1. Abstract Potentials Rare Gas Crystals References Solid and gas phase properties of argon as a test of ab initio three-body potential. František Karlický 1, Alexandr Malijevský 2, Anatol Malijevský 2 and René Kalus 1 1 Department of Physics, University of Ostrava, Ostrava, Czech Republic 2 Department of Physical Chemistry, Prague Institute of Chemical Technology, Prague, Czech Republic Three-body contributions to the interaction energy of Ar 3 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. Third Virial Coefficient where Binding energy per atom E tot = E ZPE + E 2 + E 3 + … of the crystal is a function of the nearest neighbor separation d (or lattice constant), where for N atoms in crystal is CESTC 2006 Zakopane, Poland, 24-27 September, 2006 and for zero-point energy in the quartic oscillator approximation, using only additive part of the potential (Horton, 1976) Comparison of this work with experiment (d = 3.7555 Å, Peterson et al., 1966) latticeu 2 usedE tot [J/mol] FCCAziz 1993-7703.2 HCPAziz 1993-7703.8 FCC Slavicek et al. 2003 -7676.7 HCP Slavicek et al. 2003 -7677.2 FCC, experiment Tessier et al. 1982 -7730.9±13 AXILROD, B. M., TELLER, E., 1943. J. Chem. Phys., vol. 11, p. 299 AZIZ, R. A., 1993. J. Chem. Phys., vol. 9, p. 4518 BLANCETT, A. L., HALL, K. R., CANFIELD, F. B., 1970. Physica (Utrecht), vol. 47, p. 75 DORAN, M. B., ZUCKER, I. J., 1971. J. Phys., vol. C4, p. 307 DYMOND, J. H., ALDER, B. J., 1971. J. Chem. Phys., vol. 54, p. 3472 GILGEN, R., KLEINRAHM, R., WAGNER, W., 1994. J. Chem. Thermodyn., vol. 26, p.383 HORTON, G. K., 1976. In KLEIN, M. L., VENABLES, J. A. (eds.) Rare Gas Solids. vol. 1, Academic Press, New York, 1976 KALFOGLOU, N. K., MILLER, J. G., 1967. J. Phys. Chem., vol. 71, p. 1256 LECOCQ, A., 1960. J. Rech. CNRS, vol. 50, p.55 Theory Third virial coefficient C depends on pair and three-body potentials only – this quantity is thus well suited to test these potentials. Results Three-body potential Theory 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. Neglecting remaining atoms, lying outside the sphere, is reasonable, because the energy correction due to these outer atoms is negligibly small even for not too large radii (see below). Comparison with experimentComparison with other calculations 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 W lmn were derived from third-order perturbation theory (e.g. Doran and Zucker, 1971), force constants Z lmn are taken from previous independent ab initio calculations (Thakkar, 1992). 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 Ar 3 triangle. 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 Crystal lattice 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”). Comparison of this work with recent calculations (for d = 3.7508 Å) u 2 usedu 3 usedlatticeE2E2 E3E3 E ZPE E tot [J/mol] Aziz 1993 This workFCC-9083.5612.0767.7-7703.8 Aziz 1993 This workHCP-9084.6612.6767.7-7704.3 Aziz 1993 Lotrich et al. 1997a FCC-9082.9569.6760.4-7752.9 Aziz 1993 Lotrich et al. 1997a HCP-9083.2570.5760.6-7752.1 Unfortunately, theory still favors HCP over FCC. Work in progress… 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. 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 ) 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 Nearest neighbor separation and components of binding energy for optimized E tot (d) latticeu 2 usedu 3 usedd [Å]E2E2 E3E3 E ZPE E tot [J/mol] FCCAziz 1993This work3.7494-9087.0613.6770.2-7703.2 HCPAziz 1993This work3.7501-9085.9613.3768.9-7703.7 FCC Slavicek et al. 2003 This work3.7636-9042.8596.4768.7-7677.8 HCP Slavicek et al. 2003 This work3.7650-9039.5595.1766.1-7678.3 FCCAziz 1993 Doran and Zucker, 1971 3.7729-9007.2782.5728.7-7495.9 FCCAziz 1993 Axilrod and Teller, 1943 3.7542-9072.3577.05761.7-7733.6 LOTRICH, V. F., SZALEWICZ, K., 1997a. J. Chem. Phys., vol. 106, p. 9688 LOTRICH, V. F., SZALEWICZ, K., 1997b. Phys. Rev. Lett., vol. 79, p. 1301 PETERSON, O. G., BATCHELDER, D. N., SIMMONS, R. O., 1966. Phys. Rev., vol. 152, p. 703 SLAVÍČEK, P., KALUS, R., PAŠKA, P., ODVÁRKOVÁ, I., HOBZA, P., MALIJEVSKÝ, A., 2003. J. Chem. Phys., vol. 119, p. 2102 V. ŠPIRKO, V., KRAEMER, W. P., 1995. J. Mol. Spec., vol. 172, p. 265 TEGELER, CH., SPAN, R., WAGNER, W., 1999. J. Phys. Chem. Ref. Data, vol. 28, p.779 TESSIER, C., TERLAIN, A., LARHER, Y., 1982. Physica A, vol. 113, p. 286 THAKKAR, A. J. et al., 1992. J. Chem. Phys., vol. 97, p. 3252 Results Analytical formula FCC: HCP: