J. Phys. Chem. 1993,97,49704973
4970
Effect of Phosphine Substituents in Gold(1) Complexes: A Theoretical Study of MeAuPR3, R = H, Me, Ph Oliver D. Hiberlen and Notker Rbch’ Lehrstuhl f”ur Theoretische Chemie, Technische Universitat Mfinchen, W-8046 Garching, Germany Received: December 4, 1992; In Final Form: February 9, 1993
Electronic structure investigations on triphenylphosphine (PPh3) ligated gold clusters are commonly carried out with model phosphine ligands. To explore the validity and the limitations of this approach, we have studied the effects of phosphine substituents in a series of gold(1) compounds: MeAuPR3, R = H, Me, Ph. We used the recently developed scalar-relativistic version of the linear combination of Gaussian-type orbitals (LCGTO) local density functional (LDF)method which allows an all-electron treatment of all systems under study. For structural properties the PH3 ligand provides a satisfactory model of the full PPh3 ligand. But the trimethylphosphine ligated models have to be employed if good agreement is desired for energy properties and for the dipole moment.
1. Introduction
2. Computational Details
Recently, an increasing number of polynuclear gold clusters arebeiig synthesizedandcharacterized.’-ll Someoftheseclusters feature unusual structural arrangements of their basic building blocks, triphenylphosphine-gold(1) moieties, around a central main group element.3-9 Due to their size, these cluster compounds pose quite a challenge to quantum chemical methods. Since for gold compounds a relativistic description is mandatory,12computational procedures become rather expensive. Therefore these clusters have been described by model compounds with simplified phosphine ligandsl3-15 or even by naked clusters.I6 The effect of the phosphine ligands on the bonding in these clusters is wellknown;’4J7J8 in some cases, they are required even for a qualitatively correct description of the electronic structure. However, little is known about errors introduced when the full experimental triphenylphosphineligands are modeled by simpler phosphine ligands. To examine the reliability of model calculations we have investigated the influence of the phosphine substituents in the series MeAu MeAuPH3 MeAuPMe3 MeAuPPh3 (Me = CH3, Ph = C ~ H S )One . reason for using this particular class of systems derives from the fact that the structural parameters of MeAuPPh31ghave been referred to as “important standard dimensionsfor organogoldcompounds”in the Gmelin handbook.20 The next smaller compound MeAuPMe3 is also experimentally well ~ h a r a c t e r i z e d ~sol -that ~ ~ a comparison with thecalculations is possible. Last but not least, all compounds mentioned above are computationally accessible by the theoretical method used here, sothat the present study aquiressome benchmarkcharacter. To the best of our knowledge this is the first relativisticelectronic structure investigation of the compound MeAuPPh3. Few calculations have been carried out on the molecule MeAuPMe,: LCAO-MO HartreeFockSlater (HFS) calculations at the experimental geometryz4and unpublished HartreeFock calculations where thegold-rbon distance w a s ~ a r i e d .Both ~ ~ studies also included the model MeAuPH3. A further common aspect between them is the fact that relativistic effects were taken into account by first-order perturbation theory. Severalinvestigations have examinedsubstituenteffects for free phosphines2f-28although no results seem to be available for PPh3. In one of these studies,28 the role of phosphorus d orbitals in the bonding of phosphines to transition metals, especially their importance in contributing to the A bonding, has been analyzed.
