Modal optimisation within the time-independent eigenstate-free Raman wavefunction formalism

Abstract

The time-independent eigenstate-free Raman wavefunction approach, which is based on the vibrational inhomogeneous Schrödinger equation (ISE), is a promising alternative to the well-known sum-over-states and time-dependent methods for the calculation of optical bandshapes and resonance Raman intensities. The solution of the ISE, the Raman wavefunction (RWF), can be obtained within a vibrational configuration interaction (VCI) ansatz. In this method, the optimisation of vibrational modals can provide a better convergence of the calculated RWF towards the full VCI limit. For this purpose, the variational principle for the ISE problem is formulated. The variational condition for the modal functions leads to the complex inhomogeneous vibrational self-consistent field equations. The key aspects of the implementation of this approach are discussed. The performance of this method in comparison with the conventional scheme involving VCI bases of different quality is illustrated for the X ~ 2 A 2 ⟵ X ~ 1 A 1 transition in furan. The quantitative effects due to the modal optimisation are found to be relatively small, as compared to the impact of moderate extension of the configuration basis.