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 …

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 …

We present the field of computational chemistry from the standpoint of numerical analysis.
We introduce the most commonly used models and comment on their applicability. We …

We consider a Dirac operator in three space dimensions, with an electrostatic (ie, real-
valued) potential V (x), having a strong Coulomb-type singularity at the origin. This operator …

The Dirac equation for H 2+ is solved numerically by expansion in a basis set of two-center
exponential functions, using different kinetic balance schemes. Very high precision (27 to 32 …

Publisher Summary This chapter focuses on computational approaches of relativistic models
in quantum chemistry. The chapter illustrates that the use of ab initio relativistic calculations …

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate
spheroidal coordinates for an electron–molecular two-center system. The initial state is …

A numerical method is developed to solve the time-dependent Dirac equation in cylindrical
coordinates for 3-D axisymmetric systems. The time evolution is treated by a splitting …

Analysis, modeling and simulation of multiscale problems Page 2 Mielke (Ed.) Analysis, Modeling
and Simulation of Multiscale Problems Page 3 Alexander Mielke Editor Analysis, Modeling and …

Two numerical methods are used to evaluate the relativistic spectrum of the two-center
Coulomb problem (for the H 2+ and Th 2 179+ diatomic molecules) in the fixed nuclei …