- #141

DrDu

Science Advisor

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Nevertheless, the situation should be clear: at least c(R) is an ordinary function as T^N is diagonal and if it is small everywhere, it can be treated as a perturbation. You first determine the eigenvalues and eigenstates of the unperturbed hamiltonian (Sigma and Pi states times the vibrational states) and then calculate the matrix elements of c.BillKet said:Also ##a(R), b(R)## and ##c(R)## do contain ##T^N##. This is what gives the kinetic energy of the vibrational states after the vibrational averaging.

You can't start and first diagonalize the matrix of the a, b and c, as they aren't numbers, but non-commuting operators. The notation a(R) is missleading in this respect. Better would be ##a(P_\mathrm{N}, R)##, where ##P_\mathrm{N}=-id/dR## is the nuclear momentum operator.

The above mentioned van Vleck method tries to diagonalize this operator perturbatively, but I think in the situation at hand this is rather overkill.