The calculation of vibrational energy levels by semiclassical and quantum methodology: A review

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Abstract
In this review the four best techniques that answer the question ‘Given an analytical potential-energy surface, how does one calculate the (J = 0) vibrational energy levels?’ are discussed. The methods examined are (i) the fully variational matrix procedure, (ii) the semiclassical approaches relying on quantisation of the Einstein action integrals, (iii) the adiabatic switch-on method, and (iv) the quantum Monte Carlo method applied to vibrations. In particular, the usefulness of each procedure is examined with regard to the number of atoms (N  3), and the calculation of highly excited vibrational levels.