J. Phys. Chem. 1988,92, 4853-4859
‘b
b-IEo+hl -+ U - Eo Figure 11. The dynamics underlying the solvent time scale function +(z) (eq 111-19 and VII-8). We start with a fluctuation of the solvation coordinate at the transition state (curve crossing) U = -Eo. If the system is in the la) state (R,and R4),this fluctuation will relax to S,(U) with a characteristic time scale s [ ( E o A)/A]. If the system is in the Ib) state (R,and Rz), it will relax to S,(U) and the characteristic time scale is + [ ( E o- X)/A]. 4: IEO-AI
+
7 [ ( E 0 - X)/A] is thus the average time it takes for a solvent fluctuation at the transition state (U = - E o ) to relax to thermal equilibrium in the state Ib), whereas 7 [ ( E 0+ X)/A] is the average time it takes for the same fluctuation to relax to thermal equilibrium in the state la). This is represented schematically in Figure 11. If these times are fast, the fourth-order contribution to the rate vanishes and the rate is adiabatic. The transition from the nonadiabatic to the adiabatic limit is therefore a result of the finite relaxation time of the solvent which results in a change of the distribution of the solvation coordinate Uduring the course of the
4853
rate process. It should be stressed that eq VII-8 were obtained by a careful evaluation of the nonlinear response functions. We did not have to assume a priori that the reaction takes place at the transition-state configuration U = -Eo. It should further be noted that, in fluorescence measurements, the Stokes shift depends on solvent relaxation in the excited state (R, and R2).In hole burning, we probe a difference between the ground and the excited states and therefore all pathways R,,R2, R3,and R4 contribute. Hole-burning spectroscopy is thus a probe for ground-state as well as excited-state r e l a ~ a t i o n . ~ ~ The present formulation is based on a generalized master equation, and we have derived a frequency-dependent rate K ( s ) . The s scale over which K(s) varies is determined by the solvation time scales. The values of s, relevant in the generalized master equation, are approximately equal to the inverse reaction time scale (the rate). Reactions with large activation barriers are slow, and a separation of time scales is expected to hold, resulting in ordinary rate equations (eq 11-22), For barrierless reactions this separation of time scales may not hold. Several optically induced electron-transfer and isomerization reactions show a time evolution which does not follow a simple rate Our generalized rate equation provides an adequate method for treating these reactions by keeping the s dependence of K ( s ) and allowing for an initial nonequilibrium distribution of the solvation coordinate.
Acknowledgment. The support of the National Science Foundation, the Office of Naval Research, the U S . Army Research Office, and the donors of the Petroleum Research Fund, administered by the American Chemical Society, is gratefully acknowledged.
ARTICLES A Theoretical Study of the Interaction of Acetylene with Copper and Silver Monoions Josefa Miralles-Sabater,+Manuela MerchPn, Ignacio Nebot-Gil,* and Pedro M. Viruela-Mardn Departament de Qufmica Fjsica, Universitat de ValPncia, Dtor. Moliner 50, Burjassot, 461 00, Valencia, Spain (Received: July 13, 1987)
The interaction of copper and silver monoions with acetylene has been studied including the effect of electron correlation. Geometries of the minima and binding energies have been determined by using properly localized molecular orbitals in the configuration interaction. Although the main interaction is due to the presence of a positive charge, inclusion of electron correlation is needed if accurate results are desired. In the light of the present results, and considering previous works on metal-ligand bonding, the validity of the two-way donor-acceptor model is analyzed.
Introduction The model proposed by Dewar’ in 1951 to explain the bonding in a-coordinated metal-olefin complexes has been considered as a useful scheme to rationalize this type of bonding.2 The interaction between an olefin and a metal located above the ligand molecular plane and equidistant from the two carbon atoms is attributed by Dewar’s model to the two-way donor-acceptor interaction. On the one hand, u-bonding charge donation takes place from ligand to metal and, on the other hand, a-bonding backdonation of metal electrons to the ligand (a and a referring to rotational symmetry of the orbitals implied). In 1953 the “a+Present address: Departament de QuImica, Facultat de QuImiques de Tarragona, P1. Imperial Tarraco No. 1, 43005 Tarragona, Spain.