The present investigation has been performed using the scalarrelativistic v e r ~ i o n ~ ~of- ~ the I linear combination of Gaussiantype orbitals (LCGTO) local density functional (LDF) method.32~~~ The relativistic extension of the LCGTO-LDF method is based on the Douglas-Kroll tran~formation~~ which affords a variationally stable reduction of the four-component formalism to a two-component form and treats relativistic effects self-consistently. This methodology has been used previously in the context of wave function based electronic structure m e t h o d ~ . ~The ~ J ~approximate density functional treatment of the present investigation has been applied successfully to gold d i a t o m i ~ s .The ~ ~ local density approximation used here employs the Vosko-Wilk-Nusair functionaP7 which shares the tendency to overestimate binding energies with other local density approximation~.~~ The scalar-relativistic version of the LCGTOLDF method is computationally very efficient so that all-electron calculations are feasible even for the molecule MeAuPPh3. This system comprises 15 symmetry inequivalent atoms (in C3, symmetry) and, with 680 contracted Gaussian-type MO basis functions, is probably one of the largest heavy-metal complexes so far treated relativistically. The geometry optimizations of the present study focused on the bonds formed by the gold atom. The Au-C and Au-P distances were varied in 0.05-A steps on a regular 5-by-5 grid. The bond lengths and force constants were determined from a fourth-order Chebychevpolynomialfit. In the case of MeAuPPh3 both bond lengths were varied separately ( 5 points), holding the other bond distance at the value determined for MeAuPMe,. The geometric structures of the various ligands were kept fixed. Thestructural parametersused for thefreephosphines wered(PH) = 1.415 A, f(HPH) = 93.3’ for PH3;39d(PC) = 1.846 A, L(CPC) = 98.6’ for PMe3,4O and d(PC) = 1.825 A, L(CPC) = 104.7O for PPh3.I9 In the metal complexes the values d(PC) = 1.829 A and L(CPC) = 103.2’ 22 were used for PMe3, whereas PH3and PPh3 remained unchanged. Thegeometry of the methyl groups was characterized by d(CH) = 1.078 A and L(HCH) = 108.0° 22 and that of the phenyl groups by d(CC) = 1.397 A and d(CH) = 1.084 i4.39 In all cases C3” symmetry was assumed. For the gold atom a 21s/17p/lld/7f basis4’was contracted to 1 ls/lOp/7d/3f according to a spin-restricted atomic calcul a t i ~ n . ~ ~The J O starting orbital basis set for carbon, of 9s/5p q~ality,~2 was augmented by a d exponent of 0.643(all exponents are given in a.u.) and contracted in analogous fashion to a 7s/ 4p/ld basis (to 5s/4p/ld for the five carbon atoms of the phenyl group bonded to hydrogen). The starting orbital basis set for
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* Author
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to whom correspondence should be addressed.
0 1993 American Chemical Society 0022-3654/93/2097-4970%04.000/0
The Journal of Physical Chemistry, Vol. 97, No. 19, 1993 4971
Phosphine Substituents in Gold(1) Complexes
TABLE I: Spectroscopic Constants of the Gold Compounds MeAuPRh R = H, Me, Ph
system
bond lengths [AI Au-C Au-P
force constants' [mdYn/Al ' Au-C Au-P
dipole moment6
[DI
IPC[eVl
Theory Au atom MeAu MeAuPH3 MeAuPMe3 MuAuPPh, MeAuPHf'
1.96 2.00 2.03 2.02 1.99
2.40 2.64 2.85 3.14 2.78
2.29 2.25 2.28 2.34
1.58 2.18 1.91 1.32
-0.14 3.84 5.57 5.80 4.57
9.89 9.96 9.10 8.34 8.13 8.89
Experiment Au atom MeAuPMe, MeAuPPh3
2.09 2.12k
2.2w 2.27k
2.308 2.42'
1.969
5.4-5.6h 5.6/
9.22e 8.24'
Only diagonal force constants are displayed. Positive values of the dipole moment correspond to the polarity C-AuP+. e First ionization potential, calculated as difference of total energies (spin unrestricted calculation where appropriate). The value of the H-P-H bond angle isidentical to thatofthec-P-C bondanglefoundinMeAuPMe3 (103.2'), see ref 24. Reference 12. Reference 22. g Reference 21. Reference 48. Reference 23. Reference 19. Reference 49. The force constant was calculated from the frequency given in ref 49, but neglecting any coupling to other degrees of freedom.
