Organometallics 1995,14, 1284-1291
1284
Relativistic Effects in Cationic Gold(1) Complexes: A Comparative Study of ab Initio Pseudopotential and Density Functional Methods Jan HruSak,* Roland H. Hertwig, Detlef Schroder, Peter Schwerdtfeger,+ Wolfram Koch,* and Helmut Schwarz" Institut fur Organische Chemie der Technischen Universitat Berlin, Strasse des 17, Juni 135, 0-10623 Berlin, Germany Received September 9, 1994@ The cationic gold(1) complexes Au+(HzO), Au+(CO), Au+(NH3), and Au+(CzH4)have been examined by different ab initio and density functional methods using nonrelativistic and relativistic ECPs and a quasi-relativistic approach, where relativistic effects are explicitly taken into account. On the one hand, Au+(HzO)and Au+(CO)exhibit binding energies (35.9 and 44.1 kcaymol, respectively, a t the CCSD(T) level of theory) which are comparable with those of the complexes of the group 11 congeners Cu+ and Ag+. While for Au+(NH3) and Au+(C2H4)a large relativistic stabilization is observed, such that the binding energies (65.3 and 68.8 kcaymol, respectively, a t the CCSD(T) level of theory) are almost twice as high as for M+(NH3)and M+(CzH4)for M = Cu and Ag. With respect to the computational methods applied, structural features and energetics obtained with different ab initio (MP2, CCSD(TI) and DFT (ADF/BP, B3LYP) methods are in reasonable agreement with each other. In general, the relativistic effects on structures and energetics of these gold(1) compounds are quite large, and the interplay of electron correlation and relativistic effects is discussed.
Introduction Complexes of transition-metal cations with small ligands L, e.g., water, ammonia, and small hydrocarbons, deserved considerable interest within the last decade, especially with respect to bond activations and other catalytic processes. Numerous experimental studies1,2have established accurate bond dissociation energies (BDEs) of M+(L) complexes, thus providing a detailed insight into the nature of the metal-ligand b ~ n d i n g .Due ~ t o the large amount of data available for first-row transition-metal cations, these compounds represent valuable test systems for theoretical invest i g a t i o n ~ . ~Nowadays, -~ the results of quantum-mechanical calculations are in good agreement with the + Permanent address: Computational Material Science and Engineering Research Centre, Department of Chemistry and the School of Engineering, University of Auckland, Private Bag 92019,Auckland, New Zealand. Abstract published in Advance ACS Abstracts, January 15, 1995. (1)(a) Armentrout, P. B. Annu. Rev. Phys. Chem. 1990,41, 313. (b) Eller, K.;Schwarz, H. Chem. Rev. 1991,91,1121. (c) Weishaar, J. C. Acc. Chem. Res. 1993,26,213. (2)(a) Irikura, K. K.; Beauchamp, J. L. J . Am. Chem. SOC.1989, 111, 75. (b) Buckner, S. W.; MacMahon, T. J.; Byrd, G. L.; Freiser, B. S. Inorg. Chem. 1989,28, 3511. (c) Ashcroft, T.;Cheetham, A. K.; Foord, J. S.; Green, M. L. H.; Grey, C. P.; Murrell, A. J.;Vernon, P. D. F. Nature 1990,334,319. (d) Stojka, Z.;Herman, R. G.; Klier, K. J . Chem.SOC., Chem. Commun. 1991,185.(e) Irikura, K. IC;Beauchamp, J . L. J . Am. Chem. SOC.1991,113,2769.( f l Irikura, K. K.; Beauchamp, J . L. J.Phys. Chem. 1991,95, 8344. (g) Clemmer, D.E.; Armentrout, P. B. J . Phys. Chem. 1991,95,3084. (h) Capitln, M. J.; Malet, P.; Centeno, M. A.; Munoz-PBez, A,; Carrizos, I.; Odriozola, J . A. J . Phys. Chem. 1993,97,9233. (3)(a)Schilling, J. B.; Goddard, W. A,, 111;Beauchamp, J . L. J . Am. Chem. SOC.1987,109,5573. (b) Rosch, N.;Gorling, A,; Ellis, D. E.; Schmidbaur, H. Angew. Chem. 1989,101,1410;Angew. Chem., Int. Ed. Engl. 1989,28,1357. ( c ) Hill, Y. D.; Freiser, B. S.; Bauschlicher, C. W., Jr. J . A m . Chem. SOC.1991,113,1507. (4)(a) Li,J.; Pyykko, P. Inorg. Chem. 1993,32,2630.(b) Haberlen, 0.D.; Rosch, N. J . Phys. Chem. 1993,97,4970. (5)(a) Fiedler, A.; HruSak, J.; Schwarz, H. Z . Phys. Chem. 1992, 175,15. (b) Magnusson, E.; Moriaty, N. W. J . Comput. Chem. 1993, 8,961. @
experimental findings, provided the basis set is sufficiently flexible and the effects of electron correlation are adequately described, which usually requires sophisticated methods such as multireference configuration interaction (MRCI) or coupled-cluster (CC) technique~.~-~' Much less is known experimentally about metalligand interactions for singly charged second- and thirdrow transition metals, as for example for gold(1) compounds. Wilkins et a1.12reported lower bounds of bond energies for a number of Au+(L) complexes as derived from gas-phase reactions of Au+ with a series of organic compounds and made comparisons with the behavior (6)(a) Mavridis, A.; Herrera, F. L.; Harrison, J . F. J . Phys. Chem. 1991,95,2854.(b) Sodupe, M.; Bauschlicher, C . W., Jr. Chem. Phys. Lett. 1993,212,624. (7)(a) Merchan, M.; Nebot-Gill, I.; Gonzalez-Luque, R.; Orti, E. J. Chem. Phys. 1987,87,1690.(b) Barnes, L.A,; Rosi, M.; Bauschlicher, C. W., Jr. J . Chem. Phys. 1990,93,609. (c) Smith, G. W.; Carter, E. A. J . Phys. Chem. 1991,95,2327. (8)(a) Nicolas, G.; Barthelat, J . C. J . Phys. Chem. 1986,90,2870. (b) Miralles-Sabater, J.; Merchan, M.; Nebot-Gil, I.; Viruela-Martin, P. M. J . Phys. Chem. 1988,92,4853. (c) Nicolas, G.;Spiegelman, F. J . Am. Chem. SOC. 1990,112,5410. (d) Sodupe, M.; Bauschlicher, C. W., J r . J . Phys. Chem. 1991,95,8640. (e) Guo, B. C.; Castleman, A. W., J r . Chem. Phys. Lett. 1991,181,16.(f) Basch, H.; Hoz, T. (private communication) In The chemistry of tripZe bonded functional groups; Patai, S., Ed.; Wiley: New York, Vol. 2,Suppl. C, in press. (9)(a) Alvarado-Swaisgood, A. E.; Harrison, J . F. J . Phys. Chem. 1985,89,2517.(b) Alvarado-Swaisgood, A. E.; Harrison, J . F. J . Phys. Chem. 1988,92,2757. (10)(a) Bauschlicher, C. W., Jr.; Partridge, H.; Sheehy, J. A.; Langhoff, S. R.; Rosi, M. J. Phys. Chem. 1992,96,6969.(b) Bauschlicher, C. W., Jr.; Partridge, H.; Scuseria, G. E. J . Chem. Phys. 1992, 97,7471. (11)(a) Musaev, G. D.; Morokuma, K.; Koga, N.; Nguyen, K. A.; Gordon, M. S.; Cundari, T. R. J . Phys. Chem. 1993,97,11435. (b) Musaev, D.G.; Koga, N.; Morokuma, K. J . Phys. Chem. 1993,97,4064. ( c ) Musaev, D. G.; Morokuma, K. Isr. J . Chem. 1993,33, 307. (d) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J . Phys. Chem. 1994,98,2062. (12)(a) Weil, D. A,; Wilkins, C. L. J . Am. Chem. SOC.1985,107, 7316. (b) Chowdhury, A. K.; Wilkins, C. L. J . Am. Chem. SOC.1987, 109,5336.
