J. Phys. Chem. 1996, 100, 12253-12260
12253
A Comparative Computational Study of Cationic Coinage Metal-Ethylene Complexes (C2H4)M+ (M ) Cu, Ag, and Au) Roland H. Hertwig, Wolfram Koch,* Detlef Schro1 der, and Helmut Schwarz Institut fu¨ r Organische Chemie der Technischen UniVersita¨ t Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany
Jan Hrusˇa´ k Academy of Sciences of the Czech Republic, J. HeyroVsky Institute of Physical Chemistry, DolejsˇkoVa 3, CZ-18223 Prague 8, Czech Republic
Peter Schwerdtfeger Computational Material Science and Engineering Research Center, Department of Chemistry and the School of Engineering, UniVersity of Auckland, PriVate Bag 92019, Auckland, New Zealand ReceiVed: October 16, 1995; In Final Form: May 21, 1996X
The cationic (C2H4)M+ complexes (M ) Cu, Ag, and Au) have been examined by different ab initio molecular orbital, density functional (DFT), and density functional/Hartree-Fock (DFT/HF) hybrid methods using relativistic effective core potentials and a quasi-relativistic approach to account for relativistic effects. For (C2H4)Au+ a substantial relativistic stabilization is observed, such that the computed binding energies are almost twice as high than for (C2H4)Ag+ and still significantly higher than for (C2H4)Cu+. Structural features and energetics obtained at the various computational levels, although they differ significantly in their computational demands, are in satisfying agreement with each other, adding to the level of confidence that can be attributed to the computationally economic DFT and DFT/HF hybrid methods. In order to determine the nature of the bonding in these (C2H4)M+ complexes, an energy decomposition scheme is applied to the DFT results. For all three metal cations, the interaction with ethylene shows large covalent contributions. The major part of the covalent terms stems from σ-donor contribution from the ligand to the metal, whereas π-acceptor bonding (back-bonding) is less important. An atoms-in-molecules (AIM) analysis of the charge density distribution reveals cyclic structures for (C2H4)Au+ and (C2H4)Cu+, whereas (C2H4)Ag+ is T-shaped.
Introduction Transition-metal complexes with organic ligands are of paramount interest,1 especially with respect to their possible implications in bond-activation processes and catalysis. The complexes of ethylene are of particular importance, since ethylene represents a prototype for unsaturated organic ligands. The bonding in ethylene complexes is often described by the Dewar-Chatt-Duncanson2,3 model of synergistic combination of σ-donor and π-acceptor interaction between the metal and the olefinic π-system, i.e. electron donation from a filled π-orbital of the olefin into vacant s-, p-, or d-orbitals (or their hybrids) of the metal (σ-donation) and a binding overlap between an occupied d-orbital of the metal with the empty π*orbital of the olefin (π-back-donation). This classical description has widely been used for a qualitative understanding of chemical properties in other metal-olefin complexes. An early work of Ziegler and Rauk4 described the bonding in (C2H4)M+ complexes for M ) Cu, Ag, and Au and found σ-donation and π-back-donation to be important in (C2H4)Cu+, while for M ) Ag+ and Au+ the contributions of π-backdonation are much smaller. The corresponding neutral (C2H4)M complexes have recently been studied by Nicolas and Spiegelman,5 who concluded that all three systems possess C2Vsymmetrical 2A1 ground states with predominant van der Waals interaction and bond dissociation energies (BDEs) of less than 12 kcal mol-1. Miralles-Sabater et al.6 performed configuration X
Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(95)03064-4 CCC: $12.00
interaction (CI) calculations on (C2H4)Cu+ and (C2H4)Ag+ and characterized the bonding as being mainly electrostatic. The latter description is also in agreement with calculations by Sodupe et al.7 which revealed BDE values of 36 and 40 kcal mol-1 for (C2H4)Cu+ using modified coupled pair function (MCPF) and coupled cluster (CCSD(T)) approaches, respectively. Experimental information for these (C2H4)M+ complexes is more limited: In the case of (C2H4)Cu+ there exists for the time being only a lower limit of BDE g 23 kcal mol-1.8 For (C2H4)Ag+, Guo and Castleman9 determined a BDE of 33.7 kcal mol-1 in a combined mass spectrometric and theoretical study and argued that the interaction should have large covalent contributions. Following the previous gas-phase bracketing experiments by Wilkins et al.,10 we recently11 evaluated a lower limit of 59 kcal mol-1 for the BDE of (C2H4)Au+; note that even this lower limit exceeds the values for the analogous Cu+ and Ag+ complexes almost by a factor of 2. Upon completion of the present investigation, we became aware of a recent, yet unpublished, computational work by Basch and Hoz,12 who used relativistic effective core potentials (RECPs) and second order Møller/Plesset perturbation theory (MP2) for geometry optimization, and quadratic configuration interaction (QCISD(T)) for the energetics. After correction for zero-point vibrational energy (ZPVE), they obtained BDEs of 43.2 kcal mol-1 for (C2H4)Cu+, 33.8 kcal mol-1 for (C2H4)Ag+, and 62.5 kcal mol-1 for (C2H4)Au+. Also, Frenking and co-workers13 have very recently investigated both cationic and neutral complexes of copper and © 1996 American Chemical Society
12254 J. Phys. Chem., Vol. 100, No. 30, 1996 the copper dimer with several unsaturated small hydrocarbons. For (C2H4)Cu+, they find a BDE of 46.8 kcal/mol at the MP2 level and 41.9 kcal/mol employing the CCSD(T) method based upon geometries obtained at the MP2 level of theory. An adequate quantum chemical description of (C2H4)M+ complexes requires a balance between the one- and manyparticle problem, i.e. flexible basis sets and a sophisticated treatment of electron correlation effects. In addition, systems containing heavy elements (Z > 50) exhibit relativistic effects,14 which may have significant influences on physicochemical properties. In fact, for third-row transition metals the relativistic contributions to the bonding are of the same order as the effects of electron correlation, and they are of particular relevance in gold compounds.15 The most convenient possibilities to approximate relativistic effects is the use of RECPs16 or explicit one-component schemes. Although both approaches do not cover spin-orbit interactions, the (C2H4)M+ complexes investigated in the present study are closed-shell singlets such that spin-orbit contributions should be of only minor importance. Here, we report a computational study of the complexes of the group 11 coinage metal cations Cu+, Ag+, and Au+ with ethylene at different levels of theory,17 including correlated MO methods, density functional techniques, and DFT/HF hybrid methods using flexible basis sets, ECPs and RECPs, and an explicit quasi-relativistic scheme. In addition to providing accurate complex stabilities, we discuss the qualitative character of the bonding, the equilibrium structures, and relativistic effects, which have been subject to controversial discussion in the literature. Theoretical Methods Optimized geometries, constrained to C2V symmetry, were determined by employing second-order Møller/Plesset perturbation theory,18 the local density approximation (LDA)19 augmented by nonlocal corrections for exchange and correlation due to Becke20 and Perdew21 (LDA/BP), and the B3LYP22 hybrid functional. Harmonic frequencies were obtained with MP2/RECP and B3LYP/RECP in order to identify each structure as a genuine minimum and to estimate ZPVEs. Additional calculations were carried out at the CCSD(T) level based on the MP2 optimized geometries. The MP2, CCSD(T), and B3LYP calculations were performed with GAUSSIAN92/ DFT,23 using energy adjusted scalar RECPs for the metals,24 in the case of (C2H4)Au+ a nonrelativistic ECP was also applied. The (R)ECPs covered a [Ne]-core for copper, an [Ar]3d10-core for silver, and a [Kr]4d104f14-core for gold, leaving in each case 19 electrons to be treated by the respective quantum mechanical procedure. The basis sets were augmented by two additional diffuse d- and one f-polarization function resulting in [10s/8p/ 7d/1f]/(9s/5p/6d/1f) contractions. For the carbon atom we used the standard Dunning TZ2P basis set25 with an additional f-polarization function, i.e. [10s/6p/2d/1f]/(5s/3p/2d/1f), and a [5s/2p/1d]/(3s/2p/1d) basis set for hydrogen. While basis sets of this size are required for MP2 and CCSD(T) procedures, much smaller basis sets would suffice without deterioration of the results in DFT or DFT/HF hybrid calculations.26,27 However, for the sake of comparability we used the same basis sets throughout. The basis set superposition error (BSSE) has not been considered in the present study, since (a) for DFT and DFT/HF hybrid methods, this error is usually small27 and (b) in the case of the MP2 and CCSD(T) calculations it is, at least to some extent, counterbalanced by the basis set incompleteness error (BSIE).28 The LDA/BP calculations were performed with the ADF suite of programs.29 Inner-shell electrons ([He] for C, [Ar] for Cu,
Hertwig et al. [Kr] for Ag, and [Xe]4f14 for Au) were treated in the frozencore approximation,30 and the valence orbitals were expanded as linear combinations of Slater type-orbital basis functions. Triple-ζ basis sets were used for the metals, since there are no polarized basis sets available for transition metals in ADF, whereas triple-ζ plus polarization basis sets were used for carbon and hydrogen, respectively. For a scalar relativistic treatment the ADF program offers the quasi-relativistic approach of Ziegler et al.,31 employing relativistic core potentials generated with the auxiliary program DIRAC.29 In addition, the KohnSham Hamiltonian was augmented by a first-order relativistic Hamiltonian to account for scalar relativistic effects, thereby affording a self-consistent relativistic treatment of the valence electrons. This procedure has been successfully applied to investigate relativistic effects before.32 If not stated otherwise we refer to quasi-relativistic LDA/BP results. Since the revision of the ADF program employed in the present investigation does not provide gradients in the quasi-relativistic scheme, geometries were optimized in a two-step procedure: First, the nonrelativistic minimum was located employing analytic gradient techniques, and afterwards only the metal-ligand distances were reoptimized by a sequence of quasi-relativistic single point energy calculations, keeping the ligand geometry fixed. To analyze the different contributions to the BDEs of the C2H4-M+ bonds, the ADF implementation33 of Morokuma’s34 decomposition scheme was applied to the LDA/BP results. Here, the total binding energy ∆Eb is expressed as a sum of the steric interaction ∆Esteric and the orbital interaction ∆EOI. The first term is composed of an electrostatic (∆Eelstat) and a Pauli component (∆EPauli) which is due to the antisymmetry of the wave function. ∆Esteric represents the energy gain (or loss) molecular fragments undergo, if they are brought together with the determinantal wave function simply taken as an antisymmetrized product of the unrelaxed fragment orbitals. Correspondingly, ∆EOI accounts for the change in energy arising from the presence of the bonding partner in terms of orbitalrelated contributions, like donor-acceptor and charge-transfer interactions as well as relaxation of the individual fragment orbitals. To further investigate the bonding situation we performed an AIM analysis of the charge density distribution as advocated by Bader35 to locate critical points of the charge density of the (C2H4)M+ complexes under investigation. Critical points are points where the gradient of the charge density with respect to the spatial coordinates vanishes. By calculation of the Hessian matrix of the charge density at a critical point, it can be further identified as either a bond (3,-1), a ring (3,1), or a cage (3,3) critical point. The numbers in parentheses reflect the rank of a critical point, which is usually three, since the charge density is a three-dimensional quantity, and its signature, respectively. The signature indicates the number of negative eigenvalues of the Hessian and is determined as the arithmetic sum of the signs of the three eigenvalues. A negative eigenvalue denoting a maximum is counted as -1; a positive as +1, pointing at a minimum of the charge density. A bond critical point represents a local minimum in one direction of space and a maximum in the remaining two. Using the nomenclature outlined above it is therefore a (3,-1) critical point and denotes a covalent bond between two atoms or nonnuclear attractors. The situation is reversed in the case of ring (3,-1) critical points. The charge density is at a maximum in two dimensions and a minimum in the remaining one. This analysis will enable us to decide whether bonding between the metal and the ligand occurs in the sense of a T-shape or a cyclic (metallacyclopropane) structure.35
Cationic Coinage Metal-Ethylene Complexes
J. Phys. Chem., Vol. 100, No. 30, 1996 12255
TABLE 1: Calculated Total Energies (Etot, Hartree) and Zero-Point Vibrational Energies (kcal/mol), Geometries (Å and deg), and Bond Dissociation Energies (BDE, kcal/mol) for (C2H4)M+ Using RECP for MP2, CCSD(T), and B3LYP and the Quasirelativistic Approach for LDA/BP (C2H4)Cu+ a
(C2H4)Ag+
(C2H4)Au+
MP2
CCSD(T)
B3LYP
LDA/BP
MP2
CCSD(T)
B3LYP
LDA/BP
MP2
CCSD(T)a
B3LYP
LDA/BP
rM-C rC-C rC-H RCCH θHCHCd
2.016 1.375 1.081 120.6 167.9
2.016 1.375 1.081 120.6 167.9
2.098 1.370 1.084 121.0 168.5
2.06 1.383 1.096 116.8 168.2
2.255 1.363 1.081 120.7 169.8
2.255 1.363 1.081 120.7 169.8
2.373 1.361 1.083 121.1 170.4
2.343 1.367 1.095 121.3 189.8
2.099 1.403 1.078 119.9 163.2
2.099 1.403 1.078 119.9 163.2
2.231 1.390 1.083 120.7 166.1
2.18 1.371 1.096 121.1 170.0
BDE ZPVE BDE(0 K)c
53.5 1.3 52.2
46.7
51.2 1.5 49.7
58.3
38.6 1.7 36.9
34.6
36.8 1.5 35.3
38.5
73.1 1.8 71.3
64.1
68.6 0.7 67.9
69.7
exptl
>23
45.4b
a
57.0b
a
32.9b
36.8b
67.9b
>59
33.7 b
62.3b
Calculated at the MP2 optimized geometry. Using ZPVE determined at the MP2 level. BDE corrected for ZPVE contributions at 0 K. d As compared to 180° in ethylene.
