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Theoretical prediction of the structure and the bond energy of the gold (I) complex Au+ (H2O)
5 August 1994
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 225 ( 1994) 416-420
Theoretical prediction of the structure and the bond energy of the gold (I) complex Au+ ( H20) Jan Hrukik, Detlef Schriider, Helmut Schwarz Institutfir OrganischeChemie der TechnischenUniversitiit Berlin, D-10623 Berlin, Germany Received 28 February 1994
The Au+ (HsO) complex has been studied by ab initio MO calculations using a relativistic effective core potential with a large polarized basis set. Geometry optimixations at the MP2 and the CISD levels of theory lead to a non-planar C.-symmetrical structure 1 withan Au-O bond length of 2.133 A and a hardly distorted water substructure with a wag angle 0, of 47”. In contrast to other cationic transition-metal hydrates, the corresponding planar structure 2 with &,. symmetry is slightly higher in energy and exhibits one imaginary frequency (V= i270 cm-’ ). Thus 2 is a transition structure and its further analysis reveals that the transition corresponds to the ‘umbrella’ vibration of the pyramidalized water substructure (le2). The pyramidalization of 1 can be attributed to m-hybridization of the water molecule upon complexation by the Au+ cation, due to the relativistically enlarged ionization energy of the gold atom. The calculated bond dissociation energies of the Au+ ( Hz0 ) complex converges to 36.0 kcal/mol at the CCSD(T) level of theory. Similar energetic and structural results are obtained using a density functional theory approach, i.e. BDE=37.0 kcal/mol, r(Au-0) =2.196 A, and 6,=49’.
1. Introduction The solvation of ions by dipolar solvents represents a fundamental phenomenon in chemistry and biology. At the molecular level complexes of main group and transition-metal cations with small dipolar ligands as the water molecule, have attracted considerable interest in the last decade ‘. A series of experimental studies established accurate bond dissociation energies (BDE) of M+ (H,O) complexes of transition metals [ 2 1, and theoretical studies of these systems are in good agreement with the experimental findings, provided correlation and polarization effects are taken into account by appropriate theoretical methods [ 3,4]. Recently, a systematic ’ For recent theoretical approaches to main group element hydrates, see Ref. [ 11.
study of the M+ ( HzO) complexes of the first-row transition-metal series has been published, and the effects of different methods and basis sets were discussed in great detail [ 4 1. Heavy elements exhibit additional relativistic effects which affect the structures and stabilities of M+ (H,O) complexes. These relativistic effects on structure and bonding are not yet fully understood in all its consequences, and they are expected to be exceptionally large for gold compounds [ $61. In the comparison of Au with its lower homologues, i.e. Cu and Ag, the situation is referred to as the gold anomaly [ 61. Since accurate all-electron relativistic calculations for molecules containing heavy elements are extremely time-consuming, the use of relativistic effective core potentials (RECP) offers a comfortable and reliable alternative to account for relativistic effects, such as mass-velocity and Darwin terms. Re-
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZOOO9-2614(94)00664-C
J. I-In&k et al. /Chemical Physics Letters 225 (1994) 416420
cently, Schwerdtfeger et al. [ 7 ] used a relativistic effective core potential (RECP) parameter set [ 8 ] for the gold atom, which permits calculation of structures, binding energies and vibrational frequencies for a series of diatomic gold compounds with reasonable accuracy [ 7 1. In fact, it has been demonstrated [ 9 ] that the theoretically predicted bond dissociation energy of the elusive gold (I) fluoride agrees well with the experimental value as derived from Fourier transform ion cyclotron resonance mass spectrometry. Here, we report a computational study of the monocationic complex of Au+ with a water molecule. The accurate calculation of BDE (Au+-H20) will guide experimentalists to determine binding energies for a series of Au(L)+ complexes with various ligands L by using the ion/molecule reaction bracketing technique ‘.