0 1995 American Chemical Society
Relativistic Effects in Cationic Au(I) Complexes
of the analogous Cu+ and Ag+ ions. Similar techniques have been applied for the determination and characterization of the bond energy of the elusive gold(1) fluoride13by Schroder et al.14 Here, the predicted bond energy is in excellent agreement with results of ab initio calculations by Schwerdtfeger et al.I5 In addition to the problem caused by correlation energy, systems containing heavy elements (2 > 50) exhibit relativistic effects,16 which have significant influence on physicochemical properties such as bond lengths, energetics, and ionization energies in particular. In fact, for third-row transition metals, the relativistic contributions to the bonding are of the same order as the effects of correlation energy. As pointed out by Pyykko and Desclaux,17relativistic effects reach a local maximum for group 11 compounds within a period of the periodic table. A convenient possibility t o introduce relativistic effects into theoretical approaches is the use of spin-orbit averaged relativistic effective core potentials (RECPs).18 In this paper, the corresponding nonrelativistic potential is denoted as ECP. The relativistic effect (AR) on an atomic or molecular property P is defined as A# = PNR- PR;where PNRis the property as derived from the nonrelativistic (NR) calculation and PR is derived from the scalar relativistic ( R )calculation at a certain level of theory. Whereas a number of theoretical calculations on neutral gold compounds have been performed using a variety of methods (for a review, see ref 16c), so far only a few ab initio studies addressed structures and energetics of cationic gold compounds. The smallest positively charged, diatomic system, i.e., the AuH+ cation, has been studied in great detail,1g-21establishing a theoretical prediction for BDE (Au+-H) in the order of 44 kcallmol. Furthermore, the Au+(PH3) system has been examined at the HF level by Schwerdtfeger et a1.,20aleading to a relativistic BDE of 47 kcallmol, whereas the nonrelativistic bond energy was calculated to 25 kcal/mol only. Recently, Veldkamp and Frenking22 performed MP2 and QCISD(T)calculations on Au+(CO), systems and found the first CO molecule ( n = 1) to be (13) Saenger, K. L.; Sun, C. P. Phys. Rev. 1992, 46, 670. (14) Schroder, D.; HruBak, J.; Tornieporth-Oetting, I. C.; Klapotke, T. M.; Schwarz, H. Angew. Chem. 1994,106, 223;Angew. Chem., Int. Ed. Engl. 1994, 33, 212. (15) Schwerdtfeger, P.; McFeaters, J. S.; Stephens, R. L.; Liddell, M. J.; Dolg, M.; Hess, B. A. Chem. Phys. Lett. 1994,218, 362. (16) (a) Barthelat, J . C.; Durand, P.; Pelissier, M. Phys. Rev. A 1980, 21, 1773. (b) Balasubramanian, K.; Pitzer, K. S. Adu. Chem. Phys. 1987, 67, 287. (c) Pyykko, P. Chem. Reu. 1988, 88, 563. (d) Pisani, L.; Andr6, J.-M.; Andr6, M.-C.; Clementi, E. J . Chem. Educ. 1993, 70, 894. (17) Pyykko, P.; Desclaux, J. P. Acc. Chem. Res. 1979, 12, 276. (18) (a) Durand, P.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (b) Ermler, W. C.; Ross, R. B.; Christiansen, P. A. Int. J . Quantum Chem. 1991, 40,829. (c) Kuchle, W.; Dolg, M.; Stoll, H.; Preuss, H. Mol. Phys. 1991, 74, 1245. (d) Dolg, M.; Kuchle, W.; Stoll, H.; Preuss, H.; Schwerdtfeger, P. Mol. Phys. 1991, 74, 1245. (e) Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J . Chem. 1992, 70, 612. (0 Cundari, T. R.; Stevens, W. J. J . Chem. Phys. 1993, 98, 5555. (19) (a) Ohanessian, G.; Brusich, M. J.; Goddard, W. A,, I11 J . Am. Chem. Soc. 1990, 112, 7179. (b) Ohanessian, G.; Goddard, W. A,, I11 Acc. Chem. Res. 1990, 23, 386. (c) Ishikawa, Y.; Malli, G. L.; Pyper, N. C. Chem. Phys. Lett. 1992, 194, 481. (20) (a) Schwerdtfeger, P.; Dolg, M.; Schwarz, W. H. E.; Bowmaker, G. A.; Boyd, P. D. W. J . Chem. Phys. 1989,91, 1762. (b) Schwerdtfeger, 1989,111,7261. (c) Schwerdtfeger, P.; Boyd, P. P. J.Am. Chem. SOC. D. W.; Burrell, A. K.; Robinson, W. T.; Taylor, M. J. Inorg. Chem. 1990, 29,3593. (d) Ishikawa, Y.; Malli, G. L.; Pyper, N. C. Chem. Phys. Lett. 1992,194,481. (21) A recent relativistic MR-CCSD approach leads to BDE(Au+H) = 45.2 kcalimol: Kaldor, U.; Hess, B. A,, private communication. (22) Veldkamp, A.; Frenking, G. Organometallics 1993, 12, 4613.