To locate and further analyze critical points of the charge density, one can in principle use techniques similar to those used for the characterization of potential energy surfaces.36 The search starts at some point that can be chosen arbitrarily as long as it is not too far from the estimated critical point employing a quasi-Newton-Raphson approach to locate the critical point iteratively by calculating the gradient of the charge density. The whole procedure can be completed within a few seconds of CPU time on a standard workstation. Once a critical point has been located, the Hessian matrix is calculated analytically and diagonalized to determine the three eigenvalues. Results and Discussion Table 1 summarizes the optimized geometries, total energies, and BDEs obtained at the various computational levels employed. In this section we first discuss the energetics of the (C2H4)M+ complexes for M ) Cu, Ag, and Au and then refer to the calculated geometries. Finally, we apply the Morokuma decomposition scheme as well as the AIM analysis and examine the bonding situation in these complexes and discuss the role of relativistic effects. A. Energetics. In the following we refer to 0 K values for all BDEs; i.e., ZPVE contributions are included. For the ZPVE corrections at the CCSD(T)/RECP and LDA/BP levels the MP2/ RECP frequencies were used; these corrections are, however, in all cases very small and range from 0.7 to 1.8 kcal/mol. The following general trends should be noted. The theoretically predicted values for the BDEs of C2H4-M+ (M ) Cu, Ag, and Au) are not very dependent on the methods applied; the largest deviation of 11.6 kcal/mol arises between the CCSD(T) and LDA/BP data for copper. Similar discontinuities for copper compounds have been reported previously and have been ascribed to the presence of a considerable amount of nondynamic correlation37 which is not recovered by the onedeterminantal approaches used here. The coupled cluster method is an exception, being able to account for nondynamic correlation up to a certain extent.38 Throughout all three complexes the LDA/BP and the MP2 approaches lead to BDEs which are consistently at the upper limit of the computed data, thus following in the case of approximate DFT the known trend to overestimate BDEs.19 The B3LYP/RECP and CCSD(T)/RECP approaches lead to lower BDEs, which are more consistent with available experimental data. For the lightest homologue, (C2H4)Cu+, only a lower bound for the BDE of 23 kcal/mol has been determined experimentally.8 Irrespective of the method applied, our calculated results are at least twice as high, ranging from 45.4 kcal/mol (CCSD-
c
(T)/RECP) to 57.0 kcal/mol (LDA/BP). This compares well with the recent QCISD(T)/RECP study by Basch and Hoz12 (43.2 kcal/mol) and the CCSD(T)/RECP value (43.9 kcal/mol) of Frenking and co-workers.13 Whereas the quantum mechanical procedures used by Frenking and co-workers are similar to ours, the basis sets employed are of slightly lesser quality. In the CCSD(T) single point calculation a [8s/7p/6d/1f]/(6s/5p/ 3d/1f) basis set in combination with a Hay and Wadt RECP was employed for copper along with a standard 6-31G(d) basis set augmented by a diffuse function on carbon. A previous value of 40 kcal/mol by Bauschlicher and co-workers using CCSD(T) and SCF optimized geometries7 is a only few kilocalories per mole lower.39 The internal consistency of the theoretical findings, together with the good agreement between our computed and the experimentally determined BDE found for M ) Ag and Au (see below), points to a BDE of (C2H4)Cu+ which is indeed much higher than the lower bound of 23 kcal/mol. Therefore, we tried to determine BDE (C2H4-Cu+) experimentally by applying mass-spectrometric techniques as described in detail in ref 11. To this end, we reacted (H2O)Cu+ with a ca. 500:1 mixture of water and ethylene in order to establish an equilibrium between (H2O)Cu+ and (C2H4)Cu+. However, at long reaction times (e.g. 60 s at 1 × 10-6 mbar), no (H2O)Cu+ could be detected within the signal-to-noise limit (1%) and all ions were converted to (C2H4)nCu+ (n ) 1, 2) or (C2H4)(H2O)Cu+, respectively. Hence, assuming room temperature, we can conclude from this observation that BDE(C2H4-Cu+) exceeds the well-known BDE40(H2O-Cu+) or 37.6 kcal mol-1 by at least 6 kcal/mol. On the other hand, only (NH3)nCu+ (n ) 1, 2) was observed, while no (C2H4)Cu+ could be detected within the signal-to-noise limit (1%), when (C2H4)Cu+ was equilibrated in a ca. 500:1 mixture of ethylene and ammonia. Consequently, BDE(NH3-Cu+) exceeds BDE(C2H4-Cu+) also by at least 6 kcal/mol. Combining these findings with a theoretical estimate for BDE(NH3-Cu+) of ca. 56 kcal/mol,41 we arrive at a BDE(C2H4-Cu+) of between 44 and 50 kcal/mol. This interval agrees well with the BDEs computed using CCSD(T) and B3LYP, but is indisputably below the BDEs determined with MP2 and LDA/BP, in particular. Experimentally, the BDE of (C2H4)Ag+ has been determined9 as 33.7 kcal/mol. The fact that all our calculated values are close to the experimental figure lends further support to the confidence of our theoretical approach: The CCSD(T)/RECP result is off the experimental value by less than 1 kcal/mol, and also the B3LYP/RECP result misses the experiment by 1.6 kcal/mol. At the MP2/RECP and the quasi-relativistic LDA/ BP levels the BDEs are slightly larger, as also found for (C2H4)Cu+. For (C2H4)Au+ all methods agree within 9 kcal/mol,
12256 J. Phys. Chem., Vol. 100, No. 30, 1996
Hertwig et al.