0022-3654/88/2092-4853$01.50/0
complex theory of metal-olefin c ~ m p l e x e s ”was ~ first applied by Chatt and Duncanson4 to explain the nature of the chemical bond in platinum-olefin complexes. After that, great efforts have been devoted to analyze the metal-ligand bond in terms of u- and a-bonding. It is worthwhile to recall that the metal-ligand interactions are involved in many fields of current chemical research. The study of such complexes may produce some insight into relevant aspects of homogeneous and heterogeneous catalysis, (1) Dewar, M. J. S . Bull. SOC.Chim. Fr. 1951, 18, C71. (2) Cotton, F. k.;Wilkinson, G. Aduanced Inorganic Chemistry, 3rd. 4.; Wiley: New York, 1972. (3) See comments in: Dewar, M. J. S.; Ford, G. P. J . Am. Chem. SOC. 1979, 101, 783. (4) Chatt, J.; Duncanson, L. A. J . Chem. SOC.1953, 2939.
0 1988 American Chemical Society
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organometallic chemistry, and surface chemistry, areas closely related.s To what relative extent the u and n bonding take place in a complex has been subject of experimental as well as theoretical attention. In the past few years, many studies with zerovalent transition metals and ethylene or acetylene in cryogenic matrices have carried The experimental information represents very useful test cases and offers several challenges from a theoretical point of view. Thus, this type of data has in part encouraged many theoreticians to analyze the type of between zerovalent transitions metals and ethylene and acetylene, representing the simplest unsaturated hydrocarbons. In general, quite weak interactions are involved. The important role played by electronic correlation to obtain a proper metal-ligand distance and binding energy has been s h ~ w n . ~ ' - ~ ~ However, the interaction of a metal-cation atom with olefin has not been subject of much attention. Apart from the pioneer ab initio study on the Ag+-C2H4 system by B a ~ c honly , ~ ~a few ab initio works concerning M"+-unsaturated hydrocarbons complexes are available,25in spite of their implication in many important reaction^.^^^^^ On the other hand, although the Dewar's model was proposed as a general theory to explain the bonding in olefin complexes, the original work' suggests that would be especially suited for the group IB metal monoions interacting with olefin. This is supported by chemical intuition since in those ions the valence s orbital is empty (u-bonding could be expected, no a-repulsion) and some n-back-bonding would reasonably be accomplished from the dl0 filled shell. Moreover, it would be quite interesting to see how including electronic correlation affects the description of this type of bond. The theoretical model was chosen as simple as possible with use of a copper (and silver) atom without any ligands. The main reason is to use as much refined theoretical methods as possible and analyze the model system without any remaining questions. If the metal bears the same electronic ( 5 ) (a) Muetterties, E. L.; Stein, J. Chem. Rev. 1979, 79, 479. (b) NitschkB, F.; Ertl, G.; Kiippers, J. J . Chem. Phys. 1981, 74, 5911. (c) Canning, N. D. S.; Madix, R. J. J . Phys. Chem. 1984,88, 2437. (d) Shustorovich, E. Quantum Chemistry. The Challenge of Transition Metals and Coordination Chemistry, NATO AS1 Series, Serie C., Vol. 176; Veillard, A,, Ed.: Reidel: Dordrecht. 