Optimisation of the variational method for vibrational Hamiltonian eigenvalues computation

We propose here an efficient method to define a representative approximation subspace to compute the first eigenvalues of the vibrational Hamiltonian which are those of interest in the experimental results. In the Born Oppenheimer approximation, calling by x = (x1, . . . xN ) the dimensionless normal coordinates [4], ωi the angular frequency associated with the coordinate xi and ~ the reduced Planck constant, the vibrational Hamiltonian H writes as a sum of the nuclear kinetic and potential energies: H(x) = H0 + V