Theoretical Study of Transition-Metal Ions Bound to Benzene

J . Phys. Chem. 1992, 96, 3213-3218

3273

Theoretical Study of Transition-Metal Ions Bound to Benzene Charles W. Bauschlicher, Jr.,* Harry Partridge, and Stephen R. Langhoff NASA Ames Research Center, Moffett Field, California 94035 (Received: October 4, 1991)

Theoretical binding energies are reported for all first-row and selected second-row transition metal ions (M+) bound to benzene. The calculations employ basis sets of at least double-{ plus polarization quality and account for electron correlation using the modified coupled-pair functional method. While the bonding is predominantly electrostatic, the binding energies are significantly increased by electron correlation, because the donation from the metal d orbitals to the benzene A* orbitals is not well described at the self-consistent-field level. The uncertainties in the computed binding energies are estimated to be about 5 kcal/mol. Although the calculated and experimental binding energies generally agree to within their combined uncertainties, it is likely that the true binding energies lie in the lower portion of the experimental range. This is supported by the very good agreement between the theoretical and recent experimental binding energies for AgC6H6+.

Introduction Gas-phase organometallic ion chemistry is an active area of experimental research.l Metal-ligand bond energies can be determined by a variety of methods, but the most common techniques are collision-induced dissociation (CID), ligand-exchange reactions, and guided ion beam experiments. More recently, photodissociation techniques have been used to place upper bounds on the binding energy. This technique yields an accurate value for the binding energy only when the dissociative state lies at an energy near the threshold for dissociation. The binding energies for many of the first- and second-row transition metal ions bound to benzene have been measured by these There is a greater variation in the binding energies than would have been expected based on the trends observed for M H 2 0 +Io or MNH3+." For example, Ni+ is bound to both H 2 0and NH3 by only a few kcal/mol more than Cu+.Although there are rather large error bars for the MC6H6+measurements, the corresponding difference from e ~ p e r i m e n t for ~ . ~ the benzene ligand is 18 kcal/mol. Another interesting feature is that the binding energy of AgC6H6+is much smaller than for the other metal ions. This observation is expected to be reliable as three independent experimental give comparable results. In fact, the binding energy of AgC6H6+is only slightly larger than the value of 33-35 kcal/mol estimated for MgC6H6+from a b initio calculations.'* Comparable binding energies for MgC6H6+and AgC6H6+have also been obtained experimentally by Duncan and co-worker~.~ Ab initio calculations have been used extensively to obtain insight into the nature of transition metal ion-ligand bonding, as well as to compute quantitative binding energies.I3 Because the calculations are of nearly uniform accuracy for all metal ions, they have been very useful for establishing trends and in identifying (1) Russell. D. H., Ed. Gas Phase Inorganic Chemistry; Plenum Press: New York, 1989. (2) Lech, M. L.; Freiser, B. S.,personal communication. (3) Hettich, R. L.; Freiser, B. S. J. Am. Chem. SOC. 1987, 109, 3537. (4) Hettich, R. L.; Jackson, T. C.; Stanko, E. M.; Freiser, B. S. J. Am. Chem. SOC.1986, 108, 5086. ( 5 ) Duncan, M. A., personal communication. (6) Buckner, S. W.; Freiser, B. S. Polyhedron 1988, 7 , 1583. (7) Willey, K. F.; Cheng, P. Y.; Bishop, M. B.; Duncan, M. A. J. Am. Chem. SOC.1991, 113, 4721. (8) Chen. Y.; Armentrout, P. B., personal communication. (9) Attributed to McMahon, T. B., by Freiser, B. S.(personal communication). (IO) Rosi, M.; Bauschlicher, C. W. J. Chem. Phys. 1990, 92, 1876 and references therein. ( I I ) Langhoff, S.R.; Bauschlicher, C. W.; Partridge, H.; Sodupe, M. J. Phys. Chem. 1991, 95, 10677. (12) Bauschlichcr, C. W.; Partridge, H. Chem. Phys. fett. 1991,18l, 129. (13) Bauschlicher, C. W.; Langhoff, S. R. Int. Rev. Phys. Chem. 1990.9, 149.

incorrect experimental measurements. In this work we consider the first-row and selected second-row transition-metal ions bonded to benzene.