Organometallics, Vol. 14, No. 3, 1995 1285 bound by 45 kcdmol. Further, HruS6k et al.23reported CCSD(T) calculations on the Au+(HzO)complex, possessing a nonplanar geometry with a BDE of 36 kcal/ mol. Most recently, Basch and Hozsfcomputed the BDE of Au+(C2H4)as 71.2 and 62.5 kcal/mol at the MP2 and QCISD(T)//MP2levels, respectively. In a previous we used the radiative association reaction of bare Au+ cations with hexafluoroben~) zene (eq 1) for the formation of the A u + ( C ~ Fcomplex
in the low-pressure regime of a Fourier-transform ion cyclotron resonance mass spectrometer. Due to the relatively small bond dissociation energy O f AU+(csFs), this complex can be used as a versatile precursor for the generation of other Au+(L)complexes by subsequent ligand-exchange reactions. Ion-molecule reactions employing the bracketing technique provided a relative gold(1)cation affinity scheme for the various ligands L, which follows the order C6F6 < H2O < CO < C2H4 = C6H6 X NH3 C3H6 < C4H6.24 Here, we report a computational study of the cationic complexes of Au+ with the small ligands CO, HzO, NH3, and C2H4. The principal aims of this study are to evaluate the BDEs at a uniform level of theory and to discuss the relativistic effects on the energetics and structures of these cationic species. In addition to the standard ECP and RECP ab initio calculations performed at the SCF as well as correlated levels, approximate density functional theory (DFT)25has been applied, where relativistic effects were either accounted for through the use of a RECP or through an explicit quasirelativistic approach. Recently, it has been shown that gradient-corrected DFT methods can give accurate binding energies for both main-group and transitionmetal systems.26 The inclusion of DFT methods is of particular interest in order to obtain further information on the performance of these methods in the theoretical description of bare metal-cation complexes with respect t o the relativistic effects.
Theoretical Methods Ab initio calculations have been performed by employing the GAUSSIAN92 program.27 For the gold atom we used the multi-electron adjusted relativistic (RECP) and nonrelativistic (ECP)effective core potentials derived by Schwerdtfeger et a1.20 covering 60 electrons ([Kr14d1O4P4).The original basis set was augmented by additional diffuse and polarization function^.^^^^^ resulting in a [lOs/8p/7d/lfY(9~/5p/6d/l~ basis set for both the relativistic and nonrelativistic calculations. For the other atoms we used Dunning TZ2P basis setsz8with an additional f-polarization function (af= 1.85)for the oxygen, nitrogen, and carbon atoms, i.e., the [lOs/6p/2d/lfl/(5~/3p/2d/l~ contraction (23) HruSbk, J.; Schroder, D.; Schwarz, H. Chem. Phys. Lett. 1994, 225, 416. (24) Schroder, D.; HruSak, J.; Hertwig, R. H.; Koch, W.; Schwerdt-
feger, P.; Schwarz, H. Organometallics, in press. (25) Ziegler, T. Chem. Reu. 1991, 91, 651. (26) (a) Tschinke, V.; Ziegler, T. Theor. Chim. Acta 1991, 81, 65. (b) Becke, A. D. J . Chem. Phys. 1992, 96, 2155. (27) GAUSSIAN92-DFT Rev. F.2 Frisch, M. J.; Trucks, G. W.; Schlegel, H. W.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN Inc.: Pittsburgh, PA, 1992. (28)Feller, D.; Davidson, E. P. In Reviews in Computational Chemistry; VCH Publishers: New York, 1990; Vol. I.
HruScEk et al.
1286 Organometallics, Vol. 14, No. 3, 1995 scheme. For hydrogen atoms, a [5~/2p/ld1/(3~/2p/ld) contracted basis set was used. The RECP corrects due t o the parametrization procedure only for the relativistic Darwin and mass velocity terms. The spin-orbit interaction (SO) is not included. However, since all the systems under study are closed shell singlets, resulting from the gold (IS)interaction with singlet ligands, the SO contribution to the bond energy is zero. Full geometry optimizations have been performed by using standard procedures at the SCF and MP2 levels of theory for both the relativistic and nonrelativistic approaches. Further improvement of the geometries was obtained by optimization at the CCSD(T)level of theory; here, the 1s electrons of oxygen, carbon, nitrogen, and also the 5s and 5p electrons of gold were kept frozen in the CC calculations. Due t o the technical limitations, no CCSD(T) geometry optimization for AuYCzH4) and Au+(NH3)was possible, and we restricted ourselves to the MP2-optimized geometry in the CCSD(T) energy calculation. However, as can be seen from the comparison of optimized geometries for the other ligands (vide infra), the MP2 and CCSD(T) computed structures do not differ substantially. Furthermore, since all systems under study correspond to closed-shell singlets, it can be assumed that a limited perturbational treatment such as MP2 should be a sufficient approach t o account for the correlation effects on the geometriesZ2For the same reasons, the harmonic frequencies have been calculated at the MP2 level of theory only. The DFT calculations were carried out using the Amsterdam density functional (ADF) suite of programsz9 with the innershell electrons ([He] for C, 0, N, and [Xe]4P4for Au) treated in the frozen core a p p r o ~ i m a t i o n The . ~ ~ valence orbitals were expanded as linear combinations of Slater-type basis functions. Triple-5 basis sets with additional polarization functions on carbon, oxygen, nitrogen, and hydrogen were used throughout, while for the gold atom a triple-5 basis set was employed. All molecular and atomic energies were calculated using the local spin density approximation (LDA) with Slater’s exchange functional and the Vosko-Wilk-Nusair parametrization ( V W N I 3 I on the homogeneous electron gas for c o r r e l a t i ~ n , ~ ~ augmented by BeckeY3 and Perdew’s3*(BPI gradient corrections for the exchange and correlation potential, re~pectively,~~ this method will be referred to as ADFBP. In the ADFBP scheme, relativistic effects on the electronic structures were evaluated by using the quasi-relativistic approach of Ziegler et al.36 This leads to a quasi-relativistic SCF procedure, resulting in quasi-relativistic densities and corresponding energies, which involves the sum of the relativistic Darwin and mass velocity operators. Applications of this quasi-relativistic m e t h ~ d o l o g yhave ~ ~ demonstrated that it can be successfully employed to investigate relativistic effects on bonding; this holds true in particular for third-row transition metals and heavier elements for which relativistic influences on the valence density become essential.16 Since our ADF program implementation does not allow a gradientoriented geometry optimization within the relativistic treatment, only the gold ligand distance was optimized by a series (29) ADF (version 1.0.2): (a) Baerends, E. J.; Ellis, D. E. Chem. Phys. 1973,2,71. (b) teVelde, G.; Baerends, E. J. J . Comput. Phys. 1992, 99,84, and references cited therein. (30) Snijders, J . G.; Baerends, E. J. Mols. Phys. 1977,33,1651. (31) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J . Phys. 1980,58,1200. (32) Parr, R. G.; Yang, W. Density Functional Theory ofAtoms and Molecules, Oxford University Press: New York, 1989. (33) Becke, A. D. J . Chem. Phys. 1986,84,4524. (34) Perdew, J. P. Phys. Rev. B 1986,33,8822. (35) Levy, M.; Perdew, J. P. Int. J . Quantum Chem. 1994,49,539. (36) (a) Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. G.; Ravenek, W. J . Phys. Chem. 1989,93,3050. For earlier relativistic calculations by these authors, see: (b) Snijders, J. G.; Baerends, E. J . Mol. Phys. 1978,36, 1789. ( c ) Snijders, J. G.; Baerends, E. J.; Roos, P. J . Mol. Phys. 1979,38, 1909. (d) Ziegler, T.; Snijders, T. G.; Baerends, E. J. J . Chem. Phys. 1981,74, 1271. (37) van Wezenbeek, E. M.; Baerends, E. J.; Snijders, J . G. Theor. Chim. Acta 1991, 81,139.
