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Aurophilic attraction: the additivity and the combination with hydrogen bonds
Chemical Physics Letters 370 (2003) 733–740 www.elsevier.com/locate/cplett
Aurophilic attraction: the additivity and the combination with hydrogen bonds Fernando Mendizabal b
a,b,1
, Pekka Pyykk€ o
b,* ,
Nino Runeberg
b
a Departamento de Quımica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile Department of Chemistry, University of Helsinki, P.O.B. 55 (A.I. Virtasen aukio 1), FIN-00014 Helsinki, Finland
Received 13 December 2002; in final form 15 January 2003
Abstract The coexistence of gold–gold contacts and hydrogen bonding is studied in the model system ½H2 PðOHÞAuCl2 and ½H2 PðOHÞAuPH2 ðOÞ2 . The two interactions are found to be comparable. The possible non-additivity of the aurophilic, Au(I)–Au(I) interaction is studied at MP2 level for the pentagonal ½AuðSHÞ2 ðAuSHÞ5 Þ and hexagonal ½AuðSHÞ2 ðAuSHÞ6 clusters. The possibilities of Ômechanical cooperativityÕ between different aurophilic attractions and of Au. . .S attractions are also considered. Ó 2003 Published by Elsevier Science B.V.
1. Introduction As recently reviewed [1–5], an ÔaurophilicÕ [6] (or, more generally, ÔmetallophilicÕ [7]) attraction can take place between closed-shell metal ions in compounds, even when they carry the same formal charge, like a pair of Au(I) cations. The strength of this attraction can be comparable with that of a good hydrogen bond and increasing evidence [7–11] points to a Ôvan der WaalsÕ or ÔdispersionÕ mechanism behind it, with additional allowance for virtual charge-transfer terms [12]. *
Corresponding author. Fax: +358-9-191-50169. E-mail addresses: [email protected] (F. Mendizabal), Pekka.Pyykko@helsinki.fi (P. Pyykk€ o), Nino.Runeberg@csc.fi (N. Runeberg). 1 Fax: +56-2-271-3888.
These attractions are experimentally found in pairs, oligomers, infinite chains and infinite twodimensional sheets. This raises the question of additivity, which becomes highly relevant when many pair-wise interactions coexist. The recently synthesized pentagonal and hexagonal systems of Wiseman et al. [13] provide, in idealized form, a potential system for testing that additivity. For the experimental structures, see Tables 1 and 2. We here carry out the first such test at MP2 level. Although the Axilrod–Teller–Muto non-additive terms [14,15] would involve higher-order virtual excitations than the double ones present in MP2, this test was nevertheless interesting. Due to the size of the system, higher-order many-body calculations must be deferred to later work. The question of non-additive induction terms was briefly considered for simple model trimers, both
0009-2614/03/$ - see front matter Ó 2003 Published by Elsevier Science B.V. doi:10.1016/S0009-2614(03)00115-5
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Table 1 Experimental values for the aurophilic attraction and hydrogen bonding System
Au(I)–Au(I)
D–A
A–H
\X–Au–Y
Ref.
½PH2 PðOHÞAuPPh2 ðOÞ2 ½Ph2 PðOHÞAuCl2 ½Au2 ðl-SHÞðPH2 OÞðPH2 OH2 ½ðAuðSpyHÞðPPh2 ÞÞ2 ÞðPF6 2 ½ClðMe4 piperidineÞAu2 ½ClðdicyclohexylamineÞAu2
303.1 311.1 307.4 298.7 327.9 326.8
243.2 299.9 241.0 286.0 341.7 339.1
149.5 206.7 147.0 176.6 254.0 246.0
172 170 175 173 177 177
[16] [17] [18] [19] [20] [21]
Distances in pm. The donor (D) and acceptor (A) atoms refer to the hydrogen bond. ÔPhÕ ¼ phenyl.
Table 2 Experimental average values for the Au–Au distance (in pm) Parameter
½AuðSC6 H4 –p–CMe3 Þ10
½AuðSC6 H4 –p–CMe3 Þ12 a
Au(Central)–Au(Eq.) Au(Eq.)–Au(Eq.) Au(Central)–S Au(Eq.)–S \Au(Eq.)–S–Au(Eq.)
305.2 359.8 234.3 230.9 102.4
332.1 332.8 231.2 230.9 92.3
a
Angles in degrees. These two cases are simplified here to 4 and 5, respectively. Values for a pseudo-hexagonal ring.
theoretically and at HF or MP2 levels, in [9]. A dominant R6 behavior was found. Second, there are systems where the aurophilic attraction coexists with normal hydrogen bonds [16–22] (see Tables 1 and 2). The only previous theoretical treatment of such systems is that of Codina et al. [22]. The general area where all these interactions count is crystal engineering or more precisely the prediction of crystal structures from the known interactions [23–25].
