Inorg. Chem. 2003, 42, 1599−1603 2- The Electronic Spectrum of Re2Cl8 : A Theoretical Study Laura Gagliardi*,† and Bjo1rn O. Roos‡ Dipartimento di Chimica Fisica F. Accascina, Viale delle ScienzesParco d’Orleans II, I-90128 Palermo, Italy, and Department of Theoretical Chemistry, Chemical Center, P.O. Box 124, S-221 00 Lund, Sweden Received October 14, 2002 2- One of the prototype compounds for metal−metal multiple bonding, the Re2Cl8 ion, has been studied theoretically using multiconfigurational quantum chemical methods. The molecular structure of the ground state has been determined. It is shown that the effective bond order of the Re−Re bond is close to three, due to the weakness of, in particular, the δ bond. The electronic spectrum has been calculated with the inclusion of spin−orbit coupling. Observed spectral features have been reproduced with good accuracy, and a number of new assignments are suggested. 1. Introduction In 1965, F. A. Cotton and C. B. Harris reported the crystal 1 structure of K2[Re2Cl8]‚2H2O. A surprisingly short Re-Re distance of 2.24 Å was found. This was the first example of 2- a multiple bond between two metal atoms, and the Re2Cl8 ion has since then become the prototype for this type of complexes. A new era of inorganic chemistry was born. Cotton analyzed the bonding using simple molecular orbital 2- (MO) theory and concluded that a quadruple Re-Re bond Figure 1. Structure of Re2Cl8 . 1,2 was formed. Two parallel ReCl4 units are connected by order depends on the relation between the occupation of the the Re-Re bond. The dx2-y2,px,py, and s orbitals of the valence shell of each Re atom form the σ bonding to each bonding and antibonding orbitals, respectively. Such a description is, however, only possible if a quantum chemical Cl atom. The remaining dz2 and pz orbitals with σ symmetry model is used that goes beyond the Hartree-Fock model. relative to the Re-Re line, the dxz and dyz with π symmetry, Such a model will be used here, and we shall demonstrate and the dxy with δ symmetry form the quadruple Re-Re bond: one σ bond, two π bonds, and one δ bond. Because that the true bond order between the two Re atoms is closer there are eight electrons to occupy these MOs, the ground to three than to four. - state configuration will be σ2π4δ2. The presence of the δ Considering its fundamental character, the quadruple Re 2- bond explains the eclipsed conformation of the ion. In a Re bond in the dirhenium complex Re2Cl8 (Figure 1) has staggered conformation, the overlap of the δ atomic orbitals been a subject of several later studies both experimentally is zero, and the δ bond disappears. The visible spectrum was and theoretically. 3,4 also reported in these early studies. The notion of a quadruple In 1977 and 1978, Trogler et al. measured the single- 2- bond is based on the inherent assumption that four bonding crystal polarized electronic absorption spectrum of Re2Cl8 , orbitals are doubly occupied. Today we know that this is and they assigned various bands. 5 2- not the case for weak intermetallic bonds. The true bond More recently, Blaudeau et al. have studied Re2Cl8 by ab initio quantum chemical methods, following previous * To whom correspondence should be addressed. E-mail: laurag@ ciam.unibo.it. (3) Trogler, W. C.; Cowman, C. D.; Gray, H. B.; Cotton, F. A. J. Am. † Viale delle Scienze. Chem. Soc. 1977, 99, 2993. ‡ Chemical Center. (4) Trogler, W. C.; Gray, H. B. Acc. Chem. Res. 1978, 11, 232. (1) Cotton, F. A.; Harris, C. B. Inorg. Chem. 1965, 4, 330. (5) Blaudeau, J.-P.; Ross, R. B.; Pitzer, R. M.; Mougenot, P.; Be´nard, M. (2) Cotton, F. A. Inorg. Chem. 1965, 4, 334. J. Phys. Chem. 1994, 98, 7123. 10.1021/ic0261068 CCC: $25.00 © 2003 American Chemical Society Inorganic Chemistry, Vol. 42, No. 5, 2003 1599 Published on Web 01/25/2003 Gagliardi and Roos theoretical work by Hay.6 They performed multiconfigura- with the expansion coefficients optimized in CASSCF/CASPT2 tional self-consistent field (MCSCF) and configuration calculations on different spectroscopic states of the atom and interaction (CI) calculations with relativistic effective core positive ion (for Cl on the negative ion). The DK Hamiltonian was potentials at the experimental geometry of the complex.1,7 used to include scalar relativistic effects. We note that such a basis The ground state and the two lowest excited states were set can only be used in relativistic calculations. For Re, the primitive studied. set 24s20p15d11f3g was contracted to 8s7p5d3f in a first set of calculations (basis set B1) and also to 8s7p5d3f1g (basis set B2). However, none of these earlier studies gave a more For Cl, the primitive set 17s12p5d3f was