of single-point calculations, while the ligand substructure was kept frozen at the nonrelativistic geometry. For the analysis of the different contributions to the bonding, the decomposition scheme developed by Morokuma, Ziegler, and co-workers3*was employed: The total binding energy BDE is expressed as the sum of the steric interaction AEsteric and the orbital interaction The orbital interaction term AEOI contains all contributions arising from donor-acceptor interactions as well as the relaxation of the individual fragments due t o the presence of the bonding partner. In order to check the suitability of standard ab initio ECP parametrizations in density functional approaches, relativistic and nonrelativistic DFT calculations have been performed with the GAUSSIAN92-DFTZ7 program by using both the RECP and ECP augmented with basis sets as described above. In these calculations we employed the ECP and RECP, respectively, and a hybrid HF-DFT method, in which the exchange functional consists of a mixture between HF and LDA exchange corresponding to a three-parameter fit according to Becke. The correlation functional uses a combination of the nonlocal functional derived by Lee, Yang, and Parr40 and the local correlation functional from the homogeneous electron gas. In analogy to the GAUSSIAN keyword, this semiempirical hybrid method will be referred t o as B3LYP. Most recently, Pople and c o - ~ o r k e r shave ~ ~ shown that for main-group elements B3LYP reproduces physical properties of polyatomic molecules with accuracy (i.e., &2 kcavmol) similar to the G2 contraction scheme.4z In addition, we performed test calculations with the GAUSSIAN92-DFT program using the following: (i) the BP method mentioned above; however, instead of the quasirelativistic approach of ADF, the RECP was applied; (ii) Becke’s three-parameter fit and the VWN functional for correlation (to be referred as B3P); and (iii) for Au+(H20),we also performed geometry optimization on the CISD level of theory.
Results and Discussion Atomic gold assumes a 2S1,~(dlosl),while the cation has a ‘SO (dlOsO) ground state. The experimental ionization energy (IE) of gold amounts to 9.225 eV,43whereas the calculations result in 8.54 (CCSD(T)/RECP),8.61 (MPBRECP), and 9.34 eV (B3LYPRECP). As far as these discrepancies are concerned, we refer to previous studies,44which have shown that polarization functions of higher Z-quantum number (i.e., g-type functions in the case of Au) are needed in order t o describe the IEs with an accuracy better than 0.2 eV. With respect to the species of interest, Le., Au+(H20), Au+(CO),Au+(C2H4),and Au+(NH3),our previous experimental study revealed the following:24Whereas the BDEs of Au+(H20) and Au+(CO) are moderate and within the range of the BDE values for first- and secondrow transition-metal cations, the BDEs of Au+(NH3)and (38)(a) Kitaura, K.; Morokuma, K. Int. J . Quantum Chem. 1976, 10,325. (b) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977,46,1. (39) Becke, A. D. Phys. Rev. A 1988,38,3098. (40) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988,37,785. (41) Gill, P. M. W.; Johnson, B. G.; Pople, J. A. Chem. Phys. Lett. 1992,197,499. (42) (a) Pople, J . A,; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtis, L. A. J . Chem. Phys. 1989,90,5622. (b) Curtis, L. A.; Raghavachari, K.; Jones, C.; Trucks, G. W.; Pople, J . A. J . Chem. Phys. 1990,93,2537. (43) Additional thermochemical deta were taken from: (a) Lias, S. G.; Bartmess, J . E.; Liebman, J . F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J . Phys. Chem. Ref. Data 1988, 17,Suppl. 1. (b) Moore, C. E. Atomic Energy Levels; National Standard Reference Data Series; National Bureau of Standards: Washington DC, 1971; NSRDS-NBS 35. ( c ) Herzberg, G. Electronic Spectra and Electronic Structure of Polyatomic Molecules; Van Nostrand: New York, 1966. (44) (a)Bauschlicher, C. W. Jr., J . Chem. Phys. 1987,86,5591. (b) Schwerdtfeger, P. Chem. Phys. Lett. 1991,183,457.
Relativistic Effects in Cationic Au(Z) Complexes
Organometallics, Vol. 14, No. 3, 1995 1287
Table 1. Geometries (r in bi, angles in degrees) and Bond Dissociation Energies (kcaVmol) for Au+(OH*) r(Au-0) r(0-H)
a(Au-O-H) 86
BDE
R NR R NR R NR R NR R NR
SCF
MP2 CISD CCSD(T)a ADF/BP B3LYP
2.306 2.505 0.944 0.944 126.0 126.7 180.0 180 25.9 21.4
2.132 2.377 0.964 0.963 118.8 127.1 133.3 180 38.8 25.5
2.133
2.158
0.964
0.964
119.9
119.9
133.3
133.3
38.5
35.9
2.175 1.992 0.997 0.997 113.5 113.5 125.9 180 41.2 4.7
2.198 2.397 0.968 0.964 117.4 119.9 131.0 180 37.0 23.6
Only the r(Au-0) distance optimized at the CCSD(T) level; the geometry of the water ligand is frozen at the CISD geometry.23 The planar structure is a TS at the quasi-relativistic MP2 and B3LYP levels (bl i270 cm-I).