2. Models and methods 2.1. Simplified models For a model combining aurophilic attractions and hydrogen bonds, we have optimized the structure of the monomers [H2 P(OH)AuCl] and [H2 PðOHÞAuPH2 (O)] at Hartree–Fock (HF) and MP2 levels. The phenylphosphine ligand of the original experimental structure is thereby replaced by the phosphine group. This monomer geometry is then used for studying the Au–Au and hydrogen
bonding intermolecular interactions in the dimers 1–3, see Fig. 1. The interaction energy, V ðRÞ, between the monomers was obtained including a counterpoise correction. The nature of the interaction was studied in detail by performing calculations at the local MP2 (LMP2) level. Besides reducing the computational cost and the amount of BSSE compared to MP2, LMP2 also offers the possibility to decompose the correlation energy into different classes according to different double-excitation patterns [12]. For our unbridged models with almost non-overlapping monomers (M(A). . .M(B)), we can uniquely ascribe all localized orbitals to the subspaces with both monomers occupied (A,B) or both monomers virtual (A0 ,B0 ). In addition to the intramolecular correlation (double-excitations localized on either monomer), this partition gives rise to excitation classes of ionic (A ! A0 , B ! A0 ) and dispersion (A ! A0 , B ! B0 ) type. The energy contribution from the exchange–dispersion class (A ! B0 , B ! A0 ) is usually negligible. To approach the question of additivity of the Au–Au interactions, thiolate catenane models have been studied with the simplified clusters
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Fig. 1. The theoretical ½H2 PðOHÞAuCl2 models with and without O–H. . .Cl hydrogen bonding, 1 and 2, respectively. The O–H. . .O hydrogen-bonded model [H2 P(OH)Au(PH2 (O)]2 , 3. The five- and six-ring models 4 and 5, respectively, with the ½AuðSHÞ2 ðAuSHÞn at experimental geometry. The five-ring system has an idealized D5h symmetry in 6–8). The structure 6 is an idealized 4 with D5h symmetry. Model 7 has only one peripheral Au. . .Au interaction. Model 8 is the idealized five-ring. The models 9–11 refer to Au. . .S interactions between H2 S and AuðSHÞ 2.
½AuðSHÞ2 ðAuSHÞ5 Þ and ½AuðSHÞ2 ðAuSHÞ6 , 4–7 in Fig. 1. We have thereby replaced the – (SC6 H4 –p–CMe3 ) groups in the experimental work by Wiseman et al. [13] by –SH groups. The re-
maining monomer molecular structures in the theoretical models were taken from there. Single-point HF and MP2 level calculations were performed on the models. Alternatively, we
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have fully optimized the ½AuðSHÞ2 ðAuSHÞ5 Þ 6 and [ðAuSHÞ5 ] 8 models at a D5h symmetry. The Au–Au interaction energy was obtained, including a counterpoise correction, between the central or adjacent ½AuðSHÞ2 fragment and the surrounding or adjacent [ðAuSHÞn ] ring with n ¼ 5; 6. 2.2. GA U S S I A N 98 calculations The GA U S S I A N 98 package was used [26]. The 19 valence-electron (VE) quasi-relativistic (QR) pseudopotential (PP) of Andrae et al. [27] was employed for gold. The f orbitals are necessary for the weak intermolecular interactions between d-elements, as demonstrated previously for gold [8,10]. We employed two f-type polarization functions. This is desirable for a more accurate description of the interaction energy. Also, the atoms C, O, P, S, and Cl were treated through PPs [27], using doublezeta basis sets and adding one d-type polarization function. For the H atom, a double-zeta basis plus one p-type polarization function was used. 2.3. Localized MP2 calculations LMP2 calculations on the ½H2 PðOHÞAuCl2 system have been done as implemented in the MO L P R O program package [28]. We have used the same PPs and basis sets as described in Section 2.2. The localized molecular orbitals (LMOs) were obtained through a Pipek–Mezey localization procedure [29]. The orbital domains are determined at large distances and kept fixed for all other distances.
Fig. 2. Calculated ½H2 PðOHÞAuCl2 interaction energies V ðRÞ at HF and MP2 levels for the models 1–2.
This value has also been reproduced by our calculations, as shown in Fig. 3. Two ½H2 PðOHÞAuCl2 models were tested: the first had the experimental Cl–Au–P angle of 170° and the second had the ideal angle of 180° for the monomers. The results are found in Table 3. The better results, as compared with the experimental structure, are found for the systems with the bent, experimental Cl–Au–P angle. At MP2 level the energy minimun has Re ¼ 310 pm and V ðRe Þ ¼ 93:6 kJ/mol. This energy includes a realistic estimate for both the hydrogen bond and the aurophilic attraction, possibly exaggerating the latter for MP2 and large basis sets (see e.g. Fig. 9 of [8]).
3. Results and discussion 3.1. Aurophilicity and hydrogen bonding The interaction–energy curves, V ðRÞ, for ½H2 PðOHÞAuCl2 1 and 2 as a function of R(Au– Au), calculated at HF and MP2 levels, are shown in Fig. 2. Of these models, 1 does and 2 does not have a hydrogen bond (HB); the change is obtained by rotating the –PH2 ðOHÞ group through 120°. Furthermore, the experimental average dihedral angle Cl–Au–Au–Cl of 132.2° was used.
Fig. 3. The interaction potential for ½H2 PðOHÞAuCl2 as a function of the dihedral angle Cl–Au–Au–Cl.
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Table 3 Optimized Au–Au distances and hydrogen bonding geometries for dimers at the HF and MP2 levels Model ½H2 PðOHÞAuCl2
½H2 PðOHÞAuPH2 ðOÞ2
Method a
MP2 HFa MP2a; b HFa ;b MP2c HFc MP2c;b HFc;b MP2d HFd
Au(I)–Au(I)
O–A
H–A
V ðRe Þ
310.3 348.2 305.7 375.6 357.4 386.2 329.1 387.1 316.8 353.4
314.4 344.5 485.2 537.5 311.1 334.1 470.0 511.8 269.5 301.0
218.5 249.1 522.9 571.5 215.1 239.1 511.7 550.6 181.6 219.8
)93.6 ()0.03568) )54.8 ()0.02087) )45.9 ()0.01751) )14.8 ()0.00565) )84.4 ()0.03217) )56.1 ()0.02136) )44.8 ()0.01707) )19.2 ()0.00730) )110.7 ()0.04210) )67.9 ()0.02587)
Distances in pm, interaction energies, V ðRe Þ, in kJ/mol (and a.u.). The donor (D) and acceptor (A) atoms refer to the hydrogen bond. a The \Cl–Au–P set at 170° (exp. value). b Without hydrogen bond, 2. c The \Cl–Au–P set at 180°. d The \P–Au–P is set at 172° (exp. value).
