1 - Basic Principles of Quantum Chemistry

Abstract

This chapter provides a background knowledge of some of the basic concepts and mathematical tools of quantum mechanics and matrix mechanics that are used in subsequent chapters. Without going into mathematical details, the reader is introduced to topics such as time-dependent and time-independent Schrödinger wave equations and their solution in spherical polar coordinates. The concepts of atomic orbitals, spin orbitals, and the charge-cloud interpretation of the wavefunction, which are basics to the development of quantum chemistry, have been developed by considering the problem of hydrogen-like atoms. Heisenberg’s operator formalism of quantum mechanics, operator representation of classical dynamical variables, general properties of linear operators, commutation relations, eigenvalues, eigenvectors, and expectation values have been described. This is followed by linear vector space, Dirac’s ket and bra notations and matrix representation of operators. Since the problems of quantum mechanics need approximate methods for their solution, both the perturbation theory and the variation method have been described. A brief outline of general principles of molecular symmetry and representation of point group is given at the end of the chapter to familiarize the reader with this powerful tool for simplifying several problems in quantum chemistry and for drawing general conclusions about molecular properties without calculations.