TABLE 2: Relativistic Effects (∆r, in Å) on the Metal-Carbon Bond Lengths (Å) in (C2H4)M+ Complexes
(C2H4)Cu+ (C2H4)Ag+ (C2H4)Au+ a
BP/nr
BP/qra
∆r
MP2/ RECP
MP2/ ECP
∆r
2.096 2.343 2.378
2.06 2.34 2.18
0.036 0.00 0.20
2.099
2.442
0.344
Manual geometry optimization was restricted to a step size of 0.01
Å.
predicting a BDE of 62-71 kcal/mol. Lacking more accurate experimental data, these results are in concert with the lower bound of 59 kcal/mol determined experimentally in our laboratory.11 B. Geometries. As implied by the Dewar-Chatt-Duncanson model,2,3 the olefin structure is affected by the presence of the metal cations. Both σ-donor and π-acceptor contributions lead to an elongation of the carbon-carbon bond by removal of electron density from the bonding π orbital and increase of the electron density in the antibonding π* orbital, respectively. Thus, mere inspection of the ligand geometries does not allow for a separation of these two effects. As compared to free ethylene (MP2/TZ2P, rC-C 1.328 Å; B3LYP/TZ2P, rC-C ) 1.324 Å, rC-C(exptl) ) 1.33942), the C-C bond lengths in (C2H4)Cu+ and (C2H4)Ag+ are increased by roughly the same amount at the MP2/RECP (∆rC-C ) 0.047 and 0.035 Å, respectively) and B3LYP/RECP (∆rC-C ) 0.046 and 0.037 Å, respectively) levels of theory, while in (C2H4)Au+ the elongation is somewhat larger (MP2/RECP, ∆rC-C ) 0.075 Å; B3LYP/ RECP, ∆rC-C ) 0.066 Å3). A different, but related effect of the presence of M+ on the ethylene ligand is the rehybridization of the carbon centers from sp2 toward sp3 resulting in a partial pyramidalization of the two carbon centers. As shown in Table 1, this pyramidalization is more pronounced in (C2H4)Au+ than in the Cu+ and Ag+ complexes. Hence, the interaction of ethylene with Au+ seems to be stronger and with larger covalent contributions than for Ag+ or Cu+. Unfortunately, the current version of the ADF program is not capable of optimizing geometries within the quasi-relativistic scheme; therefore, C-C bond elongations and pyramidalizations of the carbon atoms caused by relativistic effects could not be assessed at the LDA/ BP level of theory. The MP2/RECP level consistently predicts metal-carbon bond distances that are shorter than those obtained with B3LYP/ RECP and LDA/BP, but the qualitative trend is identical at all three levels of theory. The M-C distances increase in the order Cu < Au < Ag; i.e., even though gold is the heaviest among the three elements, the Au-C distance is significantly shorter than the Ag-C bond length. To which extent are relativistic effects responsible for this unusual result? To answer this question, we compare the metal-carbon bond distances of the standard, nonrelativistic LDA/BP scheme with the results of the quasi-relativistic LDA/BP calculations (Table 2); in addition, the optimized geometry of (C2H4)Au+ at the MP2 level employing a nonrelativistic ECP is included. It is well known that relativity causes contraction of atomic s-orbitals due to the nonzero probability of finding electrons with l ) 0 at the nucleus, and expansion of atomic d-orbitals due to an increased shielding effect of the s-core orbitals.14d In most cases, the interplay between these opposite effects on orbital sizes leads to a net contraction of bond lengths,43 as bonding very frequently is dominated by s-orbital contributions. For (C2H4)Cu+, a slight bond shortening of 0.04 Å emerges from the comparison of the nonrelativistic and the quasirelativistic LDA/BP calculations, while for (C2H4)Ag+ hardly any effect is seen. In contrast, (C2H4)Au+ exhibits a significant
relativistic bond contraction of the Au-C bond length by as much as 0.20 Å using LDA/BP and even 0.35 Å with MP2/ ECP and MP2/RECP, respectively. While the two methods yield the same qualitative effect, they differ in the quantitative amount of the relativistic bond shortening. Since gold is the element where relativistic effects peak throughout the periodic table,15 it could well be that relativity indeed has an explicit effect on the valence electrons, which are, albeit approximatively, covered by the quasi-relativistic scheme, but are neglected in the RECP approach. However, since relativistic and electron correlation effects are important and by no means independent from each other and neither effect is treated at an extraordinary high level of theory in the present study, we cannot decide which approach is the more reliable one. Finally, it should be noted that for (C2H4)Cu+ the possibility of a Cs symmetric complex, corresponding to an end-on coordination of the metal ion to ethylene, was examined at the LDA/BP level by scanning the C-C-M angles from 0 to 180° while fully optimizing all other parameters. This scan revealed no indication for minima other than the C2V symmetric structure. C. Bond Decomposition. Does the Dewar-Chatt-Duncanson model2,3 indeed provide a qualitative description of the nature of the metal-ethylene bonding in these complexes? Is the interaction mainly electrostatic or covalent in nature? How do the relativistic effects influence the various components of the bonding interaction? To answer these questions, we analyzed the LDA/BP results employing Morokuma’s34 bond decomposition scheme as implemented in ADF33 at the quasirelativistic and the nonrelativistic levels (Table 3). In their early Hartree-Fock-Slater study, Ziegler and Rauk performed a similar analysis for (C2H4)M+ complexes (M ) Cu, Ag, and Au);4 however, a reevaluation based on the more advanced LDA/BP functional is certainly desirable, since (i) the HFS level employed by Ziegler and Rauk wassmeasured by current standardssfairly low and (ii) relativistic effects were not included, even though they are of particular importance for (C2H4)Au+. First, we discuss the results obtained from the quasirelativistic scheme, which will be followed by an analysis of the relativistic contributions to the various components. We note in passing that all numbers but those in the last row of Table 3 are based on the optimized geometries obtained at the nonrelativistic level. Although we partially reoptimized the geometries of all three (C2H4)M+ complexes for an accurate determination of the BDE on the relativistic level, as outlined above, this procedure is not favorable when it comes to separating the interaction between metal and ligand into its components and comparing them for the relativistic and the nonrelativistic case.44 As this splitting of the BDE is in fact artificial, one has to keep the geometries fixed when comparing the results of different methods. However, since the decomposition scheme should be applied to reveal trends, rather than to be taken as quantitatively accurate, the minimum structures optimized at the nonrelativistic level are a sufficiently accurate approximation to the true relativistic minimum. In every case the steric interaction (∆Esteric) is only slightly repulsive, since the stabilizing electrostatic contribution (∆Eelstat) is of the same order of magnitude as the destabilizing Pauli repulsion (∆EPauli). The magnitude of this term decreases in the order Cu > Ag > Au as complexating metals. The attractive ∆EOI term can be further devided into the contributions from the distinct irreducible representations of C2V, i.e. A1, A2, B1, and B2, with the z-axis being the 2-fold rotation axis and the C-C bond situated along the x-axis. For all three molecules the same general features emerge: The major part of the
Cationic Coinage Metal-Ethylene Complexes
J. Phys. Chem., Vol. 100, No. 30, 1996 12257
TABLE 3: Morokuma Bond-Decomposition Analysis for Nonrelativistic (NR) and Quasi-Relativistic (QR) Calculations of (C2H4)M+ with LDA/BP (Values in kcal/mol and As Percentages of the Total BDEs) (C2H4)Cu+ NR ∆Esteric ∆EPauli ∆Eel.stat.
