Group-theoretical Methods in Quantum-chemical Calculations

Group-theoretical methods used in quantum chemistry have been reviewed. The method for constructing the basis functions of the irreducible representations of finite groups by means of projection operators has been examined in detail. Particular attention has been paid to the use of the theory of permutation groups for constructing the eigenfunctions of the operator of the square of the total spin S² and obtaining closed equations for the matrix elements of the Hamiltonian in a state having a definite value of S. A method has been described for finding the allowed molecular states and the orders of the secular equations obtained in variation quantum-chemical calculations. The use of the mathematical apparatus of continuous groups in quantum-chemical calculations has been discussed.
The bibliography contains 60 references.