2 - Quantum Properties of Small Systems at Equilibrium: First Principle Calculations

Abstract

Transport properties of strongly spatially inhomogeneous quantum systems near equilibrium or in their steady states can be expressed self-consistently and from the first principles in terms of equilibrium correlation functions and/or two-time temperature Green's functions (EGFs) using ZT-projection operator method (see Chapter 1 for details). In their turn, the correlation functions and EGFs can be calculated analytically, in particular using an appropriate version of the ZT method for EGF calculations, and/or numerically. Analytical tools for such calculations have been briefly discussed in Chapter 1. This chapter is focused on the first-principle computational tools of statistical mechanics, and in particular on ab initio quantum chemistry methods used to characterize the equilibrium state (i.e., the ground state) of a bounded quantum system. In this approach the time-independent Schrödinger equation for N-particle system (all atomic nuclei and electrons of the system included) is solved using extended variation methods based on the variation theorem. Self-consistent field (SCF), Hartree-Fock (HF), configuration interaction CI method [including the complete active space (CAS), CASSCF, multiconfiguration SCF (MCSCF) approximations, and the Møller-Plesset (MP) perturbation theory], and the coupled-cluster (CC) method are discussed in detail. A reader would be enabled to use intelligently the existing ab initio software packages for virtual synthesis of electronic materials, such as those discussed in Chapters 3 to 8. A brief overview of available ab initio quantum chemistry software and the virtual synthesis method are also provided.