2. Computational details For the gold atom we used a multi-electron adjusted, spin-orbit averaged RECP [ 81 and augmented the basis set with additional diffuse and polarization functions resulting in a contracted [ lOs/ 8p/7d/ If] / (9s/5p/6d/ If) basis set. For the other atoms the Dunning TZ2P basis sets were employed, augmented with an additional f-polarization function (&= 1.85) for the oxygen atom, [ lOs/6p/2d/
lfl/(WWWW,
and [Ss/2p/ld1/(3s/2p/ld)
for the hydrogen atom (t = 0.156) [ 111. Full geometry optimizations have been performed using standard procedures at the SCF, MP2 and CISD levels of theory, accounting for the effect of correlation energy. Since the inclusion of correlation energy did not result in substantial changes to the geometry (see below), only the Au-O bond length has been partially re-optimized for the CCSD (T ) approach; harmonic frequencies have been calculated at the MP2 level of theory. In addition, we performed density functional theory (DFT) [ 121 computations by using the same RECP and basis sets for all atoms. We applied Becke’s three parameter fit with the functional of Lee, Yang and Parr, which accounts for both local and non-local ’ For an experimental observation of a structurally unspecified Au+(H*O) complex, see Ref. [lo].
417
terms [ 13 1. As recently evaluated by Johnson et al. [ 14 1, this hybrid functional results in reliable structures and energetics for a series of di- and poly-atomic molecules. All valence electrons were correlated both by perturbational (MP2) and configuration interaction (CI ) treatments. Bond dissociation energies (BDEs) were computed as the differences between the total energies of the complex and the isolated species. All calculations were performed using the GAUSSIAN 92 DFT program package [ 151 on either IBM/R!3 6000 workstations or a CRAY-YMP computer of the Konrad Zuse Rechenzentrum, Berlin.
3. Results and discussion Table 1 displays the geometries and energetics of Au+ ( H20) for the C,-symmetrical structure 1 and the C2,-symmetrical species 2 as obtained at various computational levels. It is well known that the SCF procedure overestimates metal ligand bond distances significantly and may lead to erroneous results as far as minimum geometries and transition structures are concerned [ 161. In fact, r(Au-0) decreases significantly if the correlation energy is taken into account by applying second-order Msller-Plesset perturbation theory ( MP2 ) ; furthermore, at the MP2 level the planarity of Au+ ( H20) vanishes and the global minimum corresponds to the non-planar C,-symmetrical structure 1 (Table 1, Fig. 1). Since the Au+ ( H20) complex represents a closed-shell system which results from the interaction of Au+ ( ‘S) with the dipolar Hz0 ( *Ai) molecule, even a relatively simple perturbational treatment,such as MP2 is expected to yield reasonable structural features and energetics [ 17 1. Accordingly, the structural and energetical differences for 1 as computed at the MP2 and the CISD levels of theory are almost negligible, i.e. r(Au0) = 2.132 and 2.133 A, respectively; BDE= 38.8 and 38.5 kcal/mol. Upon re-optimizationof r(Au-O), for 1 at the highest level of theory applied, i.e. CCSD(T), the bond distance only slightly increases from 2.133 to 2.159 A, accompanied by a further stabilization of 1 by 0.1 kcal/mol; similar effects are found for the transition structure 2. Thus, we conclude that the geometry optimization at the MP2 level of theory is
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et al. /Chemical
Physics Letters 225 (1994) 416-420
Table 1 Geometries of the Au+ (HsO) complexes for the C,-symmetrical minimum structure 1 and the transition structure 2 at various levels of theory. (Bond lengths in A and bond angles in deg, bond dissociation energies in kcal/mol) r(Au-0)
W-H)
(Y
6,
BDE .
1
SCF MP2 CISD+D CCSD(T) CCSD(T) DFT
2.306 2.132 2.133 2.133 = 2.159 * 2.198
0.944 0.964 0.964 0.964 = 0.964 = 0.968
126.0 118.8 119.9 119.9 c 119.9 c 117.4
180 46.7 46.1 46.7 = 46.1’ 49.0
25.9 b 38.8 38.5 35.9 36.0 37.0
2
SCF MP2 CISD+D CCSD(T) CCSD(T)
2.306 2.138 2.196 2.196= 2.152*
0.944 0.962 0.953 0.953 c 0.953 =
126.0 125.7 125.9 125.9 c 125.9 =
180 180 180 180 180
25.9 36.7 37.9 35.1 35.3
~BDEwithrespecttoisolatedAu+(‘S)andHzO(’A,). b At the SCF level of theory, a C,,-symmetrical structure corresponds to the global minimum. c Single-point energy calculation at the CISD optimized geometries. * r(Au-0) has been optimized at this level of theory.