*
particularly Au+(C2H4)are much higher as compared t o their group 11 congeners Cu+ and Ag+. Unfortunately, the ion-molecule reaction bracketing technique did not allow a precise evaluation of experimental bond energies, since these were either too large or accurate thermochemical reference data were not known. However, it was observed experimentally that ethene is capable of replacing not only the benzene ligand in Au+(CsHs),but also the covalently bound iodine in AuI+ to yield Auf(C2H4). The latter observation implies that BDE (Auf-C2H4) exceeds 59 kcal/mol.12 In contrast, ~ ) Ag+(C2H4)are 36 and 34 the BDEs of C U + ( C ~ Hand kcavmol, respectively.8 These results further emphasize that relativistic effects are essential in gold(1)chemistry. In the following sections, we first address the computational results for each species separately and then discuss the interplay of relativistic and correlation effects on structures and energetics. In addition, we compare our theoretical results to some experimental findings to shed more light on the accuracy of our computational approach. Au+(HzO). Table 1 summarizes the results for the cationic gold-water complex. As stated in our previous study, the relativistic MP2/RECP calculation^^^ predict the complex to deviate from planarity by 49”. The planar structure was found to be a transition structure with an imaginary frequency of i270 cm-l, being less stable by 3.1 kcaVmol than the corresponding minimum. The nonplanarity of this system can be attributed to the relativistic stabilization of the gold 6s orbital leading t o a relatively high ionization energy (9.225 eV) as compared to Cu (7.726 eV) and Ag (7.576 eV), resulting in a larger covalent contribution t o the bonding in Au+(HzO). In terms of the Lewis acidity, this high ionization energy forces a significant electron transfer from H2O toward Au and thus, in analogy t o H30+, a rehybridization of the water ligand leads t o the nonplanar structure. The fact that the distortion (CzUto C,) of Au+(H20) is caused by relativistic effects is verified by the results of an MP2 geometry optimization using the nonrelativistic ECP, which predicts a planar C2,-sy”etrical structure as the minimum (Table 1). Furthermore, the relatively long Au-0 distance of 2.377 A obtained in the nonrelativistic scheme is in line with the mainly electrostatic nature of the interaction and is reflected by the low stabilization energy of only 25.5 kcaYmo1. When the RECP is applied, the geometrical changes of Au+(HzO) are quite small when either the MP2,
CISD, or CCSD(T) methods is used for the geometry optimization, whereas on the SCF level, the Au-0 distance is lengthened significantly. Furthermore, it is not surprising that the largest differences are observed for the Au-0 distance (Ar = 0.025 A), while the ligand geometry is only slightly changed. However, the magnitude of these geometry differences indicates that all theoretical approaches beyond SCF suffice for the geometry optimization of the gold(1) water complex. A similar conclusion applies for the DFT methods: The RECP-based B3LYP density functional predicts a nonplanar Au+(H20) structure which is very close to the CCSD(T)results. The Au-0 distance is slightly elongated from 2.158 to 2.198 A, and the ligand substructure is almost unperturbed. The deviation in the Au-0 bond length (Ar = 0.040 A) by using the B3LYP method (as compared t o CCSD(T))is probably caused in the evaluation of the correlation by the LYP f u n ~ t i o n a lsince ,~~ a test calculation using the B3PRECP procedure, where the correlation effects are described by a different functional, predicted the Au-0 bond length to be shorter (2.167 A) as compared to B3LYP. The results of the nonrelativistic ADF/BP calculation lead to erroneous data: Similar to the other nonrelativistic approaches, the optimized Au+(H20) structure is planar; however, the optimized Au-0 distance is much too short as compared to other methods (Table 1). Further, according to the NR calculation, the stabilization energy is only 4.7 kcaYmo1. This failure of the ADF program for the nonrelativistic Au+(H20) structure can most likely be traced back to the implemented optimizer which is not capable to deal with potential energy surfaces that are very flat, such as here. As a consequence, numerical problems hamper the geometry optimization procedure. However, as compared to the other relativistic approaches, the salient geometrical features of the Au+(H20) complex are well reproduced by the quasi-relativistic ADF/BP method. With respect to the nonrelativistic computation, the Au-0 bond is significantly elongated (2.175 A)and differs by only 0.017 A as compared to the CCSD(TIRECP calculation. In addition to the geometries, a uniform picture can be deduced for the BDEs from the data in Table 1. Independent of the method used for the electron correlation treatment, the bond energies scatter around the CCSD(T)value of ca. 36 kcdmol, with a slight tendency for overbinding as compared to CCSD(T). The difference between MP2- and CCSD(T)-calculatedBDEs is small (2.9 kcaYmol), and the values compare well also to the B3LYP/RECP results. A slightly larger deviation as compared to the CCSD(T) result (35.9 kcaYmo1) is calculated with the quasi-relativistic ADFBP density functional method (41.2 kcaYmo1). In fact, it is wellknown from previous studies that this method tends to overestimate stabilization e n e r g i e ~ . Note, ~ ~ , ~however, ~ that the NR values are severely too low, further emphasizing that the inclusion of relativistic effects is essential in the evaluation of the energetics of gold compounds.17 Au+(CO). Ligand-exchange experiment^^^ have demonstrated that the CO molecule exhibits a larger gold(I) affinity than H2O. This finding is in agreement with the QCISD(T)//MP2-calculatedrelativistic bond energy for AuYCO) of 45.1 kcaYmol as reported by Veldkamp
1288 Organometallics, Vol. 14,No. 3, 1995
HruSak et al.
Table 2. Geometries (r in A, angles in degrees) and Bond Dissociation Energies (kcdmol) for Au+(CO) SCF r(Au-C) r(C-0) a(Au-CO) BDE
MP2
MP2a CCSD(T) ADFiBP B3LYP
R 2.175 1.907 1.975 NR 2.679 2.347 R 1.088 1.125 1.143 NR 1.092 1.125 R 180 180 180 NR 180 180 R 18.5 50.1 45.1 18.9 NR 8.4
1.954 1.119 180 44.1
1.890 2.249 1.125 1.125 180 180 59.5 18.4
1.972 2.396 1.113 1.113 180 180 43.6 18.0
Data taken from ref 22. A single-point calculation with an additional f-polarization function leads to BDE (Au+-CO) = 51.1 kcal/mol.
and Frenking.22 These authors used the relativistic effective core potential parametrization of Hay and Wadt,45 a slightly smaller basis set on gold, and the 6-31G(d) basis set on C and 0 atoms, such that the differences (especially in the CO bond length) can be attributed to basis set effects and the different RECP parameters used. For comparative purposes, the results of their calculations are also included in Table 2, which contains our theoretical predictions. Both, the relativistic and nonrelativistic calculations result in linear C,,-symmetrical structures46for Au+(CO); however, the relativistic changes in the Au-C bond lengths are significant. For example, at MP2 the relativistic contraction of the Au-C bond (ARr = 0.440 A) is much lar er as compared to the Au+(H20)complex (ARr = 0.245 ) and is also accompanied by a sizable stabilization ( A d = 31.2 kcaymol). Similar to the Au+(H2O) case, the relativistic B3LYF' density functional method predicts a slightly longer Au-L distance (1.972 A) as compared t o the CCSD(T) result (1.954 A). By using the complementary density functional (ADF/BP), the relativistic Au-C bond distance is calculated shorter (1.890 A) as compared t o the RECP-based CCSD(T)and B3LYP methods; however, these geometry changes are within the computational error of the methods as indicated by the comparison of the Au-C bond lengths obtained with the MP2 approach described in ref 22 and our MP2 results. The C-0 bond length as calculated using different correlated methods compare well within 0.01 A; the slight increase of the C - 0 bond distance in the previous study22is probably due to basis set effects (vide supra). Because our ADFBP calculation is an entirely different approach (Slater orbitals, a direct evaluation of the mass velocity and Darwin terms), the agreement in structure is a further verification for the reliability of the present results. When RECPs are used, the binding energy of Au+(CO) converges at CCSD(T) and B3LYF'to 44 kcaymol; this is also in agreement with the QCISD(T)/RECP// MP2/RECP value of 45.1 kcal/mol given in ref 22. In contrast, the BDE (Au+-CO) is calculated as 59.5 kcal/ mol by using the quasi-relativistic ADF/BP method; i.e., the ligand seems to be strongly overbound. As mentioned above, the same tendency holds true in the comparison of the calculated BDEs for the Au+(H20) complex. Finally, in the comparison of the results for Au+(HzO)and Au+(CO),it becomes apparent that the interplay between correlation and relativistic effects is very different for both gold(1) complexes. These differ-
1
(45)Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985,82,299. (46) Schwerdtfeger, P.; Bowmaker, G . A. J . Chem. Phys. 1994,100, 4487.
