J. Am. Chem. SOC.1994, 116, 8241-8248
8241
Stability of Main-Group Element-Centered Gold Cluster Cations Oliver D. HPberlen,? Hubert Schmidbaur,* and Notker Rasch'++ Contribution from the Lehrstuhl f i r Theoretische Chemie and Anorganisch-Chemisches Znstitut, Technische Universitiit Miinchen, 0-85747 Garching, Germany Received February 22, 1994"
Abstract: Relativistic electronic structure calculations have been carried out for the main-group element-centered octahedral gold cluster cations [(LAU)6Xm]" (with central atoms X1 = B, X2 = C, and X3 = N and ligands L = PH3 or P(CH3)3) as wellas for thecorrespondingseries of four- and five-coordinateelement-centeredcations[(LAu)~,](*~)+ and [(LAu)5Xm](*1)+. Geometry optimization shows that the phosphine-ligated clusters have an X-Au bond which, on the average, is about 4 pm larger than that of the analogous naked clusters; the corresponding force constant is concomitantlyweaker. The contribution of the ligands to the overall stability of the clusters is significant, as the cluster cations are stabilized more the higher the cluster charge; the effect is even more pronounced for trimethylphosphine ligands. When the central atom of the naked cluster core is varied, an opposite trend is found as the cluster stability decreases along the series B C N. Both effects compounded lead to a maximum of stability for the cluster cations [(AuL)dN]+, [(AuL)sC]+, and [(AuL)6CIZ+,in agreement with the experimental results. Furthermore, all ligated octahedral clusters are calculated to be stable with respect to the loss of an AuL+ moiety while the corresponding reaction leading to a five-coordinate cluster core is energetically feasible for the naked metal clusters. Thus the study of ligand-free models is not meaningful for an analysis of the electronic structure of gold phosphine compounds.
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1. Introduction
In recent years a wide variety of higher coordinated maingroup element-centered gold cluster cations have been synthesized,' e.g. the four-coordinate tetrahedral [(LAu)4N]+ and square-pyramidal [(LAu)&s]+ 3 clusters, the five-coordinate L L L trigonal bipyramidal clusters [(LAu)sC]+,4 [ ( L A U ) ~ N ] ~ + , ~ and [ (LAu)sP]*+,6 and the six-coordinate octahedral clusters Figure 1. Decompositionof the octahedral cluster cations into their lower coordinate trigonal bipyramidal and tetrahedral analogues by successive [(LAu)&]2+ 7 and [(LAu)6P]3+.*89 As a common structural loss of AuLt units (XI = B, Xz = C, X3 = N). pattern, most of these clusters feature several gold(1) triphenylphosphine moeties AuL (with L = P(C6H5)s) around a mainTable 1. Known n-Coordinate Main-Group Element-Centered Gold group element X, (see Figure 1) although some unusual Clusters of the Form I(LAuLX,l(h+m-6)t with L = PPhP coordinations have also been found, e.g. the square pyramidal coordination cluster charge [(n+md)+] complex ([p(c&)~Au]&)+.~ Strong efforts are being madel number 0 1+ 2+ 3+ to complete this series of the general formula [(LAu),J,] with respect to the central atoms X, from the groups I11 to V 1 Clb 2 sec Cld ( m = 1, 2, 3, respectively) or to extend the series to even higher Of s/ Sd 3 coordinationnumbers. A tabular survey of the presently known 4 N,x Ash 0' clusters (see Table 1) exhibits an "island of stability" along its 5 (3 N,k PI 6 Cm Nn(?), Po * Author to whom correspondence should be addressed. Lehrstuhl fIir Theoretische Chemie. The corresponding central atoms X, are displayed. XIE group 111, ~~