q-o.88
0.964
q= -0.72
1 W,) Fig. 1. Geometries and Mulliken charges of 1 and 2 calculated at the CISD level of theory (bond lengths in A,bond angles in deg ) .
sufficient for a proper description of gold (I) compoundssuchasland2 [7,17]. The bonding in 1 can be described as a combination of electrostatic ion/dipole interaction and significant covalent contributions. The geometry of the water ligand in 1 (r(O-H) ~0.964 A, HOH angle= 105.6”) is hardly perturbed as compared to the isolated molecule (r(O-H) =0.959 A, HOH angle= 104.4”), and despite the relatively high ionization energy IE of Au (IE = 9.23 eV [ 18 ] ) the atomic charges as derived from a Mulliken population analysis are comparable to water complexes of other transition metal cations and main group element cations as well (Fig. 1) [ 1,3,4]. The planar structure 2 is characterized by a larger HOH angle (108.2” for CISD) with a slightly enhanced Au-O bond length (r(Au-0)=2.196 A). However, at the correlated computational levels 2 corresponds to a transition structure, since it exhibits
one imaginary frequency at the MP2 level of theory (i270 cm-‘, Table 2), pointing to a degenerate rearrangement 1+2. This frequency corresponds to a wagging or ‘umbrella’ motion of the pyramidalized water substructure [ 19 1. At all levels of theory the energy difference between 1 and 2 does not exceed 2 kcal/mol, indicating a flat potential energy surface for this wagging motion; this is also implied by the magnitude of the imaginary frequency of 2. The structures of neutral and ionic hydrates constitutes a long-standing topic in coordination chemistry and the origin of the effects is not yet fully understood. Almost all previous ab initio MO calculations of cationic water complexes of transition metals M revealed planar Cz,-symmetrical structures as minima [ 3,4,19]. The planarity of the transition Table 2 Harmonic vibrational frequencies (cm-i, unscaled) of 1 and 2 calculated numerically at the MP2 level of theory Symmetry
1
Symmetry
2
A A’ A” A’ A’ A”
351.5 418.2 655.2 1645.1 3782.2 3881.1
b, a1 bz ai a1 bz
i270.2 342.5 575.8 1635.2 3812.5 3916.8
J. Hndik et al. /Chemical Physics Letters 225 (1994) 416420
metal complexes was rationalized by the operation of a predominant ion/dipole, rather than covalent interactions, being indicated by relatively large M-O distances. However, some hydrates of main group element cations [ 3,4,20] also possess non-planar geometries, which result from covalent contributions to the bonding; this latter effect is accompanied by decreased M-O bond distances and increased stabilization energies (see also Ref. [ 2 1 ] ) . The finding that 2 exhibits an imaginary frequency at the MP2 level implies that the deviation from planarity is indeed a characteristic feature of this cationic gold complex. In 1988, Davy and Hall [ 191 proposed that the deviation from CzVsymmetry in M+ ( HzO) complexes can be attributed to the acidity of the metal cations, but all cations and dications studied by these authors were not sufficiently acidic to cause deviations from planar structures. Due to relativistic effects, the ionization energy of atomic gold is relatively high compared to the lower homologues copper and silver, leading to a larger covalent character of the bonding of A+ to the water ligand compared to M+ (H,O) complexes of other transition metals. In terms of Lewis acidity the high ionization energy of Au forces the Hz0 molecule to undergo rehybridization to yield the C,-symmetrical non-planar structure in analogy to the CsV structure of HjO+
WI. The larger covalent character of 1 is in line with the magnitude of the electrostatic interactions in 1 and 2. According to a simple point-charge model, the Coulombic part of the interaction amounts to 28 kcal/ mol in the ion-dipole complex 2; this term decreases to 19 kcal/mol in 1, due to the bent orientation of the water dipole and the positive charge. In addition, we examined 1 by using a density functional theory approach [ 12 1, and the DFI results serve as a further verification of our results. Considering that DFT is a fundamentally different computational method, the findings for 1 are similar using DFT as compared to the other approaches. Neither the binding energy nor the structural features of 1 differ much from the MP2 and CISD levels of theory, i.e. BDE= 37.0 kcal/mol, r(Au-0) = 2.196 A, r(O-H) =0.968 A, (Y= 117.4”, and 8,=49.0”. Thus, a combination of DFT with a RECP seems to offer a versatile alternative for the computational description of cationic gold complexes.
