Publisher Summary This chapter discusses basic modeling. The chapter illustrates that
quantum chemistry aims at understanding the properties of matter through the modeling of …

This review is devoted to the study of stationary solutions of linear and nonlinear equations
from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as …

Abstract The familiar unrestricted Hartree-Fock variational principles is generalized to
include quasi-free states. As we show, these are in one-to-one correspondence with the one …

We derive and assess two new classes of regularizers that cope with offending
denominators in the single-reference second-order Møller–Plesset perturbation theory …

This article is concerned with the numerical solution of subspace optimization problems,
consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed …

The present work is a mathematical analysis of two algorithms, namely the Roothaan and
the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations …

We present an overview of some works on the models of computational quantum chemistry.
We examine issues such as the existence of ground states (both for the electronic structure …

Geometric techniques have played an important role in the seventies, for the study of the
spectrum of many-body Schrödinger operators. In this paper we provide a formalism which …

We explore a variety of unsolved problems in density functional theory, where
mathematicians might prove useful. We give the background and context of the different …

Using recent calculations we review some well‐known aspects of density functional theory:
the Hohenberg–Kohn theorems, the Kohn–Sham method, the adiabatic connection, and the …