Methods In view of the large number of degrees of freedom in the M+-benzene systems, we first optimized all of the geometrical parameters for selected systems at the self-consistent-field (SCF) level. On the basis of these SCF calculations, we restricted the correlated studies to C, symmetry. Although for selected systems we optimized all four symmetry-independent degrees of freedom at the modified coupled-pair functional (MCPF) level,I4for most systems only the metal ion-benzene and C-C distances were optimized, because the binding energies were sensitive only to these geometrical parameters. For computational convenience, there are some differences in the basis sets used in the S C F optimization and in the MCPF calculations. The specific calculations are described in more detail below. In the MCPF calculations the first transition row metal atom basis sets consist of the [8s4p3d] contraction of the (14s9pSd) primitive sets of Wachters,Is augmented with two diffuse p and a d function,16 as well as a three-term fit to a Slater 4f function. The 4f Slater exponents vary from 1.6 to 4.8 in steps of 0.4 from Sc to Cu. Thus the metal basis sets are of the form (14sllp6d3f)/[8~6p4dlfl.In the triple-{ plus two sets of polarization (TZ2P) calculation on CuC6H6+, the three-term f function is contracted as (21). The final Cu basis set uses a general contraction of the s, p, and d functions based on an S C F calculation for Cu+. The coefficients from the Is, 2s, 3s, 2p, 3p, and 3d orbitals are used to contract the tight functions: the outermost three s, three p, and three d primitives are uncontracted. The (3f)/[2fl contraction is also used in this basis set giving a final basis set of the form (14sllp6d3f)/[6~5p4d2fl.In the S C F optimizations the 4f functions are deleted. For the second-row transition-metal atoms we used the relativistic effective core potentials (RECP) developed by Hay and Wadt." These RECPs include the outermost core orbitals, the 4s and 4p, in the valence shell; this results in a node in the 5s orbital and therefore the valence electrons can be correlated.]* The supplemented valence basis and the (3f)/[ I f ] polarization sets described in ref 19 are employed, yielding final basis sets of the form (6s6pSd3f)/[5s4p4dlfll. We fully optimize the geometry (14) Chong, D. P.; Langhoff, S.R. J. Chem. Phys. 1986, 84, 5606. See also: Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J. Chem. Phys. 1985, 82, 890. (15) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (16) Hay, P. J. J. Chem. Phys. 1977, 66, 4377. (17) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299. (18) Rohlfing, C. M.; Hay, P. J.; Martin, R. L. J. Chem. Phys. 1986,85, 1447. (19) Langhoff.

S.R.; Pettersson, L. G . M.; Bauschlicher, C. W.; Partridge, H . J. Chem. Phys. 1987, 86, 268.

This article not subject to U S . Copyright. Published 1992 by the American Chemical Society