7.24 96.39 -89.15
∆EOI -64.37 A1 -36.22 A2 -2.18 B1 -20.82 B2 -4.93 nonlocal corra -0.22
% bond
QR
58
5.91 96.08 -90.81
24 1 14 3
-68.77 -39.87 -2.19 -21.49 -4.97 -0.25
(C2H4)Ag+ % bond
57 25 1 14 3
∆
NR
% bond
QR
63
2.46 63.56 -61.10
-1.33 4.69 -0.31 64.44 -1.03 -59.75 -4.40 -35.29 -3.65 -23.13 -0.01 -1.42 -0.67 -7.29 -0.04 -2.51 -0.03 -0.32
24 1 8 3
-43.81 -30.71 -1.49 -8.65 -2.61 -0.34
(C2H4)Au+ % bond
58 29 1 8 2
∆
NR
-2.23 9.66 -0.88 79.89 -1.35 -70.23 -8.52 -37.23 -7.58 -23.88 -0.07 -1.49 -0.73 -8.49 -0.10 -2.57 -0.02 -0.35
% bond
QR
66
2.21 75.82 -73.62
22 1 8 2
-71.25 -54.81 -1.76 11.22 2.94 1.53
% bond
∆
50
-7.45 -4.07 -3.39
38 1 8 2
-34.02 -30.93 -0.27 -2.37 -0.37 -1.18
∑b
-57.1
-62.9
-5.7
-30.6
-41.4
-10.8
-27.6
-69.0
-41.5
BDE‚(-1)c
-51.8
-57.0
-5.2
-26.7
-36.8
-10.1
-23.1
-67.9
-44.8
a
This number reflects the nonlocal corrections to the ∆EOI term. b Sum over all attractive and repulsive contributions. Attractive terms are by definition negative; repulsive terms are positive. c Negative values of BDEs, resulting from fully optimized nonrleativistic geometries, and partially reoptimized relativistic geometries from Table 2.
covalent bonding originates from the A1 contribution, and within the Dewar-Chatt-Duncanson model this can be identified as σ-bonding, i.e., the interaction of the occupied π-orbital of ethylene with the appropriate orbitals on the metal (s-, dz2-, or dx2-y2-orbitals or their hybrids). π-Back-bonding via the occupied dyz orbital on the metal and the empty π*-orbital of ethylene can be identified in the B1 contribution. To give an estimate of the importance of the respective attractiVe terms discussed here, we give the percentage of each term as fraction of the sum of all attractive terms in Table 3. According to these numbers the electrostatic term comprises in each case at least half of all contributions to the bond (Cu, 57%; Ag, 58%; Au, 50%). The other half (or slightly less for Cu and Ag) is shared among bonding and back-bonding covalent contributions. Here, we can see differences between copper and the other two metals: π-back-bonding is responsible for about one-third of the covalent contribution in (C2H4)Cu+. For both (C2H4)Ag+ and (C2H4)Au+, back-bonding amounts to only one-fifth of all covalent contributions. Hence, while within this scheme in all three complexes π-back-bonding is less important than σ-bonding, its relevance is actually somewhat higher for Cu. This is in contrast to the analysis given by Ziegler and Rauk,4 who identified back-bonding to be of utmost importance for copper, but hardly relevant for silver and gold. As expected, the contributions of the remaining two irreducible representations, A2 and B2, are virtually negligible. Consequently, in all three cases, electrostatic and covalent contributions are to first order equally important in the C2H4-M+ interaction. The amount of π-back-bonding ranges between one-fifth and one-third of all covalent fractions. Coming back to (C2H4)Ag+, we found the absence of relativistic bond contraction earlier in the geometry section in contrast to both the copper and gold compounds. How could the bond decomposition analysis provide an explanation for this finding? To answer this question we slightly distorted the Ag-C bond length, repeated the quasirelativistic BP calculation, and performed the bond decomposition analysis. Upon bond lengthening the steric interaction (∆Esteric) becomes slightly less repulsive since Pauli repulsion is reduced, but due to worse overlap the attractive orbital overlap term (∆EOI) becomes less stabilizing to a larger amount. Therefore the net BDE is lower. If, on the other hand, the Ag-C bond is contracted, the opposite effect is observed: the steric interaction term (∆Esteric) becomes more repulsive due to larger Pauli repulsion, whereas the orbital interaction term (∆EOI) shows an increased amount of stabilization, however in this case to a lesser extent than the increase of repulsive forces
from ∆Esteric. Again, the net BDE is lower than the one of the undistorted geometry. From these observations we are able to derive the following qualitative picture. Relativistic bond contraction occurs for the most part if the increase of orbital interactions and the resulting stabilizing effect exceeds the increase of repulsion of the ∆Esteric term. This is not the case for (C2H4)Ag+, being the reason why no relativistic bond shortening can be observed and the Ag-C bond length is governed by the interplay of the steric interaction orbital interaction and the orbital interaction term (∆Esteric and ∆EOI). Moreover, it is now obvious that in the case of (C2H4)Au+, where we have observed significant bond shortening, the energy gain from the increased interaction of the π-bond on ethylene and the empty s-orbital on gold is so substantial that it can compensate an increased ∆Esteric term, even if the bond is contracted by as much as 0.2 Å. The same bond decomposition analysis has also been performed at the nonrelativistic level and the results are included in Table 3 along with the differences compared to the quasirelativistic treatment (listed in the ∆ column of Table 3). Relativistic effects slightly reduce the repulsive ∆Esteric terms in every case. This is obviously a result of the contracting effect of relativity of the valence s-orbital which reduces the Pauli repulsion and increases electrostatic interactions of the electrons with the positive core charges. In all cases the major contribution to the relativistic stabilization, however, originates from increase of ∆EOI, in particular, the A1 term. This can be rationalized by inspection of the orbital energies of the bare metal cations. In the case of Au+, where this effect is most pronounced, the Kohn-Sham orbital energy of the set of 5dorbitals rises slightly upon inclusion of relativistic effects (0.5 eV), while the 6s-orbital is substantially lowered in energy by 2.6 eV. Thus, the donor-acceptor interaction of the occupied π-orbital on ethylene with the formally empty gold 6s-orbital becomes more favorable, due to the diminished energy gap separating these orbitals. For (C2H4)Cu+, the relativistic stabilization due to ∆EOI is only marginal, in line with the observation that for the copper cation the 4s Kohn-Sham orbital energy is only slightly lowered (0.3 eV), and virtually no effect on the orbital energies of the 3d-orbitals is seen upon inclusion of relativistic effects. The impact of relativistic effects on the BDEs as a whole can be estimated by comparing the nonrelativistic LDA/BP results with the quasi-relativistic data using the with reoptimized metal-ligand bond lengths in the last row of Table 3. Note that the sum over all contributions of the bond decomposition scheme in Table 3 is approximate due to the
