Interaction of chemical bonds: Strictly localized wave functions in orthogonal basis

Abstract

A second-quantized theory is presented with the aim to study the nature and interactions of well-localizable chemical bonds in molecules. The basis set is partitioned by assigning each basis function to a chemical bond possessing two electrons. The Schr\"odinger equation within each limited basis subset is solved exactly for each bond, leading to correlated, strictly localized, intrabond wave functions. The total many-electron wave function $\ensuremath{\Psi}$ is defined as the antisymmetrized product of these strictly localized geminals. The second-quantized Hamiltonian $\stackrel{^}{H}$ is partitioned as $\stackrel{^}{H}={\stackrel{^}{h}}^{0}+\stackrel{^}{W}$, where the zeroth-order Hamiltonian ${\stackrel{^}{h}}^{0}$ contains all terms which contribute to the energy of the strictly localized wave function $\ensuremath{\Psi}$, while the expectation value of $\stackrel{^}{W}$, as calculated by $\ensuremath{\Psi}$, is zero. Since ${\stackrel{^}{h}}^{0}$ is not simply the sum of intrabond Hamiltonians, the strictly localized wave function accounts for certain interbond interactions (inductive effects). The concept of bond creation and annihilation operators is introduced which formally shows Bose-type behavior since they refer to a two-electron composite system.