419
4. Conclusion The geometries and energetics of Au+ ( HzO) are well described at the MP2 level of theory, ifan appropriate RECP is used to account for relativistic effects. As far as transition metals are concerned, 1 represents the first example of a non-planar cationic M+(H20) complex, exhibiting the interplay between electrostatic and covalent bonding in this class of compounds. The convergence of the binding energy of 1 at various levels of theory may serve as a reliable anchor point for forthcoming ion/molecule reactions aimed at bracketing Au+ (ligand) bond dissociation energies.
Acknowledgement Continuous financial support was provided by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. We are grateful to DEGUSSA AG, Hanau, for the generous assistance of our ‘gold project’, Dr. Peter Schwerdtfeger, Auckland, New Zealand, is acknowledged for providing us with the relativistic pseudopotential for the gold atom.
References [ 1] F. Ramondo, L. Bencivenni, V. Rossi and R. Caminiti, J. Mol. Struct. THEOCHEM 277 (1992) 185; K Hashimoto and S. Iwata, J. Phys. Chem. 93 (1989) 2165; K. Hashimoto, N. Yoda, Y. Gsamura and S. Iwata, J. Am. Chem. Sot. 112 (1990) 7261; M. Sodupe and C.W. Bauschlicher Jr., Chem. Phys. Letters 192 (1992) 185; J. HruUk, D. Stiickigt and H. Schwatz, Chem. Phys. Letters 221 (1994) 518; M. Sodupe and C.W. Bauschlicher Jr., Chem. Phys. Letters 212 (1993) 624; P.R. Chattaraj and P. von R. Schleyer, J. Am. Chem. Sot. 116 (1994) 1067. [ 2 ] T.F. Ma8nera,D.E. David and J. Michl, J. Am. Chem. Sot. 111 (1989) 4100; P.J. Marinelli and R.R. Squires, J. Am. Chem. Sot. 111 (1989) 4101; T.F. Magnera, D.E. David, D. Stulik, R.G. Orth, H.T. Jonkman and J. Michl, J. Am. Chem. Sot. 111 (1989) 5036; R.H. Schultz and P.B. Armentrout, J. Phys. Chem. 97 (1993) 596; M.S. El-Shall, ICE. Schriver, R.L. Whetten and M. MeotNer, J. Phys. Chem. 93 (1989) 7969;
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N.F. Dalleska, K. Hinma, L.S. Sunderlin and P.B. Armentrout, J. Am. Chem. Sot. 116 ( 1994) 35 19. [ 31 M. Rosi and C.W. Bauschlicher Jr., J. Chem. Phys. 90 (1989) 7264; 92 (1990) 1876; A. Fiedler, J. Hrugak and H. Schwarx, Z. Physik. Chem. 175 (1992) 15; E. Magnusson and N.W. Moriarty, J. Comput. Chem. 14 (1993) 961. [4] C.W. Bauschlicher Jr. and S. Langhoff, in: Gas-phase metal reactions, ed. A. Fontijn (Elsevier, Amsterdam, 1992) p. 277. [ 51P. Pyykkii and J.P. Desclaux, Nature 266 (1977) 337; N. Riisch, A. G&ling, D.E. Ellis and H. Schmidbaur, Angew. Chem. 101 (1989) 1410; Angew. Chem. Intern. Ed. Engl. 28 (1989) 1402; A. Grohmann, J. Riede and H. Schmidbaur, Nature 345 (1990) 140; E. Zeller, H. Beruda, A. Kolb, P. Bissinger, J. Riede and H. Schmidbaur, Nature 352 (1991) 141. [6] P. Pyykko, Chem. Rev. 88 (1988) 563. [ 71 P. Schwerdtfeger, M. Dolg, W.H.E. Schwarx, G.A. Bowmaker and P.D.W. Boyd, J. Chem. Phys. 91 (1989) 1762; P. Schwerdtfeger, J. Am. Chem. Sot. 111 (1989) 7261; P. Schwerdtfeger, P.D.W. Boyd, AK. Burrell, W.T. Robinson and M.J. Taylor, Inorg. Chem. 29 ( 1990) 3593. [ 81 U. Wedig, Ph.D. Thesis, Univertitiit Stuttgart ( 1988). [9] D. Schr&ler, J. Hi-&k, LC. Tomieporth-Oetting, T.M. Klap&ke and H. Schwarx, Angew. Chem. 106 (1994) 223; Angew. Chem. Intern. Ed. Engl. 33 (1994) 212; P. Schwerdtfeger, J.S. McFeaters, R.L. Stephens, M.J. Liddell, M. Dolg and B.A. Hess, Chem. Phys. Letters 218 ( 1994) 362.