Table 3. Geometries (r in A, angles in degrees) and Bond Dissociation Energies ( k d m o l ) for Au+(C,&) r(Au-C) r(C-C) r(C-H) a(C-C-H) B(H-CC-H) BDE a
R NR R NR R NR R NR R NR R NR
SCF
MP2
CCSD(T)a
ADFBP
B3LYP
2.381 2.690 1.356 1.331 1.074 1.075 120.9 121.4 169.5 173.6 34.5 12.3
2.098 2.451 1.402 1.358 1.077 1.080 119.9 120.8 162.7 171.2 73.1 30.2
2.098
2.070 2.395 1.365 1.365 1.097 1.097 121.1 121.1 169.9 169.9 70.0 26.0
2.231 2.582 1.390 1.351 1.083 1.083 120.7 121.3 165.8 171.6 68.6 27.2
1.402 1.077 119.9 162.7 68.8
Calculated at the MP2-optimized geometry.
ent contributions of relativistic and correlation effects on the structure and energetics of Au+(CO)as compared to Au+(H20) and other complexes are probably due to the different nature of the bonding in Au+(CO),as will be discussed below. Au+(C2&). Neutral Au(C2H4) has been recently studied by Nicolas and Spiegelmanscin the context of a comparison with the analogous copper and silver M(C2I14) complexes (M = Cu, Ag, Au). It has been found that all three systems possess CzUsymmetrical minima with weakly bound (ca. 12 kcaymol) 2A1 ground states. Miralles-Sabater et a1.8bperformed CI calculations on Cu+(C2H4)and Ag'(C2H4) complexes and found that the bonding can be described mainly in terms of electrostatic forces. In contrast, Guo and CastlemanBedetermined by a combination of mass spectrometric experiments and theoretical calculations the BDE of Ag+(C2H4)as 33.7 kcal/mol and argued that the interaction should have a large covalent contribution. As mentioned above, our previous experimental study demonstrated that the BDE (Au+-C~H~) is surprisingly high and is almost twice that of the analogus copper and silver complexes.24 Most recently, Basch and Hozsf reported a BDE of 62.5 kcaYmol for the Au+(C2H4)complex by using a QCISD(T)/RECP//MP2/RECPmethod, which could also reproduce the experimental binding energies of Cu+(C2H4) and Ag+(C2H4). The results of our calculations (Table 3) support these previously reported findings. For example, at the highest level of theory applied, i.e., CCSD(T),the bond dissociation energy of Au+(C2H4)is calculated as 68.8 kcallmol, indicating a much larger gold(1) aflnity of C2H4, as compared t o H20 and CO. Furthermore, the computed BDE (Au+-C2H4) agrees well with the lower bound of 59 kcaymol as derived from the displacement of the iodine ligand in AuI+ by ethene24and is slightly higher then the QCISD(T)value.8f As far as structural features of Au+(CzH4) are concerned, most of the conclusions drawn for Au+(H20)also hold true. For example, the relativistic MP2 and ADF/ BP geometries agree quite well with each other, whereas the B3LYP functional leads to a somewhat longer bond distance to the ligand, e.g., r~,-c(MP2) = 2.098 A and rA,-c(mF/BP) = 2.070 A versus r~,-c(B%w) = 2.231 A. Albeit the geometry was optimized with restriction to CzU symmetry, at all levels of theory applied, frequency analyses reveal that these structures are indeed true minima (Table 4). Whereas the ligand substructures in Au+(H20)and Au+(CO)were found to be hardly perturbed by the presence of the Au+ cation, in the Au+-
Organometallics, Vol. 14,No. 3, 1995 1289
Relativistic Effects in Cationic Au(I) Complexes Table 4. Calculated Harmonic Frequencies (cm-l) for Au+(CdL) mode
MP2"
BPb
ADF/BPC
B3LYP
b2 ai bi bi a2 bz ai
37 1 350 667 832 1053 1073 1099 1232 1260 1488 1575 3187 3174 3272 3289
346 356 605 842 1013 1068 1083 1232 1280 1482 1571 3136 3 140 3227 3245
445 45 1 590 679 763 924 1146 1268 1307 1676 1907 2908 2918 3123 3132
317 322 620 812 932 1037 1051 1183 1223 1428 1503 3053 3054 3 145 3162
a2
al bz ai bz ai a2 bi
a Calculated by Basch and Hoz using a relativistic potential (ref 8f; private communication). Calculated with the GAUSSIAN program using the RECP. Calculated with the ADF program in the quasi-relativisticscheme.
(C2H4) complex the C-C bond distance is elongated significantly as compared to free ethene (MP2,1.336 A; experimental, 1.339 A43c)and the ethene substructure is pyramidalized significantly (OHCCH (MP2) 17.31, indicating covalent contributions to the bonding in terms of the formation of a metallacy~lopropane.~~ A plausible explanation for the large distortion of the ligand is the relativistically increased donation-back-donation interaction as proposed in the Dewar-Chatt-Duncanson Both components of this electron transfer (i.e., the donation of the n electrons of ethene into an sp or sd hybrid of Au and the back-donation of the 5d electrons into the n* orbital) lead to a weakening of the C-C double bond. Moreover, the small energy gap (AIE = 1.28 eV) between the gold 6s orbital (IE = 9.225 eV) and the ethene n orbital (IE = 10.51 eV) result in significant charge transfer from the ethene t o the gold; this is also reflected in the Mulliken population analysis in which the partial positive charge of the gold atom is only 0.58.24 This charge transfer also accounts for the significant stabilization of Au+(CzH4) as compared t o Cu+(CzH4)(AIE = 2.78 eV) and &+(C2H4) (AIE = 2.93 eV), which cannot be explained by geometrical arguments only. The large relativistic distortion of the C2H2 =P7.5") ~) moiety (Awc-c(MP2) = 0.044 A,A R ~ H C C H ( M can be viewed as a further verification of this proposed interaction scheme. Except for the SCF result, the BDE (Au+-C2H4) is ca. 70 kcaVmol at all levels of theory, when relativistic contributions are included. In contrast, the nonrelativistic BDEs are only of the magnitude of an electrostatic interaction. The relativistic effects are also quite large as far as geometry is concerned; for exam le, the relativistic bond contraction ARrAu-c is 0.353 f f a t the MP2 level of theory concomitant with an increase of the BDE from 30.2 (ECP) t o 73.1 kcaVmol (RECP), i.e., a relativistic stabilization of A d = 42.9 kcaVmol. In fact, it becomes apparent that the relativistic bond amplification even exceeds the effect of electron correlation. As mentioned above, the differences between the optimized (47) Spackman, M. A. J . Phys. Chem. 1989,93,7594. (48)(a) For the formation of metallacycles in gas-phase ionmolecule reactions, see: Jacobson, D. B.; Freiser, B. s.Organometallics 1983,3, 513. (b) For theoretical aspects, see: Swanstrom, P.; J0rgensen, K. A. J. Chem. SOC.,Dalton Trans. 1990,115. (49) (a) Dewar, M. J. S. Bull. SOC.Chim. Fr. 1961, C79, 18. (bj Chatt, J.; Duncanson, L. A. J . Chem. SOC.1953,2939.
