Special Topics in Quantum Chemistry

Courses in “Special Topics in Quantum Chemistry” is an Advanced course in Quantum Chemistry. Specifically, the subjects which are examined are: 1) linear algebra, orthogonal functions, eigenfunctions and operators, 2) the electronic problem, orbitals, Slater determinants, and basis functions, operators and matrix elements, second quantization, spin-adapted configurations, 3) the Hartree-Fock equations, derivation of the Hartree-Fock equations, interpretation of solutions to the Hartree-Fock equations, the Roothan equations, model calculations on H2 and HeH+, polyatomic basis sets, some illustrative closed-shell calculations, the Pople-Nesbet equations, 4) multiconfigurational wave functions and the structure of the Full Configuration Interaction (CI) matrix, doubly excited CI, some illustrative calculations, natural orbitals, the Multiconfiguration Self-Consistent Field (MCSCF) and Generalized Valence Bond (GVB) methods, truncated CI and the size-consistency problem. 5) the Independent Electron Pair Approximation (IEPA), coupled-pair theories, 6) Rayleigh-Schrödinger (RS) Perturbation Theory, Orbital Perturbation Theory-one particle perturbations, perturbation expansion of the correlation energy, the N-dependence of the RS perturbation expansion. After successful completion of this course the student is expected to familiarize with classical problems of quantum chemistry, the way of approaching and solving multielectron problems, and finally understanding the formalistic treatment of the above cases.

Objectives

The main objective of the course is to familiarize students with basic concepts of quantum chemistry, namely: 1) linear algebra, orthogonal functions, eigenfunctions and operators, 2) the electronic problem, orbitals, Slater determinants, and basis functions, operators and matrix elements, second quantization, spin-adapted configurations, 3) the Hartree-Fock equations, derivation of the Hartree-Fock equations, interpretation of solutions to the Hartree-Fock equations, the Roothan equations, model calculations on H2 and HeH+, polyatomic basis sets, some illustrative closed-shell calculations, the Pople-Nesbet equations, 4) multiconfigurational wave functions and the structure of the Full Configuration Interaction (CI) matrix, doubly excited CI, some illustrative calculations, natural orbitals, the Multiconfiguration Self-Consistent Field (MCSCF) and Generalized Valence Bond (GVB) methods, truncated CI and the size-consistency problem. 5) the Independent Electron Pair Approximation (IEPA), coupled-pair theories, 6) Rayleigh-Schrödinger (RS) Perturbation Theory, Orbital Perturbation Theory-one particle perturbations, perturbation expansion of the correlation energy, the N-dependence of the RS perturbation expansion. After successful completion of this course the student is expected to familiarize with classical problems of quantum chemistry, the way of approaching and solving multielectron problems, and finally understanding the formalistic treatment of the above cases.

Prerequisites

• Very good knowledge of calculus • Introductory linear algebra is greatly recommended • Good knowledge of Quantum Mechanics • ΧΗΥ-014, ΧΗΥ-025, ΧΗΥ-033, ΧΗΥ-061.

Syllabus

• Mathematical review. • Many electron wave functions and operators. • The Hartree-Fock approximation. • Configuration interaction and multiconfiguration self-consistent field method. • Pair and coupled-pair theories. • Many-body perturbation theory.