Interpolating moving least-squares methods for fitting potential energy surfaces: using classical trajectories to explore configuration space.

We develop two approaches for growing a fitted potential energy surface (PES) by the interpolating moving least-squares (IMLS) technique using classical trajectories. We illustrate both approaches by calculating nitrous acid (HONO) cis-->trans isomerization trajectories under the control of ab initio forces from low-level HF/cc-pVDZ electronic structure calculations. In this illustrative example, as few as 300 ab initio energy/gradient calculations are required to converge the isomerization rate constant at a fixed energy to approximately 10%.

Interpolating moving least-squares methods for fitting potential energy surfaces: a strategy for efficient automatic data point placement in high dimensions.

An accurate and efficient method for automated molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating moving least-squares (IMLS) method is developed with the flexibility to fit various ab initio data: (1) energies, (2) energies and gradients, or (3) energies, gradients, and Hessian data. The method is automated and flexible so that a PES can be optimally generated for trajectories, spectroscopy, or other applications.

Interpolating moving least-squares methods for fitting potential energy surfaces: Improving efficiency via local approximants.

The local interpolating moving least-squares (IMLS) method for constructing potential energy surfaces is investigated. The method retains the advantageous features of the IMLS approach in that the ab initio derivatives are not required and high degree polynomials can be used to provide accurate fits, while at the same time it is much more efficient than the standard IMLS approach because the least-squares solutions need to be calculated only once at the data points. Issues related to the implementation of the local IMLS method are investigated and the accuracy is assessed using HOOH as a test case.

Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points.

A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications.

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.

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

In standard applications of interpolating moving least squares (IMLS) for fitting a potential-energy surface (PES), all available ab initio points are used. Because remote ab initio points negligibly influence IMLS accuracy and increase IMLS time-to-solution, we present two methods to locally restrict the number of points included in a particular fit. The fixed radius cutoff (FRC) method includes ab initio points within a hypersphere of fixed radius.

Interpolating moving least-squares methods for fitting potential energy surfaces: Analysis of an application to a six-dimensional system.

The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are applied to a six-dimensional potential energy surface (PES) of the HOOH molecule, for which an analytic ("exact") potential is available in the literature. The results of systematic investigations of the effects of weight function parameters, the degree and partial degree of IMLS, the number of data points allowed, and the optimal automatic point selection of data points up to full third-degree IMLS fits are reported. With partial reduction of cross terms and automatic point selection the full six-dimensional HOOH PES can be fit over a range of 100 kcal/mol to an accuracy of less than 1 kcal/mol with approximately 1350 ab initio points.

Interpolating moving least-squares methods for fitting potential energy surfaces: applications to classical dynamics calculations.

As a continuation of our efforts to develop efficient and accurate interpolating moving least-squares (IMLS) methods for generating potential energy surfaces, we carry out classical trajectories and compute kinetics properties on higher degree IMLS surfaces. In this study, we have investigated the choice of coordinate system, the range of points (i.e.

Improving the accuracy of interpolated potential energy surfaces by using an analytical zeroth-order potential function.

We present a method for improving the accuracy and efficiency of interpolation methods, in which an analytical zeroth-order potential-energy surface is employed as a reference surface. To investigate and test the method, we apply it to hydrogen peroxide where there exists an accurate analytical surface which we take as the "exact" surface for obtaining the energies and derivatives for fitting and assessing the accuracy. Examples are given for four-dimensional and six-dimensional surfaces interpolated by using either the modified Shepard or second-degree interpolating moving least-squares approach, with comparisons for cases with and without using the zeroth-order potential.