12258 J. Phys. Chem., Vol. 100, No. 30, 1996
Figure 1. AIM analysis of (C2H4)Au+. Thin lines are gradient vector paths; thick lines are bond paths or bond separation curves. Critical points are marked with a circle.
Figure 2. AIM analysis of (C2H4)Ag+. Thin lines are gradient vector paths; thick lines are bond paths or bond separation curves.
restrictions that had to be applied in order to perform this analysis, as mentioned earlier. As expected, the relativistic contributions to the BDEs increase with increasing atomic numbers. For Cu+, the nonrelativistic BDE is 5.2 kcal/mol below the quasi-relativistically determined one, for Ag+ relativistic effects increase the BDE by 10.1 kcal/mol, and the largest effect of 44.8 kcal/mol is seen for Au+, where 64% of the binding energy is due to relativistic effects. An extraordinary magnitude of relativistic effects on both the BDE and equilibrium geometry has also been found recently in an investigation of the neutral monohydrides of Cu, Ag, and Au,45 where relativistic effects were found to contribute about 40% of the BDE of AuH. The results of the AIM analysis are shown in Figures 1-3. In this study we used the charge density resulting from our MP2/ RECP calculations throughout.46 We would like to stress that it is necessary to use the charge density obtained at the MP2
Hertwig et al.
Figure 3. AIM analysis of (C2H4)Cu+. Thin lines are gradient vector paths; thick lines are bond paths or bond separation curves. Critical points are marked with a circle. The bond critical points of the Cu-C bonds almost coincide with the ring critical point.
level for the AIM analysis; using the HF density may produce false results.47 The figures show the gradient vector field. Each of the thin lines lead into the direction indicated by the vector ∇F(r) at each point on the trajectory, similar to a tangent of the density surface and terminate where ∇F(r) vanishes (critical point). These trajectories are perpendicular to lines of constant density. The bond paths (thick line connecting two atoms) are gradient paths that connect two nuclei through the corresponding bond critical point marking the ridge of the electron density surface between two atoms. The bond separation curves (also given as thick lines intercepting bond paths) consist of two special gradient vector paths located in the valley between two atomic basins and terminating at a (3,-1) bond critical point. Electron density within such an atomic basin is considered to “belong” to the atom in the center of that basin. A bond critical point is the terminus of bond separation curves and the origin of bond paths. For an excellent in-depth discussion see ref 35. If one starts with (C2H4)Au+ from Figure 1, it is apparent that ethylene in fact forms a nearly triangular structure when complexing with gold. We were able to identify a ring (3,+1) critical point positioned on the C2-axis of the molecule. It is surrounded by three bond (3,-1) critical points, belonging to two separate bond paths which connect gold and the carbon centers of ethylene and a third between the two carbon atoms. In distinct difference to the foregoing is the mode of bonding in (C2H4)Ag+ shown in Figure 2. Besides the bond critical point between the two carbon centers, we were able to locate only one more critical point positioned on the C2-axis of the molecule. Analysis of the curvature revealed a bond (3,-1) critical point, meaning that the mode of bonding in (C2H4)Ag+ is in fact T-shaped rather than triangular. This finding is emphasized by bond paths and bond separation curves. There is one straight line connecting the silver atom with the bond midpoint of the ethylene ligand, perpendicular to the bond paths of the two carbon centers. (Note that in this case the bond paths of Ag and C2H4 is overlayed by the bond separation curve of the C-C double bond.) In the case of copper the situation is somewhat ambiguous. The bond paths give clear indication that copper is bound to
Cationic Coinage Metal-Ethylene Complexes the two carbon atoms, leading from copper two either carbon atom. However, they are bend toward the C2-axis thus giving the triangle a very narrow shape. Also, the fact that the ring critical point and the two Cu-C bond critical points are very close suggests that in the case of (C2H4)Cu+ we are dealing with a bond situation located somewhere between a triangular and a T-shaped structure. Frenking and co-workers also performed an AIM analysis on (C2H4)Cu+ and arrive at a different conclusion, namely that (C2H4)Cu+ has a T-shaped structure.13 Increasing the basis set on the ligand to TZP quality, however, also led to a ring structure.48 At this point, the reasons for this discrepancy are not fully clear; however our results agree with Frenking’s in so far that if (C2H4)Cu+ adopts a triangular shape, it is not very pronounced, and the topology of the charge density is near a so-called bifurcation point,35 where ring and bond critical points would coalesce. Comparing these results with the pyramidalization angles that arise from the optimized structures, we find agreement with the amount of pyramidalization observed for the three compounds: gold induces the strongest pyramidalization tendency (16.8°), being in line with a cyclic structure. Less pronounced is copper (12.1°), and finally, silver-ethylene (10.2°) exhibits the least pyramidalization tendency. The fact that (C2H4)Ag+ exhibits a nonnegligible pyramidalization tendency, although from the AIM analysis it cannot be regarded as a cyclic structure, hints to the existence of other effects that mediate the actual amount of bending of the sp2-centers, such as repulsion of