Static spin correlations in alternant quantum cell models

Abstract

Static-spin-correlation functions 4〈$s_{\mathrm{pz}}$ $s_{\mathrm{qz}}$〉 are evaluated via diagrammatic valence-bond theory for exact states of finite Hubbard, Pariser-Parr-Pople (PPP), and related quantum cell models. Several properties of 〈$s_{\mathrm{pz}}$ $s_{\mathrm{qz}}$〉 that are independent of intersite potentials $V_{\mathrm{pp}\mathcal{’}}$ in the Hartree-Fock (HF) approximation for half-filled alternant systems are shown to be sensitive to correlations in the ground state of N≤12 Hubbard and PPP chains. Accurate N→∞ extrapolations are found for near neighbors. The correct ground-state charge density 〈$n_p$〉=1 is a property of half-filled alternant systems and thus not a test of HF or other one-electron approximations. Spin correlations in PPP models with standard molecular parameters and long-range Coulomb interactions are approximately given by on-site interactions of U≃2‖t‖ in Hubbard models, although the general semiempirical PPP approach to conjugated molecules is preferable for wide-band systems.