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Journal of the Chilean Chemical Society

versión On-line ISSN 0717-9707

J. Chil. Chem. Soc. v.49 n.4 Concepción dic. 2004 

Chil. Chem. Soc., 49, N 4 (2004): págs: 361365




aAvenida Libertadores 848, El Monte, Región Metropolitana, Chile. e-mail:
*Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Andrés Bello, Santiago, Chile,


Dirac molecular spinor calculations on the Re2Cl82-, Re2Br82-, Os2Cl82- (both staggered and eclipsed isomers), Os2Br82- and Os2I82- cluster ions are reported. Here we report the calculations of the spin-orbit splitting affecting the metal and ligand core-like states and also affecting the p and d metal-metal bonds. We also compare the calculated molecular spin-orbit splitting against the calculated atomic spin-orbit splitting, and, against available experimental data.


The existence of multiple bonds between transition metal atoms has been recognized for about three decades [1-23]. Since the discovery of the prototype quadruple bonded Re2Cl82- ion [1,2,5], characterized by a s2p4d2 ground state configuration arising from d4-d4 interactions, there has been an enormous experimental and theoretical interest to elucidate the details of its electronic spectrum [4,13,18-20] due to fact that posses a rich manifold of excited states that are responsible for its luminescent behavior. However, the intense lowest absorption band characterized by a d´ d* (1A1g «1A2u) transition at 14700 cm-1 has represented a major challenge to sophisticated quantum mechanical methods, since this transition is still calculated with significant errors [13,18-20]. Obviously, metal-metal quadruple bonded systems possess the same low-lying excited states that involve complicated configuration interaction (CI) mechanisms, which are difficult to deal with. On the other hand, the electron-rich triply bonded metal-metal complexes, characterized by a s2p4d2d*2 ground state configuration arising from d5-d5 interactions, do not exhibit low-lying excited states with the same symmetry and do not involve the complex configuration interaction mechanisms which are operative in quadruply bonded systems [5,13,18-20].

Besides numerous theoretical studies aimed toward the understanding of the electronic structure and spectral properties of these molecular systems [5,10,13,14-18,20], photoelectron spectroscopy (PES) has also played an important role in the experimental investigation of the electronic structure in these compounds, particularly for the study of the s, p and d type metal-metal bonds in the quadruply bonded W2Cl4(PMe3)4 , W2(mph)4, where mph= 2-oxy-6-methylpyridine ion; W2(OCMe3)6, and, the electron-rich triply bonded Re2Cl4(PMe3)4 complexes [21-24]. Valence photoelectron spectral studies have provided experimental information about spin-orbit effects acting on the p and d type bonds, and, about the location of the s, p and d bond ionizations, but these studies are limited only to meta-metal multiply bonded compounds which can be volatilized, thus permitting the measurement of their valence photoelectron spectra. Unfortunately, the Re2Cl82-, Re2Br82-, Os2Cl82-, Os2Br82- and Os2I82- complex ions are not possible to volatilize.

With the purpose of obtaining information on the nature, ionization and spin-orbit splitting of the metal-metal bonds and core-like states, we report here the first Dirac molecular calculations on the quadruple bonded Re2Br82-, and the triple bonded Os2Br82- and Os2I82- anions. We also compare our current results with those previously published for W2Cl84- [14] and the two isomers of Os2Cl82- [17].


