Sampling general distributions with quasi-regular grids: Application to the vibrational spectra calculations

We introduce a new method for sampling a general multidimensional distribution function Px using a quasiregular grid (QRG) of points xi (i = 1, …, N). This grid is constructed by minimizing a pairwise functional, ∑u(xi, xj) → min, with the short-range pair pseudopotential u(xi, xj), defined locally according to the underlying distribution P(x). While QRGs can be useful in many diverse areas of science, in this paper, we apply them to construct Gaussian basis sets in the context of solving the vibrational Schrödinger equation. Using some 2D and 3D model systems, we demonstrate that the resulting optimized Gaussian basis sets have properties superior to other choices explored previously in the literature.