At HF level the aurophilic attraction, being a dispersion effect, disappears while substantial parts of the hydrogen bonding survive, only a part of the hydrogen bonding coming from dispersion. In the present dimer, the latter contribution amounts to 27.4 kJ/mol per hydrogen bond. We estimate the aurophilic interaction as the difference of the MP2 and HF energies at the equilibrium distance of 310.3 pm. The result is 50 kJ/mol, at the upper end of the typical range (cf. e.g. [8, Table 6]). For the model without HB, 2, we obtain at MP2 level a shorter equilibrium Au–Au distance of 305 pm but a smaller interaction energy of 45.9 kJ/mol. At HF level, there is no evident minimum. The electrostatic and induction contributions would still be there. In Table 3, we have included the corresponding results using the idealized P–Au–Cl angle of 180°. Analogous trends are found as with the experimental P–Au–Cl angle, but the Au–Au distance is now greater. The hydrogen bonding is comparable to that obtained with the experimental P–Au–Cl angle. For the O–H. . .O hydrogen bonds in 3 the HB energy at HF level is )67.9 kJ/mol, much larger than the O–H. . .Cl one. The remaining (MP2–HF) estimate for the aurophilic energy is now )42.8 kJ/mol, comparable with the values for 1–2.
Fig. 4. LMP2 interaction potential for model dimers 1 and 2.
The main conclusion becomes that both the aurophilic attraction and the hydrogen bonds are indeed there and that their magnitudes are comparable. The interaction–energy curves obtained at LMP2 level, for the model dimers 1 and 2, are shown in Fig. 4. The LMP2 calculations were done with dimers having linear Cl–Au–P units. At LMP2 level the equilibrium Au-Au distance for the HB dimer 1 is 368 pm compared with the MP2 value of 357 pm. The corresponding interaction energies are 76 and 84 kJ/mol, respectively. For the model dimer without hydrogen bonds 2, the calculated LMP2 equilibrium Au-Au dis-
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Table 4 Interaction energies, V ðRe Þ, in kJ/mol System
½AuðSHÞ2 ðAuSHÞ5 Þ 4 ½AuðSHÞ2 ðAuSHÞ6 5 ½AuðSHÞ2 ðAuSHÞ5 Þ 6 ½AuðSHÞ2 ðAuSHÞ5 Þ 7
Method
V ðRe Þ
Au–Au pair
HF MP2 HF MP2 HF MP2 HFa ;b MP2a ;b
+84.0 (+69.6) )131.1 ()317.9) +40.9 (+27.1) )145.0 ()302.8) +15.7 (+18.13) )264.1 ()499.8) +5.8 (+0.34) )46.9 ()92.5)
+16.8 (+13.9) )26.3 ()63.6) +6.8 (+4.52) )24.2 ()50.5) +3.14 (+3.63) )52.80 ()99.9) +5.8 (+0.34) )46.9 ()92.5)
The values in parentheses were obtained without counterpoise (CP) correction. We have used the geometry of the model 6. b The optimized intermolecular Au–Au distance is 332 pm. a
Table 5 Optimized parameters at the HF and MP2 levels Parameters
½AuðSHÞ2 ðAuSHÞ5 Þ 6
Au(Central)–Au(Eq) Au(Eq)–Au(Eq) Au(Central)–S Au(Eq)–S \Au(Eq)–S–Au(Eq) S(Eq.)–H S(Axial)–H
322.3 378.8 227.5 226.8 113.3 134.1 133.4
[ðAuSHÞ5 ] 8
(360.4) (423.7) (242.1) (241.9) (122.1) (132.4) (133.1)
[AuðSHÞ2
395.6 (423.1) 230.9 (245.7) 228.2 (239.8) 120.2 (123.8) 134.2 (133.1) 133.0 (132.6)
Distances in pm, angles in degrees. The HF values are between parentheses.
tance is 324 pm. The interaction energy at LMP2 level is 51 kJ/mol. The corresponding equilibrium values obtained at MP2 level are 329 pm and 45 kJ/mol, respectively. The part of the BSSE arising already at SCF level can be significant for overlapping systems described by moderate-sized basis sets. This is the reason for the stronger and shorter interaction obtained at LMP2 level for the more compact model 2. The correlation contribution to the interaction energy for the two model dimers is shown in Table 3.
The results for the [AuðSHÞ2 ðAuSHÞ5 ] and [AuðSHÞ2 ðAuSHÞ6 ] models are shown in Table 4. Both models produce an attraction at MP2 level. If the interaction energy, V ðRe Þ, is divided by the number of Au–Au contacts present in the models, pair-wise energies of )26.3 and )24.2
3.2. Gold thiolate catenane models Here the AuðSHÞ 2 ÔstickÕ can be placed at the midpoint of the n-membered ring or outside its periphery, in contact with just one gold atom, and the question is whether the former case gives n times the attraction energy of the latter? The Au–S–H angles can be taken as linear or bent.
Fig. 5. The interaction potential for the Ôstick-outside-ringÕ, 7. The dashed curve gives the MP2-level charge-polarizability part.
