Abstract
We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation procedure that is exact for harmonic systems and considered two possible mesh types: Delaunay triangulation and an alternative anisotropic triangulation designed to improve performance in anharmonic systems. The mesh is generated and updated on the fly during the simulation. The procedure is tested on two-dimensional quartic oscillators and on the path integral Monte Carlo evaluation of the HCN/DCN equilibrium isotope effect.
Highlights
Accurate evaluation of the Born-Oppenheimer potential energy surface of a molecular system is essential for predicting its dynamical and equilibrium properties
We aimed for a procedure that would interpolate energies from stored data evaluated at points of a simplicial mesh and that would be comparable to the Shepard interpolation in terms of simplicity and generality
While we focus on classical Monte Carlo and path integral Monte Carlo applications, similar interpolation procedures can be used with molecular dynamics or path integral molecular dynamics methods
Summary
Accurate evaluation of the Born-Oppenheimer potential energy surface of a molecular system is essential for predicting its dynamical and equilibrium properties. Numerous advances in the algorithms used for the problem[1,2] combined with increasing computational power available to researchers have made it possible to combine on-the-fly ab initio evaluation of the potential energy even with path integral[3,4,5] or semiclassical[6,7,8,9,10,11] dynamics algorithms Such approaches are still computationally expensive, and for long simulations requiring a very large number of potential energy values in the same region of configuration space, it is reasonable to instead generate a mesh of points at which accurate ab initio calculations are made and fit a function to reproduce their potential energy values or some other quantities that become bottlenecks of the calculation, such as Hessians of the potential energy.[12,13] For that purpose, a multitude of methods have been proposed, from the modified Shepard interpolation[14,15,16,17] to more sophisticated approaches,[18] including those based on interpolating moving least squares,[19,20] Gaussian process regression,[21,22] and neural networks.[23–26]. While we focus on classical Monte Carlo and path integral Monte Carlo applications, similar interpolation procedures can be used with molecular dynamics or path integral molecular dynamics methods
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