Keiran C. Thompson

Polyatomic molecular potential energy surfaces by interpolation in local internal coordinates

We present a method for expressing a potential energy surface (PES) for polyatomic molecules as an interpolation of local Taylor expansions in internal coordinates. This approach extends and replaces an earlier method which was only directly applicable to molecules of no more than four atoms. In general, the local Taylor expansions are derived from ab initio quantum calculations. Here, the methodology is evaluated by comparison with an analytic surface for the reactions H+CH4⇌H2+CH3. Approximately 1000–1300 data points are required for an accurate 12-dimensional surface which describes both forward and backward reactions, at the energy studied.

Convergence of molecular potential energy surfaces by interpolation: Application to the OH+H2→H2O+H reaction

A recently proposed scheme for interpolating and iteratively improving molecular potential energy surfaces [Ischtwan and Collins, J. Chem. Phys. 100, 8080 (1994)] is evaluated by comparison with an analytic surface for the OH+H2→H2O+H reaction. An improvement in the procedure for constructing the potential surface is suggested and implemented. The most efficient means of converging the surface is determined. It is found that the probability of reaction, for example, may be accurately calculated using of the order of 200–400 data points to define the potential energy surface.

The utility of higher order derivatives in constructing molecular potential energy surfaces by interpolation

In this paper we evaluate the use of higher order derivatives in the construction of an interpolated potential energy surface for the OH+H2→H2O+H reaction. The surface construction involves interpolating between local Taylor expansions about a set of known data points. We examine the use of first, second, third, and fourth order Taylor expansions in the interpolation scheme. The convergence of the various interpolated surfaces is evaluated in terms of the probability of reaction. We conclude that first order Taylor expansions (and by implication zeroth order expansions) are not suitable for constructing potential energy surfaces for reactive systems. We also conclude that it is inefficient to use fourth order derivatives. The factors differentiating between second and third order Taylor expansions are less clear. Although third order surfaces require substantially fewer data points to converge than second order surfaces, this faster convergence does not offset the large cost incurred in calculating numeri...

Molecular potential energy surfaces by interpolation in Cartesian coordinates

We present a new method for expressing a molecular potential energy surface (PES) as an interpolation of local Taylor expansions. By using only Cartesian coordinates for the atomic positions, this method avoids redundancy problems associated with the use of internal coordinates. The correct translation, rotation, inversion, and permutation invariance are incorporated in the PES via the interpolation method itself. The method is most readily employed for bound molecules or clusters and is demonstrated by application to the vibrational motion of acetylene.

Supercollision events in weak collisional energy transfer of highly excited species

The results are reported of a series of trajectory studies on Xe colliding with highly excited azulene, obtained using the method of Lim and Gilbert. These show a small fraction (about 1%) of supercollisions (ones which transfer an abnormally large amount of energy), in accord with results from several different experimental techniques. The trajectories show that these rare supercollisions occur when a hydrogen atom is compressed between the bath gas and part or all of the carbon framework. This produces a strong repulsion between the Xe and H as the relative coordinate is driven high up the repulsive wall; if vibrational phases, or rotation, of the substrate framework are such that the bath gas and substrate separate during this compression, the final energy transfer is large.

Molecular potential-energy surfaces by interpolation: Furtherrefinements

We present some refinements of a recently developed scheme for interpolating and iteratively improving molecular potential-energy surfaces (PES). By comparison with an analytic surface for the OH+H 2 →H 2 O+H reaction, we show that an accurate and smooth PES may be constructed using of the order of 100–200 calculations of the energy, energy gradient and second derivatives. The refinements rely, in part, on improved methods for determining the optimum locations for these calculations.

A classical trajectory study of the photodissociation of T1 acetaldehyde: the transition from impulsive to statistical dynamics.

Previous experimental and theoretical studies of the radical dissociation channel of T(1) acetaldehyde show conflicting behavior in the HCO and CH(3) product distributions. To resolve these conflicts, a full-dimensional potential-energy surface for the dissociation of CH(3)CHO into HCO and CH(3) fragments over the barrier on the T(1) surface is developed based on RO-CCSD(T)/cc-pVTZ(DZ) ab initio calculations. 20,000 classical trajectories are calculated on this surface at each of five initial excess energies, spanning the excitation energies used in previous experimental studies, and translational, vibrational, and rotational distributions of the radical products are determined. For excess energies near the dissociation threshold, both the HCO and CH(3) products are vibrationally cold; there is a small amount of HCO rotational excitation and little CH(3) rotational excitation, and the reaction energy is partitioned dominantly (>90% at threshold) into relative translational motion. Close to threshold the HCO and CH(3) rotational distributions are symmetrically shaped, resembling a Gaussian function, in agreement with observed experimental HCO rotational distributions. As the excess energy increases the calculated HCO and CH(3) rotational distributions are observed to change from a Gaussian shape at threshold to one more resembling a Boltzmann distribution, a behavior also seen by various experimental groups. Thus the distribution of energy in these rotational degrees of freedom is observed to change from nonstatistical to apparently statistical, as excess energy increases. As the energy above threshold increases all the internal and external degrees of freedom are observed to gain population at a similar rate, broadly consistent with equipartitioning of the available energy at the transition state. These observations generally support the practice of separating the reaction dynamics into two reservoirs: an impulsive reservoir, fed by the exit channel dynamics, and a statistical reservoir, supported by the random distribution of excess energy above the barrier. The HCO rotation, however, is favored by approximately a factor of 3 over the statistical prediction. Thus, at sufficiently high excess energies, although the HCO rotational distribution may be considered statistical, the partitioning of energy into HCO rotation is not.

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo

A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.

The response of a molecule to an external electric field: predicting structural and spectroscopic change

Abstract The accuracy of expanding the response of a molecule to an external electric field, E , as a power series in the field is investigated in the model hydrogen-bonded complex, ClH:NH 3 . Even at field strengths large enough to cause dramatic structural change in the complex, both the structure and vibrational frequencies are quantitatively predicted using only terms linear in E . These results suggest that knowledge of the zero-field molecular potential energy and dipole moment surfaces may be sufficient to accurately model the interactions of molecules in a wide range of external electric fields.