Sequences of basis sets that systematically converge towards the complete basis set (CBS) limit have been developed for the coinage metals (Cu, Ag, Au) and group 12 elements (Zn, Cd, Hg). These basis sets are based on recently published small-core relativistic pseudopotentials [Figgen D, Rauhut G, Dolg M, Stoll H (2005) Chem Phys 311:227] and range in size from double- through quintuple-ζ. Series of basis sets designed for valence-only and outer-core electron correlation are presented, as well as these sets augmented by additional diffuse functions for the accurate description of negative ions and weak interactions. Selected benchmark calculations at the coupled cluster level of theory are presented for both atomic and molecular properties. The latter include the calculation of both spectroscopic and thermochemical properties of the homonuclear dimers Cu2, Ag2, and Au2, as well as the van der Waals species Zn2, Cd2, and Hg2. The CBS limit results, including the effects of core-valence correlation and spin-orbit coupling, represent some of the most accurate carried out to date and result in new recommendations for the equilibrium bond lengths of the group 12 dimers. Comparisons are also made to a limited number of all-electron Douglas–Kroll–Hess (DKH) calculations (second and third order) carried out using new correlation consistent basis sets of triple-ζ quality.

http://tyr0.chem.wsu.edu/~kipeters/pages/pdfs/tca114.283.2005.pdf

Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements

New correlation consistent-like basis sets have been developed for the post-d group 13–15 elements (Ga–As, In–Sb, Tl–Bi) employing accurate, small-core relativistic pseudopotentials. The resulting basis sets, which are denoted cc-pVnZ-PP, are appropriate for valence electron correlation and range in size from (8s7p7d)/[4s3p2d] for the cc-pVDZ-PP to (16s13p12d3f2g1h)/[7s7p5d3f2g1h] for the cc-pV5Z-PP sets. Benchmark calculations on selected diatomic molecules (As2, Sb2, Bi2, AsN, SbN, BiN, GeO, SnO, PbO, GaCl, InCl, TlCl, GaH, InH, and TlH) are reported using these new basis sets at the coupled cluster level of theory. Much like their all-electron counterparts, the cc-pVnZ-PP basis sets yield systematic convergence of total energies and spectroscopic constants. In several cases all-electron benchmark calculations were also carried out for comparison. The results from the pseudopotential and all-electron calculations were nearly identical when scalar relativity was accurately included in the all-electron wo...

http://tyr0.chem.wsu.edu/~kipeters/Pages/pdfs/JCP119.11099.2003.pdf

Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13–15 elements

Two-component relativistic pseudopotentials (i.e., scalar-relativistic and spin–orbit (SO) potentials) of the energy-consistent variety have been adjusted for the group 11 and 12 atoms Cu, Zn; Ag, Cd; Au, Hg, replacing the 1s–2p; 1s–3d; and 1s–4f cores, respectively. The adjustment has been done for the valence-energy spectrum of (near-)neutral atoms, to reference data from numerical all-electron four-component multi-configuration Dirac–Hartree–Fock (MCDHF) calculations, including the two-electron Breit interaction. For use in molecular calculations, the potentials have been supplemented by energy-optimized (12s12p9d3f2g)/[6s6p4d3f2g] valence basis sets. First benchmark applications of the potentials and basis sets are presented for atomic excitation energies and SO splittings at a correlated level, and for ground and excited state spectroscopic properties of group 11 monohalides and group 12 dimers.

Energy-consistent pseudopotentials for group 11 and 12 atoms: adjustment to multi-configuration Dirac–Hartree–Fock data

We review recent progress in developing potential energy and dipole moment surfaces for polyatomic systems with up to 10 atoms. The emphasis is on global linear least squares fitting of tens of thousands of scattered ab initio energies using a special, compact fitting basis of permutationally invariant polynomials in Morse-type variables of all the internuclear distances. The computational mathematics underlying this approach is reviewed first, followed by a review of the practical approaches used to obtain the data for the fits. A straightforward symmetrization approach is also given, mainly for pedagogical purposes. The methods are illustrated for potential energy surfaces for , (H2O)2 and CH3CHO. The relationship of this approach to other approaches is also briefly reviewed.

Permutationally invariant potential energy surfaces in high dimensionality

A review of the theoretical and computational modeling of bimolecular reactions is given. The review is divided into several sections which are as follows: gas-phase thermal reactions; gas-phase state-selected reactions and product state distributions; and condensed-phase bimolecular reactions. The section on gas-phase thermal reactions covers the enthalpies and free energies of reaction, kinetics, saddle points and potential energy surfaces, rate theory for simple barrier reactions and bimolecular reactions over potential wells. The section on gas-phase state-selected reactions focuses on electronically adiabatic reactions and electronically nonadiabatic reactions. Finally, the section on condensed-phase bimolecular reactions covers reactions in liquids, reactions on surfaces and in solids and tunneling at low temperature.

Modeling the Kinetics of Bimolecular Reactions

The many-body expansion ${V}_{\mathrm{int}}={\ensuremath{\sum}}_{ilj}{V}^{(2)}({r}_{ij})+{\ensuremath{\sum}}_{iljlk}{V}^{(3)}({r}_{ij},{r}_{ik},{r}_{jk})+\ensuremath{\cdots},$ in terms of interaction potentials between rare-gas atoms converges fast at distances $rg{r}_{\mathit{HS}}$, with ${r}_{\mathit{HS}}$ 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 ${r}_{\mathit{HS}}$, 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 (1925)], 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 (2000)]. 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 $15\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ three-body effects become very important for argon and good agreement is reached with experimental high-pressure density measurements up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, 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.

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Extension of the Lennard-Jones potential: Theoretical investigations into rare-gas clusters and crystal lattices of He, Ne, Ar, and Kr using many-body interaction expansions

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 A, 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 A, 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 A, 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.

The potential energy curve and dipole polarizability tensor of mercury dimer

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.

Properties of small- to medium-sized mercury clusters from a combined ab initio, density-functional, and simulated-annealing study.

A potential energy surface for H5+ has been constructed by a modified Shepard interpolation on a sparse set of data points, using second order Moller–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.

/pdf/interpolated-potential-energy-surface-and-classical-dynamics-1c9npq3qip.pdf

Interpolated potential energy surface and classical dynamics for H3++HD and H3++D2

An ab initio interpolated potential energy surface for the hydrogen abstraction and exchange reactions between ammonia and a hydrogen atom is reported. The interpolation is constructed over a set of data points calculated at the unrestricted coupled cluster approximation, using single and double excitations, and including the triple excitations non-iteratively. New data point selection methods were used to improve the convergence and accuracy of the interpolated surface.

Gloria E. Moyano

Papers

Extension of the Lennard-Jones potential: Theoretical investigations into rare-gas clusters and crystal lattices of He, Ne, Ar, and Kr using many-body interaction expansions

The potential energy curve and dipole polarizability tensor of mercury dimer

Properties of small- to medium-sized mercury clusters from a combined ab initio, density-functional, and simulated-annealing study.

Interpolated potential energy surface and classical dynamics for H3++HD and H3++D2

Interpolated potential energy surface for abstraction and exchange reactions of NH 3 + H and deuterated analogues