Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

The potential energy surface (PES)
describes the energy of a chemical
system as a function of its geometry and is a fundamental concept
in modern chemistry. A PES provides much useful information about
the system, including the structures and energies of various stationary
points, such as stable conformers (local minima) and transition states
(first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate
reduced-dimensional PESs using sparse interpolation along chemically
significant reaction coordinates, such as bond lengths, bond angles,
and torsion angles. These surrogates used a single interpolation basis,
either polynomials or trigonometric functions, in every dimension.
However, relevant molecular dynamics (MD) simulations often involve
some combination of both periodic and nonperiodic coordinates. Using
a trigonometric basis on nonperiodic coordinates, such as bond lengths,
leads to inaccuracies near the domain boundary. Conversely, polynomial
interpolation on the periodic coordinates does not enforce the periodicity
of the surrogate PES gradient, leading to nonconservation of total
energy even in a microcanonical ensemble. In this work, we present
an interpolation method that uses trigonometric interpolation on the
periodic reaction coordinates and polynomial interpolation on the
nonperiodic coordinates. We apply this method to MD simulations of
possible isomerization pathways of azomethane between cis and trans
conformers. This method is the only known interpolative method that
appropriately conserves total energy in systems with both periodic
and nonperiodic reaction coordinates. In addition, compared to all-polynomial
interpolation, the mixed basis requires fewer electronic structure
calculations to obtain a given level of accuracy, is an order of magnitude
faster, and is freely available on GitHub.