1986: D 445. (6) Parker, S. F.; Peden, C.'H. F.; Barret, P. H.; Pearson, R.G. Inorg. Chem. 1983, 22, 2813. (7) Chenier, J. H. B.; Howard, J. A,; Mile, B.; Sutcliffe, R.J . Am. Chem. SOC.1983, 105, 788. (8) Kasai, P. H. J. Am. Chem. SOC.1983, 105, 6704. (9) Howard, J. A,; Sutcliffe, R.; Tse, J. S.; Mile, B. Organometallics 1984, 3, 859. (10) Kasai, P. H. J . Am. Chem. SOC.1984, 106, 3069. ( 1 1 ) Zoellner, R. W.; Klabunde, K. J. Chem. Reu. 1984,84, 545. (12) Kafafi, Z. H.; Hauge, R. H.; Margrave, J. L. J. Am. Chem. SOC. 1985, 107, 7550 and references cited therein. (13) Kline, E. S.; Kafafi, Z. H.; Hauge, R. H.; Margrave, J. L. J . Am. Chem. SOC.1985, 107, 7559 and references cited therein. (14) Swope, W. C.; Schaefer, H. F., 111 Mol. Phys. 1977, 34, 1037. (1 5 ) Ozin, G. A,; Power, W. J.; Upton, T. H.; Goddard, W. A., 111J. Am. Chem. SOC.1978, 100, 4750. (16) Novaro, 0.; Blaisten-Barojas, E.; Clementi, E.; Giunchi, G.; RuizVizcaya, M. E. J . Chem. Phys. 1978, 68, 2337. (17) Pitzer, R. M.; Schaefer, H. F., I11 J . Am. Chem. SOC.1978, 101, 7 176. (18) Garcia-Prieto, J.; Novaro, 0. Mol. Phys. 1980, 41, 205. (19) Daudey, J. P.; Jeung, G.; Ruiz, M. E.; Novaro, 0. Mol. Phys. 1982, 46, 67. (20) Cohen, D.; Basch, H. J . Am. Chem. SOC.1983, 105, 6980. (21) Widmark, P. 0.; Roos, B. 0.;Siegbahn, P. E. M. J . Phys. Chem. 1985, 89, 2180. (22) Widmark, P. 0.;Sexton, G. J.; Roos, B. 0. J . Mol. Struct. THEUCHEM. 1986, 135, 235. (23) Nicolas, G.; Barthelat, J. C. J . Phys. Chem. 1986, 90, 2870 (24) Basch, H. J . Chem. Phys. 1972, 56, 441. (25) (a) Kelber, J. A.; Harrah, L. A.; Jennison, D. R. J . Urganomet. Chem. 1980, 199, 281. (b) Merchln, M.; Gondez-Luque, R.; Nebot-Gil, I.; Tomls, F. Chem. Phys. Lett. 1984, 112, 412. ( c ) Vitovskaya, N. M.; Bernshtein, V. G.; Schmidt, F. M. Kine?. Katal. 1984, 25, 1000. (d) Gonzilez-Luque, R.; Merchln, M.; Nebot-Gil, I.; Tomis, F.; MontaAana, R. J . Mol. Strucf. THEOCHEM 1985, 57, 121. (e) Merchln, M.; Gonzllez-Luque, R.; Nebot-Gil, I.; Tomis, F. Chem. Phys. Lett. 1985, 114, 516. ( f ) Merchin, M.; AndrBs, J.; Nebot-Gil, I.; Silla, E.; Tomls, F. J . Phys. Chem. 1985, 89, 4769. (26) Heck, R. F. Organotransition Metal Chemistry, a Mechanistic Approach; Academic, New York, 1974.
Miralles-Sabater et al. configuration, similar meaningful conclusions from the study with ligands on the metal would probably always be achieved, as far as the analysis of the two-way donor-acceptor model is concerned, but without introducing an unnecessary complexity. Thus, in our approach, and in order to analyze the model proposed by Dewar, we choose to interact copper and silver monoions with one of the more simple unsaturated hydrocarbons; for the sake of convenience, acetylene is considered. A priori, it can be assumed that copper monoion interaction with acetylene presents the same basic type of bonding as other metal-olefin bonding, e.g., Cu+-C2H4, since in the two cases the atomic and molecular orbitals implied have the same character, in agreement with our previous and present findings with these particular charged group IB metals, as will be discussed below. In this paper a study of the Cu+/C2H2and Ag+/C2H2at S C F level is presented to determine quantitatively the importance of u-bonding with respect to n-bonding. Also, the main electronic correlation effects, using high-quality correlated wave functions, are analyzed. Special attention has been paid to build as much as possible size- and distance-consistent potential energy curves in order to avoid the major problems implied in C I approaches. Moreover, adequate optimal valence virtual orbitals are used for the C I calculations, leading to a level of accuracy similar to the MC S C F MO's. The overall process allows us to obtain reliable binding energies and optimal metal-C2H2 interaction distances. Also, usefulness of the language of localized molecular orbitals and decomposition of wave functions in terms of VB contributions are stressed in order to make intuitive the electron correlation analysis. From the results obtained, and taking into account previous results on related systems, the validity of the two-way donor-acceptor model is analyzed.
Details of the Calculations Restricted Hartree-Fock (RHF) calculations were carried out with the PSHONDO program27which is a modified version of the HONDO program package2*including the pseudopotential method proposed by Durand and B a r t h e l a ~ ~ ~ qThe ~ O calculations have been restricted to the valence electrons of the carbon and metal atoms, 2s and 2p shells, and valence s and d shells, respectively; the inner electrons have been represented by a nonempirical potential function. The specific parameters for carbon are the ones obtained from standard calculation^.^^ The parameters used for copper32aand ~ i l v e r ~ ~ % edetermined re by Pelissier and Barthelat, respectively. The basis sets e m p l ~ y e d ~are ' , ~slightly ~ better than a double-[ quality. The primitive set of Gaussian-type orbitals (3s,lp,5d/4~,4p/4s)is contracted to [2s,lp,2d/2~,2p,/2s],where the information separated by slashes belongs to the metal, carbon, and hydrogen atoms, respectively. This somewhat limited basis set takes into account the more important features of the interaction of metal with ethylene and acetylene, in other systems, e g , A1/C2H4,33aA1/C2H2,33aand Pd/C2H2.33bIn fact, introducing d- and p-functions on the carbon and hydrogen atoms, respectively, does not significantly change the quantitative and qualitative conclusions. The corresponding orbital tran~formation~~ has been performed to determine quantitatively how much the occupied S C F MO's of the separate systems (acetylene and metal) are contained in the S C F MO's of the complex. The canonical MO's of the complex (AB) and fragment (A) are transformed in two new sets of MO's by a proper unitary transformations. The corresponding eigenvalues (A,) are (i) A, = 0, orbitals of AB which do not belong (27) Daudey, J. P., private communication. (28) Dupuis, M.; Rys, J.; King, H. F. J . Chem. Phys. 1976, 65, 111. (29) Durand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (30) Barthelat, J. C.; Durand, Ph. Gazz. Chim. Ital. 1978, 108, 225. (3 1) Molecular Ab Initio Calculations Using Pseudopotentials; Technical Report; Laboratoire de Physique Quantique: Toulouse, France, 198 1. (32) (a) Pelissier, M. J . Chem. Phys. 1981, 75, 775. (b) Barthelat, J. C., private communication. (33) (a) Miralles-Sabater, J.; Merchln, M.; Nebot-Gil, I. Chem. Phys. Lett. 1987, 142, 136. (b) Garcia-Cuesta, I.; Miralles-Sabater, J.; Merchln, M.; Nebot-Gil, I., to be submitted for publication. (34) Amos, A. T.; Hall, G. C. Proc. R . Soc. London 1981, A263,483. (b) Martin, R. L ; Davidson, E. R. Phys. Rev. 1977, A16, 1341.
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988 4855
Interaction of CzH2 with Cu and Ag Monoions
,,
E'Ehf
- E, 1 0 7 ~
t 41
.
m
n
.
-
c
-0.80
-l.O2I I
0
50
I
100
I
150
NCF
Figure 1. Variational (lower part) and second-order corrected (upper
- 1.06
t
part) correlation energies of the (CuC2H2)+complex as a function of the number of determinants in the variational wave function (NCF) (CIPSI algorithm): (-0-) canonical M O s ; (-+-) canonical occupied MOs and valence virtual MO's obtained from the P A 0 procedure; (-O-) canonical occupied M O s and virtual MO's using the HAO's following localization of the valence occupied and the P A 0 procedure; (-A-) virtual MO's using the HAO's.
to A; (ii) Xi = 1, orbitals of A which have not changed in AB; or (iii) 0 < Xi < 1 orbitals which have been modified in AB in relation with A. The 1 - Xi values give a quantitative measure to the extent of the change, which can be reasonably be attributed to the interaction of A with B.35 The CI calculations were performed with the CIPSI alg~rithrn,'~ which proceeds by an iterative selection of the reference determinants. The multireference wave function is then perturbed to the second order in a Rayleigh-Shriidinger Merller-Plesset perturbation expansion.'' As it is ~ e l l - k n o w n the , ~ ~canonical HF virtual orbitals are in general not well suited for CI purposes, mainly because of their diffuse character. Optimization of the valence virtual space have been carried out using hybridized atomic orbitals39 (HAO), an improvement in the efficient projected atomic orbital (PAO) procedure.40 The HAO's are obtained by a diagonalization of the ground-state H F molecular density operator restricted to the atom.39 These procedures have been proved to give results almost identical with those obtained by a comparable MCSCF calculat i ~ n . ~ ~ *On ' " 'the other hand, a proper projection of the fragments MO's into the molecular (occupied or virtual) space has been undertaken in order to gather the same physical meaning for the correlation energy along a potential energy curve, as has recently been s ~ g g e s t e d . ' ~ To show the efficiency of these procedures a few test calculations were carried out for the Cu+/C2H2 system at a metal-ligand distance of 4.0 ao, using the experimental geometry for the acetylene unit.41 Figure 1 shows the convergence of the different procedures when the number of configurations (NCF) included in the reference space is increased. The results are quite impressive. For instance, when valence virtual M O s defined by the (35) Bagus, P. S.;Nelin, C.J.; Bauschlicher, Jr., c. W. P h p . Rev. 1983, 828,5423. (36)Huron, B.; Malrieu, J. P.; Rancurel, P. J . Chem. Phys. 1973,58, 5745.
(37) (a) Moller, C.; Plesset, M. S . Phys. Rev. 1934,46,618.(b) See,e.g.: Daudley, J. P.; Malrieu, J. P. Studies in Physical and Theoretical Chemistry; Car&, R., Ed.; Elsevier: Amsterdam, 1982;Vol. 21,pp 35-64. (38) See, e.g.: Fantucci, P.;BonaCiE-Kouteckg, V.; Kouteckg, J. J . Comput. Chem. 1985,6,463 and references cited therein. (39)Illas, F.; MerchPn, M.; Pelissier, M.; Malrieu, J. P. Chem. Phys. 1986, 107, 361. (40)Chambaud, G.;Gtrard-Ah, M.; Kassab, E.; Levy, B.; Pernot, P. Chem. Phys. 1984,90, 271. (41) Herzberg, G. Electronic spectra of Polyatomic Molecules; Van Nostrand: Princeton, NJ, 1966.
4.0
5.0
6.0
7.0
r/ao
Figure 2. From top to bottom: S C F (A),variational (O), and corrected up to the second order (0) ( N C F = 86) potential energy curves vs r(Cu+-C2H2). The energies are relative to -61.000000 ao. TABLE I: Optimal Metal-Acetylene Distances, z(M),, and Binding Energies, Eb,at SCF and CI Levels, for the (MC2H2)+Complexes dM)llliIl/a0
Ebc/eV
approach
M = Cu
M = Ag
M = Cu
M = Ag
SCF Cha: CItotb
4.338 4.126 4.220
5.083 5.274 5.018
0.99 0.64 1.16
0.58 0.43 0.64
'From diagonalization of the reference space. Including the second-order perturbation corrections. Binding energies are referred to z(M) = 20.0 ao.
PAOs procedure are used, 45 determinants are necessary to obtain a first-order correlation energy of -0.2104, while 158 are needed from canonical MOs. The use of the HAO's to obtain the valence virtual MO's gives a slight improvement with respect to the standard PAO's procedure. Also, the HAO's, which bear the molecular information, allow us to localize the bond MO's by projecting the adequate linear combination of HAO's (within the C , symmetry constraints) in the molecular Fock space. As Figure 1 reflects the improvement is not so pronounced due mainly to the previous optimization of the corresponding antibonding counterparts. The values of the energies corrected to second order are less disperse than the variational results. This fact shows once more the accuracy of the second-order multireferential algorithms, such as CIPSI one. Hereafter, all the results reported were carried out by using the HAO's to localize the valence virtual and occupied molecular Me's*
and Discussion The r-coordinated structures of the complexes considered belong to c2u the symmetry being x z and yz* The acetylene unit is located in the x axis and in a first approximation the experimental geometr?' is used. The metal is placed in the z axis,'and so the coordinated value corresponds td the distance of the metal from the C-C bond, namely, z(M). The potential energy curves with respect to z(M) are shown in Figures 2 and 3 for the Cu+/C2H2and Ag+/C2H2systems, respectively. The
4856
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988
TABLE 11: Net Atomic Charges and Total Overlap Population of CzHz and (MCZH2)' Ground States at the SCF Optimal Metal-Ligand Distance Interaction
E/Eh -.28
atom C M H
\\ -.3 6
Miralles-Sabater et al.
