Donald L. Thompson

Ground‐ and lower excited‐state discrete abinitio electronic potential‐energy surfaces for doublet HeH2+a)

Ab initio electronic energy calculations are reported for 596 nuclear configurations of HeH2+ (in Cs symmetry). The lowest four doublet spin‐state eigenfunctions for HeH2+ were computed by partially diagonalizing a subset of the full‐configuration interaction Hamiltonian matrix, selected by perturbation theory estimation, relative to a reference set of configurations including the Hartree–Fock configuration and all appropriate single excitation occupations. Trial wave functions corresponding to ground and excited states were constructed from 30 molecular orbitals expanded in a twice‐double‐zeta‐plus polarization contracted Gaussian basis. Two basis sets were employed: one constructed to produce greater accuracy for the ground‐state (principal quantum number n equal to one) surface, and a second more contracted set in the n=1 space and augmented with n=2 basis functions to describe low‐lying excited states. Absolute accuracy estimates of the ground‐ and excited‐state surfaces are within 5 and 10 millihartr...

Semiclassical calculations of tunneling splitting in malonaldehyde

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 o...

A quasiclassical trajectory study of vibrational predissociation of van der Waals molecules: Collinear He⋅⋅⋅I2(B3Π)

Vibrational predissociation of the van der Waals molecule He⋅⋅⋅I2(B 3Π) has been investigated using quasiclassical trajectories. The study was restricted to collinear motion to allow comparisons with the quantum mechanical calculations of Beswick and Jortner [J. Chem. Phys. 68, 2277 (1978); 69, 512 (1978)]. The unimolecular dissociation of He⋅⋅⋅I2(B 3Π) confined to a single adiabatic electronic potential‐energy surface was studied as a function of the initial I2 vibrational quantum state, where a zeroth‐order approximation of the separation of the I–I and He–I2 oscillators was made for the purpose of assigning initial states. The computed trajectory results show that the unimolecular decay as a function of time obeys the exponential decay law quite well. The computed decay rates are in accord with the quantum mechanical values and with experimental measurements.

Analysis of the zero‐point energy problem in classical trajectory simulations

We examine methods for dealing with the flow of zero‐point energy in classical trajectory simulations and identify some of the problems associated with their use. Fundamental issues which must be considered, both in assessing the extent of the zero‐point energy problem and in the development of useful remedies, are discussed.

Dynamics of the Molecular and Atomic Mechanisms for the Hydrogen‐Iodine Exchange Reaction

Theoretical treatment of both the molecular and atomic mechanisms for the hydrogen‐iodine exchange reaction (H2+I2→ 2HI) is accomplished by means of extensive classical trajectories calculated on a reasonable potential‐energy surface in which the single adjustable parameter is the iodine‐core effective charge. The analysis shows the molecular mechanism to be dynamically forbidden, but gives an over‐all rate constant for the atomic mechanism in substantial agreement with the experimental values. The formation of a weak H2I complex is predicted to play an important dynamical role if the atomic mechanism is limited to reactions with collision complexes involving no more than two hydrogen atoms and two iodine atoms. Excellent agreement with experiment is obtained for the rate constant for the recombination I+I+H2→ I2+H2 and its negative temperature coefficient. Trajectories for the latter reaction are rich in multiple exchange of internal energy between the molecular species, but the formation of H2I is predi...

Molecular dynamics study of the melting of nitromethane

Molecular dynamic studies of melting of nitromethane have been carried out using two methods: (1) void-nucleated melting with the gradual heating of the lattice and (2) equilibration of coexisting liquid and solid phases. The results are in near agreement with each other; the small difference is attributed to the hysteresis effect associated with the direct heating process. The values of the melting temperature Tm computed by using the intermolecular interaction potential of Sorescu et al. [J. Phys. Chem. B 104, 8406 (2000)] are found to be in good agreement with the experimental data at various values of pressure ranging from 1 atm to 30 kbar. The computed values of the melting temperature satisfy the Simon–Glatzel equation P(kbar)=aTmb+c, where a=1.597×10−5, b=2.322, c=−6.74, and Tm is in kelvin. A comparison of computed Tm with and without the presence of molecular vibrations reveals that Tm is insensitive to the intramolecular interaction term of the potential energy function, but depends strongly on ...

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. 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.

Interpolating moving least-squares methods for fitting potential energy surfaces: Detailed analysis of one-dimensional applications

We present the basic formal and numerical aspects of higher degree interpolated moving least-squares (IMLS) methods. For simplicity, applications of these methods are restricted to two one-dimensional (1D) test cases: a Morse oscillator and a 1D slice of the HN2→H+N2 potential energy surface. For these two test cases, we systematically examine the effect of parameters in the weight function (intrinsic to IMLS methods), 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 degree) 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.

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. 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.

Molecular dynamics studies of melting and some liquid-state properties of 1-ethyl-3-methylimidazolium hexafluorophosphate [emim][PF6].

Molecular dynamics simulations are used to study the liquid-state properties and melting of 1-ethyl-3-methylimidazolium hexafluorosphosphate [emim][PF6] using the force field of Canongia Lopes et al. [J. Phys. Chem. B 108, 2038 (2004)] and geometric constants from crystallographic data. The structures of the solid and liquid states are characterized by carbon-carbon, carbon-phosphorous, and phosphorous-phosphorous radial distribution functions. Spatial correlations among the ions are strong in the liquid state. The cohesive energy density and the temperature dependences of the molar volume and density of the liquid have been computed. The melting point is determined by equilibrating the solid-state supercells in which void defects have been introduced to eliminate the free-energy barrier for the formation of a solid-liquid interface. The computed melting point is 375+/-10 K, which is approximately 10% higher than the experimental value of 333 K.