New index functions for storing Gaunt coefficients

Gaunt coefficients express angular momentum conservation rules. They are therefore required in the combination of atomic orbitals. In this case, the angular factors are real spherical harmonics and the Gaunt coefficients appear when their products are linearized. The Gaunt coefficients may be pre-calculated and stored. This work describes new index functions for storing and retrieving the required Gaunt coefficients which are (almost) all nonzero. This strategy is closely related to that of Rasch and Yu, who have compared retrieval to that using recurrence relations and found it to be at least 20 times faster. Some corrections and improvements to their work will be found here and the index functions used are different. Only a few arithmetic operations are required to generate the index, therefore its evaluation and handling takes a negligible time compared to its applications, notably molecular electronic integral evaluation.