\
c-c C-M C-H
M = Cu
M = An
-0.130 0.764 0.248 0.681 0.075 0.399
-0.172 0.887 0.228 0.754 0.035 0.404
0.171 0.871 0.404
TABLE III: Total Population of Atomic Valence Orbitals of CzHz and (MC2H2)+Complexes at the SCF Optimal Metal-Ligand Distance Interaction
-.44
-.52
C,H, -0.171
AO's
\
-.6 0
-.68 I
I
I
I
4.0
5.0
6.0
7.0
*
C,H,
(MC2H2)+ M = Cu M = Ag. 1.335 0.898 0.992 0.906 0.149 0.002 0.012 0.078 2.001 1.998 2.000 1.993 2.003
1.330 0.895 0.999 0.948 0.094 0.000 0.003 0.022 2.000 1.999 2.000 1.996 2.000
ria,
Figure 3. From top to bottom: SCF (A),variational (m), and corrected up to the second order ( 0 ) (NCF = 117) potential energy curves vs r(Ag+-C2H2). The energies are relative to -49.000 000 ao.
C I curves were built with the reference space selected at z(M) = 4.0 ao, involving 86 and 1 1 7 configurations, for Cu+ and Ag+ complexes, respectively. The overall process used to obtain localized molecular orbitals (LMO's) allows us to keep the same reference spaces along the C I curves. The second-order energy correction takes into account the contribution of about 1.8 X lo6 determinants for the Cu+/C2H2,and 2.3 X lo6 for the Ag+/C2H2. Figures 2 and 3 show that the optimal z(M) distances and binding energies are quite dependent on the approach used. The values are summarized in Table I. It can be noted how the part of the correlation energy which has been calculated variationally increases the optimal z(M) value and diminishes the binding energy in relation to the S C F results, and on the contrary, inclusion of the second-order perturbation corrections works in the opposite way. In what follows, we try to analyze the reasons for these behaviors. Let us consider first the factors influencing bonding at S C F level. In a first approximation, the S C F model should be adequate to describe the major effects in these types of interactions. The (MC2H2)+( M = Cu, Ag) 'Al ground state may be described in terms of a acetylene ligand '2: and a M+(dlO)metal atom. Thus, there are two contributions to be considered: (i) the electrostatic interaction and (ii) the u- and/or a-charge transfer. The strong electric field produced by the positive charge of (MC2H2)+allows us to suggest that the electrostatic interactions are dominant. In order to estimate the importance of these interactions, we have replaced the metal ion by a simple point charge at the SCF optimal metal-ligand distance, z(M)-. Binding energies of 0.87 and 0.55 eV for the analogues of (CuC2H2)+and (AgC2H2)+complexes, respectively, are obtained. Comparison with the S C F results in Table I indicates that this simple model is quite reasonable and gives a forward picture on the nature of the M+-C2H2interaction. It is also in agreement with the results on the Ag+/C2H424and C U + / C ~ systems. H ~ ~ ~ Moreover, ~ the present z(M)- value and binding energy obtained at SCF level for the (CuC2H2)+complex can be compared with the previously reported for the C, structure of ( C U C ~ H ~ )at' , the ~ ~same ~ level of quality. Only on the grounds of merely ionization potential of ethylene and acetylene one could
