The Resonating Valence Bond Model of Molecules and Reactions

• Main Author: Voter, Arthur Ford
• Format: Others
• Language: en
• Published: 1983
• Online Access: https://thesis.library.caltech.edu/5376/1/Voter_af_1983.pdf; Voter, Arthur Ford (1983) The Resonating Valence Bond Model of Molecules and Reactions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/d754-h174. https://resolver.caltech.edu/CaltechTHESIS:11132009-133042163 <https://resolver.caltech.edu/CaltechTHESIS:11132009-133042163>

<p>This thesis presents an ab initio generalization of Pauling's theory of resonance, the generalized resonating valence bond (GRVB) method. In GRVB, we optimize a wavefunction of the form</p> <p>Ψ_<i>TOT</i> = C_<i>A</i> Ψ_<i>A</i> + C_<i>B</i> Ψ_<i>B</i></p> <p>where Ψ_<i>A</i> and Ψ_<i>B</i> are multiconfigurational wavefunctions with arbitrary overlap. This type of wavefunction has been considered unfeasible for more than a few electrons due to the <i>n</i>! computational dependence of evaluating the matrix element &lt; Ψ_<i>A</i> | <i>H</i> | Ψ_<i>B</i> &gt;. We reduce this dependence to ~n⁵ by biorthogonalizing the orbitals in each determinant pair. GRVB is ideally suited to describing systems which require a resonance of more than one bonding structure, such as benzene, molecules with three-electron bonds, and reaction transition states. Besides yielding a conceptually simple avefunction, we find that GRVB yields quantitative results for processes in which the dominant differential correlation is a resonance effect. For example, the GRVB barrier heights for the HCl + H and HF + H exchange reactions are each within one kcal of the basis set limit, in contrast to the orthogonal configuration interaction (CI) approaches which require hundreds or thousands of configurations to achieve the same accuracy. We also present application to the three-electron bonding in noble gas dimer ions, and various other examples.</p>