phosphorus, a 12s/9p basis,44was augmented by a d exponent of 0.3443 and contracted similarly to a 8s/6p/ld basis. The 6s hydrogen basis44was augmented with a p exponent of 1.0 and contracted to 4s/lp. The auxiliary basis sets for fitting the charge density and the exchange-correlation potential were constructed in standard f a ~ h i o n . ~ *The .~~ ,~~ s exponents of the molecular orbital basis sets were scaled by 2 and 213, respectively, to generate atom centered s-type functions. The p orbital exponents were scaled in the same way to generate atom-centered +type fitting functions. In the case of gold, only every second p exponent was used. To fit angular variations around the atoms, two geometric series of 5 p- and d-type functions were used, the exponents being 0.1,0.25,0.625, 1.5625, and 3.90615 for the former and twice as large for the latter. In the case of hydrogen, no d-type exponents were used. The usage of d-type fitting functions in the auxiliary basis sets turned out to be essential for the proper description of the rather flat gold-phosphorus potential curves.
3. Results and Discussion A comparison of calculated and experimental results for MeAuPMe3 reveals a good agreement for the bond lengths, a satisfactory description of the force constants, and very good agreement for the dipolemoment and the first ionization potential (see Table I). These results provide further evidence for the quality of the scalar-relativistic LCGTO-LDF approach to the electronic structure of heavy-element ~ y s t e m s . ~ ~In- ~the ' case of MeAuPPh3 the agreement between theory and experiment is of similar quality with a striking exception of the gold-carbon bond length. There is quite a smooth trend in the calculated gold-carbon bond length along the series MeAu MeAuPH3 MeAuPMe3, essentially reproducing the experimental value of 2.03 A in the latter compound. Thus the experimental value of2.124Ai9forMeA~PPh~seemsquestionable. Given thepivotal nature of this compound,20 it might be worth consideringto repeat the rather difficult measurement of this quantity. The spectroscopic constants for the gold-phosphorus bond in MeAuPR3 (see Table I) show no monotonic trend along the series R = H, Me, Ph; the methyl-substituted compound marks, in a sense, an extremum position. As a consequence, the PH, ligand may be taken as a satisfactory model ligand for the full PPh3 ligand with respect to structural aspects. The values of the dipole moment and the first ionization potential show a clear convergence along the series of substituents R = H, Me, Ph. For PH3, the
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TABLE Ik Dissociation Energies (in kJ/mol) for the Gold-Carbon and Cold-Phosphorus Bond in MeAuPRh AuPRk and AuPR3+, R = H, Me, Ph
--- ++ -- + reaction
R=H
R=Me
R=Ph
MeAuPR, MeAu + PR3 MeAuPR3 Me AuPR3 MeAuPR3 Me Au PRs A u P R ~ AU PR3 A u P R ~ + Au+ + PRs HPR3+ H + + PR,
182 432 556 124 40 1 762 782
236 434 610 176 553 906 935
246 436 620 184 580 924
4
+
calc" expb
The phosphonium ion PH4+ was calculated in Td symmetry, the geometries of PMe3 and PPh3 were taken as described in section 2. Reference 27.