expect that (CuC2H2)+has a weaker bonding than (CuC2H4)+ since acetylene would not be as good a donor as ethylene because acetylene has a much higher ionization energy than ethylene. However, Cu+-C2H2 and Cu+-C2H4binding energies are of the same order of magnitude which gives forward support to the view of these metal-ligand interactions as mainly due to the presence of a positive charge, the two-way donoracceptor mechanism being less important. In order to understand better the S C F description of bonding, in Table I1 are shown the M ~ l l i k e net n ~ ~atomic charges and total overlap population for the (MC2H2)+complex at the optimal S C F metal-ligand distance, along with C2H2,for the sake of comparison. Charge transfer from C2H2to the metal seems to take place more for the copper complex, since the net atomic charge of the metal is less positive for the copper than for the silver atom. Moreover, the M-C overlap population is larger and the C-C overlap population lesser for the (CuC2H2)+ than for the (AgC2H2)+complex. Table 111 shows total population of atomic valence orbitals. Apparently, the orbitals involved in the metal-ligand bonding are the ligand ar orbital and the s, pz atomic orbitals of the metal. It must be pointed out that the value is less than 1 for the total population of the carbon pr orbitals, and the role of the metal pz orbitals is nonnegligible. If a-back-bonding would be present, a value less than 2.0 for the d,, atomic population might be expected. That is not the case and a-back-bonding is negligible, which appears to be a characteristic finding in the copper monoion-ligand interaction^.^^ Also, some diminishing from 2.0 is found for the dg atomic orbital of metal, which could be ascribed to s, dZ2or s, pz, dz2 metal hybridization. In order to check if the above qualitative conclusions on the M+-C2H2 bonding are correct, determining in a quantitative way the extent to which the 6- and a-bonding take place, the corresponding orbital t r a n ~ f o r m a t i o n ' ~was , ~ ~carried out. Corresponding orbitals depend only upon the nature of the two S C F orbital sets considered and are not subject to any artifact. Table IV shows the (1 - A) highest values of the smallest nonzero A's for the (MC2H2)+complexes; the remaining x's being essentially 1. The C2H,/(MC2H2)+analysis shows a very small change of the C2H2orbitals. The corresponding orbitals associated with the (42) Mulliken, R. S . J . Chem. Phys. 1955, 23, 1833, 1841, 2338, 2343.
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988 4857
Interaction of C2H2with Cu and Ag Monoions TABLE IV: The Highest (1 - X) Values of the Smallest Nonzero Corresponding Orbital Eigenvalues, X, Related to C2H2and (MC2Hz)+ (1) and Mt and (MC2H2)' (2) Occupied Orbitals, at the SCF Optimal Metal-Ligand Distance (1 - A) x 102
-E.IO'/E,,
t /---
13 -
Ag a
1.732
0.053
c
0.107
Penultimate M+-(MC2H2)+corresponding eigenvalue.
TABLE V: Weights in the Variational Wave Function (WWF's) for the (MC2H2)' Complexes WWF's. 5%
Me a12(r,)
-
2.4 1.o
0.2 0.1
__________~
(MC,H,)' M = Cu M = Ag
GS" 92.0 91.7
C2H2b 5.4 7.2
" Represents the ground-state determinant. Weight in the variational wave function involving the intramolecular correlation of the ligand. Weight in the variational wave function involving the intraatomic correlation of the metal. It accounts for the u charge transfer.