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Table 6 Counterpoise-corrected MP2 geometries and interaction energies for three H2 S . . . AuðSHÞ 2 models 9–11 (see text) Model
Au–S
DE (MP2)
DE (HF)
Increment (MP2–HF)
9 10 11
342.6 413.8 391.0
7.35 10.80 )17.33
16.32 15.19 )5.18
)8.97 )4.39 )12.15
Distances in pm, energies in kJ/mol.
kJ/mol are found for [AuðSHÞ2 ðAuSHÞ5 Þ ] 4 and [AuðSHÞ2 ðAuSHÞ6 ] 5, respectively. At HF level, the interaction energies are positive, i.e. repulsive. Furthermore, as indicated in Table 4, the interaction energies without CP are strongly overestimated at all levels. We have fully optimized at the HF and MP2 levels the geometry for [AuðSHÞ2 ðAuSHÞ5 ] 6, assuming a D5h point symmetry. The interaction energies are shown in Table 4 and the structures in Table 5. The MP2-level interaction energies per Au–Au pair are comparable for the centered fiveand six-rings with idealized experimental geometries, 4 and 5, respectively. They nearly double upon optimization the centered five-ring 6, or the Ôstick-outside-ringÕ 7. The Au–Au distance between the central fragment, ðAuðSHÞ2 Þ , and the peripheral ring, ðAuSHÞ5 , shows a dramatic reduction of 38 pm from HF to MP2 level, see Table 5. The Au–Au pair energy at MP2 level is )52.80 kJ/ mol. The optimized MP2-level Au(central)–Au(eq) distance of 322 pm in Table 5 is still longer than the experimental average value of 305 pm in Table 2. The low symmetry makes the analysis less clearcut, but the charge-polarizability term is clearly important in Fig. 5. Could we have here, not electronic, but mechanical cooperativity? With this we mean that the radial Au-Au interactions in 6 would lead to shorter intra-ring Au–Au distances and, through that, to a further energy decrease. To check this hypothesis, we calculated the MP2–HF energy difference for the five-ring part of 6. The bending of the S–Au–S angle from 120.2° to 113.3° lowers that energy difference by in all 33.9 kJ/mol. One-fifth of this is only 6.8 kJ/mol and is hence not enough to explain the apparent doubling of the pairwise Au–Au attraction from 4 to 6.
Two further contributions were considered: Induction and Au...S interactions. If the central [AuðSHÞ2 ] unit of 4 is replaced by a point charge of )1 without basis functions at the midpoint, the total energy is lowered by )110.0 and )116.4 kJ/ mol at HF and MP2 levels, respectively. The increment of )6.4 kJ/mol is not sufficient as explanation. Finally we modelled the possible Au. . .S inter action [2] by a simple H2 S . . . AuðSHÞ2 model in three orientations of C2v symmetry, 9: both molecules in the same plane, 10: H2 S in the equatorial plane of AuðSHÞ 2 , S–H hands out, and 11 dito, S–H hands in. The results are shown in Table 6. The MP2–HF increment of 9 or 11 would help to explain the large MP2–HF increment of the interaction between the central ion and the ring in 6. We thus cautiously suggest that both Au. . .Au and Au. . .S interactions may be important in that case. This is to our knowledge the first theoretical study of the Au. . .S interaction.
Acknowledgements P.P. and N.R. were supported by The Academy of Finland. The stay of F.M. at Helsinki was partially financed by the Centre for International Mobility (CIMO), Finland, and the Fondecyt Project No. 1020141, Chile. Computer resources at CSC, Finland, were used.
References [1] H. Schmidbaur, Gold Bull. 23 (1990) 11. [2] P. Pyykk€ o, Chem. Rev. 97 (1997) 597. [3] H. Schmidbaur (Ed.), Gold: Progress in Chemistry, Biochemistry and Techology, Wiley, New York, 1999.
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[4] M. Bardajı, A. Laguna, J. Chem. Ed. 76 (1999) 201. [5] L.H. Gade, Angew. Chem. Int. Ed. 40 (2001) 3573. [6] F. Scherbaum, A. Grohmann, B. Huber, C. Kr€ uger, H. Schmidbaur, Angew. Chem., Int. Ed. 27 (1988) 1544. [7] P. Pyykk€ o, J. Li, N. Runeberg, Chem. Phys. Lett. 218 (1994) 133. [8] P. Pyykk€ o, N. Runeberg, F. Mendizabal, Chem. Eur. J. 3 (1997) 1451. [9] P. Pyykk€ o, F. Mendizabal, Chem. Eur. J. 3 (1997) 1458. [10] P. Pyykk€ o, T. Tamm, Organometallics 17 (1998) 4842. [11] L. Magnko, M. Schweizer, G. Rauhut, M. Sch€ utz, H. Stoll, H.-J. Werner, Phys. Chem. Chem. Phys. 4 (2002) 1006. [12] N. Runeberg, M. Sch€ utz, H.-J. Werner, J. Chem. Phys. 110 (1999) 7210. [13] M.R. Wiseman, P.A. Marsh, P.T. Bishop, B.J. Brisdon, M.F. Mahon, J. Am. Chem. Soc. 122 (2000) 12598. [14] B.M. Axilrod, E. Teller, J. Chem. Phys. 11 (1943) 299. [15] Y. Muto, Proc. Phys. Soc. Jpn. 17 (1943) 629. [16] C. Hollatz, A. Schier, H. Schmidbaur, J. Am. Chem. Soc. 119 (1997) 8115. [17] C. Hollatz, A. Schier, J. Riede, H. Schmidbaur, J. Chem. Soc. Dalton Trans. (1999) 111. [18] W.J. Hunks, M.C. Jennings, R.J. Puddephatt, Inorg. Chem. 39 (2000) 2699. [19] L. Hao, M.A. Mansour, R.J. Lachicote, H.J. Gysling, R. Eisenberg, Inorg. Chem. 39 (2000) 5520.