The self-consistent-field Dirac scattered-wave method has been developed by Yang, Case and Arratia-Perez [14,17,25-32]. This method employs the molecular Dirac equation in the multiple scattering approximations to generate the one-electron molecular spinors, and thus includes all the non-quantum electrodynamical relativistic effects at the SCF stage. In this formalism, the cluster wave function is taken as a Slater determinant of four-component molecular spinors [33] determined by an effective Coulomb and exchange-correlation potential. For the exchange-correlation potential we used a local density potential [34] relativistically modified according to MacDonald and Vosko [35-37]. The calculations presented here include the principal relativistic effects: mass-velocity, Darwin, and spin-orbit at the SCF stage. This method uses a radial differential equation rather than a basis set expansion to determine the radial behavior of its molecular spinors to obtain flexible numerical wavefunctions. In the present study, angular momentum expansions were truncated at l= 2 on the metal, and X atoms, and l = 4 on the outer sphere to stabilize the numerical solution. The symmetrized basis functions for the D4d* and D4h* double point groups were generated by the usual relativistic projection methods [17]. The bond symmetry representations and group correlation between the D4h* and D4d* double point groups are discussed below. The structural parameters used for the calculations are listed in Table 1.


A. Symmetry considerations. The D4h point group belongs to one of the 32-crystallographic point groups and it is compatible with translational symmetry. However, the D4d point group is only compatible with rotational symmetry and thus is not a crystallographic point group. This may be one of the reasons that double point-group character tables are scarce [40]. A simple reduction of the direct products of the single-valued irreducible representations (hereafter irreps) with the double-valued spin representations, chosen as the rotation matrices Dj= 1/2 of each point group, gives the extra irreps of the D4h* double point group (E2g, E2u, E3g, E3u), and, the extra irreps of the D4d* double point group (E4, E5, E6, E7) [17,40]. Furthermore, the descent in symmetry from the full rotation group to the double point group gives the irreps correlations between the D4h*and the D4d* groups. The group relations thus obtained and the corresponding metal-metal bond symmetries are given in Table 2. It can be seen from this table that for eclipsed (D4h) multiply bonded M2X8 systems the metal-metal pu bond splits by spin-orbit interaction into the E2g Ä E3g irreps. Similarly, the metal-metal pg* bond splits by spin-orbit interaction into the E2g E3g irreps. While, in the staggered (D4d) triple bonded M2X8 systems the nonrelativistic degenerated p, (d,d*), p* metal-metal bonds splits by spin-orbit interaction into : p = E5 Ä E6; (d,d*) = E5 Ä E7; and, p*= E4 Ä E7 [17]. Then, double point group symmetry dictates that d and d* electronic states are no longer degenerate when the MX4 units are fully staggered with respect to each other. As can be seen from Table 2, the actual relativistic molecular spinors spanning the double group irreps contain mixtures of bond symmetries and spin due to spin-orbit coupling. These bond and spin mixtures in the p metal-metal bond (that couples with the sj = 1/2, and, dj = 3/2, metal-metal bonds) may explain the fact that two spin-orbit components have different band envelopes and cross sections seen in the photoelectron spectra of W2Cl4(PMe3)4 [22].

B. Electronic Structure. The quadruply bonded M2X8 systems which posses eclipsed (D4h) conformations are characterized by the nonrelativistic s2p4d2 configuration, but the relativistic configuration due to spin-orbit coupling is s2p1/22p3/2 2d3/2,5/22. Each HOMO (d) and each LUMO (d*) for W2Cl84- [14], Re2Cl82-, and Re2Br82-, are mainly localized on each metal center (with more than 60% d-character). The calculated HOMO-LUMO separations are 1.02, 0.70 and 0.73 eV, respectively. This calculated one-electron energy difference for Re2Cl82-is quite far from the observed intense lowest absorption band characterized by a d «d* (1A1g «1A2u) transition at 14700 cm-1 [3,4,13,18-20]. As indicated above, more elaborated CI procedures are needed to characterize fully this intense absorption band [13,18-20]. Moreover, recent scalar relativistic Douglas-Kroll multiconfigurational CI (CASSCF/CASPT2) calculations for Re2Cl82- by Gagliardi and Roos concluded that the Re-Re bond has an effective bond order of 3.2 mainly due to the large occupation of the antibonding d* orbital, thus describing the Re-Re bond as a "weak" quadruple bond [20].