σ-C-H bonds with populated orbitals on the metal. An interpretation of the results of the AIM analysis is not obvious; however, it seems from the bond decomposition analysis that the interplay of Pauli repulsion and electrostatic interaction enforces a relatively large Ag-C bond length, overruling orbital interaction terms. Therefore the formation of two separate Ag-C bonds which would require relatively short metal-carbon bond distances at the expense of increased Pauli repulsion is less favorable than a long Ag-C bond allowing only interaction of metal orbitals with the π-bond as such. Conclusion Our theoretically predicted metal-ethylene binding energies and corresponding minimum structures are probably among the most accurate energetical and structural information on these systems available today. In particular, it should be mentioned that the hybrid functional applied here (B3LYP), yields results that show remarkable agreement with the CCSD(T) data at a fraction of the computational effort. The bond decomposition scheme reveals a half-covalent, half-electrostatic nature of the total bonding force between metal and ligand. Back-bonding plays an important role in all three complexes, constituting approximately one-third of all covalent bonding contributions for (C2H4)Cu+ and one-fifth for (C2H4)Ag+ and (C2H4)Au+. As for relativistic effects, these are dominating the bond between gold and ethylene, contributing two-thirds to the overall BDE. In the case of copper and silver relativistic stabilization is observed to a much lesser degree. Regardless of the overall amount of the relativistic stabilization, it is almost exclusively exerted through orbitals belonging to the A1 irreducible representation in all three complexes. The AIM analysis revealed only (C2H4)Ag+ to have a T-shaped structure, (C2H4)Au+ is a metallacyclopropane, and (C2H4)Cu+ shows a tendency to form a cyclic structure. In the case of the cationic gold(I) compounds the role of electron transfer from the ligand to the metal needs to be further examined. Because of the prevalence of relativistic effects for gold a more accurate description going
J. Phys. Chem., Vol. 100, No. 30, 1996 12259 beyond mass-velocity and Darwin terms should enhance the accuracy of the results. In particular, it is desirable to include an adequate, yet easy, description of spin-orbit effects in the calculations of elements for which relativistic effects are important. Acknowledgment. We appreciate financial support by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie, and the Gesellschaft von Freunden der Technischen Universita¨t Berlin. P.S. is grateful to the Auckland University Research Committee and to the NY/FRG for financial support. Furthermore, we thank Dr. C. Heinemann and Dr. M. C. Holthausen for helpful comments. Grad. Math. Heidi Grauel is thanked for help with the implementation of f-functions into the set of Bader programs. Prof. H. Basch and Prof. G. Frenking are acknowledged for providing us with copies of their work prior to publication (refs 12 and 13). We would also like to thank Prof. K. Morukuma for fruitful discussions. References and Notes (1) (a) Freiser, B. S. Chemtracts: Anal. Phys. Chem. 1989, 1, 65. (b) Armentrout, P. B. Annu. ReV. Phys. Chem. 1990, 41, 313. (c) Eller, K.; Schwarz, H. Chem. ReV. 1991, 91, 1121. (d) Tsipis, C. A. Coord. Chem. ReV. 1991, 108, 163. (e) Veillard, A. Chem. ReV. 1991, 91, 743. (f) Weishaar, J. C. Acc. Chem. Res. 1993, 26, 213. (2) Dewar, M. J. S. Bull. Soc. Chim. Fr. 1951, C79, 18. (3) Chatt, J.; Duncanson, L. A. J. Chem. Soc. 1953, 2939. (4) Ziegler, T.; Rauk, A. Inorg. Chem. 1979, 18, 1558. (5) Nicholas, G.; Spiegelman, F. J. Am. Chem. Soc. 1990, 112, 5410. (6) Miralles-Sabater, J.; Merchan, M.; Nebot-Gil, I.; Viruela-Martin, P. M. J. Phys. Chem. 1988, 92, 4853. (7) (a) Sodupe, M.; Bauschlicher, C. W., Jr. J. Phys. Chem. 1991, 95, 8640. (b) Sodupe, M.; Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H. J. Phys. Chem. 1992, 96, 2118. (8) Fisher, E. R.; Armentrout, P. B. J. Phys. Chem. 1990, 111, 4251. (9) Guo, B. C.; Castleman, Jr., A. W. Chem. Phys. Lett. 1991, 181, 16. (10) (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. (11) Schro¨der, D.; Hrusˇa´k, J.; Hertwig, R. H.; Koch, W.; Schwerdtfeger, P.; Schwarz, H. Organometallics 1995, 14, 312. (12) Basch, H.; Hoz, T. Private communication. To be published in The chemistry of triple bonded functional groups; Patai, S., Ed.; Wiley: New York, Vol. 2, Suppl. C. (13) Bo¨hme, M.; Wagener, T.; Frenking, G. J. Organomet. Chem., in press. (14) (a) Barthelat, J. C.; Durand, P.; Pelissier, M. Phys. ReV. A 1980, 21, 1773. (b) Balasubramanian, K.; Pitzer, K. S. AdV. Chem. Phys. 1987, 67, 287. (c) Pyykko¨, P. Chem. ReV. 1988, 88, 563. (d) Schwarz, W. H. E. In Theoretical Models of Chemical Bonding, Vol. II; Maksic´, Z. B., Ed.; Springer Verlag: Berlin, Heidelberg, Germany, 1990. (e) Pisani, L.; Andre´, J.-M.; Andre´, M.-C.; Clementi, E. J. Chem. Educ. 1993, 70, 894. (15) Pyykko¨, P.; Desclaux, J. P. Acc. Chem. Res. 1979, 12, 276. (16) (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) Ku¨chle, W.; Dolg, M.; Stoll, H.; Preuss, H. Mol. Phys. 1991, 74, 1245. (d) Dolg, M.; Ku¨chle, W.; Stoll, H.; Preuss, H.; Schwerdtfeger, P. Mol. Phys. 1991, 74, 1265; (e) Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J. Chem. 1992, 70, 612. (f) Cundari, T. R.; Stevens, W. J. J. Chem. Phys. 1993, 98, 5555. (17) For earlier investigations see: (a) Hrusˇa´k, J.; Schro¨der, D.; Schwarz, H. Chem. Phys. Lett. 1994, 225, 416. (b) Hrusˇa´k, J.; Schro¨der, D.; Hertwig, R. H.; Koch, W.; Schwerdtfeger, P.; Schwarz, H. Organometallics 1995, 14, 1284. (c) Hertwig, R. H.; Hrusˇa´k, J.; Schro¨der, D.; Koch, W.; Schwarz, H. Chem. Phys. Lett. 1995, 236, 194. (18) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 46, 618. (19) Ziegler, T. Chem. ReV. 1991, 91, 651. (20) Becke, A. D. Int. J. Quantum Chem. 1983, 23, 1915; J. Chem. Phys. 1986, 86, 4524; Phys. ReV. A 1988, 33, 3098. (21) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (22) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648; (b) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (23) 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.