[20] J.J. Guy, P.G. Jones, M.J. Mays, G.M. Sheldrick, J. Chem. Soc., Dalton Trans. (1977) 8. [21] B. Ahrens, P.G. Jones, A.K. Fischer, Eur. J. Inorg. Chem. (1999) 1103. [22] A. Codina, E.J. Fernandez, P.G. Jones, A. Laguna, J.M. L opez-de-Luzuriaga, M. Monge, M.E. Olmos, J. Perez, M.A. Rodriguez, J. Am. Chem. Soc. 124 (2002) 6781. [23] G.R. Desiraju, Angew. Chem. Int. Ed. 34 (1995) 2311. [24] D. Braga, F. Grepioni, G.R. Desiraju, Chem. Rev. 98 (1998) 1375. [25] D. Braga, F. Grepioni, Acc. Chem. Res. 33 (2000) 601. [26] M.J. Frisch et al., Gaussian Inc., Pittsburgh PA, 1998. [27] D. Andrae, U. H€ausserman, M. Dolg, H. Stoll, H. Preuss, Theor. Chim. Acta 77 (1990) 123, with af ¼ 0:20 and 1.19 added, QR (8s6p5d2f)/[7s3p4d2f]. P, O, C, and Cl: A. Bergner, M. Dolg, W. K€ uchle, H. Stoll, H. Preuss, Mol. Phys. 80 (1993) 1431, (4s4p1d)/[2s2p1d], with ad ¼ 0.340, 1.154, 0.800, and 0.514 added for P, O, C, and Cl, respectively. Value for ad from S. Huzinaga, Gaussian Basis Sets for Molecular Calculations, Elsevier, Amsterdam, 1984, p. 16. For hydrogen, we used the Huzinaga 4s basis set, with a set of p polarization functions with a ¼ 0:8. [28] MO L P R O is a package of ab initio programs written by H.-J. Werner, P.J. Knowles et al. [29] J. Pipek, P.G. Mezey, J. Chem. Phys. 90 (1989) 4916.
Aurophilic attraction: the additivity and the combination with hydrogen bonds Fernando Mendizabal b
a,b,1
, Pekka Pyykk€ o
b,* ,
Nino Runeberg
b
a Departamento de Quımica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile Department of Chemistry, University of Helsinki, P.O.B. 55 (A.I. Virtasen aukio 1), FIN-00014 Helsinki, Finland
Received 13 December 2002; in final form 15 January 2003
Abstract The coexistence of gold–gold contacts and hydrogen bonding is studied in the model system ½H2 PðOHÞAuCl2 and ½H2 PðOHÞAuPH2 ðOÞ2 . The two interactions are found to be comparable. The possible non-additivity of the aurophilic, Au(I)–Au(I) interaction is studied at MP2 level for the pentagonal ½AuðSHÞ2 ðAuSHÞ5 Þ and hexagonal ½AuðSHÞ2 ðAuSHÞ6 clusters. The possibilities of Ômechanical cooperativityÕ between different aurophilic attractions and of Au. . .S attractions are also considered. Ó 2003 Published by Elsevier Science B.V.
1. Introduction As recently reviewed [1–5], an ÔaurophilicÕ [6] (or, more generally, ÔmetallophilicÕ [7]) attraction can take place between closed-shell metal ions in compounds, even when they carry the same formal charge, like a pair of Au(I) cations. The strength of this attraction can be comparable with that of a good hydrogen bond and increasing evidence [7–11] points to a Ôvan der WaalsÕ or ÔdispersionÕ mechanism behind it, with additional allowance for virtual charge-transfer terms [12]. *
Corresponding author. Fax: +358-9-191-50169. E-mail addresses: [email protected] (F. Mendizabal), Pekka.Pyykko@helsinki.fi (P. Pyykk€ o), Nino.Runeberg@csc.fi (N. Runeberg). 1 Fax: +56-2-271-3888.
These attractions are experimentally found in pairs, oligomers, infinite chains and infinite twodimensional sheets. This raises the question of additivity, which becomes highly relevant when many pair-wise interactions coexist. The recently synthesized pentagonal and hexagonal systems of Wiseman et al. [13] provide, in idealized form, a potential system for testing that additivity. For the experimental structures, see Tables 1 and 2. We here carry out the first such test at MP2 level. Although the Axilrod–Teller–Muto non-additive terms [14,15] would involve higher-order virtual excitations than the double ones present in MP2, this test was nevertheless interesting. Due to the size of the system, higher-order many-body calculations must be deferred to later work. The question of non-additive induction terms was briefly considered for simple model trimers, both
0009-2614/03/$ - see front matter Ó 2003 Published by Elsevier Science B.V. doi:10.1016/S0009-2614(03)00115-5
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F. Mendizabal et al. / Chemical Physics Letters 370 (2003) 733–740
Table 1 Experimental values for the aurophilic attraction and hydrogen bonding System
Au(I)–Au(I)
D–A
A–H
\X–Au–Y
Ref.
½PH2 PðOHÞAuPPh2 ðOÞ2 ½Ph2 PðOHÞAuCl2 ½Au2 ðl-SHÞðPH2 OÞðPH2 OH2 ½ðAuðSpyHÞðPPh2 ÞÞ2 ÞðPF6 2 ½ClðMe4 piperidineÞAu2 ½ClðdicyclohexylamineÞAu2
303.1 311.1 307.4 298.7 327.9 326.8
243.2 299.9 241.0 286.0 341.7 339.1
149.5 206.7 147.0 176.6 254.0 246.0
172 170 175 173 177 177
[16] [17] [18] [19] [20] [21]
Distances in pm. The donor (D) and acceptor (A) atoms refer to the hydrogen bond. ÔPhÕ ¼ phenyl.