The triply bonded eclipsed (D4h) Os2Cl82- anion is characterized by the nonrelativistic configuration s2p4d2d*2 , but the relativistic configuration due to spin orbit coupling is s2p1/22p3/2 2d3/22d* 5/22, in which the HOMO (d*) is mainly localized on each Os center with more than 65% d-character and it is 0.61 eV apart from the LUMO (p*1/2).

The triply bonded staggered (D4d) Os2Cl82-,Os2 Br82- and Os2I82- anions are characterized by the nonrelativistic s2p4(d,d*)4 configuration, but, the relativistic configuration due to spin orbit coupling is s2p1/22p3/2 2d3/22d* 5/22. The HOMO's (d*) of Os2Cl82- and Os2Br82- are mainly localized on each Os center with more than 60% d-character. The HOMO of Os2I82- is delocalized around the ligand atoms and it is almost pure iodine in character. The metal d* orbital is located just below the HOMO about 0.3 eV apart.

C. Spin-orbit Effects. All the compounds calculated here are amenable to be studied by XPS photoelectron spectroscopy, which provide information about "core and core-like states" ionizations and hence about electronic states energy differences. To our knowledge, the only compound, studied by XPS spectroscopy is the prototype Re2Cl82-anion. The measured rhenium (4f5/2-4f7/2) spin-orbit splitting (lso) is 2.39 eV [39]. The calculated molecular value is 2.49 eV, and the calculated atomic (Re) value is 2.70 eV. In Table 3 we list the calculated "core-like" molecular lso values for Re2Cl82-, Os2Cl82-, Os2Br82-, and Os2I82-, and, the corresponding atomic lso values for each atom forming part of these cluster complexes. It can be seen from Table 3 that the molecular lso values are always reduced from the atomic lso values by about 10%. Obviously, these lso reduction effects arise due to bonding effects. The information listed in Table 3 could be of utility for the interpretation of XPS data.

Table 3. Core states spin-orbit splitting (lso in eV).

a Atomic Dirac Slater calculations. See Ref. 38.
b Experimental XPS: 2.39 eV. See Ref. 39.

In Table 4 we show the calculated spin-orbit splitting of the metal-metal p bond for the eclipsed M2X8 complexes, and the spin-orbit splitting of the metal-metal p and d bonds for the staggered triply bonded M2X8 complexes. We also show here the measured HeI/HeII PES data for comparable complexes. It can be seen that the calculated p1/2-p3/2 spin-orbit splitting values are in good agreement with those measured in comparable eclipsed complexes. The calculated value of the p1/2-p3/2 spin-orbit splitting of the staggered complexes are similar to the calculated values for the eclipsed complexes, but, the calculated values of the d3/2 - d5/2* spin-orbit splitting are quite small suggesting that ligand- ligand electrostatic effects tends to diminish the spin-orbit effects. So, the current Dirac molecular calculations predicts a near degeneracy of the d and d* levels since these levels still exist as separate types, in contrast to nonrelativistic single point group interpretations that indicates that these energy levels should be degenerated [10]. The small d3/2 - d5/2* energy separation clearly suggests the OsX4 units should overcome a small electronic rotational barrier when proceeding from a eclipsed to a fully staggered conformation. It should be noted that a very small rotational barrier has been computed by Hay [10] for the rotation of the ReCl4 units around the Re-Re bond.


We have reported here vectorial relativistic calculations within the Dirac Slater multiple scattering approximation on the eclipsed and staggered M2X8 complexes obtaining new results on spin-orbit effects affecting the core-like and valence electronic states that can provide a better understanding of molecular systems having multiple metal-metal bonds.



We dedicate this work to our friend Professor Carlos Andrade Plaza. This work has been supported in part by Fondecyt No.1030148 and UNAB-DI 10-02, and the Millennium Nucleus of Applied Quantum Mechanics and Computational Chemistry, P02-004-F.


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(Received: September 1, 2004 - Accepted: November 3, 2004)

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