t Anorganisch-Chemisches Institut. *Abstract published in Advance ACS Abstracts. August 1, 1994. (1) Schmidbaur, H.Gold Bull. 1990, 23, 11. (2) Slovokhotov, Y.L.; Struchkov, Y . T. J. Organomet. Chem. 1984,277, 143. (3) Zeller, E.; Beruda, H.; Kolb, A.; Bissinger, P.; Riede, J.; Schmidbauer, H.Narure 1991, 352, 141. (4) Scherbaum, F.;Grohmann, A.; Maller, G.; Schmidbaur, H.Angew. Chem., Int. Ed. Engl. 1989, 28, 463. (5) Grohmann, A.; Riede, J.; Schmidbaur, H.Nature 1990, 345, 140. (6) Schmidbaur, H.;Weidenhiller, G.; Steigelmann, 0. Angew. Chem., Int. Ed. Engl. 1991, 29, 433. (7) Scherbaum, F.; Grohmann, A,; Huber, B.; Krfiger, C.; Schmidbaur, H. Angew. Chem., Inr. Ed. Engl. 1988,27, 1544. ( 8 ) Schmidbaur, H.Pure Appl. Chem. 1993,65, 691. (9) Zeller, E.; Schmidbaur, H.J. Chem. Soc., Chem. Commun. 1993,69. (IO) Schmidbaur, H.; Weidenhiller,G.; Steigelmann, 0.;MIiller, G. Chem. Ber. 1990, 123, 285. (11) Jones, P. G.; Thbe, C. Chem. Eer. 1991, 124, 2725. (12) Jones, P. G.;Sheldrick, G. M.; Uson, R.; Laguna,A. Acta Crystallogr. E 1980, 36, 1486. (13) Nesmeyanov, A. N.; Perevalova, E. G.; Struchkov, Y.T.; Antipin, M. Y.;Grandberg, K. I.; Dyadchenko, V. P. J . Organomet. Chem. 1980, 210, 343. (14) Lensch, C.; Jones, P. G.; Sheldrick, G. M. Z . Naturforsch. E 1982, 37, 944.
~
Xz E group IV, X3 E group V, X4 E group VI, Xs E group VII. b Reference 10. Reference 11. d Reference 12. e Reference 13. /Reference 14. Reference 2. Reference 3 (quadratic pyramidal structure &). 1 Reference 8. Reference 4. Reference 5. I Reference 6. Reference 7. n Reference 15, but see also the comments in ref 6 and 8. References 8 and 9.
*
diagonal, Le. an approximate correlation between the charge of the cluster cations and the number of AuL units. In the present work we investigated the electronic structure and the stability of a variety of element-centeredgold phosphine clusters and have focused on the isoelectronic series of sixcoordinate clusters [(LAu)6Xmlm+(XI = B, X2 = C, X3 = N). Only the carbon-centered member of this series has been synthesized so far; the existence of the nitrogen-centeredcluster15 is still under discussion.638 To further probe the arguments put forward in this quantum chemical analysis, we have also applied the same line of reasoning to the four- and five-coordinateclusters, arriving finally at a rationalization of the "island of stability". (15) Brodbeck, A.; Strihle, J. Acta Crysrallogr. A 1990, 46. C-232.
OOO2-7863/94/1516-8241$04.50/00 1994 American Chemical Society
8242 J. Am. Chem. SOC.,Vol. 116, No. 18, 1994 The electronic structure of gold phosphine compounds has been previously studied in several quantum chemical investigations. Indeed, the six-coordinate carbon-centered cluster was originally predicted on the basis of extended Hiickel calculations.16 These calculations have recently been extended to include also the boronand nitrogen-centered cluster^.'^ However, one should keep in mind that a reliable quantitative evaluation of binding energies and bond lengths is not feasible in extended Hiickel theory, particularly when stretching motions are of importance. Therefore, results obtained with this method will remain essentially of a qualitative nature. Relativistic pseudopotential Hartree-Fock calculations have been carried out on the bare clusters [Au&,lm+ (X, = B,C, N)1* with the aim to investigate the size of the metal cage for different central atoms. Since electron correlation and the ligand influence were neglected in that work, the