The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

A method is presented, which allows for the rigorous use of symmetry within the construction of multidimensional potential energy surfaces (PESs). This approach is based on a crude but very fast energy estimate, which retains the symmetry of a molecule. This enables the efficient use of coordinate systems, which mix molecular and permutational symmetry, as, for example, in the case of normal coordinates with subsets of localized normal coordinates. The impact of symmetry within the individual terms of an expansion of the PES is studied together with a symmetry consideration within the individual electronic structure calculations. A trade between symmetry within the surface and the electronic structure calculations has been observed and has been investigated in dependence on different coordinate systems. Differences occur between molecules belonging to Abelian point groups in contrast to non-Abelian groups, in which further benefits can be achieved by rotating normal coordinates belonging to degenerate vibrational frequencies. In general, the exploitation of surface symmetry was found to be very important within the construction of PESs of small and medium-sized molecules—irrespective of the coordinate system. Benchmark calculations are provided for formaldehyde, ethene, chloromethane, and cubane.

The impact of localized CH-stretching normal coordinates in comparison to canonical normal coordinates on the performance of accurate vibrational structure calculations has been studied for simple molecules of up to eight atoms. Two aspects have been considered in detail, (a) the (pre)screening of coupling terms within an n-mode expansion of the multidimensional potential energy surface and (b) the demands in vibrational configuration interaction calculations (VCI). All calculations have been performed in a realistic setup, and the effect of any approximation has been measured in deviations of the final VCI frequencies, which allows for a direct comparison with experimental data.

No abstract

The fundamental vibrational modes of 11B2H6, 11B2D6, 10B2H6, and 10B2D6 have been obtained from vibrational configuration interaction calculations including up to 6-tuple excitations. An n-mode expansion of the underlying potential energy surface obtained from explicitly correlated coupled cluster theory was truncated after the 4-mode coupling terms, which were found to be very important for these particular systems. All molecules are strongly affected by Fermi resonances, which are discussed in detail. The final results are in very good agreement with the available experimental data.