Configuration-Space Sampling in Potential Energy Surface Fitting: A Space-Reduced Bond-Order Grid Approach

Abstract

Potential energy surfaces (PESs) for use in dynamics calculations of few-atom reactive systems are commonly modeled as functional forms fitting or interpolating a set of ab initio energies computed at many nuclear configurations. An automated procedure is here proposed for optimal configuration-space sampling in generating this set of energies as part of the grid-empowered molecular simulator GEMS (Laganà et al., J. Grid Comput. 2010, 8, 571-586). The scheme is based on a space-reduced formulation of the so-called bond-order variables allowing for a balanced representation of the attractive and repulsive regions of a diatom configuration space. Uniform grids based on space-reduced bond-order variables are proven to outperform those defined on the more conventional bond-length variables in converging the fitted/interpolated PES to the computed ab initio one with increasing number of grid points. Benchmarks are performed on the one- and three-dimensional prototype systems H2 and H3 using both a local-interpolation (modified Shepard) and a global-fitting (Aguado-Paniagua) scheme.

On the temperature dependence of the rate coefficient of formation of C$_2^+$ from C + CH+

“…Configuration-space sampling (i.e., the choice of these geometries) was accomplished according to the space-reduced bond-order (SRBO) grid approach of Rampino (2016). In the SRBO scheme, use is made of opportunely defined diatomic bond-order (BO) variables (Garcia & Laganà 1985a,b) n = e −β BO (r−r e ) (4) with r being the diatom internuclear distance and r e its equilibrium value.…”

“…SRBO variables are obtained by fixing two boundary r min and r max values and relaxing β BO so as to reach a desired ratio f between the sampled attractive (e −β BO (r max −r e ) < n < 1) and repulsive (1 < n < e −β BO (r min −r e ) ) regions of the diatom configuration space (see also . Reasonable boundary values can be obtained via a Morse modeling of the diatom potential through parameters V fact and V thrs (set here to 1.0 and 0.01, respectively) for which the reader is referred to Rampino (2016). The diatom configuration space is then conveniently sampled by a uniform grid in BO variables which is denoted by (N r , N a ) with N r and N a being the number of points in the repulsive and attractive regions, respectively, resulting in a space ratio parameter f = N a /N r .…”

“…For that purpose, we make use of the gridempowered molecular simulator GEMS (Laganà 2005;Laganà et al 2010;Rampino 2011; designed to enable the coordinated execution of different codes on distributed platforms by properly selecting compute resources among the high-performance computing (HPC) and high-throughput computing (HTC) available ones on the ground of the quality of the service provided . GEMS is articulated into four highly interoperable Rossi et al 2014) modules:…”

“…Accordingly, we start by illustrating the ab initio calculations of the electronic structure of the molecular system leading to Reaction 1 performed using standard procedures on an optimized regular space-reduced bond-order (SRBO) mesh (Rampino 2016) of molecular geometries and fitting the computed potential energy values to the well-known Aguado-Paniagua (AP) functional form (Aguado & Paniagua 1992;Aguado et al 1998). Then we discuss the outcomes of extended QCT calculations carried out on the resulting analytic, single-sheeted PES to the end of working out the related observables.…”

A General User-Friendly Tool for Kinetic Calculations of Multi-Step Reactions within the Virtual Multifrequency Spectrometer Project

“…A rigorous treatment of the time evolution of a chemical reaction should be based on quantum-dynamics calculations modeling the motion of the involved nuclei on ab initio potential-energy surfaces [1][2][3]. However, exact quantum-dynamics methods are only applicable to very small systems made up of three or four atoms (see, for instance, Refs.…”