The symbols within parentheses give the main component of each MO. greatest (1 - A) are mainly related to the T, M O of the C2H2, the participation of the s atomic orbital of the metal in the complex with p, hybridization somewhat polarized toward the carbon sM, but the coratoms. There is some charge a-donation, x, responding eigenvalue shows that is very little. In fact, assuming that the deviation from 1 is due entirely to C2H2to metal u-donation, at the optimal SCF metal-ligand distance, we can estimate that as only 0.042,0.035 electrons (2(1 - A)) for (CuC2H2)+and (AgC2H2)+,respectively. The (MCzH2)+analysis is also consistent with the results from Mulliken population analysis. The smallest A is associated with the dg orbital of the metal, which shows some hybridization with the s atomic orbital being the role of the p, orbital less important. Table IV also shows the penultimate 1 - A value which is associated to the d,, orbital. It could be related and to the ?r-back-donation, appearing to be negligible (3 X electrons at the S C F Z(M),,,~, value for (CuC2H2)+and (AgC2H2)+,respectively). Let us consider now which are the main effects when electronic correlation is taken into account. As can be seen from Table V, apart from the HF determinant, the most important contributions to the variational wave function comes from the intramolecular correlation of the C2H2unit. Hence, the analysis of the main electron correlation effects on the free C2Hzshould be useful to be compared with the complexes considered. Localized MO's (LMO's) are used, and in Figure 4 the variational and total C I energies vs N C F for the C2H2are shown. Usefulness of the LMO's is again evident. Table VI shows the most important contributions in decreasing order in the C I wave function using LMO's, and also the corresponding coefficients with CMO's (canonical MO's). These two wave functions pick up nearly the same variational correlation energy, about -0.1 10Eh, N C F being equal to 31 and 99 with LMO's and CMO's, respectively. These more important contributions have a larger weight with L M O s than with CMO's because the valence virtual L M O s have a maximum overlap with the HAO's, which involves the maximization of the virtual-occupied exchange interaction. These more important contributions account for the correlation within the bond MO's and their antibonding counterparts. Since we use LMO's, we have a valence space defined, which is isomorphic to a minimal basis set. Then, we can analyze the various physical contributions implying valence MO's in the VB language. This analysis has been shown as a nice too143-45to
-
(43) Spiegelmann, F.; Malrieu, J. P.; Maynau, D.; Zurru, J. P. J . Chim. Phys. 1986, 83, 69. (44) Karafiloglou, P.; Malrieu, J. P. Chem. Phys. 1986, 104, 383. (45) Sevin, A. Quantum Chemistry: The Challenge of Tranrition Metals and Coordination Chemistry, NATO AS1 Series, Serie C, Vol. 176; Veillard, A,, Ed., Reidel: Dordrecht, 1986; pp 235-252.
,
I
0
a12(sM)d
50
I
100
150
NCF
Figure 4. Variational (lower part) and second order corrected (upper part) correlation energies of the C2H2as function of the number of determinants (NCF) in the variational wave function ( ~ 1 s algorithm): t (-O-)
canonical MO's; (-+-)
localization of the valence occupied
and virtual MO's using the HAO's.
TABLE VI: The More Important Singular Contributions, by Spin or Symmetry Constraints, to the Multideterminantal CI Wave Function for C2H2,Using Localized Molecular Orbitals (LMO's), as Well as the Canonical Orbitals (CMO's)
tvDe of contribution" ground state
I. -:,a 11. 111. T"i,*
IV.
v.
--?r* Bx
61 H$-
?r*
-* p
Bx= T*BxT2
w
u*,c-
i&ruy2-?r*gXriT*
W
VI. ugc b2(d*y,)zy XI. al(d,z)2 a*l(d*,z)2 XII. bl(d,J2 b*l(d*xr)2 charge transfer from C2H2to Cu' XW. a21(rz) a21(scu)
3.500 a,
4.220 a,
6.000 a.
0.962
0.960
0.958
-0.091 -0.105 -0.066 -0.041 -0.032 0.025 0.031 0.03 1 -0.030
-0.093 -0.105 -0.067 -0.041 -0.035 0.026 0.03 1 0.03 1 -0.03 1
-0.100 -0.104 -0.068 -0.041 -0.036 0.028 0.032 0.032 -0.032
-0.034 -0.034 -0.033 -0.032 -0.026
-0.035 -0.034 -0.034 -0.032 -0.028
-0.034 -0.034 -0.034 -0.034 -0.033
-0.025
-0.040
-0.032
TABLE VIII: The More Important Singular Wave Function Coefficients (WCF) in the Multideterminantal CI Wave Function (NCF = 117) for the (AgC2H2)+Complex for Various Metal-Ligand Distances
WFC type of contribution ground state intramol correln of C2H2 I. a I 2 b*12(r,) b22 a*22(7ry) 11. a16, b*lL*z(r) 111. alb2 b*la*2(r) IV. b21 b*I2(C-H) V. a21b22 b*lza*22(r)VI. al,~l(rJ b*IC
