Praha

1. R q r Accurate ab initio three-body potential for argon František Karlický and René Kalus Department of Physics, University of Ostrava, Ostrava, Czech Republic Praha Ostrava Abstract Three-body contributions to the interaction energy of Ar3 have been calculated using the HF – CCSD(T) method and multiply augmented basis sets due to Dunning and co-workers [1]. The calculations have been performed using the MOLPRO 2002 suite of quantum-chemistry programs. The basis set superposition error has been treated through the counterpoise correction by Boys and Bernardi [2], the convergence to the complete basis set has been analyzed, and both the triple-excitation and core-electron contributions to the three-body energy of Ar3 have been assessed. A complete nonaditive potential has been fitted to 330 computed points and compared with other points. Ab initio calculations Calculations Choice of points Analysis of convergence Three-body energies for D3h geometry and perimeter = 3 x 3.757 A. For each choice of Ar3 geometry, three-body energies have been calculated at the CCSD(T) + d-aug-cc-pVQZ level for a sufficiently broad range of perimeters. The calculations seem to be converged within about several tenths of K at this level. To save computer time, the following procedure has been adopted: • The geometry of Ar3 has been described by the perimeter of the Ar3 triangle, p, and by the two smaller angles in this triangle, a and b. • Angles a and b used in our ab initio calculations have been chosen so that they spread over all the relevant three-body geometries in both an fcc and an hcp argon crystal. • A small set of energies has been calculated for a small number of perimeters, at both the aug-cc-pVTZ and the d-aug-cc-pVQZ level. This has usually taken 7 – 10 days of computer time. • Differences between the aug-cc-pVTZ and the d-aug-cc-pVQZ energies have been fitted to an analytical formula. • A much larger set of energies has been calculated (20 – 40) at the aug-cc-pVTZ level (about one hour of computation). • Finally, the aug-cc-pVTZ energies have been corrected. Differences between t-aug-cc-pVQZ and d-aug-cc-pVQZ. Differences between the aug-cc-pVTZ and d-aug-cc-pVQZ energies for a selected C2v geometry, and the corresponding least-square fit. Examples of results Methods and basis sets Contributions due to triple-excitations and core correlations. • correlation method – CCSD(T) • only valence electrons have been correlated • basis sets – x-aug-cc-pVNZ with N = D,T,Q and x = s,d,t • MOLPRO 2002 suite of ab initio programs • computer – PIV 2.3 GHz, 2 GB RAM, and about 10 GB HDD requested Potential energy surface fit Hypersurface Analytical formula V3(r,R,q = p/2) sections of three-body potential for argon comparison Our three-body potential (2-D cut) for argon compared with Axilrod-Teller-Muto uDDD term Three-body potential has been represented by a sum of short-range [3] and long-range terms expressed in Jacobi coordinates, suitably damped by function F.Geometrical factors Wlmn were derived from third-order perturbation theory [4], force constants Zlmn are taken from previous independent ab initio calculations [5]. Axilrod-Teller-Muto uDDD term our potential l, m, n = D-dipole, Q-quadrupole, O-octupole Tests The least-square fit compared with additionally calculated points - 1D cut along a line in the a-b plane (see section “choice of points”), perimeter of Ar3 triangle is fixed. The Axilrod-Teller (uDDD) term is also added. 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. Method 1D cut for fixed r,q Jacobi coordinates • least-square fit using Newton-Raphson method • achieved standard deviation 0,4 K • maximum fit deviation 1 K from ab initio points V3(r = 3.757 Å,R,q) sections of three-body potential for argon References Outlooks [1] see, e.g., T. H. Dunning, J. Phys. Chem. A 104 (2000) 9062. [2] S. F. Boys and F. Bernardi, Mol. Phys. 19 (1970) 553. [3] inspired by V. Špirko and W. P. Kraemer, J. Mol. Spec. 172 (1995) 265. [4] see, e. g., M. B. Doran and I. J. Zucker, Sol. St. Phys. 4 (1971) 307. [5] A. J. Thakkar et al., J. Chem. Phys. 97 (1992) 3252. [6] P. Slavicek et al., J. Chem. Phys. 119 (2003) 2102. • This work is the first step in a series of calculations of the three-body non-additivities we plan for heavier rare gases, argon – xenon. The aim of these calculations consists in obtaining reliable three-body potentials for heavier rare gases to be employed in subsequent molecular simulations. • Firstly, a thorough analysis of methods and computations is proposed for the argon trimer. In addition to the all-electron calculations presented here, which use Dunning’s multiply augmented basis sets of atomic orbitals, further calculations will be performed for argon including mid-bond functions, effective-core potentials, and core-polarization potentials. • Secondly, properly chosen mid-bond functions, optimized for dimers, will be combined with effective-core potentials and with core-polarization potentials to calculate three-body energies for krypton and xenon. Our previous work on krypton and xenon two-body energies [6] indicates that this way may be rather promising. • Our potential will be tested by computing experimentally measurable results: vibrational spectra of trimers, third virial coefficient, crystal structures and their binding energies. 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 Faculty of Science, University of Ostrava (grant. no. 1052/2005)