12260 J. Phys. Chem., Vol. 100, No. 30, 1996 L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN Inc.: Pittsburgh, PA, 1992. (24) (a) Schwerdtfeger, P.; Dolg, M.; Schwarz, W. H. E.; Bowmaker, G. A.; Boyd, P. D. W. J. Chem. Phys. 1989, 91, 1762. (b) Schwerdtfeger, P. J. Am. Chem. Soc. 1989, 111, 7261. (c) Schwerdtfeger, P.; Boyd, P. 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. (25) Feller, D.; Davidson, E. P. In ReViews in Computational Chemistry, Vol. I; Lipkowitz, K. B., Boyd, D. B. Eds.; VCH Publishers: New York, 1990. (26) Hertwig, R. H.; Koch, W. J. Comput. Chem. 1995, 16, 576. (27) Hertwig, R. H.; Dargel, T. K.; Koch, W. Unpublished results. (28) (a) Frenking, G.; Antes, I.; Bo¨hme, M.; Dapprich, S.; Ehlers, E. W.; Jonas, V.; Neuhaus, A.; Otto, M.; Stegmann, R.; Veldkamp, A.; Vyboishchikov, S. F. ReV. Comput. Chem. 1996, 8. (b) Helgaker, T.; Taylor, P. R. In Modern Electronic Structure Theory, Part II; Yarkony, D. R., Ed.; World Scientific: Singapore, 1995. (29) ADF, version 1.1: (a) Baerends, E. J.; Ellis, D. E. Chem. Phys. 1973, 2, 71. (b) te Velde, G.; Baerends, E. J. J. Comp. Phys. 1992, 99, 84, and references cited therein. (30) Snijders, J. G.; Baerends, E. J. Mol. Phys. 1977, 33, 1651. (31) Ziegler, T.; Tschinke, V.; Baerends, E. J.; Snijders, J. G.; Ravenek, W. J. Phys. Chem. 1989, 93, 3050. (32) (a) van Wezenbeek, E. M.; Baerends, E. J. Chem. Phys. Lett. 1991, 74, 1271. (b) Heinemann, C.; Hertwig, R. H.; Wesendrup, R.; Koch, W.; Schwarz, H. J. Am. Chem. Soc. 1995, 117, 495. (33) Ziegler, T.; Rauk, A. Theor. Chim. Acta 1977, 46, 1. (34) Kiaura, K.; Morukuma, K. Int. J. Quantum Chem. 1976, 10, 325. (35) Bader, R. F. W. Atoms in Molecules; Clarendon Press: Oxford, England, 1994. (36) Bader, R. F. W.; Laidig, K. E. MacMaster University, Hamilton Ontario, Canada. For the analysis we used a modified version of the original
Hertwig et al. set of programs to account for the f-type basis functions that have been employed. (37) Bo¨hme, M.; Frenking, G. Chem. Phys. Lett. 1994, 224, 195. (38) See, e.g.: (a) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. Symp. 1989, 23, 199. (b) Lee, T. J.; Rendell, A. P.; Taylor, P. R. J. Phys. Chem. 1990, 94, 5463. (c) Bartlett, R. J. In Modern Electronic Structure Theory, Part II; Yarkony, D. R., Ed.; World Scientific: Singapore, 1996. (39) Since the metal-carbon distance is much larger at the SCF level (2.35 Å) than at the correlated levels presented here (1.896-2.06 Å), the bonding interaction between cationic copper and ethylene is probably underestimated at the SCF geometry. (40) Armentrout, P. B.; Kickel, B. L. In Organometallic Ion Chemistry; Freiser, B. S., Ed.; Kluwer: Dordrecht, 1996. (41) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H. J. Phys. Chem. 1991, 94, 2068. (42) Herzberg, G. Electronic Spectra and Electronic Structure of Polyatomic Molecules; Van Nostrand: New York, 1966. (43) A counter example is given in: Van Wezenbeek, E. M.; Baerends, E. J.; Snijders, J. G. Theor. Chim. Acta 1991, 81, 139. (44) Morukuma, K. Personal communication to R.H.H., June 1995. (45) Collins, C. L.; Dyall, K. G.; Schaefer, H. F. J. Chem. Phys. 1995, 102, 2024. (46) The gradient lines do not convolute at the point of the atomic core as an indication of a pseudocritical (3,-3) point in the case of the metal. This is due to the use of the pseudopotential to describe the properties of the innermost electrons, resulting in an artificial decline of charge density near the metal core. (47) Using the HF density at the MP2 optimized geometry leads to a T-shaped mode of bonding for (C2H4)Cu+ in the AIM analysis. (48) Frenking G. Personal communication to W.K., February 1996.
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