On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods

TLDR

The approach is discussed in relation to configuration‑interaction and quantum‑field perturbation theory. The authors propose a method to compute matrix elements of the logarithm of an operator that yields the exact wavefunction in the one‑electron approximation. The method employs creation and annihilation operators, hole–particle formalism, Wick’s theorem, and Feynman‑like diagrams, and is applied to nitrogen and benzene models. The resulting matrix elements are compared with full configuration‑interaction calculations for nitrogen and benzene, demonstrating consistency.

Abstract

A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman-like diagrams. The connection of this method with the configuration-interaction method as well as with the perturbation theory in the quantum-field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration-interaction method considering all possible configurations within the chosen basis of one-electron functions.