[lo] D.A. Weiland C.L. Wilkins, J. Am. Chem. Sot. 107 (1985) 7318. [ 111 S. Huzinaga, J. Chem. Phys. 42 (1965) 1293; R.A. Kendall, T.H. Dunning Jr. and R.J. Harrison, J. Chem. Phys. 96 (1992) 6796. [ 121 T. Ziegler, Chem. Rev. 91 (1991) 651. [ 131 A.D. Becke, J. Chem. Phys. 96 (1992) 2155; C. Lee, W. Yang and R.G. Parr, Phys. Rev. B 37 (1988) 785. [ 141 B.G. Johnson, P.M.W. Gill and J.A. Pople, J. Chem. Phys. 98 (1993) 5612. [ 151 M.J. Frisch, G.W. TrucM, H.W. Schlegel, P.M.W. Gill, B.G. Johnson, M.W. Wang, J.B. Foresman, M.A. Robb, M. HeadGordon, E.S. Replogle, R. Gomperts, J.L. A&es, K. Raghavachari, J.S. Binkley , C. Gonzales, R.L. Martin, D.J. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92 DFT, Revision F.2 (Gaussian Inc., Pittsburg, 1993). [ 16 ] W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986). [ 17 ] A. Veldkamp and G. Frenking, Organometallics 12 ( 1993) 4613. [ 181 S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, R.D. Levin and W.G. Mallard, J. Phys. Chem. Ref. Data 17 (1988) Suppl. 1. [19]R.D.DavyandM.B.Hall, Inorg.Chem.27 (1988) 1417. [20] G. Bouchoux, MassSpectrom. Rev. 7 (1988) 1; D. Schrtier, F. Grandinetti, J. Hrugak and H. Schwarx, J. Phys. Chem. 96 (1992) 4841. [ 2 1 ] M. Kaupp, P. von R. Schleyer, H. Stoll and H. Preuss, J. Am.Chem.Soc. 113 (1991)6012. [ 221 R.S. Drago, D.C. Ferris and N. Wong, J. Am. Chem. Sot. 112 (1990) 8953.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 225 ( 1994) 416-420
Theoretical prediction of the structure and the bond energy of the gold (I) complex Au+ ( H20) Jan Hrukik, Detlef Schriider, Helmut Schwarz Institutfir OrganischeChemie der TechnischenUniversitiit Berlin, D-10623 Berlin, Germany Received 28 February 1994
The Au+ (HsO) complex has been studied by ab initio MO calculations using a relativistic effective core potential with a large polarized basis set. Geometry optimixations at the MP2 and the CISD levels of theory lead to a non-planar C.-symmetrical structure 1 withan Au-O bond length of 2.133 A and a hardly distorted water substructure with a wag angle 0, of 47”. In contrast to other cationic transition-metal hydrates, the corresponding planar structure 2 with &,. symmetry is slightly higher in energy and exhibits one imaginary frequency (V= i270 cm-’ ). Thus 2 is a transition structure and its further analysis reveals that the transition corresponds to the ‘umbrella’ vibration of the pyramidalized water substructure (le2). The pyramidalization of 1 can be attributed to m-hybridization of the water molecule upon complexation by the Au+ cation, due to the relativistically enlarged ionization energy of the gold atom. The calculated bond dissociation energies of the Au+ ( Hz0 ) complex converges to 36.0 kcal/mol at the CCSD(T) level of theory. Similar energetic and structural results are obtained using a density functional theory approach, i.e. BDE=37.0 kcal/mol, r(Au-0) =2.196 A, and 6,=49’.
