where the quantum numbers are the usual ones for this basis. For example, these could be harmonic-oscillator functions in normal coordinates of a potential minimum. More sophisticated 1-mode bases are used currently, but the details of these are not relevant. The interested reader can consult relevant chapters in a recent book on computational approaches to vibrational dynamics. In applications, the values of these quantum numbers for each 1mode basis is restricted. In addition, the sum of quantum numbers of all modes is typically bounded. This is probably the most common method to restrict the basis and goes back 40-50 years. More fine-grained restriction methods are used in the code MULTIMODE, where the excitation space is restricted, as in electronic structure methods, to "singles", "doubles", "triples", "quadruples", etc. Then separate excitation bounds are applied to each level of excitation. Also, when applicable, point-group symmetry is also used to block-diagonalize the H-matrix.