3274 The Journal of Physical Chemistry, Vol. 96, No. 8, 1992

of two second-row transition metal-benzene systems at the SCF level. The f function was not included in the NbC6H6+calculation, and the (3f)/[lfl contraction was replaced by a single f function with an exponent of 1.1 in the AgC6H6+calculations. At the SCF level we used 6-31G and 31G sets20for carbon and hydrogen, respectively. In some calculations a 3d ( a = 0.8) polarization function was added to C (denoted 6-31G*). At the MCPF level a double-f plus polarization (DZP) basis was used with the contraction proposed by Dunning.21 For hydrogen, the scaled basis set was used. The polarization functions for carbon and hydrogen were a(d) = 0.75 and a(p) = 1.O. The DZP basis sets were of the form ( 9 ~ 5 p l d ) / [ 4 ~ 2 p l and d ] (4slp)/[2slp] for C and H, respectively. To reduce the basis set superposition errors (BSSE), another C basis set of approximately DZP quality was constructed. The basis set was a truncated version of our standard22atomic natural orbita12j (ANO) basis set, namely, (13~8p6d)/[4~3pld].While this contraction combined with the large primitive set reduced the C6H6 BSSE, this basis set, like the DZP basis set, underestimated the polarizability. This deficiency was corrected in the basis set donated ANO+d, where the most diffuse d primitive was uncontracted. The general contraction of the Cu basis set was used in conjunction with the ANO+d carbon set. In the TZ2P calibration calculation on CUC&,+, the (lOs6p)/[5s3p] basis set of Dunning24was supplemented with two d functions with exponents of 1.40 and 0.40. The hydrogen basis set is the (5s)/[3s] contraction of Dunning24 with a 2p function ( a = 1.0) added. Previous workI2 on Mg+-benzene has shown that the bonding, which is due primarily to charge-induced dipole interactions, is well described at the S C F level. However, the bonding is more complex for the transition-metal ions, because there is considerable donation of the d electrons into the A* orbitals of benzene. An accurate description of the donation requires that electron correlation be included. In this work we use the MCPF method, which has been shown13to yield good binding energies for transition-metal ions with other ligands. Also, as we show below, the MCPF and the single and double excitation coupled-cluster method2s with a perturbational estimate of the triple excitations26 [CCSD(T)] approaches agree well for the transition metalbenzene systems. In the MCPF calculations we correlated 36 electrons on benzene (i.e., all but the C 1s-like electrons) and the metal valence d and s electrons. For the second transition row we include the effect of the mass-velocity and Darwin terms through the use of the RECP. Thus the change in the size of the valence orbitals due to relativistic effects should be accounted for. For the first transition row the change in orbital size is small, especially for the dn+l occupation, and therefore we have neglected these terms. The atomic ion spin-orbit splittings2' are relatively small for Sc+ but grow in magnitude with Z. The spin-orbit splittings for the molecular ions can be estimated by neglecting the second-order (off-diagonal) spin-orbit contributions, assuming that the open-shell orbital is localized entirely on the metal yielding a system with pseudolinear symmetry, and estimating the magnitude of the spin-orbit matrix elements using the atomic l values.2s This correction reduces the De Values O f FeC&6+, CoC&,+, NbC&+, and RUC&,+ by 1.6, 2.0, 1 S,and 4.0 kcal/mol, respectively; the reduction is less than 1.0 kcal/mol for the other ions studied. Given the (20) Hehre. W. J.; Radom, L.; Schleyer. P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986, and ref-

erences .......therein ......... (21) Dunning, T . H . J . Chem. Phys. 1970, 53, 2823. (22) Bauschlicher, C. W.; Langhoff, S. R.; Taylor, P R. J . Chem. Phys

Bauschlicher et al. TABLE I: Benzene Geometry

(A) as a Function of the Level of

Treatment method

r(C-C)

r(C-H)

SCF 6-31G SCF 6-31G' MCPF DZP MCPF AN0

1.388 1.386

1.073 1.076

1.407 1.401 1.397

1.083 1.084

expta

1.087

a ro values from: Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand Reinhold Company: New York, 1966; Vol.

111.

qualitative nature and relatively small size of the correction, we do not incorporate it into our De values but increase our error bars accordingly. Only the pure spherical harmonic components of the basis functions were included in the SCF/MCPF calculations, while all functions were included in the SCF geometry optimizations. The calculations were performed using the MOLECULE-SWEDEN,~~ TITAN,^^ and GRADSCF~' program systems on the NASA Ames Research Center Central Computing Facility CRAY Y-MP/832.

Calibration Calculations The benzene geometry is rather insensitive to improvements in both the one-particle basis set and correlation treatment, and the structures a t all levels of theory are in good agreement with experiment (see Table I). Since the bonding is primarily electrostatic, the binding energy depends strongly on the metal-ligand distance, and it is essential to accurately describe the polarizability of the benzene ligand along the c6 axis. At the MCPF level the results for the polarizability along the c6 axis of benzene are (in ai): DZP(26.2), AN0(32.6), TZ2P(35.7), and ANO+d (41.3), compared with the experimental value32 of 42.9. While the dominant bonding term is charge-induced dipole, which is proportional to a/#,previous work has shown13that such effects as promotion, hybridization, and orientation of the singly or doubly occupied d orbitals on the metal ion can significantly enhance the bonding. For metal ions, such as Fe+, with a ground state derived from the 3dn4s1occupation, it is often energetically favorable to promote to a low-lying state derived from the 3dn+I occupation, as the more compact d orbital reduces the effective size of the ion, thereby allowing it to approach closer to the ligand. Whether this promotion is favorable depends on the promotion energy and strength of the metal-ligand interaction. The metal d to benzene r* donation is another important factor in determining the relative ordering of the electronic states. In c6, symmetry, where the metal ion lies along the c 6 axis of benzene, the r* orbitals transform according to the b, and e2 representations. The d orbitals on the metal ion transform as de2(6), de,(*), and da,(u). Thus it is most favorable to occupy the de2(S)orbitals, as this maximizes donation into the T* orbitals on benzene. Due to the symmetry, it is not possible for the metal to donate into the b, A* orbital. Thus additional electrons must go into orbitals that overlap with the benzene A orbitals, which increases the metal-benzene repulsion. The dal(u) orbital has a smaller overlap with the A orbitals on benzene than does the de,(*) orbital. This is opposite to the usual trend, as the da,(u) orbital generally has the largest overlap with the ligand. The da,(o) overlap is small for benzene, because the orbital is relatively compact and points into the 'hole" in the center of the benzene a ring. The ordering of states in the MC6H6+ions is determined by the filling order de2(6),da,(u), and de,(*). The dH1occupation,

