Modeling of high-order terms in potential energy surface expansions using the reference-geometry Harris–Foulkes method

Abstract

The reference-geometry Harris-Foulkes (RGHF) approach has been used to model high-order terms within the expansion of multi-dimensional potential energy surfaces (PES) as needed within the calculation of accurate vibrational frequencies beyond the harmonic approximation. The key step of this method is a localization of the electron density to the atoms of the molecule at a given reference structure and a subsequent transfer of these atom-centered partial densities to the atom positions of distorted structures. This concept has been used to evaluate the 3-mode coupling terms of a multi-mode expansion of the PES as arising in the Watson Hamiltonian. Systematic benchmark calculations for vibrational frequencies obtained from vibrational configuration interaction (VCI) theory have been performed in order to study the effects of this approximation on the fundamental modes of a test suite of 28 molecules.

The Molpro quantum chemistry package

“…274 In particular the modeling of high-order terms of the PES expansion leads to substantial accelerations. 275,276 These potentials can be dumped as ASCII files to be used in any other program. In a subsequent transformation program the grid representation of the PES can be transformed to an analytical sum-of-products representation of multivariate polynomials, B-splines or distributed Gaussians.…”

Linear-scaling generation of potential energy surfaces using a double incremental expansion

“…If we, for example, consider a chain like system ABCD, the FCR up to three-fragment interactions reads FCR 3F = {{}, {A}, {B}, {C}, {D}, {A, B}, {A, C}, {A, D}, {B, C}, {B, D}, {C, D}, {A, B, C}, {A, B, D}, {A, C, D}, {B, C, D}}. (24) Restricting this FCR to direct neighbor coupling, we obtain FCR 3F,NB = {{}, {A}, {B}, {C}, {D}, {A, B}, {A, C}, {B, C}, {B, D}, {C, D},…”

“…Accordingly, the n-mode representation has been combined with a number of approaches further reducing the number of required SPCs, such as screening schemes [11][12][13][14][15][16] and adaptive choice of the grid points [17][18][19] . Another possibility to reduce the computational scaling for PES generations is to obtain the expensive higher-order mode couplings in a more approximate manner 12,[20][21][22][23][24] .…”

“…This can, for example, be achieved by using lower-cost electronic structure methods 12,[20][21][22] , derivative information 23 , or other approximate ways to calculate the individual single point energies 24 . In special cases, effective linear scaling of the number of required SPCs has been observed with an adaptive grid approach 25 .…”

A novel system-bath Hamiltonian for vibration-phonon coupling: Formulation, and application to the relaxation of Si–H and Si–D bending modes of H/D:Si(100)-(2 × 1)

“…The brute force inclusion of three-phonon terms in the system-bath Hamiltonian (terms proportional to Q i Q j Q k , coefficients j ijk ðqÞ), however, would be challenging. Such terms are needed for anharmonic couplings and in this case, further approximations are necessary as suggested, e.g., for anharmonic vibrational analysis of polyatomics [45]. Fortunately, for a large class of problems (including the one studied here), the two-phonon expansion is sufficient.…”