contracted to 5s4p2d (B1) complete treatment of the low-lying excited states, and the and to 5s4p2d1f (B2). computed energies were not accurate enough to give an The geometry of the ground state was optimized at the CASSCF unambiguous assignment of the experimental spectrum. level using analytical first derivatives24 and assuming that the Today more advanced methods are available for such studies, molecule has D4h symmetry. Since MOLCAS works in subgroups which also include relativistic effects and spin-orbit cou- of D2h, all calculations were performed in D2h symmetry. A pling. Therefore, it should be possible to give a rather numerical optimization of the three degrees of freedom of the complete account of the electronic spectrum. Because the molecule, the Re-Re and Re-Cl bonds and ClReRe angle, was 2- Re2Cl8 ion is such an important entity in inorganic also carried out at the CASPT2 level. chemistry, we decided to study its structure and electronic The choice of the active space is the crucial step in a CASSCF/ spectrum using multiconfigurational quantum chemistry, the CASPT2 calculation. Initially, an active space formed by 12 only approach that can deal with the complexity of the electrons in 12 active orbitals (12/12) was used. This comprises multiple bond. The same approach used in the present work one 5dσ, two 5dπ, and one 5dδ Re-Re bonding orbitals and the has earlier been used to describe successfully the properties corresponding antibonding orbitals and two Re-Cl δ bonding orbitals and the corresponding two antibonding MOs. This active and electronic spectrum of the Cr2 molecule, which formally has a sextuple bond,8,9 and dichromium tetraformate.10 The space can only describe electronic states where the excitations are - main difference here is that we include relativistic effects in located in the Re Re bond. An extension is needed to cover also the ligand-to-metal charge-transfer (LMCT) excitations. It would a more adequate way, and also spin-orbit coupling. be impossible to include all the Cl 3p orbitals in the active space. 2. Details of the Calculations Therefore, a more limited procedure was followed: The active space was enlarged with two orbitals in one of the eight irreps of D The study was performed using the complete active space (CAS) 2h and four extra electrons. Thus, eight sets of calculations were SCF method11 with dynamic correlation added by multiconfigura- performed with a 16/14 active space. Calculations were only tional second-order perturbation theory (CASPT2).12-14 Scalar performed for allowed transitions (symmetries 1A and 1E ). This relativistic effects were included via a Douglas-Kroll (DK) 2u u procedure will have the effect that a number of excited states are Hamiltonian.15,16 The effects of spin-orbit (SO) coupling were computed with different active spaces, which can be used to check calculated employing a newly developed method based on the whether the results are stable when the active space is enlarged. CASSCF state interaction method (CASSI).17,18 Here, the CASSCF wave functions generated for a number of electronic states are allowed to mix under the influence of a spin-orbit Hamiltonian. 3. Results The method has recently been described, and we refer to this article 3.1. The Ground State. The geometry of Re Cl 2- for details.19 It has been shown to be successful in the study of 2 8 actinide compounds.20,21 All calculations have been performed with obtained at the CASSCF and CASPT2 levels of theory with the software MOLCAS-5.22 two different basis sets is reported in Table 1, together with A newly developed basis set of ANO type has been used for Re the experimental values. and Cl atoms.23 They are of the atomic natural orbital (ANO) type The small basis, B1, reproduces reasonably well the Re- Re distance, while it gives a too long Re-Cl distance. The (6) Hay, P. J. J. Am. Chem. Soc. 1982, 104, 7007. (7) Chakravarty. A. R.; Cotton, F. A.; Cutler, A. R.; Walton, R. A. Inorg. CASSCF and CASPT2 results obtained with the B1 basis Chem. 1986, 25, 3619. set are very similar. With the large basis, on the other hand, (8) Andersson, K. Chem. Phys. Lett. 1995, 237, 212. - (9) Roos, B. O.; Andersson, K. Chem. Phys. Lett. 1995, 245, 215. the Re Cl distance improves substantially in going from (10) Andersson, K.; Bauschlicher, C. W., Jr.; Persson, B. J.; Roos, B. O. CASSCF to CASPT2. It thus seems that the inclusion of Chem. Phys. Lett. 1996, 257, 238. (11) Roos, B. O. In AdVances in Chemical Physics; Ab Initio Methods in Quantum Chemistry-II; Lawley, K. P., Ed.; John Wiley & Sons Ltd.: (20) Gagliardi, L.; Roos, B. O.; Malmqvist, P.-Å.; Dyke, J. M. J. Phys. Chichester, U.K., 1987; p 399.