agreement with the target quantities is rather approximate, whereas PMe3provides an almost quantitative model for theligand PPh3. The monotonic decrease in the ionization potential from 9.96 eV for MeAu to 8.13 eV for MeAuPPh3 corresponds to an increase in the electron-donating capability of the ligands.Z4 As for the ionization potential and the dipole moment a similar convergence is observed for the energy change associated with breaking the gold-phosphorus bond in MeAuPR3 and in AuPR3 (see Table 11). The gold-carbon bond dissociationenergy is nearly unaffected by the type of phosphine ligand attached to the gold atom although there is an increase compared to the dissociation energy of 374 kJ/mol for MeAu. As an aid to understand the stabilization of gold cluster compounds by phosphine ligands, it is illuminating to compare the dissociation energies of AuPR3 and AuPR3+ (see Table 11). The binding energy of PR3 to a gold cation is more than 3 times larger as to a neutral gold atom. The propensity increases along the series R = H, Me, Ph: in the neutral case a gain of 60 kJ/mol is achieved when going from PH3 to PPh3; in the charged case this gain amounts to 180 kJ/mol. Since no experimental data seem to be available for the "gold ion affinities" of phosphines, these results might be compared to the proton affinities of PR3 moieties where good agreement between experimental and calculated values is found. The absolute values of the energy changes are almost a factor of 2 larger in the case of a proton, but the gain from PH3 to PPh3 with about 160 kJ/mol is comparable to that calculated for gold. Leaving aside for the moment the importance of steric factors for the existence of yporcupine"3+46gold clusters, this quite pronounced differencein the "gold affinity" points to an additional stabilizing effect of triphenylphosphine ligands. Furthermore, this effect is expected to be more pronounced for more positively charged clusters. For element-centered octahedral goId clusters this topic will be discussed more thoroughly el~ewhere.~' To gain a more detailed picture of the similarity and difference of the bonding in the various gold phosphine compounds MeAuPR3, their relativistic one-electron level spectra are compared in Figure 1 together with the orbital characters as determined in a Mulliken population analysis. A pseudo-axial terminology (u,r,6) is used to denote the orbitals, the correspondence in C3, symmetry being u al, u e, and 6 e. Of course, it is not possible to separate the levels into pure Au-C and pure Au-P bonding orbitals, but a qualitative assignment is helpful. The valence orbitals pertinent to the Au-P and Au-C bonds are the Au 6s and 5d orbitals as well as the highest lying occupied u and r valence orbitals of the methyl and phosphine moieties. The Au 6p orbitals play a minor role in bonding, their participation in molecular orbitals according to a Mulliken population analysis is less than 5%. In MeAu the bonding is essentially due to the interaction between the u(Me) orbital and the Au 6sand Sd,orbitals, entailing a significant energy lowering of the d,-derived level. The degeneracy of the Au 5d, and 5da levels is lifted slightly by a weakinteractionofthe Au 5d,and theu(Me) levels. Theaddition
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4972 The Journal of Physical Chemistry, Vol. 97, No. 19, 199I3
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9
\
n 1410/86/0
p4o(MeAuPR3
n (MeAu)
'' 'u'u''u /II 16101681
14/5130151 u(AuPRJ
Figure 1. One-electron level spectrum (KohnSham eigenvalues) and first ionization potentials of the compounds MeAu and MeAuPR3 (R = H, Me Ph). For clarity of presentation, only the levels pertinent to the Au-C and Au-P bonds are displayed. Also shown are Mulliken populations (in percent) in the form Me/Au(s)/Au(d)/PR3. A pseudoaxial notation (c,*,6) is used to characterize the orbitals.
