Interpolating moving least-squares methods for fitting potential-energy surfaces: Further improvement of efficiency via cutoff strategies

Interpolation Methods for Molecular Potential Energy Surface Construction

The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

Interpolating moving least-squares methods for fitting potential energy surfaces: An application to the H2CN unimolecular reaction

Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.

Quasiclassical trajectories on a finite element density functional potential energy surface: The C++H2O reaction revisited

A new method for the representation of potential energy surfaces (PESs) based on the p version of the finite element method is presented and applied to the PES of the [COH2]+ system in order to study the C++H2O-->[COH]++H reaction through the quasiclassical trajectory method. Benchmark ab initio computations have been performed on the most relevant stationary points of the PES through a procedure that incorporates basis set extrapolations, the contribution of the core correlation energy, and scalar relativistic corrections. The electronic structure method employed to compute the many points needed to construct the PES is a hybrid density functional approach of the B3LYP type with geometry-dependent parameters, which improves dramatically the performance with respect of the B3LYP method. The trajectory computations shed light on the behavior of the COH2+ complex formed in the collision. At a fixed relative translational energy of 0.62 eV, which corresponds to the crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], the complex dissociates significantly into the reactants (37%). However, the behavior for a thermal sampling at T=300 K is significantly different because only 9% of the trajectories where capture occurs lead to dissociation into the reactants. The latter kind of behavior is coherent with the view that simple ion-molecule reactions proceed quite often at the capture rate provided it is corrected by the fraction of the electronic states which, being nearly degenerate for the reactants, become attractive at short distances. For both T=300 K and crossed beam conditions, the trajectory computations indicate that COH2+ is the critical intermediate, in agreement with a recent work [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003)] and in contrast with the interpretation of the crossed beam experiments. Besides, virtually all trajectories generate COH++H (>99%), but a significant proportion of the isoformyl cation is formed with enough vibrational energy as to surmount the COH+-HCO+ isomerization barrier, about 37% at T=300 K.