main Methods:

  • A perfect quadruples (PQ) model is proposed, truncating CC theory with quadruple excitations (CCSDTQ).
  • The model operates in a pairing active space with one virtual orbital per occupied orbital.
  • Amplitudes in the PQ model are scaled by the fourth root of CCSDTQ amplitudes.

Main Results:

  • The PQ model accurately approximates complete active space self-consistent field (CASSCF) results.
  • Validation was performed on molecular systems including H(4) deformations, H(2)O dissociation, ethene, and N(2).
  • The PQ model exhibits favorable computational scaling (fourth order with system size).

Conclusions:

  • The PQ model provides a significant improvement in accuracy over previous active space CC truncations.
  • Its computational efficiency allows for the study of larger molecular systems.
  • This method offers a balance between accuracy and computational cost for electronic structure calculations.