1987 -.-, 87 - 3x7

(23) Aimlof, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (24) Dunning, T. H. J . Chem. Phys. 1971, 55, 716. (25) Bartlett, R. J . Annu. Reo. Phys. Chem. 1981, 32, 359. (26) Raghavachari, K.; Trucks, G.W.; Pople, J. A,; Head-Gordon, M. Chem. Phys. Lett. 1989, l 5 7 , 479. (27) Moore, C. E. Atomic energy levels; US.National Bureau of Standards (U.S.) Circular No. 467; 1949. (28) Lefebvre-Brion, H.; Field, R. W. Perturbations in the Spectra of Diatomic Molecules; Academic Press: Orlando, FL, 1986.

(29) MOLECULE-SWEDEN is an electronic structure program system written by J. Almlof, C. W. Bauschjicher, M . R. A. Blomberg, D. P. Chong. A. Heiberg, S. R. Langhoff, P.-A. Malmqvist, A. P. Rendell, B. 0. Roos, P. E. M . Siegbahn, and P. R. Taylor. (30) TITAN is a set of electronic structure programs written by T. J . Lee, A. P. Rendell, and J. E. Rice. ( 3 I ) GRADSCF is a vectorized SCF first- and second-derivative code written by A. Komornicki and H. King. (32) Landolt-Biirnstein, Zahlenwerte und Funkrionen; 1951. Vol. I, p 5 1 I .

The Journal of Physical Chemistry, Vol. 96, No. 8, 1992 3275

Transition-Metal Ions Bound to Benzene

TABLE 11: Structures (A and deg) and Binding Energies (kcal/mol) for the First-Row Transition-Metal Ions Bound to Benzene (Values in Parentbeses Are Not Optimized)

metal sc sc sc Ti V

Cr Mn

Fe Fe Fe co Ni

cu cu cu cu cu cu

state' 'E2(3dei4s')' 3E2(3dei4s') 'Ez(3de;4s') 4A2(3dei3dai) 3dei3da;3de;) 6AI(3deg3dai3de:) 'A I (3dei3dai 3de:4s I) 'A2( 3de:3da 3dei) 4A,(3de:3da! 3de:) 6E2(3de~3da;3de~4sl) 'Az( 3dej3dai3de;) 2El(3dei3da:3de:) ]Al(3de:3da:3de:) 'A, (3de:3da:3de:) 'A, (3de:3da:3de:) !A,(3dej3daf3de:) ,Al(3dei3dai3de:) 'Al (3de:3da:3de:)

level SCF 6-31G MCPF DZP MCPF AN0 MCPF DZP MCPF DZP MCPF DZP MCPF DZP MCPF DZP MCPF AN0 MCPF DZP MCPF DZP MCPF DZP SCF 6-31G SCF 6-3 1 G* MCPF DZP MCPF TZ2P MCPF ANO+d MCPF AN0

r(M-ring) 2.565 2.260 2.300

2.059 1.964 2.1 IO

2.300 1.830 (1.830)

2.153 I .854

r(C-C) 1.398 1.415 1.409 1.424 1.420

1.417 1.415 1.421 (1.421) 1.416

r(C-H) 1.072 (1.074)

H bend

(1.074)

(1.074) (1.074) (1.074)