of the PH3 ligand results in a strong interaction of the lower u(MeAu) orbital with the u(PH3) orbital which leads to a stabilized molecular orbital of simultaneous Au-C and Au-P bonding character.24 If one replaces the phosphine hydrogen atoms by methyl groups (in PMe3), all levels shift upward, a trend which is reversed in part by the phenyl substitution (in PPh3). It is interesting to note that this nonmonotonic behavior correlates with the changes of the bond lengths and of the force constants. As can be seen from Figure 1, the first ionization potential follows closely the energy of the u-HOMO. Concomitantly with the growing delocalization of the HOMO the relaxation shift decreases along the series (from 3.6 to 2.5 eV) leading to the smallest ionization potential for MeAuPPh3. As is well-known, the Au 5d orbitals contribute substantially to the bonding of gold ~ompounds.~3-'5~1~~~8~Z~ DeKock et al.24 have shown that 40% of the gold-phosphine binding energy in MeAuPH3 results from the participation of the gold 5d orbitals. This is in line with the present findings: the a(PR3) orbital, for example, rises significantly in energy upon substitution R = H Me -+ Ph and thus acquires Au d, character, whereas PR3 admixtures appear in the Au d, and d6 orbitals. Thus, part of the stabilizing effect of the phosphine ligands can be correlated with their ability to induce a participation of the Au 5d orbitals in the bonding.'3-l5~1*.Z4 Finally,we address an interesting aspect of the ligand influence on the electronic structure of these gold compounds which has been pointed out previously. It has been suggestedz4that the ability of the PH3 ligand to model a PMe3 ligand is improved if the H-P-H bond angle is increased from its experimental value of 93.3" to 1OSo,a value close to that of the C-P-C bond angle in MeAuPMe3 (103.2O). As a consequence, all but one of the valence orbitals participating in the bonding rise in energy, bringing the level spectrum into better agreement with that of MeAuPMe3. This improves the calculated photoelectron spect r ~ m Inspired . ~ ~ by this success we have optimized the structure of MeAuPH3 with the H-P-H bond angle fixed at an increased value (see Table I). With the exception of the Au-C force constant, the values for the bond lengths and force constants compare worse to MeAuPMe3. A possible explanation for this failure may be connected to the downward shift of the a(PH3) orbital when the H-P-H bond angle is increased. This shift results in a decreased participation of the Au d, orbitals in r(PH3) but is at variance with the behavior of the r(PMe3) and a(PPh3) orbitals, which rise in energy (see Figure 1). 4. Conclusion Triphenylphosphines are found in many of the recently synthesized gold cluster compoundsbecause they act as stabilizing
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agents. We have investigated the possibility of modeling these complex ligands by the simpler trimethylphosphine or even by pure phosphine moieties. Structural aspects are modeled satisfactorily by the simple phosphine ligands PH, while the dipole moment, the first ionization potential, and the binding energy are described only approximately. On the other hand, trimethylphosphine ligands yield an almost quantitative model for the interaction between a gold atom and triphenylphosphine. Thus a cost effective strategy is to employ simple phosphine ligands during the geometry optimization and, if desired and feasible, to use trimethylphosphine ligands at the resulting geometry to improve energetic aspects and other observables.
