Talk:GF method

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)

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)

Better explanation neccessary
I think that equations
 * $$ \mathbf{L}^\mathrm{T} \mathbf{F} \mathbf{L} =\boldsymbol{\Phi}

\quad \mathrm{and}\quad \mathbf{L}^\mathrm{T} \mathbf{G}^{-1} \mathbf{L} = \mathbf{E} $$ should be explained better than just writing "One can solve the following two matrix problems simultaneously". Maybe I overlooked something, but I think there should be some motivation why do we need to fulfill these relations. But I do not understand this method good enough to write missing explanation. Can somebody do it, please? --Irigi (talk) 15:39, 2 January 2009 (UTC)

"vibrational amplitudes of the atoms as a function of time"
The amplitudes of normal modes do not depend on time. May be, "displacements" were meant in that sentence? — Mikhail Ryazanov (talk) 00:33, 19 February 2011 (UTC)