Generalisation of a property of Hamiltonians depending linearly upon a parameter: application to a model of inert gas matrix effect on vibrational spectra

Abstract

The property that the ground state eigenvalue of a Hamiltonian, depending linearly upon a parameter, is a concave function of this parameter is generalised. It is shown that the concavity or convexity of the nth eigenvalue depends upon the relative weights of the states below the nth state, with respect to those above it, in a weighted sum of transition energies. The result is illustrated on a model of matrix effect on gas phase molecular vibrational spectra. The model is applied to the 2,3-naphthyne molecule.