1. Introduction The solvation of ions by dipolar solvents represents a fundamental phenomenon in chemistry and biology. At the molecular level complexes of main group and transition-metal cations with small dipolar ligands as the water molecule, have attracted considerable interest in the last decade ‘. A series of experimental studies established accurate bond dissociation energies (BDE) of M+ (H,O) complexes of transition metals [ 2 1, and theoretical studies of these systems are in good agreement with the experimental findings, provided correlation and polarization effects are taken into account by appropriate theoretical methods [ 3,4]. Recently, a systematic ’ For recent theoretical approaches to main group element hydrates, see Ref. [ 11.
study of the M+ ( HzO) complexes of the first-row transition-metal series has been published, and the effects of different methods and basis sets were discussed in great detail [ 4 1. Heavy elements exhibit additional relativistic effects which affect the structures and stabilities of M+ (H,O) complexes. These relativistic effects on structure and bonding are not yet fully understood in all its consequences, and they are expected to be exceptionally large for gold compounds [ $61. In the comparison of Au with its lower homologues, i.e. Cu and Ag, the situation is referred to as the gold anomaly [ 61. Since accurate all-electron relativistic calculations for molecules containing heavy elements are extremely time-consuming, the use of relativistic effective core potentials (RECP) offers a comfortable and reliable alternative to account for relativistic effects, such as mass-velocity and Darwin terms. Re-
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDZOOO9-2614(94)00664-C
J. I-In&k et al. /Chemical Physics Letters 225 (1994) 416420
cently, Schwerdtfeger et al. [ 7 ] used a relativistic effective core potential (RECP) parameter set [ 8 ] for the gold atom, which permits calculation of structures, binding energies and vibrational frequencies for a series of diatomic gold compounds with reasonable accuracy [ 7 1. In fact, it has been demonstrated [ 9 ] that the theoretically predicted bond dissociation energy of the elusive gold (I) fluoride agrees well with the experimental value as derived from Fourier transform ion cyclotron resonance mass spectrometry. Here, we report a computational study of the monocationic complex of Au+ with a water molecule. The accurate calculation of BDE (Au+-H20) will guide experimentalists to determine binding energies for a series of Au(L)+ complexes with various ligands L by using the ion/molecule reaction bracketing technique ‘.
2. Computational details For the gold atom we used a multi-electron adjusted, spin-orbit averaged RECP [ 81 and augmented the basis set with additional diffuse and polarization functions resulting in a contracted [ lOs/ 8p/7d/ If] / (9s/5p/6d/ If) basis set. For the other atoms the Dunning TZ2P basis sets were employed, augmented with an additional f-polarization function (&= 1.85) for the oxygen atom, [ lOs/6p/2d/
lfl/(WWWW,
and [Ss/2p/ld1/(3s/2p/ld)
for the hydrogen atom (t = 0.156) [ 111. Full geometry optimizations have been performed using standard procedures at the SCF, MP2 and CISD levels of theory, accounting for the effect of correlation energy. Since the inclusion of correlation energy did not result in substantial changes to the geometry (see below), only the Au-O bond length has been partially re-optimized for the CCSD (T ) approach; harmonic frequencies have been calculated at the MP2 level of theory. In addition, we performed density functional theory (DFT) [ 121 computations by using the same RECP and basis sets for all atoms. We applied Becke’s three parameter fit with the functional of Lee, Yang and Parr, which accounts for both local and non-local ’ For an experimental observation of a structurally unspecified Au+(H*O) complex, see Ref. [lo].
417
terms [ 13 1. As recently evaluated by Johnson et al. [ 14 1, this hybrid functional results in reliable structures and energetics for a series of di- and poly-atomic molecules. All valence electrons were correlated both by perturbational (MP2) and configuration interaction (CI ) treatments. Bond dissociation energies (BDEs) were computed as the differences between the total energies of the complex and the isolated species. All calculations were performed using the GAUSSIAN 92 DFT program package [ 151 on either IBM/R!3 6000 workstations or a CRAY-YMP computer of the Konrad Zuse Rechenzentrum, Berlin.