Table 2 Experimental average values for the Au–Au distance (in pm) Parameter
½AuðSC6 H4 –p–CMe3 Þ10
½AuðSC6 H4 –p–CMe3 Þ12 a
Au(Central)–Au(Eq.) Au(Eq.)–Au(Eq.) Au(Central)–S Au(Eq.)–S \Au(Eq.)–S–Au(Eq.)
305.2 359.8 234.3 230.9 102.4
332.1 332.8 231.2 230.9 92.3
a
Angles in degrees. These two cases are simplified here to 4 and 5, respectively. Values for a pseudo-hexagonal ring.
theoretically and at HF or MP2 levels, in [9]. A dominant R6 behavior was found. Second, there are systems where the aurophilic attraction coexists with normal hydrogen bonds [16–22] (see Tables 1 and 2). The only previous theoretical treatment of such systems is that of Codina et al. [22]. The general area where all these interactions count is crystal engineering or more precisely the prediction of crystal structures from the known interactions [23–25].
2. Models and methods 2.1. Simplified models For a model combining aurophilic attractions and hydrogen bonds, we have optimized the structure of the monomers [H2 P(OH)AuCl] and [H2 PðOHÞAuPH2 (O)] at Hartree–Fock (HF) and MP2 levels. The phenylphosphine ligand of the original experimental structure is thereby replaced by the phosphine group. This monomer geometry is then used for studying the Au–Au and hydrogen
bonding intermolecular interactions in the dimers 1–3, see Fig. 1. The interaction energy, V ðRÞ, between the monomers was obtained including a counterpoise correction. The nature of the interaction was studied in detail by performing calculations at the local MP2 (LMP2) level. Besides reducing the computational cost and the amount of BSSE compared to MP2, LMP2 also offers the possibility to decompose the correlation energy into different classes according to different double-excitation patterns [12]. For our unbridged models with almost non-overlapping monomers (M(A). . .M(B)), we can uniquely ascribe all localized orbitals to the subspaces with both monomers occupied (A,B) or both monomers virtual (A0 ,B0 ). In addition to the intramolecular correlation (double-excitations localized on either monomer), this partition gives rise to excitation classes of ionic (A ! A0 , B ! A0 ) and dispersion (A ! A0 , B ! B0 ) type. The energy contribution from the exchange–dispersion class (A ! B0 , B ! A0 ) is usually negligible. To approach the question of additivity of the Au–Au interactions, thiolate catenane models have been studied with the simplified clusters
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Fig. 1. The theoretical ½H2 PðOHÞAuCl2 models with and without O–H. . .Cl hydrogen bonding, 1 and 2, respectively. The O–H. . .O hydrogen-bonded model [H2 P(OH)Au(PH2 (O)]2 , 3. The five- and six-ring models 4 and 5, respectively, with the ½AuðSHÞ2 ðAuSHÞn at experimental geometry. The five-ring system has an idealized D5h symmetry in 6–8). The structure 6 is an idealized 4 with D5h symmetry. Model 7 has only one peripheral Au. . .Au interaction. Model 8 is the idealized five-ring. The models 9–11 refer to Au. . .S interactions between H2 S and AuðSHÞ 2.
½AuðSHÞ2 ðAuSHÞ5 Þ and ½AuðSHÞ2 ðAuSHÞ6 , 4–7 in Fig. 1. We have thereby replaced the – (SC6 H4 –p–CMe3 ) groups in the experimental work by Wiseman et al. [13] by –SH groups. The re-
maining monomer molecular structures in the theoretical models were taken from there. Single-point HF and MP2 level calculations were performed on the models. Alternatively, we
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have fully optimized the ½AuðSHÞ2 ðAuSHÞ5 Þ 6 and [ðAuSHÞ5 ] 8 models at a D5h symmetry. The Au–Au interaction energy was obtained, including a counterpoise correction, between the central or adjacent ½AuðSHÞ2 fragment and the surrounding or adjacent [ðAuSHÞn ] ring with n ¼ 5; 6. 2.2. GA U S S I A N 98 calculations The GA U S S I A N 98 package was used [26]. The 19 valence-electron (VE) quasi-relativistic (QR) pseudopotential (PP) of Andrae et al. [27] was employed for gold. The f orbitals are necessary for the weak intermolecular interactions between d-elements, as demonstrated previously for gold [8,10]. We employed two f-type polarization functions. This is desirable for a more accurate description of the interaction energy. Also, the atoms C, O, P, S, and Cl were treated through PPs [27], using doublezeta basis sets and adding one d-type polarization function. For the H atom, a double-zeta basis plus one p-type polarization function was used. 2.3. Localized MP2 calculations LMP2 calculations on the ½H2 PðOHÞAuCl2 system have been done as implemented in the MO L P R O program package [28]. We have used the same PPs and basis sets as described in Section 2.2. The localized molecular orbitals (LMOs) were obtained through a Pipek–Mezey localization procedure [29]. The orbital domains are determined at large distances and kept fixed for all other distances.
Fig. 2. Calculated ½H2 PðOHÞAuCl2 interaction energies V ðRÞ at HF and MP2 levels for the models 1–2.
