Gaussian2 theory: Use of higher level correlation methods, quadratic configuration interaction geometries, and secondorder Mo/ller-Plesset zeropoint energies

We have devised a semiclassical procedure based on the Makri–Miller [J. Chem. Phys. 91, 4026 (1989)] model for calculating the eigenvalue splitting in many-atom systems and have used it to calculate the ground-state splitting in several isotopomers of malonaldehyde. A potential-energy surface that includes all twenty-one vibrational degrees of freedom was constructed based on the available theoretical and experimental information. The results for calculations in which all atoms are allowed full three-dimensional motion are in good agreement with the experimentally measured values. Restricting the molecular motion to a plane leads to an increase in the splitting due to a decrease in the average height and width of the barrier to tunneling when the molecule is not allowed to vibrate transverse to the molecular plane. Low energy mode-specific excitations were used to study the sensitivity of the splitting to the motions of heavy atoms. The results show that the heavy atom motions have significant influence on the tunneling. This study demonstrates that simple semiclassical methods can be used to treat proton tunneling in large systems.

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.

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. It is shown that the local IMLS method is at the same level of accuracy as the standard IMLS method. In addition, the scaling of the method is found to be a power law as a function of number of data points N, N(-q). The results suggest that when fitting only to the energy values for a d-dimensional system by using a Qth degree polynomial the power law exponent q approximately Qd when the energy range fitted is large (e.g., E<100 kcalmol for HOOH), and q>Qd when the energy range fitted is smaller (E<30 kcalmol) and the density of data points is higher. This study demonstrates that the local IMLS method provides an efficient and accurate means for constructing potential energy surfaces.

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., the cutoff radius) used in fitting, and strategies for selections of data points and basis elements. We illustrate and test the method by applying it to hydrogen peroxide (HOOH). In particular, reaction rates for the O-O bond breaking in HOOH are calculated on fitted surfaces using the classical trajectory approach to test the accuracy of the IMLS method for providing potentials for dynamics calculations.