Finite group theory for large systems. 1. Symmetry-adaptation

The challenge of symmetry-adapting large basis sets to finite groups, apart from extensive calculations with large matrices, is obtaining linearly independent bases for frequently repeated irreducible representations, a process that is not determined by the group theory. The usual projection method is modified here to solve this problem efficiently and systematically. The resulting basis is suitably conditioned so that repeated irreducible representations are identical as required by the symmetry-generation theorem.