This value has also been reproduced by our calculations, as shown in Fig. 3. Two ½H2 PðOHÞAuCl2 models were tested: the first had the experimental Cl–Au–P angle of 170° and the second had the ideal angle of 180° for the monomers. The results are found in Table 3. The better results, as compared with the experimental structure, are found for the systems with the bent, experimental Cl–Au–P angle. At MP2 level the energy minimun has Re ¼ 310 pm and V ðRe Þ ¼ 93:6 kJ/mol. This energy includes a realistic estimate for both the hydrogen bond and the aurophilic attraction, possibly exaggerating the latter for MP2 and large basis sets (see e.g. Fig. 9 of [8]).
3. Results and discussion 3.1. Aurophilicity and hydrogen bonding The interaction–energy curves, V ðRÞ, for ½H2 PðOHÞAuCl2 1 and 2 as a function of R(Au– Au), calculated at HF and MP2 levels, are shown in Fig. 2. Of these models, 1 does and 2 does not have a hydrogen bond (HB); the change is obtained by rotating the –PH2 ðOHÞ group through 120°. Furthermore, the experimental average dihedral angle Cl–Au–Au–Cl of 132.2° was used.
Fig. 3. The interaction potential for ½H2 PðOHÞAuCl2 as a function of the dihedral angle Cl–Au–Au–Cl.
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Table 3 Optimized Au–Au distances and hydrogen bonding geometries for dimers at the HF and MP2 levels Model ½H2 PðOHÞAuCl2
½H2 PðOHÞAuPH2 ðOÞ2
Method a
MP2 HFa MP2a; b HFa ;b MP2c HFc MP2c;b HFc;b MP2d HFd
Au(I)–Au(I)
O–A
H–A
V ðRe Þ
310.3 348.2 305.7 375.6 357.4 386.2 329.1 387.1 316.8 353.4
314.4 344.5 485.2 537.5 311.1 334.1 470.0 511.8 269.5 301.0
218.5 249.1 522.9 571.5 215.1 239.1 511.7 550.6 181.6 219.8
)93.6 ()0.03568) )54.8 ()0.02087) )45.9 ()0.01751) )14.8 ()0.00565) )84.4 ()0.03217) )56.1 ()0.02136) )44.8 ()0.01707) )19.2 ()0.00730) )110.7 ()0.04210) )67.9 ()0.02587)
Distances in pm, interaction energies, V ðRe Þ, in kJ/mol (and a.u.). The donor (D) and acceptor (A) atoms refer to the hydrogen bond. a The \Cl–Au–P set at 170° (exp. value). b Without hydrogen bond, 2. c The \Cl–Au–P set at 180°. d The \P–Au–P is set at 172° (exp. value).
At HF level the aurophilic attraction, being a dispersion effect, disappears while substantial parts of the hydrogen bonding survive, only a part of the hydrogen bonding coming from dispersion. In the present dimer, the latter contribution amounts to 27.4 kJ/mol per hydrogen bond. We estimate the aurophilic interaction as the difference of the MP2 and HF energies at the equilibrium distance of 310.3 pm. The result is 50 kJ/mol, at the upper end of the typical range (cf. e.g. [8, Table 6]). For the model without HB, 2, we obtain at MP2 level a shorter equilibrium Au–Au distance of 305 pm but a smaller interaction energy of 45.9 kJ/mol. At HF level, there is no evident minimum. The electrostatic and induction contributions would still be there. In Table 3, we have included the corresponding results using the idealized P–Au–Cl angle of 180°. Analogous trends are found as with the experimental P–Au–Cl angle, but the Au–Au distance is now greater. The hydrogen bonding is comparable to that obtained with the experimental P–Au–Cl angle. For the O–H. . .O hydrogen bonds in 3 the HB energy at HF level is )67.9 kJ/mol, much larger than the O–H. . .Cl one. The remaining (MP2–HF) estimate for the aurophilic energy is now )42.8 kJ/mol, comparable with the values for 1–2.
Fig. 4. LMP2 interaction potential for model dimers 1 and 2.
The main conclusion becomes that both the aurophilic attraction and the hydrogen bonds are indeed there and that their magnitudes are comparable. The interaction–energy curves obtained at LMP2 level, for the model dimers 1 and 2, are shown in Fig. 4. The LMP2 calculations were done with dimers having linear Cl–Au–P units. At LMP2 level the equilibrium Au-Au distance for the HB dimer 1 is 368 pm compared with the MP2 value of 357 pm. The corresponding interaction energies are 76 and 84 kJ/mol, respectively. For the model dimer without hydrogen bonds 2, the calculated LMP2 equilibrium Au-Au dis-
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Table 4 Interaction energies, V ðRe Þ, in kJ/mol System
½AuðSHÞ2 ðAuSHÞ5 Þ 4 ½AuðSHÞ2 ðAuSHÞ6 5 ½AuðSHÞ2 ðAuSHÞ5 Þ 6 ½AuðSHÞ2 ðAuSHÞ5 Þ 7
Method
V ðRe Þ
Au–Au pair
HF MP2 HF MP2 HF MP2 HFa ;b MP2a ;b
+84.0 (+69.6) )131.1 ()317.9) +40.9 (+27.1) )145.0 ()302.8) +15.7 (+18.13) )264.1 ()499.8) +5.8 (+0.34) )46.9 ()92.5)
+16.8 (+13.9) )26.3 ()63.6) +6.8 (+4.52) )24.2 ()50.5) +3.14 (+3.63) )52.80 ()99.9) +5.8 (+0.34) )46.9 ()92.5)
The values in parentheses were obtained without counterpoise (CP) correction. We have used the geometry of the model 6. b The optimized intermolecular Au–Au distance is 332 pm. a
Table 5 Optimized parameters at the HF and MP2 levels Parameters
½AuðSHÞ2 ðAuSHÞ5 Þ 6
Au(Central)–Au(Eq) Au(Eq)–Au(Eq) Au(Central)–S Au(Eq)–S \Au(Eq)–S–Au(Eq) S(Eq.)–H S(Axial)–H
322.3 378.8 227.5 226.8 113.3 134.1 133.4
[ðAuSHÞ5 ] 8
(360.4) (423.7) (242.1) (241.9) (122.1) (132.4) (133.1)
[AuðSHÞ2
395.6 (423.1) 230.9 (245.7) 228.2 (239.8) 120.2 (123.8) 134.2 (133.1) 133.0 (132.6)
Distances in pm, angles in degrees. The HF values are between parentheses.
