An Analysis for Some Methods and Algorithms of Quantum Chemistry

In the field of ab-initio calculation of theproperties of atoms, molecules and solids, the solution of the electronic Schrödinger equation,an operator eigenvalue equation for the Hamiltonianof the system, plays a major role. Of utmost significance is thelowest eigenvalue of this Hamiltonian, representing the ground state energy of the system. To meet the requirements of the multitude of possibleapplications of the electronic Schrödinger equation,the last decades have seen the development of avariety of different methods designed to approximate the solution of this extremelyhigh-dimensional minimization problem. The present work delivers amathematical analysis for aspects of some of these methods used in the context of quantumchemistry calculation. Three approaches used in the algorithmic treatment ofthe electronic Schrödinger equation are analysed in detail: A "direct minimization" scheme used inHartree-Fock, Kohn-Sham and in CI calculations, the Coupled Cluster method, being of high practicalsignificance in calculations where high accuracy is demanded, and the common acceleration technique DIIS.