Table 5. Geometries (f in A, angles in degrees; optimized in C3J and Bond Dissociation Energies (kcal/mol) for Au+(NH3) r(Au-N) r(N-H) a(Au-N-H) BDE
R NR R NR R NR R NR
SCF
MP2
2.194 2.486 1.002 1.002 111.4 112.3 42.2 27.5
2.028 2.322 1.014 1.013 110.6 112.3 68.6 37.7
CCSD(T)" ADFIBP 2.028 1.014 110.6 65.3
2.062 2.325 1.026 1.026 111.0 111.0 72.5 36.0
B3LYP 2.103 2.392 1.018 1.016 110.3 111.9 63.5 38.1
Calculated at the MP2-optimized geometry.
geometries of Au'(Hz0) and Au+(CO) at the various levels of theory applied (except SCF) are small. Thus, we refrained from a complete geometry optimization of Au+(CzH4)in the CCSD(T) calculations. Furthermore, it was not possible to perform a complete geometry optimization at the quasi-relativistic ADF level, and therefore, we varied only the Au-C distance and kept the geometry of the ethene moiety frozen at the nonrelativistic optimized geometry. In order t o estimate the error made, we performed a single-point ADF/BP calculation at the MP2RECP-optimized geometry. The bond energy calculated in such a way is 70.3 kcaVmol as compared to 70.0 kcaVmo1 listed in Table 3. Within this context, it is worth mentioning that the apparent overbinding obtained for Au+(HzO)and Au+(CO)with the ADF/BP approach is not present for the Auf(C2H4) complex. Finally, we note that the harmonic frequencies of Au+(CZH4), as obtained via three different DFT approaches, are in reasonable agreement with each other (Table 4) and compare quite well with the MP2RECP values as well as the data reported in ref 8f. Thus, the nonclassical n-bridged structure is a real minimum on the potential energy surface of Au+(CzH4). Due to the high polarizability of ethene, which gives rise to the ioninduced-dipole interaction, other coordinations (i.e., inplane bridging structure or the classical o-bound system) could also be possible; however, the large quadrupole moment4' of CzH4 should lead to a large ion-quadrupole interaction and thus favor the n bridging.8f However, the low frequencies associated with the Au+-(C2H4) motion indicate a flat PES for the movement of Au along the C-C axis, and the search for other minima would need further investigations. Au+(NI&). The results for the Au+(NH3)complex are listed in Table 5; as mentioned above, the CCSD(T) energy was obtained in a single-point calculation at the MP2 geometry. Furthermore, the geometry has been optimized under the restriction of C3v symmetry; however, a subsequent frequency analysis proved the CsV structure to be a minimum. As found for the other gold(1) complexes, the structural parameters of Au+(NH3)optimized by using different methods are in good agreement with each other. Once again, B3LYF' slightly overestimates the Au-N bond length as compared to the other computational approaches; i.e., ~A,-N(B~LYP) = 2.103 A versus r ~ , - ~ ( M p 2= ) 2.028 A and rAU-N(mF/BP)= 2.062 A. The relativistic bond contraction Aw is still substantial, and ranges from 0.26 and 0.29 A,depending on the level of theory used. As far as the binding energies are concerned, the BDEs of Au+(NH3)scatter around the CCSD(T) result
HruSak et al.
1290 Organometallics, Vol. 14, No. 3, 1995 of 65 kcaymol; similar to Au+(CzH4),no overestimation of the BDE by the ADF/BP method takes place. Although the computed BDEs of Au+(CzH4)and Au+(NH3) are quite close t o another, the different nature of the bonding already becomes apparent in the comparison of nonrelativistic and relativistic calculations: Due to the dipolar character of ammonia, the ion-dipole interaction between Au+ and NH3 is quite large, such that even BDE (SCF/NR) is 27.5 kcaVmol and this effect further increases upon inclusion of correlation. However, the relativistic stabilization of the Au+-NH3 bond is still substantial, e.g., AG(MP2) = 30.9 kcaVmo1. As outlined above, part of this relativistic stabilization is due to electron transfer from amonia (IE = 10.16 eV) to the gold atom (IE = 9.225 eV); this is also evidenced by the partial positive charge of the gold atom, i.e., 0.63 according to Mulliken population analysis.24 Albeit the computed BDE for Au+(NHd is quite large, it is somewhat smaller than Au+(C2H4)for all but the ADF/BP method. For example, at the MP2 level of theory, the computed AAE (0 K) for the ligand exchange reaction of Au+(NH3)with ethene (eq 2)is +4.5 kcdmol,
+
Au+(NH3) C,H4
-
+
Au+(C2H4) NH3
(2)
and converting this value to AAG (298 K) does not affect the relative computed gold(1)affinity scheme at all; i.e., AAG (298 K) = +4.5 kcaymol, since the AAH and A A S terms cancel each other. The CCSD(T) and B3LYP calculations predict similar AAE values for the ligandexchange reaction 2 (+3.5 and f 5 . 1 kcaymol, respectively), whereas the ADF/BP procedure results in a reverse value of AAE = -2.5 kcaumol. Experimentally, it was found that ammonia exhibits a larger gold(1) affinity than ethene, i.e., BDE(Au+NH3) =- BDE(Au+-C2Hd, and measurement of the thermal equilibrium constant resulted in AAG = -2.3 kcaymol for the ligand-exchange reaction 2. As far as the relative gold(1) affinities of the ligands are concerned, only the ADF/BP approach predicts the same order as found experimentally, i.e., Hz0 < CO < C2H4 < NH3, whereas the other methods lead to the reverse order for ethene and ammonia. Relativistic Effects. A problem often addressed in the literature is the question of the interplay of relativistic andlor correlation energy contributions t o the bonding in heavy element containing systems.44a It is an accepted fact that both effects are important and lead t o significant bond stabilization. In order to evaluate both effects, often the additivity assumption (eq 3) is made. Eorr
= E L + @om
(3)
According to this approach, the total relativistic energy Et, can be obtained from the uncorrelated relativistic energy ERCFby adding the correlation energy contribution A EBOm. To a first approximation, one can assume that AE:, = AEEE and the latter term is easily derived from a nonrelativistic ab initio calculation by using any correlated method. Using this additivity assumption, it seems to be trivial to compute that total energies as E A d d (eq 4). (4)
However, the errors made by neglecting the relativistic effects on the correlated wave function can be large. Moreover, recently it has been demonstrated for group 11 dipole polarizabilities that relativistic and electron correlation contributions are not additive.46 In order to analyze this in more detail for the Au+(L)systems, we have calculated the different contributions t o the bond energy by using the advantages of the ECPRECP approach. For the purpose of this study we modified eq 3 to obtain eq
For all closed-shell ions under study, it can be assumed that the uncorrelated relativistic effect on the energy (ARE; eq 6) can be calculated from the difference of the SCF energies by use of the relativistic and nonrelativistic effective core potentials.
