Implementation of a semiclassical light-matter interaction using the Gauss-Hermite quadrature: A simple alternative to the multipole expansion

We present an analytical and numerical solution of the calculation of the transition moments for the exact semiclassical light-matter interaction for wave functions expanded in a Gaussian basis. By a simple manipulation we show that the exact semiclassical light-matter interaction of a plane wave can be compared to a Fourier transformation of a Gaussian where analytical recursive formulas are well known and hence, making the difficulty in the implementation of the exact semiclassical light-matter interaction comparable to the transition dipole. Since the evaluation of the analytical expression involves a new Gaussian, we instead have chosen to evaluate the integrals using a standard Gauss-Hermite quadrature, since this is faster. A brief discussion of the numerical advantages of the exact semiclassical light-matter interaction in comparison to the multipole expansion along with the unphysical interpretation of the multipole expansion is discussed. Numerical examples on [CuCl4](2-) show that the usual features of the multipole expansion are immediately visible also for the exact semiclassical light-matter interaction and that this can be used to distinguish between symmetries. Calculation on [FeCl4](1-) is presented to demonstrate the better numerical stability with respect to the choice of basis set in comparison to the multipole expansion and finally, Fe-O-Fe to show origin independence is a given for the exact operator. The implementation is freely available in OpenMolcas.