Correlation-Driven Orbital Optimization in One-Dimensional Hubbard Systems

Abstract

The flexibility afforded by molecular orbitals plays a central role in the development of quantum-chemical methods. In this work, we investigate the electronic structure of delocalized half-filled one-dimensional symmetric AA and asymmetric AB systems described by the Hubbard Hamiltonian through a bottom-up strategy designed to assess the performance of a two-step procedure. The proposed framework aims at constructing a correlated wave function, thereby providing a complementary perspective to conventional band-structure descriptions. In a first step, Rayleigh–Schrödinger perturbation theory is applied to a zeroth-order local valence-bond ground state in order to incorporate charge-transfer configurations and account for short-range delocalization effects. In a second step, the resulting second-order energy is minimized with respect to orbital rotations. Starting from the canonical molecular orbitals obtained from the one-electron part of the Hubbard Hamiltonian, the method is benchmarked against exact cluster calculations for both symmetric AA and asymmetric AB systems. Although the second-order energy correction in symmetric systems is insensitive to the choice of the molecular orbitals, electron–electron interactions in asymmetric systems drive departures from the canonical orbital representation, emphasizing the role of local electronic correlations in determining the optimal orbital framework. Beyond its quantitative performance, the present approach complements the conventional Bloch-function picture and offers a chemically intuitive interpretation for extended systems.