tance is 324 pm. The interaction energy at LMP2 level is 51 kJ/mol. The corresponding equilibrium values obtained at MP2 level are 329 pm and 45 kJ/mol, respectively. The part of the BSSE arising already at SCF level can be significant for overlapping systems described by moderate-sized basis sets. This is the reason for the stronger and shorter interaction obtained at LMP2 level for the more compact model 2. The correlation contribution to the interaction energy for the two model dimers is shown in Table 3.
The results for the [AuðSHÞ2 ðAuSHÞ5 ] and [AuðSHÞ2 ðAuSHÞ6 ] models are shown in Table 4. Both models produce an attraction at MP2 level. If the interaction energy, V ðRe Þ, is divided by the number of Au–Au contacts present in the models, pair-wise energies of )26.3 and )24.2
3.2. Gold thiolate catenane models Here the AuðSHÞ 2 ÔstickÕ can be placed at the midpoint of the n-membered ring or outside its periphery, in contact with just one gold atom, and the question is whether the former case gives n times the attraction energy of the latter? The Au–S–H angles can be taken as linear or bent.
Fig. 5. The interaction potential for the Ôstick-outside-ringÕ, 7. The dashed curve gives the MP2-level charge-polarizability part.
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Table 6 Counterpoise-corrected MP2 geometries and interaction energies for three H2 S . . . AuðSHÞ 2 models 9–11 (see text) Model
Au–S
DE (MP2)
DE (HF)
Increment (MP2–HF)
9 10 11
342.6 413.8 391.0
7.35 10.80 )17.33
16.32 15.19 )5.18
)8.97 )4.39 )12.15
Distances in pm, energies in kJ/mol.
kJ/mol are found for [AuðSHÞ2 ðAuSHÞ5 Þ ] 4 and [AuðSHÞ2 ðAuSHÞ6 ] 5, respectively. At HF level, the interaction energies are positive, i.e. repulsive. Furthermore, as indicated in Table 4, the interaction energies without CP are strongly overestimated at all levels. We have fully optimized at the HF and MP2 levels the geometry for [AuðSHÞ2 ðAuSHÞ5 ] 6, assuming a D5h point symmetry. The interaction energies are shown in Table 4 and the structures in Table 5. The MP2-level interaction energies per Au–Au pair are comparable for the centered fiveand six-rings with idealized experimental geometries, 4 and 5, respectively. They nearly double upon optimization the centered five-ring 6, or the Ôstick-outside-ringÕ 7. The Au–Au distance between the central fragment, ðAuðSHÞ2 Þ , and the peripheral ring, ðAuSHÞ5 , shows a dramatic reduction of 38 pm from HF to MP2 level, see Table 5. The Au–Au pair energy at MP2 level is )52.80 kJ/ mol. The optimized MP2-level Au(central)–Au(eq) distance of 322 pm in Table 5 is still longer than the experimental average value of 305 pm in Table 2. The low symmetry makes the analysis less clearcut, but the charge-polarizability term is clearly important in Fig. 5. Could we have here, not electronic, but mechanical cooperativity? With this we mean that the radial Au-Au interactions in 6 would lead to shorter intra-ring Au–Au distances and, through that, to a further energy decrease. To check this hypothesis, we calculated the MP2–HF energy difference for the five-ring part of 6. The bending of the S–Au–S angle from 120.2° to 113.3° lowers that energy difference by in all 33.9 kJ/mol. One-fifth of this is only 6.8 kJ/mol and is hence not enough to explain the apparent doubling of the pairwise Au–Au attraction from 4 to 6.
Two further contributions were considered: Induction and Au...S interactions. If the central [AuðSHÞ2 ] unit of 4 is replaced by a point charge of )1 without basis functions at the midpoint, the total energy is lowered by )110.0 and )116.4 kJ/ mol at HF and MP2 levels, respectively. The increment of )6.4 kJ/mol is not sufficient as explanation. Finally we modelled the possible Au. . .S inter action [2] by a simple H2 S . . . AuðSHÞ2 model in three orientations of C2v symmetry, 9: both molecules in the same plane, 10: H2 S in the equatorial plane of AuðSHÞ 2 , S–H hands out, and 11 dito, S–H hands in. The results are shown in Table 6. The MP2–HF increment of 9 or 11 would help to explain the large MP2–HF increment of the interaction between the central ion and the ring in 6. We thus cautiously suggest that both Au. . .Au and Au. . .S interactions may be important in that case. This is to our knowledge the first theoretical study of the Au. . .S interaction.
Acknowledgements P.P. and N.R. were supported by The Academy of Finland. The stay of F.M. at Helsinki was partially financed by the Centre for International Mobility (CIMO), Finland, and the Fondecyt Project No. 1020141, Chile. Computer resources at CSC, Finland, were used.
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