Semi-empirical Quantum-mechanical Methods for the Calculation of Molecular Geometry and Conformational Energies

The LCAO–MO approximation is considered in the Hartree–Fock problem for many-electron systems, and Roothaan's equations are given, various "simplifications" of which form the foundation for most current semi-empirical methods for calculating the electronic structure of polyatomic molecules. Accounts are given of the most popular semi-empirical schemes enabling the geometry of a molecule to be predicted and several related properties – conformational energies, barriers to internal rotation, and energies of formation – to be calculated. The possibilities and limits of application of these methods are discussed. A list of 171 references is included.