The many-body expansion V int = ͚ iϽj V ͑2͒ ͑r ij ͒ + ͚ iϽjϽk V ͑3͒ ͑r ij , r ik , r jk ͒ +¯, in terms of interaction potentials between rare-gas atoms converges fast at distances r Ͼ r HS , with r HS being the hard-sphere radius at the start of the repulsive wall of the interaction potential. Hence, for the solid state where the minimum distance is always above r HS , a reasonable accuracy is already obtained for the lattice parameters and cohesive energies of the rare-gas elements using precise two-body terms. All tested two-body potentials show a preference of the hcp over the fcc structure. We demonstrate that this is always the case for the Lennard-Jones potential. We extend the Lennard-Jones potential to obtain analytical expressions for the lattice parameters, cohesive energy, and bulk modulus using the solid-state parameters of Lennard-Jones and Ingham ͓Proc. R. Soc. London, Ser. A 107, 636 ͑1925͔͒, which we evaluate up to computer precision for the cubic lattices and hcp. The inclusion of three-body terms does not change the preference of hcp over fcc, and zero-point vibrational effects are responsible for the transition from hcp to fcc as shown recently by Rosciszewski et al. ͓Phys. Rev. B 62, 5482 ͑2000͔͒. More precisely, we show that it is the coupling between the harmonic modes which leads to the preference of fcc over hcp, as the simple Einstein approximation of moving an atom in the static field of all other atoms fails to describe this difference accurately. Anharmonicity corrections to the crystal stability are found to be small for argon and krypton. We show that at pressures higher than 15 GPa three-body effects become very important for argon and good agreement is reached with experimental high-pressure density measurements up to 30 GPa, where higher than three-body effects become important. At high pressures we find that fcc is preferred over the hcp structure. Zero-point vibrational effects for the solid can be successfully estimated from an extrapolation of the cluster zero-point vibrational energies with increasing cluster size N. For He, the harmonic zero-point vibrational energy is predicted to be always above the potential energy contribution for all cluster sizes up to the solid state at structures obtained from the two-body force. Here anharmonicity effects are very large which is typical for a quantum solid.

The cohesive energies of argon in its cubic and hexagonal closed packed structures are computed with an unprecedented accuracy of about 5 J mol(-1) (corresponding to 0.05 % of the total cohesive energy). The same relative accuracy with respect to experimental data is also found for the face-centered cubic lattice constant deviating by ca. 0.003 Å. This level of accuracy was enabled by using high-level theoretical, wave-function-based methods within a many-body decomposition of the interaction energy. Static contributions of two-, three-, and four-body fragments of the crystal are all individually converged to sub-J mol(-1) accuracy and complemented by harmonic and anharmonic vibrational corrections. Computational chemistry is thus achieving or even surpassing experimental accuracy for the solid-state rare gases.

A potential energy surface for H5+ has been constructed by a modified Shepard interpolation on a sparse set of data points, using second order Möller–Plesset perturbation theory. An improved version of the surface was also obtained by substituting the energy values at the data points with values evaluated using a coupled cluster treatment (with single and double excitations, and perturbative treatment of triple excitations). Classical simulations for the collisions between H3++HD and H3++D2 were carried out in order to calculate the total integral cross sections and rate coefficients for these systems. There is good agreement with earlier experimental data for rate coefficients at temperatures between 80 and 300 K, but the predicted rate coefficient for the reaction of H3++HD at 10 K deviates from the most recent experimental measurement, suggesting that quantum rather than classical reaction dynamics are necessary.

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Relativistic coupled-cluster and second-order many-body perturbation theories were used to construct two- and three-body potentials for the interaction between mercury atoms. A subsequent combined simulated-annealing downhill simplex and conjugate gradient-optimization procedure gave global minima for mercury clusters with up to 30 atoms. The calculations reveal magic cluster numbers of 6, 13, 19, 23, 26, and 29 atoms. At these cluster sizes, the static dipole polarizability obtained from density-functional theory has a minimum. The calculations also reveal a fast convergence of the polarizability towards the bulk limit in contrast to the singlet-triplet gap or the ionization potential.

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Scalar relativistic coupled cluster calculations for the potential energy curve and the distance dependence of the static dipole polarizability tensor of Hg2 are presented and compared with current experimental work. The role of the basis set superposition error for the potential energy curve and the dipole polarizability is discussed in detail. Our recently optimized correlation consistent valence basis sets together with energy adjusted pseudopotentials are well suited to accurately describe the van der Waals system Hg2. The vibrational–rotational analysis of the best spin–orbit corrected potential energy curve yields re=3.74 Å, D0=328 cm−1, ωe=18.4 cm−1, and ωexe=0.28 cm−1 in reasonable agreement with experimental data (re=3.69±0.01 Å, De=380±25 cm−1, ωe=19.6±0.3 cm−1 and ωexe=0.25±0.05 cm−1). We finally present a scaled potential energy curve of the form ∑ja2jr−2j which fits the experimental fundamental vibrational transition of 19.1 cm−1 and the form of our calculated potential energy curve best (re=3.69 Å, D0=365 cm−1, ωe=19.7 cm−1, and ωexe=0.29 cm−1). We recommend these accurate two-body potentials as the starting point for the construction of many-body potentials in dynamic simulations of mercury clusters.

Two ab initio interpolated potential energy surfaces have been constructed to study the dynamics of atomic hydrogen/deuterium exchange in collisions of H(3)(+) with H (D). One of the surfaces is based on energy calculations using quadratic configuration interaction with single and double excitations. The second includes a perturbative treatment of the triple excitations and an additive correction for basis set deficiency. Results from classical dynamics simulation of the exchange reaction on these surfaces are presented and discussed.