Abstract

1. Solid and gas phase properties of argon as a test of ab initio three-body potential. František Karlický1, Alexandr Malijevský2, Anatol Malijevský2 and René Kalus1 1Department of Physics, University of Ostrava, Ostrava, Czech Republic 2Department of Physical Chemistry, Prague Institute of Chemical Technology, Prague, Czech Republic Abstract Three-body contributions to the interaction energy of Ar3 have been calculated recently using the HF - CCSD(T) method and multiply augmented basis sets. Tests of new ab initio three-body potential for argon trimer are performed in this work. These tests consist in a comparison of several quantities we calculated with corresponding recent theoretical results and available experimental values. Recently published ab initio pair potential is used. The first part of the tests include data on rare-gas solids - a zero-temperature binding energy, lattice constant, and crystal structure. The second part of the tests is focused on the third virial coefficient - one of thermodynamic quantities which are influenced exclusively by two and three-body intermolecular interactions. In addition, the solid and gas phase properties considered are also calculated using semiempirical pair potential and simple Axilrod-Teller three-body term for comparison. Potentials Three-body potential Analytical formula Fitting method • included 354 ab initio points • least-square fit using Newton-Raphson method • achieved mean deviation 0.2 cm-1 from ab initio points • largest fit deviations ranging between 0.4 – 0.6 cm-1 for less than 5% of points Ab initio methods and basis sets • correlation method – CCSD(T) • only valence electrons have been correlated • basis set – d-aug-cc-pVQZ • MOLPRO 2002 suite of ab initio programs Pair potentials Potential energy surface fit Three-body potential has been represented by a sum of short-range (inspired by V. Špirko et al., 1995) and long-range terms expressed in Jacobi coordinates, suitably damped by function F. Geometrical factors Wlmn were derived from third-order perturbation theory (e.g. Doran and Zucker, 1971), force constants Zlmn are taken from previous independent ab initio calculations (Thakkar, 1992). • Ab initio potential of Slavíček et al. (2003): all-electron CCSD(T) correlation method, extended basis set aug-cc-pV6Z augmented with spdfg bond functions. • Semi-empirical HFDID potential of Aziz (1993), with parameters fitted to experimental data. Jacobi coordinates (r, R, q): r represents the “shortest” Ar-Ar separation, R denotes distance between the “remaining” Ar atom and the center-of-mass of the previous Ar-Ar fragment, and q is the angle between r and R vectors.Λ denotes perimeter and α<β two smallest angles in the Ar3 triangle. Rare Gas Crystals Theory Crystal lattice Binding energy per atom Etot= EZPE + E2 + E3 + … of the crystal is a function of the nearest neighbor separation d (or lattice constant), where for N atoms in crystal is Spherical symmetry of argon atoms (with closed electronic shells) yield close-packed structures. There are two possibilities – face centered cubic (FCC) and hexagonal closed packed (HCP) lattice. In reality, FCC lattice is favored, theory usually predicts HCP lattice (“crystal structure paradox”). and for zero-point energy in the quartic oscillator approximation, using only additive part of the potential (Horton, 1976) HCP: FCC: Results Number of atoms in crystal All calculations were performed in approximation of a crystal of infinite size (N) to eliminate surface phenomena. In numerical calculations finite number of atoms in sphere is used. 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Phys., vol. 97, p. 3252 Financial support: the Ministry of Education, Youth, and Sports of the Czech Republic (Grant No. IN04125 – Centre for numerically demanding calculations of the University of Ostrava), the Grant Agency of the Czech Republic (Grant No. 203/04/2146 ) CESTC 2006 Zakopane, Poland, 24-27 September, 2006