ARE = E!&F - Et&
(6)
On the other hand, the pure nonrelativistic correlation energy contribution (Aco,E) can be evaluated by use of the nonrelativistic wave function (eq 7).
(7)
As can be seen from a comparison of MP2-, CCSD(TI-, and B3LYP-calculatedBDEs values, the correlation energy is sufficiently described even at the MP2 level; thus, we use the ECP/MP2 data for the evaluation of Aco,ENR. The last term in eq 5 (Ami&) contains the relativistic effect on the correlation energy contribution. Assuming that correlation and relativistic effects are independent of each other and additive, the total energy can be obtained in a first approximation by setting A m k E = 0, thus eq 5 becomes equal to eq 4 leading t o E a d d = R
EC0l-I.
The contributions of the various effects to the BDEs of the Au+(L)complexes are displayed in Figure 1. As can be seen for Au+(H20),even the nonrelativistic SCF computation describes the predominantly electrostatic nature of the bonding qualitatively correct and accounts for 60% of the BDE as compared to the CCSD(T)value. As a consequence, the relativistic and correlation effects on the BDE are quite small, whereas the bond length contraction remains substantial (vide supra). In contrast, for Au+(CO),Au+(NH3),and Au+(C2H4)electron correlation and relativistic effects are much more important. For example, the contributions of ARE and AcorrENRto the total binding energy of Au+(C2H4)are 22 and 18 kcaymol, respectively. However, as can be easily seen in Figure 1, the evaluation of the BDE in terms of E a d d underestimates the bonding substantially. In fact, for Au+(CzH4),the relativistic contribution to correlation energy AmixE represents 28% of the total binding energy. Similar conclusions can be drawn for Au+(NH3),and for Au+(CO)the weight of AmixEis even more pronounced (42% of the BDE). As a consequence, the determination of BDE by combining a relativistic SCF calculation with a nonrelativistic treatment of correlation is obviously inadequate. Finally, it is evident from Figure l that the relativistic MP2 method tends to overestimate the bond energies as compared t o CCSD(T) and B3LYP; however, an ultimate evaluation of the performance of the methods is not feasible
Organometallics, Vol. 14, No. 3, 1995 1291
Relativistic Effects in Cationic Au(I) Complexes
30.0
increase of the n- and d-bonding partition (ARE01 (n)= 13.3 kcallmol, ARE01 (d) = 6.8 kcallmol), whereas the contributions of the a2 and el orbitals to the bonding in Au+(NH3) are even destabilizing. Thus, for Au+(CO), the role of the relativistic correlation energy ( A l l m i x ) is essential. Furthermore, this explanation accounts for the relatively large deviation (6 kcal/mol) of BDE ( A d CO) between the MP2 and CCSD(T)approaches. From a chemical point of view, in Au+(CO)the 5d orbitals of gold are actively involved in the bonding, whereas for Au+(NH3), the bonding is dominated by the electron transfer from the ligand to gold.24
20,o
Conclusions
c
80.0
$-
70,O
z 3
0 SCFMCP
$i 3
60.0
-0
0
m
0 SCFECP 0 MPZECP
E 3 E”,, MP2MCP H B3LYP/RECP
50,O
CCSD(T)RECP
40,O
10,o
0.0
Au+(H20)
A i (CO)
AuC(C2H4)
Figure 1. Comparison of the computed BDE (Ad-L) as obtained by various computational methods using either the nonrelativistic or relativistic potentials, i.e., SCF/ECP, SCFLRECP, MP2/ECP, MP2/RECP, B3LYPLRECP, and CCSD(T)/RECP. The term Eadd denotes the BDE obtained when correlation and relativistic effects are assumed to behave additively (see text). since precise and accurate experimental and theoretical data for Au+(L)complexes are not available. By comparing the individual energy contributions to the total BDEs, one may be surprised by the fact that the weight of the mixed term (Am&) in Au+(CO)covers almost half (42%) of the bond energy, whereas for the other ligands, i.e., H20, NH3, and C2H4, the effect of AmkE is of the order of 25%. By applying the Morokuma bond analysis38to the results of the ADFBP method, one may compare Au+(CO),for example, with the Au+(NH3) system. In Au+(CO),the Au-C bond is shorter than the Au-N bond in Au+(NH3), and further, the relativistic bond contraction (ART-)in Au+(Co) is very large (0.504 A) as compared to 0.292 A for Au+(NH3). Consequently, the changes in the repulsive steric interaction energy (AR,i?3stefic)are twice as large for Au+(CO) with respect to Au+(NH3);i.e., 94.5 and 46.3 kcall mol, respectively. On the other hand the relativistic change in the attractive 0 overlap A&OI (a),associated with the 0 orbital in Au+(CO)and the a1 orbital in Au+(NH3), is much stronger for Au+(CO)than for Au+(NH3), i.e., 197.1 and 96.4 kcal/mol, respectively. In addition, concomitant to the bond contraction in Au+(CO)is an
In general, the results of the present study demonstrate that for gold(1) compounds density functional methods are in reasonable good agreement with ab initio MP2 and CCSD(T) approaches. This applies not only for geometries and energetics, but also for relativistic effects if an appropriate RECP scheme is used or the relativistic effects are included directly as in the quasirelativistic ADFBP treatment. More precisely, the MP2 and ADFBP approaches exhibit a slight tendency to overestimate the binding energies as compared to CCSD(T) and B3LYP. In addition, the B3LYP hybrid method leads to an elongation of the corresponding Au+-L bonds as compared to the other approaches. For the Au+(L) complexes under study, correlation and relativistic effects are of the same order of magnitude and both affect the binding severely. As far as the interplay between both effects is concerned, our study emphasizes the necessity for the evaluation of correlation energy using a relativistic approach. However, the agreement of the calculated values with the scarce experimental findings in gold(1) chemistry is not excellent, and there is still room for further improvement in the future.
Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie, and the Gesellschaft von Freunden der Technischen Universitat Berlin as well as a gift of transition metals from Degussa AG, Hanau, are gratefully acknowledged. P.S. is grateful to the Auckland University Research Committee and to NY/FRG for financial support. Furthermore, we express our thanks to Dip1.-Chem. C. Heinemann for helpful discussions. H. Basch is acknowledged for providing us with a copy of his work prior publication. OM940709C
