Question

In group theory, what do we do when we have infinite group order, like in D[infinity]h or C[infinity]v but we want to mathematically determine the SALCs (symmetry adapted linear combinations) using the projection formula. If we did, we would get a function that tends towards 0 which isn't that useful. I asked my lecturer, and he suggested that it's probably because it's obvious with linear molecules so we wouldn't need to mathematically determine the SALCs. Is there some way of doing it though?

Answer 1

When dealing with infinite group orders, the mathematical determination of SALCs using the projection formula can still be useful, even if the resulting functions tend towards 0.

The need for mathematical determination depends on the complexity of the molecule's symmetry.

Step-by-step explanation:

In group theory, when dealing with infinite group orders like D∞h or C∞v and determining symmetry adapted linear combinations (SALCs) using the projection formula, it is true that the resulting functions tend towards 0.

However, this doesn't mean that the calculation is not useful.

In the case of linear molecules, the determination of SALCs using mathematical formulas may not be necessary because the symmetry is obvious, but for more complex cases, the mathematical approach is still applicable.