(1.074) (1.074) (1.074) (1.074)

1.6

D,b 29.9

(0.0)

44.1

0.2 (0.0)

40.4 60.6 51.1 37.4 35.1 47.6d

(0.0) (0.0) (0.0) 0.2 (0.2) 0.0

45.4 41.7

1.423

(1.074)

(0.0)

62.6

(1.074)

(0.0)

59.3

1.072

1.8 1.3 0.4

34.7 37.2

(1.864) (1.864)

1.423 1.399 1.398 1.420 (1.414) (1.414)

(0.5)

50.3 50.5

1.864

1.414

1.082

1.750 2.168 2.1 18

1.852

1.075 1.072 (1.082) (1.082)

(0.5)

51.1'

0.5 48.8 "The MCPF calculations are carried out in C, symmetry. As discussed in the text, the actual symmetry of the SCF geometry may be lower. bThe dissociation energies are computed relative to the ground state of the metal ion. 'The SCF has only C, symmetry, but the distortion from C, symmetry is very small-see text. dThe De with respect to the 4F asymptote is 56.8 kcal/mol. 'The CCSD and CCSD(T) binding energies are 49.4 and 53.5 kcal/mol, respectively. TABLE 111: Effect of BSSE and Basis Set Incompleteness on the CuC&,+ M C P F Binding Energy (kcal/mol)

basis DZP TZ2P AN0 ANO+d

De

51.1 50.3 48.8 50.5

BSSE 8.5

D,

- BSSE 42.6

4.6

45.7

4.9

43.9 45.8

4.7

which has a shorter metal-benzene distance and more d electrons, has a larger metal to benzene donation that increases the interaction and helps compensate for the promotion energy. To accurately describe the polarization and to keep the BSSE to a manageable level, it is necessary to employ a basis set of at least DZP quality. Using large basis sets, it is computationally expensive to fully optimize all of the geometrical parameters a t the correlated level. However, as shown below, the binding energies are insensitive to the C-H distance and the bending of the hydrogens out of the plane of the benzene. Thus in many of the calculations only the metal-benzene and C-C distances are opt i d . Another constraint imposed on the geometry is restriction to C, symmetry. As discussed in more detail later, there are cases where the preferred geometry is asymmetrical even in the absence of Jahn-Teller distortion. Nevertheless, the energy associated with this distortion never exceeds more than a few tenths of a kcal/mol at the SCF level and is not expected to be significantly larger at the correlated level. Since the remaining errors due to basis set incompleteness and limitations in the correlation treatment are much larger, this restriction does not significantly affect our results. To.estimate the accuracy of our computed binding energies, we must consider the errors in both the one-particle basis set and the correlation treatment. We use CUC6H6' to calibrate our treatment-see Tables I1 and 111. At the S C F level adding a d function to the carbon basis (6-31G* vs 6-31G)increases the binding energy by 2.5 kcal/mol but has little effect on the geometry. Correlation decreases the Cu-benzene distance and increases the &C6H6+ binding energy significantly. At the MCPF level in the DZP basis set, the total BSSE [Le., the sum of cU'(c6H6) and C,H,(CU)] is 8.5 kcal/mol, which suggests that half of the increase at the correlated level is an artifact of BSSE. Changing from the DZP to A N 0 basis set reduces the BSSE to 4.9 kcal/mol but reduces the binding energy by only 2.3 kcal/ molTable 111. The disparity between the reduction in BSSE and decrease in binding energy indicates that basis set incompleteness is still sizeable. Expanding the basis set to TZ2P quality

