Matthew P. Hodges

Global minima of protonated water clusters

Abstract Candidate global minima are obtained for H3O+⋯(H2O)n clusters with n⩽20 using a basin-hopping algorithm and an empirical, polarizable model potential. We have reoptimized the lowest minima for each system using a more accurate model and find extensive reordering of the potential energy surfaces, especially for larger n. For both model potentials a distorted dodecahedron surrounding an H2O molecule is the global minimum for n=20, in good agreement with experiment. The gap between the latter structure and the lowest minimum with H3O+ in the centre is about 10–20 kJ mol−1.

Intermolecular potential and second virial coefficient of the water-hydrogen complex

We construct a rigid-body (five-dimensional) potential-energy surface for the water-hydrogen complex using scaled perturbation theory (SPT). An analytic fit of this surface is obtained, and, using this, two minima are found. The global minimum has C2v symmetry, with the hydrogen molecule acting as a proton donor to the oxygen atom on water. A local minimum with Cs symmetry has the hydrogen molecule acting as a proton acceptor to one of the hydrogen atoms on water, where the OH bond and H2 are in a T-shaped configuration. The SPT global minimum is bound by 1097 microEh (Eh approximately 4.359744 x 10(-18) J). Our best estimate of the binding energy, from a complete basis set extrapolation of coupled-cluster calculations, is 1076.1 microEh. The fitted surface is used to calculate the second cross virial coefficient over a wide temperature range (100-3000 K). Three complementary methods are used to quantify quantum statistical mechanical effects that become significant at low temperatures. We compare our results with experimental data, which are available over a smaller temperature range (230-700 K). Generally good agreement is found, but the experimental data are subject to larger uncertainties.

Modeling small hydronium–water clusters

We have developed new potentials to model the interactions between H3O+ and H2O and used them to investigate small H3O+⋯(H2O)n clusters for n=1–7. The construction of the potentials uses monomer properties for the long-range interactions and perturbation theory for the short-range terms. We have extensively searched all the potential energy surfaces and discuss the low-energy minima that we have found. We extend the calculations for n=2, 4, and 5 by performing geometry optimizations using density functional theory, starting with minima found with the new model potential.

Intermolecular potentials and second virial coefficients of the water–neon and water–argon complexes

We construct potential-energy surfaces for the water–neon and water–argon complexes from scaled perturbation theory, and calibrate them using accurate supermolecule data. Our best estimates of the binding energies for these two systems are 66.9 and 142.7 cm−1, respectively, where the latter value is in good agreement with the spectroscopically determined AW2 potential. We calculate second virial coefficients, B12(T), and the related property φ12=B12−T(dB12/dT), and compare our results with experimental data for water–argon. The perturbation theory and AW2 B12(T) results are consistent, and demonstrate that current theoretical approaches yield more precise second virial coefficient data than any in the literature. Our φ12 calculations are in good agreement with experimental results derived from enthalpy-of-mixing data, though our estimated uncertainties are significantly smaller.

Intermolecular potential for the interaction of helium with ammonia

We develop an intermolecular potential for the interaction between helium and ammonia including flexibility in the ammonia inversion tunneling coordinate. The potential energy surface is generated by fitting to scaled perturbation theory calculations and is shown to be comparable with high-quality ab initio supermolecule calculations. We have characterized the potential energy surface for a number of ammonia geometries from planar to a highly distorted geometry. For all but the most distorted ammonia geometry, the global minimum has the helium atom in an equatorial location, equidistant from the two closest hydrogen atoms. As the ammonia molecule moves away from the planar configuration, the equatorial minima become less strongly bound while the binding energy increases in the axial regions of the potential energy surface. At the most distorted ammonia geometry, the equatorial minimum is a local minimum, and the global minimum has the helium atom on the symmetry axis of the molecule at the hydrogen end.

Structure, dynamics, and thermodynamics of benzene-Arn clusters (1⩽n⩽8 and n=19)

We use a combination of molecular dynamics, Monte Carlo and geometry optimisation techniques to study benzene-Arn clusters for 1⩽n⩽19, with particular emphasis on BzAr19. In particular, we discuss the difficulties which arise in the accurate simulation of heterogeneous clusters due to problems of ergodicity and nonadditive contributions to the energy. The sensitivity of minima, transition states and reaction pathways to parameters of the potential and the induction energy is also considered. An efficient integration scheme with adaptive step size due to Bulirsch and Stoer is employed in the molecular dynamics simulations. Both geometry optimisation and molecular dynamics are considered to evaluate the usefulness of the Jump–walking Monte Carlo method proposed by Frantz, Freeman, and Doll. This approach improves the ergodicity of canonical simulations using data from different temperatures which we achieved using multiple parallel runs. We then apply a multiple histogram method to calculate the relative nu...

Application of the overlap model to calculating correlated exchange energies

Abstract We develop methods for approximating correlated exchange energies which require only Hartree–Fock self-consistent field (SCF) exchange energies and SCF and correlated charge density overlaps. We benchmark the methods using results calculated for the water dimer at the second-order Moller–Plesset (MP2) level using symmetry-adapted perturbation theory. Assuming that the exchange/overlap ratio is transferable between SCF and MP2 calculations gives a weighted RMS error of 3.2% with no fitted parameters. Including a single overall scaling parameter gives an error of 2.3%.

The effect of anisotropy on the second virial coefficient of H2

We have calculated the second virial coefficient B(T), including quantum corrections, from a pair potential for hydrogen recently developed from ab initio calculations. Previous comparisons with experimental second virial coefficients used an isotropic simplification of the potential. We compute B(T) for the full anisotropic potential in a semiclassical expansion for temperatures above 100 K and compare the results with experiment. We find that the effect of the anisotropy at the temperatures considered is of similar magnitude to the uncertainty in the best data. Even with this more rigorous calculation, the second virial coefficient predicted by the potential is consistently too positive by an amount somewhat greater than the experimental uncertainty.

Flexible multipole models for hydrogen fluoride

We use the distributed multipole analysis method to analyse the charge density of the hydrogen fluoride molecule, including variation of the HF bond length, and taking into consideration the level of theory, the basis set, and the number of sites used. We also examine the effects of truncating the dimer electrostatic interactions at charge–charge, quadrupole–quadrupole and all interactions up to r−5 dependence in the intermolecular site–site separations. We assess the accuracy of these approximations using both the calculated multipoles and multipoles described by polynomial functions of the bond stretching coordinate. We consider two ranges of the HF bond length, one of which should be suitable for calculations of structures and energetics of hydrogen fluoride clusters, and the other for dynamical calculations on the same systems.