results are of limited relevance for the present goal. For the four-coordinate clusters with N, P, and As as “central” atoms, relativistic pseudopotential Hartree-Fock calculations were performed19 to elucidate the experimentally observed3 structural change from tetrahedral (for N) to square pyramidal (for As) coordination. These calculations included correlation by second-order perturbation theory (MP2) as well as ligands modeled by phosphines. Fully relativistic DiracSlater discrete-variational (DS-DV) X a calculations have been performed20p21on the ligated clusters using phosphines as model ligands. A central result of this investigation, which is at variance with previous models for bonding in gold cluster compounds, is the participation of gold 5d orbitals in the metal-metal bonding, similar to the dlO-d10 interaction suggested earlier for Cu(I)-Cu(I)22 and Pt(0)-Pt(0) ~omplexes.2~ Via s-d hybridization this additional interaction mechanism, which is strongly enhanced by relativistic effects, leads to an interplay between radial X-Au and Au-L u bonding on the one hand and the tangential gold-gold bonding on the other. Thus, for a proper description of the bonding in these element-centered gold cluster compounds it is essential to simultaneously take electron correlation, relativistic effects, and the influence of the ligands into account. At present, a reliable all-electron treatment of these systems by a ”first principles” method seems to be only possible a t the level of density functional theory. Our previous work*’J+21 using the DS-DV-Xa method focused on a molecular orbital analysis of octahedral gold cluster compounds but did not include a geometry optimization and the calculation of binding energies. The present investigation extends this work by means of an adequate electronic structure method, which is able to furnish geometries and binding energies, namely the quasirelativistic extension of the linear combination of Gaussian-type orbitals local density functional (R-LCGTO-LDF) method.2+26 We start our discussion by first describing the pertinent features of the R-LCGTO-LDF method as well as some computational details. Then we proceed to analyze the structural aspects of the ligand-free cluster cations. Topics of interest here are the effects of the charge on the cluster cations and the structural consequences of an atom in the center of the cluster as well as the extent of relativistic and electron correlation effects. In the next step, we investigate the influence of the phosphine ligands on the geometry and on the bonding of the cluster compounds. Then we present a detailed analysis of the energetic aspects that lead to the particular stability of the carbon-centered octahedral cluster. We (16) Mingos, D. M.P. J . Chem. SOC.,Dalton Trans. 1976, 1163. (17) Mingos, D. M. P.; Kanters, R. P. F. J. Organomet. Chem. 1990,384, 405.
(18) PyykkB, P.; Zhao, Y . Chem. Phys. Lett. 1991, 177, 103. (19) Li, J.; PyykkB, P. Inorg. Chem. 1993, 32, 2630. (20) Rbsch, N.; GBrling, A.; Ellis, D. E.; Schmidbaur,H. Angew. Chem., Int. Ed. Engl. 1989, 28, 1357. (21) GBrling, A.; RBsch, N.; Ellis, D. E.;.Schmidbaur, H. Inorg. Chem. 1991. __ - 30. - -, 39x6. - - - -. (22) Mehrotra, P. K.; Hoffmann, R. Inorg. Chem. 1978, 17, 2187. (23) Dedieu, A.; Hoffmann, R. J . Am. Chem. SOC.1978, 100, 2074. (24) Knappc, P.; RBsch, N. J . Chem. Phys. 1990, 92, 1153. (25) RBsch, N.; Hiberlen, 0. D. J. Chem. Phys. 1992, 96,6322. (26) Hiberlen, 0. D.; RBsch, N. Chem. Phys. Lett. 1992, 199, 491.
