On Relativistic Effects in Ground State Potential Curves of Zn 2 , Cd 2 , and Hg 2 Dimers. A CCSD(T) Study LUKA ´ S ˇ BUC ˇ INSKY ´ , * STANISLAV BISKUPIC ˇ , MICHAL ILC ˇ IN, VLADIMI ´ R LUKES ˇ , VILIAM LAURINC Institute of Physical Chemistry and Chemical Physics, Slovak University of Technology in Bratislava, Radlinske´ho 9, SK-81237 Bratislava, Slovak Republic Received 7 May 2007; Accepted 11 April 2008 DOI 10.1002/jcc.21030 Published online 28 May 2008 in Wiley InterScience (www.interscience.wiley.com). Abstract: The ground state potential curves of the Zn 2 , Cd 2 , and Hg 2 dimers calculated at different levels of theory are presented and compared with each other as well as with experimental and other theoretical studies. The calculations at the level of Dirac-Coulomb Hamiltonian (DCH), 4-component spin-free Hamiltonian, nonrelativistic Le ´vy–Leblond Hamiltonian and at the level of simple Coulombic correction to DCH are presented. The potential curves are calculated in an all-electron supermolecular approach including the correction to basis set superposition error (BSSE). Electron correlation is treated at the coupled cluster level including single and double excitations and noniterative triple corrections, CCSD(T). In addition, simulations of the temperature dependence of dynamic viscos- ities in the low-density limit using the obtained ground state potential curves are presented. q 2008 Wiley Periodicals, Inc. J Comput Chem 30: 65–74, 2009 Key words: Zn Cd Hg dimers; relativistic effects; van der Waals; dynamic viscosity; CCSD(T); study Introduction The ground states of Zn 2 , Cd 2 , and Hg 2 have been considered in a number of experimental 1–8 and theoretical studies. 9–17 The pa- per of Koperski 1 provides a thorough review in both experimen- tal and theoretical field of this subject. Although these dimers (Zn 2 , Cd 2 , and Hg 2 ) are in the ground state considered as weakly bound van der Waals complexes and theoretical works report a fully repulsive SCF and/or CASSCF ground state poten- tial curves, 9 the bonding character has been reported to be cova- lent 9,10,15 up to 25%. 10 This has been shown in the analysis of charge fluctuation at the CASSCF level reported by Dolg and Yu. 10 The comparison of SCF and Heitler–London Hg 2 curves presented in the study of Kunz et al. 9 yielded a similar conclu- sion on the covalent bonding in Hg 2 dimer. The symmetry adapted perturbation theory (SAPT) study of Lukes ˇ et al. 15 con- firmed larger contributions of induction and exchange-induction effects to interaction energy in the Zn 2 , Cd 2 , and Hg 2 dimers than is the case in the noble gas dimers. Nevertheless, these two effects, namely induction and exchange-induction, largely cancel each other out. 15 Most spectroscopic constants (D e , x e , x e x e ) which character- ize the ground state potential curves have been determined experimentally. The equilibrium bond length (r e ) of Hg 2 dimer has been determined from the rotational structure of vibrational bands. 3,1 The equilibrium bond lengths of Zn 2 , and Cd 2 have been estimated using empirical formulas only. 1,2 Ceccherini and Moraldi 18 have chosen a different approach to determine the val- ues of re in Zn 2 , Cd 2 , and Hg 2 dimers, namely based on fitting the Morse and the Lennard-Jones(n-6) potential to experimental low density viscosity data. 19 The results of Ceccherini and Moraldi 18 show a good agreement between experiment and theory for re of Hg 2 dimer, but the equilibrium distances of Cd 2 and especially of Zn 2 are too long. Recent articles 7,8 on the anal- ysis of rotational structure of vibrational transitions have reported direct determination of the equilibrium bond lengths of ground and excited states in Cd 2 dimer. The reported values of the ground state equilibrium bond length in Cd 2 dimer are 3.77 A ˚ 7 and 3.76 A ˚ , 8 respectively. It has been stated by Strojecki et al. 8 that a new measurement of Zn 2 species is in progress. Table 1 summarizes some of the reported experimental and calculated spectroscopic constants. Most theoretical studies of the Zn 2 , Cd 2 , and Hg 2 dimers used effective core potentials (ECPs). 10–15 The main advantage of ECPs comes from computational savings, the other advantage lays in the straightforward implementation of the scalar relativis- tic effects within the given parameterization of the potential. Several studies report calculations at the all electron Douglas– Kroll–Hess Hamiltonian (DKH) level. 9,14,16 Studies of the Zn 2 Contract/grant sponsor: Slovak Grant Agency VEGA; contract/grant numbers: 1/3566/06 Correspondence to: L. Bucinsky; e-mail: lukas.bucinsky@stuba.sk q 2008 Wiley Periodicals, Inc.