Talk:GF method

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When updating "Molecular Hamiltonian" I had a need to refer to the GF method. As far as I'm concerned this article is now finished. --P.wormer 13:51, 5 January 2007 (UTC)

[edit] Eckart conditions

Any book that I've seen implies (but never states it plainly) that Wilson's linearized coordinates satisfy the Eckart conditions. Until writing this article I was convinced that this was the case.

After reading a few books and papers on this topic, I don't believe it anymore, but I've found no confirmation of it. So, maybe I am wrong. Wilson et al. (1955) introduce in chapter 2 of their book normal coordinates that satisfy Eckart conditions. In chapter 4 they introduce normal coordinates as solutions of the GF method, but nowhere they state that these normal coordinates are not the same (as I believe).

The basic problem arises from the fact that Wilson et al. do not apply mass-weighting when they linearize valence coordinates. Therefore translation and rotation invariance conditions do not contain masses either.

I write this up in the hope that somebody, more expert than myself, reads this and will either confirm the reasoning in this article, or point out where I went wrong. --P.wormer 15:16, 7 January 2007 (UTC)

As very often, difficulties are caused by (trivial) differences in definitions. Wilson et al. work in fact with two kinds of inner products (with matrix M as metric/overlap and with unit matrix as metric/overlap).--P.wormer 16:05, 22 January 2007 (UTC)