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Habeden et al. put forth detailed arguments that the stabilizing effect of the ligands is most effective for positively charged clusters, although it competes with the increasing Coulomb repulsion within these cluster cations. In thelast section weapply theconceptselaborated in an analysis of the lower coordinated clusters. We also investigate the stability of the cluster cations with respect to the loss of AuL+ moieties, thus rationalizing the experimentally observed tendency of the lower coordinated clusters to aggregate further AuL+ units. Here again the ligand influence turns out to be crucial. 2. Method and Computational Details 2.1. Quasirelativistic LCGTO-LDF Method. The quasirelativistic extension2c26of the LCGTO-LDF m e t h ~ d is~ based ’ ~ ~ on ~ the DouglasKroll (DK) transformation.29 This transformation affords a variationally stable reduction of the four-component Dirac-type formalism to the familiar two-component formalism and permits the self-consistent treatment of relativistic effects. This methodology, based on the no-pair projection operator formalism of quantum electrodynamics, has been used previouslyin the context of wave-function-based electronic structure meth0ds.3~~~ Wemerely report theresultsof theDK transformation in the framework of the Kohn-Sham theory, correct to the second order in the effective one-particle potential u. One obtains25*26 a set of two-component KohnSham-like equations with an effective one-particle “Hamiltonian”
h 3 = E, + A,UA, + ApR,uR,,A p - -(E,@ 1 + W’E, + 2 WEpW) 2
(1)
Here, the abbreviations
E, = c(p2 + c’)~~’, A, =
+ (%) E
c2 I/’
C(
;.$)
,R, = - (2) E, + c2
have been used, where represents the vector of the Pauli spin matrices and $ is the electronic momentum operator. The integral operator W is given in the momentum representation by
(3) This type of transformation avoids the generation of highly singular operators that arise in the Foldy-Wouthuysen t r a n ~ f o r m a t i o n . ~As~ , ~ ~ a consequence, matrix techniq~es’~ may be successfullyemployed for the evaluation of the various, rather complicated operators. However, only matrix elements of the operators @u$) and @Xu$) have to be evaluated in addition to those already required in the standard nonrelativisticversion of the method. The latter matrix elements which are readily associated with the spin-orbit interaction are even needed in a scalar-relativistic variant of the method through cross terms that occur in the operator W in eq 1.26 For the present investigation, the spin-orbit interaction is neglected. Furthermore, only the dominating nuclear potential is taken into account in the DK transformation but not the costly electronic contributions to the potential. Judging from atomic results,u one expects that most of the scalar-relativistic effects are taken into account by this level of theory (termed “vn2“ in ref 26). The scalar-relativistic density functional method described above has been successfullyapplied to the gold dimer,26 to the series of mononuclear gold(1) complexes (H&)Au(PR3) with R = H, CH3, and C~HS,)’and to cerium bound endohedrally in C ~ s . 3 6 ,Judging ~~ from the results for (27) Dunlap, B.I.; Connolly, J. W.; Sabin, J. R. J. Chem. Phys. 1979, 71, 3396, 4993. (28) Dunlap, B. I.; RBsch, N. Adu. Quantum Chem. 1990, 21, 317. (29) Douglas, M.; Kroll, N. M.Ann. Phys. 1974, 82, 89. (30) Sucher, J. Phys. Rev. A 1980, 22, 348. (31) AlmlBf, J.; Faegri, K.; Grelland, H. H. Chem. Phys. Lett. 1985,114, 53. (32) Hese, B. A. Phys. Rev. A 1986, 33, 3742. (33) Foldy, L. L.; Wouthuysen, S. A. Phys. Reo. 1950, 78, 29. (34) Moss,R. E. Mol. Phys. 1984,53, 269. (35) Hiberlen, 0. D.; RBsch, N. J. Phys. Chem. 1993, 97,4970. (36) Hiberlen, 0.D.; RBsch, N.; Dunlap, B. I. Chem. Phys. Lett. 1992, 200, 418. (37) RBsch, N.; Hiberlen, 0. D.; Dunlap, B. I. Angew. Chem., Int. Ed. Engl. 1993, 32, 108.
J. Am. Chem. Soc., Vol. 116, No. 18, 1994 8243
Main-Group Element- Centered Gold Cluster Cations Au2,26 one expects the local density approximation used here3*to exhibit a tendency to overestimate binding energies.39 This deficiency of the LDFmethod is acceptable in the present investigation,sincewearemainly interested in changes of binding energies rather than in their absolute values. The scalar-relativistic version of the LCGTO-LDF method is computationallyvery efficientso that all-electroncalculations are feasible even for the complexes {[(H~C)~PAU]&,,,)"+with 85 atoms and more than 1600 contracted Gaussian-type MO basis functions. 2.2. Computational Details. Octahedral symmetry was assumed for thecluster core [A@,]"+. Theligatedmodelclusters [(R3PAu)&,]"+ were calculated in idealized D3d symmetry. The geometry optimizations of the present study focused on the distances from the gold atoms to the center of the cage and on the gold-ligand distances. These distances were varied in steps of 10 pm on a regular 5 X 5 grid. The bond lengths and force constants were determined by fitting a fourth-order Chebychev polynomial to the resulting energy values. The geometries of the various phosphine ligands were kept fixed. For PH3, standard values were employed: d(PH) = 141.5pm,