3. Results and discussion Table 1 displays the geometries and energetics of Au+ ( H20) for the C,-symmetrical structure 1 and the C2,-symmetrical species 2 as obtained at various computational levels. It is well known that the SCF procedure overestimates metal ligand bond distances significantly and may lead to erroneous results as far as minimum geometries and transition structures are concerned [ 161. In fact, r(Au-0) decreases significantly if the correlation energy is taken into account by applying second-order Msller-Plesset perturbation theory ( MP2 ) ; furthermore, at the MP2 level the planarity of Au+ ( H20) vanishes and the global minimum corresponds to the non-planar C,-symmetrical structure 1 (Table 1, Fig. 1). Since the Au+ ( H20) complex represents a closed-shell system which results from the interaction of Au+ ( ‘S) with the dipolar Hz0 ( *Ai) molecule, even a relatively simple perturbational treatment,such as MP2 is expected to yield reasonable structural features and energetics [ 17 1. Accordingly, the structural and energetical differences for 1 as computed at the MP2 and the CISD levels of theory are almost negligible, i.e. r(Au0) = 2.132 and 2.133 A, respectively; BDE= 38.8 and 38.5 kcal/mol. Upon re-optimizationof r(Au-O), for 1 at the highest level of theory applied, i.e. CCSD(T), the bond distance only slightly increases from 2.133 to 2.159 A, accompanied by a further stabilization of 1 by 0.1 kcal/mol; similar effects are found for the transition structure 2. Thus, we conclude that the geometry optimization at the MP2 level of theory is
418
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et al. /Chemical
Physics Letters 225 (1994) 416-420
Table 1 Geometries of the Au+ (HsO) complexes for the C,-symmetrical minimum structure 1 and the transition structure 2 at various levels of theory. (Bond lengths in A and bond angles in deg, bond dissociation energies in kcal/mol) r(Au-0)
W-H)
(Y
6,
BDE .
1
SCF MP2 CISD+D CCSD(T) CCSD(T) DFT
2.306 2.132 2.133 2.133 = 2.159 * 2.198
0.944 0.964 0.964 0.964 = 0.964 = 0.968
126.0 118.8 119.9 119.9 c 119.9 c 117.4
180 46.7 46.1 46.7 = 46.1’ 49.0
25.9 b 38.8 38.5 35.9 36.0 37.0
2
SCF MP2 CISD+D CCSD(T) CCSD(T)
2.306 2.138 2.196 2.196= 2.152*
0.944 0.962 0.953 0.953 c 0.953 =
126.0 125.7 125.9 125.9 c 125.9 =
180 180 180 180 180
25.9 36.7 37.9 35.1 35.3
~BDEwithrespecttoisolatedAu+(‘S)andHzO(’A,). b At the SCF level of theory, a C,,-symmetrical structure corresponds to the global minimum. c Single-point energy calculation at the CISD optimized geometries. * r(Au-0) has been optimized at this level of theory.
q-o.88
0.964
q= -0.72
1 W,) Fig. 1. Geometries and Mulliken charges of 1 and 2 calculated at the CISD level of theory (bond lengths in A,bond angles in deg ) .
