The concept behind active thermochemical tables (ATcT) is presented. As opposed to traditional sequential thermochemistry, ATcT provides reliable, accurate, and internally consistent thermochemistry by utilizing the thermochemical network (TN) approach. This involves, inter alia, a statistical analysis of thermochemically relevant determinations that define the TN, made possible by redundancies in the TN, such as competing measurements and alternate network pathways that interrelate the various chemical species. The statistical analysis produces a self-consistent TN, from which the optimal thermochemical values are obtained by simultaneous solution in error-weighted space, thus allowing optimal use of all of the knowledge present in the TN. ATcT offers a number of additional features that are not present nor possible in the traditional approach. With ATcT, new knowledge can be painlessly propagated through all affected thermochemical values. ATcT also allows hypothesis testing and evaluation, as well as discovery of weak links in the TN. The latter provides pointers to new experimental or theoretical determinations that will most efficiently improve the underlying thermochemical body of knowledge. The ATcT approach is illustrated by providing improved thermochemistry for several key thermochemical species.

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. High efficiency is achieved by employing local IMLS in which fitting coefficients are stored at a limited number of expansion points, thus eliminating the need to perform weighted least-squares fits each time the potential is evaluated. An automatic point selection scheme based on the difference in two successive orders of IMLS fits is used to determine where new ab initio data need to be calculated for the most efficient fitting of the PES. A simple scan of the coordinate is shown to work well to identify these maxima in one dimension, but this search strategy scales poorly with dimension. We demonstrate the efficacy of using conjugate gradient minimizations on the difference surface to locate optimal data point placement in high dimensions. Results that are indicative of the accuracy, efficiency, and scalability are presented for a one-dimensional model potential (Morse) as well as for three-dimensional (HCN), six-dimensional (HOOH), and nine-dimensional (CH4) molecular PESs.

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. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.

No abstract

We present the basic formal and numerical aspects of higher degree interpolated moving least-squares ͑IMLS͒ methods. For simplicity, applications of these methods are restricted to two one-dimensional ͑1D͒ test cases: a Morse oscillator and a 1D slice of the HN 2 →HϩN 2 potential energy surface. For these two test cases, we systematically examine the effect of parameters in the weight function ͑intrinsic to IMLS methods͒, the degree of the IMLS fit, and the number and placement of potential energy points. From this systematic study, we discover compact and accurate representations of potentials and their derivatives for first-degree and higher-degree ͑up to nine degree͒ IMLS fits. We show how the number of ab initio points needed to achieve a given accuracy declines with the degree of the IMLS. We outline automatic procedures for ab initio point selection that can optimize this decline.