Acknowledgment. We thank J. K. Fsegri for communicating unpublished results. O.D.H. thanks G. Malli for supporting his participation at the NATO advanced study institute held at Vancouver in August 1992where preliminary results of this study have been presented. This work has been supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 338 and by the Fonds der Chemischen Industrie. References and Notes (1) Hall, K. P.; Mingos, D. M. P. Prog. Inorg. Chem. 1984, 32, 237. (2) Manassero, M.; Naldini, L.; Sansoni, M. J . Chem. SOC.,Chem. Commun. 1979, 385. (3) Scherbaum, F.; Grohmann, A.; Huber, B.; Kriiger, C.; Schmidbaur, H. Angew. Chem., Int. Ed. Engl. 1988, 27, 1544. (4) Scherbaum, F.; Grohmann, A.; Miiller, G.; Schmidbaur, H. Angew. Chem., Inr. Ed. Engl. 1989, 28, 463. (5) Grohmann, A,; Riede, J.; Schmidbaur, H. Nature 1990,345, 140. (6) Brodbeck, A,; Strihle, J. Acta Crystallogr. A 1990, 46, C-232. (7) Schmidbaur, H. 16th International Conference on Organometallic Chemistry, Detroit, August 19-24, 1990; p 50. (8) Schmidbaur, H. Gold Bull. 1990, 23, 11. (9) Zeller, E.; Beruda, H.; Kolb, A.; Bissinger,P.; Riede, J.; Schmidbaur, H. Nature 1991, 352, 141. (10) Schmid, G.; Pfeil, R.; Boese, R.;Bandermann, F.;Meyer, S.; Calis, G. H. M.; v. d. Velden, J. W. A. Chem. Eer. 1981, 114, 3634. (1 1) Mielcke, J.; StrBhle, J. Angew. Chem., Int. Ed. Engl. 1992,31,464. (12) Pyykkd, P. Chem. Rev. 1988, 88, 563. (13) Rdsch, N.; Gdrling, A.; Ellis, D. E.; Schmidbaur, H. Angew. Chem., Int. Ed. Engl. 1989, 28, 1357. (14) Gdrling, A.; Riisch, N.; Ellis, D. E.; Schmidbaur, H. Inorg. Chem. 1991. ~ 30. , 3986. (15) Schwerdtfeger, P.; Boyd, P. D. W. Inorg. Chem. 1992, 31, 327. (16) Pyykkd, P.; Zhao, Y. Chem. Phys. Lett. 1991, 177, 103. (17) Mingos, D. M. P. J. Chem. SOC.,Dalton Trans. 1976, 1163. (18) Mingos, D. M. P.; SI=, T.; Zhenyang, L. Chem. Rev. 1990,90,383. (19) Gavens,P.D.;Guy,J. J.;Mays,M. J.;Sheldrick,G. ActaCrystallogr. B 1977, 33, 137. (20) Schmidbaur, H. In Gmelin Handbook of Inorganic Chemistry, Organogold Compounds; Slawisch, A,, Ed.; Springer-Verlag: New York, 1980. (21) Shaw, C. F.;Tobias, R. S.Inorg. Chem. 1973, 12, 965. (22) Haaland, A.; Hougen, J.; Volden, H. V. J. Organomet. Chem. 1987, 325, 311. Puddephatt, R. J.; Tse, J. S. Inorg. Chem. (23) Bancroft, G. M.; Chan, T.; 1982, 21, 2946. (24) DeKock, R. L.;Baerends, E. J.; Boerrigter, P. M.; Hengelmolen, R. J. Am. Chem. SOC.1984, 106, 3387. (25) K. Fiegri, J.; Hougen, J.; Korsell, K. Private communication. (26) Xiao,S.-X.;Trogler, W. C.; Ellis, D. E.; Berkovitch-Yellin,Z.J. Am. Chem. SOC.1983, 105, 7033. (27) Magnusson, E. Aust. J . Chem. 1985, 38, 23. (28) Pacchioni, G.; Bagus, P. S. Inorg. Chem. 1992, 32, 4391. (29) Knappe, P.; Riisch, N. J. Chem. Phys. 1990, 92, 1153. (30) HBberlen, 0. D.; Rbch, N. Chem. Phys. Lett. 1992, 199,491. (31) Rhch, N.; HPberlen, 0. D. J . Chem. Phys. 1992, 96,6322. (32) Dunlap, B. I.; Connolly, J. W.;Sabin, J. R. J. Chem. Phys. 1979, 71, 3396; 4993. (33) Dunlap, B. I.; Riisch, N. Adv. Quantum Chem. 1990, 21, 317. (34) Douglas, M.; Kroll, N. M. Ann. Phys. 1974, 82, 89. (35) Almldf, J.; Fkgri, K.;Grelland, H. H. Chem. Phys. Lett. 1985,114, 53. (36) Hess, B. A. Phys. Rev. A 1986, 33, 3142. (37) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (38) Parr, R. G.; Yang, W. Density Funetional Theory for Atoms and Molecules; Oxford University Press: New York, 1989. (39) CRC Handbook of Chemistry and Physics, 64th ed.; Weast, R. C., Ed.; CRC Press, Inc.: Boca Raton, FL, 1983. (40) Bartell, L. S.; Brockway, L. 0. J. Chem. Phys. 1960, 32, 512. (41) Hess, B. A. Private communication. (42) van Duijneveldt, F. B. IBM Res. Rep. 1971, RJ 945. 1
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