sufficient for a proper description of gold (I) compoundssuchasland2 [7,17]. The bonding in 1 can be described as a combination of electrostatic ion/dipole interaction and significant covalent contributions. The geometry of the water ligand in 1 (r(O-H) ~0.964 A, HOH angle= 105.6”) is hardly perturbed as compared to the isolated molecule (r(O-H) =0.959 A, HOH angle= 104.4”), and despite the relatively high ionization energy IE of Au (IE = 9.23 eV [ 18 ] ) the atomic charges as derived from a Mulliken population analysis are comparable to water complexes of other transition metal cations and main group element cations as well (Fig. 1) [ 1,3,4]. The planar structure 2 is characterized by a larger HOH angle (108.2” for CISD) with a slightly enhanced Au-O bond length (r(Au-0)=2.196 A). However, at the correlated computational levels 2 corresponds to a transition structure, since it exhibits
one imaginary frequency at the MP2 level of theory (i270 cm-‘, Table 2), pointing to a degenerate rearrangement 1+2. This frequency corresponds to a wagging or ‘umbrella’ motion of the pyramidalized water substructure [ 19 1. At all levels of theory the energy difference between 1 and 2 does not exceed 2 kcal/mol, indicating a flat potential energy surface for this wagging motion; this is also implied by the magnitude of the imaginary frequency of 2. The structures of neutral and ionic hydrates constitutes a long-standing topic in coordination chemistry and the origin of the effects is not yet fully understood. Almost all previous ab initio MO calculations of cationic water complexes of transition metals M revealed planar Cz,-symmetrical structures as minima [ 3,4,19]. The planarity of the transition Table 2 Harmonic vibrational frequencies (cm-i, unscaled) of 1 and 2 calculated numerically at the MP2 level of theory Symmetry
1
Symmetry
2
A A’ A” A’ A’ A”
351.5 418.2 655.2 1645.1 3782.2 3881.1
b, a1 bz ai a1 bz
i270.2 342.5 575.8 1635.2 3812.5 3916.8
J. Hndik et al. /Chemical Physics Letters 225 (1994) 416420
metal complexes was rationalized by the operation of a predominant ion/dipole, rather than covalent interactions, being indicated by relatively large M-O distances. However, some hydrates of main group element cations [ 3,4,20] also possess non-planar geometries, which result from covalent contributions to the bonding; this latter effect is accompanied by decreased M-O bond distances and increased stabilization energies (see also Ref. [ 2 1 ] ) . The finding that 2 exhibits an imaginary frequency at the MP2 level implies that the deviation from planarity is indeed a characteristic feature of this cationic gold complex. In 1988, Davy and Hall [ 191 proposed that the deviation from CzVsymmetry in M+ ( HzO) complexes can be attributed to the acidity of the metal cations, but all cations and dications studied by these authors were not sufficiently acidic to cause deviations from planar structures. Due to relativistic effects, the ionization energy of atomic gold is relatively high compared to the lower homologues copper and silver, leading to a larger covalent character of the bonding of A+ to the water ligand compared to M+ (H,O) complexes of other transition metals. In terms of Lewis acidity the high ionization energy of Au forces the Hz0 molecule to undergo rehybridization to yield the C,-symmetrical non-planar structure in analogy to the CsV structure of HjO+
WI. The larger covalent character of 1 is in line with the magnitude of the electrostatic interactions in 1 and 2. According to a simple point-charge model, the Coulombic part of the interaction amounts to 28 kcal/ mol in the ion-dipole complex 2; this term decreases to 19 kcal/mol in 1, due to the bent orientation of the water dipole and the positive charge. In addition, we examined 1 by using a density functional theory approach [ 12 1, and the DFI results serve as a further verification of our results. Considering that DFT is a fundamentally different computational method, the findings for 1 are similar using DFT as compared to the other approaches. Neither the binding energy nor the structural features of 1 differ much from the MP2 and CISD levels of theory, i.e. BDE= 37.0 kcal/mol, r(Au-0) = 2.196 A, r(O-H) =0.968 A, (Y= 117.4”, and 8,=49.0”. Thus, a combination of DFT with a RECP seems to offer a versatile alternative for the computational description of cationic gold complexes.
419
4. Conclusion The geometries and energetics of Au+ ( HzO) are well described at the MP2 level of theory, ifan appropriate RECP is used to account for relativistic effects. As far as transition metals are concerned, 1 represents the first example of a non-planar cationic M+(H20) complex, exhibiting the interplay between electrostatic and covalent bonding in this class of compounds. The convergence of the binding energy of 1 at various levels of theory may serve as a reliable anchor point for forthcoming ion/molecule reactions aimed at bracketing Au+ (ligand) bond dissociation energies.
Acknowledgement Continuous financial support was provided by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. We are grateful to DEGUSSA AG, Hanau, for the generous assistance of our ‘gold project’, Dr. Peter Schwerdtfeger, Auckland, New Zealand, is acknowledged for providing us with the relativistic pseudopotential for the gold atom.
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