significantly increases the flexibility of the basis set; the BSSE is reduced by 0.3 kcal/mol and the binding energy is increased by 1.5 kcal/mol compared to the A N 0 set. Relative to the DZP or A N 0 basis sets, the greater flexibility of the TZ2P basis increases both the metal to A* donation and the C,& polarizability along the c6 axis. However the TZ2P bask set has a polarizability that is 17% smaller than the experimental value.32 Further expansion of the basis set leads to a prohibitively large calculation. The ANO+d basis set has a C6H6 polarizability that is in very good agreement with experiment but may not be quite as flexible as the TZZP basis set for describing metal to A* donation. This ANO+d basis set has a BSSE that is only 0.1 kcal/mol larger and a binding energy that is 0.2 kcal/mol larger than for the TZ2P set. The TZ2P and ANO+d results indicate that there is significant cancellation between BSSE and basis set incompleteness when the DZP basis is employed. Because calculations using the TZZP or ANO+d basis sets are expensive, we take advantage of the cancellation of errors and use the DZP basis for all systems. From the fact that the difference between the DZP and A N 0 results for other metal systems is similar to that found for CUCSH~', we conclude that the basis set studies for CuC6H6' are representative of all MC6H6+systems. We have also assessed the limitations in the MCPF treatment of electron correlation by determining the binding energy for CUC6H6' using the CCSD(T) method. The CCSD(T) method has been shown to give excellent agreement with accurate multireference configuration-interaction methods for a variety of system^.'^ The binding energy at the CCSD(T) level is 2.4 kcal/mol larger than the MCPF value. The perturbational estimate of the triples contribution to the binding energy is about 4 kcal/mol. While the MCPF and CCSD(T) results often agree better for electrostatic systems, in this case there is a substantial increase in the binding energy due to correlation, because the donation from the metal to the benzene ligand is not well described at the S C F level. Since the MCPF De value of CUC6H6' is about 14 kcal/mol larger than the S C F value, it is not surprising that this value is increased by an additional 2 kcal/mol by improving the correlation treatment. On the basis of the calibration calculations, we estimate the uncertainties as follows. The calculations using the ANO, ANO+d, and TZZP basis sets suggest that the MCPF value in the DZP basis set could be a maximum of about 5 kcal/mol too (33) Lee,T. J.; Rendell, A. P.; Taylor, P. R. J. Chem. Phys. 1990,93,6636 and references therein.

3276 The Journal of Physical Chemistry, Vol. 96, No. 8,1992

large due to superposition error. However, the results for the TZZP, ANO+d and A N 0 basis sets suggest that the basis set incompleteness is probably about the same size as the BSSE. The CCSD(T) calculations show that higher levels of correlation treatment will increase the MCPF value. Also, optimization of the C-H bond length and the C-H bend as well as distortion from C, symmetry will increase the binding energy slightly. Therefore the real value could be 5 kcal/mol larger than our computed value. On the basis of the calibration calculations, we assign error bars of &5 kcal/mol to the D Z P basis MCPF binding energies. Furthermore, we feel that excluding Ru+,where the spin-orbit effects are large, the correct binding energy will probably lie in the upper half of our estimate.

Results and Discussion The structure of the ground state of SCC6H6' was fully optimized at the SCF level using the 6-31G basis. The benzene geometry is only slightly distorted by the interaction with the metal ion. The hydrogen atoms bend away from the ion by less than 2*, and very little energy is associated with this distortion. The ground state is derived from the 'D(3d'4s1) state of Sc+; the 3de2 orbital is singly occupied to maximize 3d to K* donation. The 3d population at the MCPF level (1.18 electrons) indicates some contribution to the wave function from the 3d2atomic state. While stronger bonds can be formed from the 3d2 asymptote of Sc+, the promotion energy is too large for this to become the dominant bonding mechanism. Jahn-Teller distortion of the 3E2state lowers the symmetry to C,, resulting in a 3A: ground state. However, this distortion is very small, leading to Sc-C distances that differ by only 0.015 A. Since the distortion is very small, the MCPF calculations were performed in C , symmetry and this symmetry is used to label the state. The inclusion of correlation at the MCPF level increases the binding energy of SCC6H6' by more than 10 kcal/mol. In contrast, electron correlation increases the binding energy of MgC6H6+by less than 2 kcal/mol. The effect is larger for the Sc+ion, because correlation enhances the donation to the benzene r* orbitals, which is unimportant for Mg+ because it has no occupied d orbitals. The optimized geometries for the 3E2state of SCC6H6' are very similar using the DZP and A N 0 basis sets. The difference in binding energy between these two basis sets is larger than for CUC6H6' but is consistent with our estimated uncertainties in the calculations. The ground state of TiC6H6+is 4A2 where two of the openshell d electrons are in the 3de2(6) orbitals to maximize donation into the T * orbitals and the third d electron resides in the 3dal(a) orbital. The Mulliken d population (2.97 electrons) shows that this state is derived almost exclusively from the 4F(3d3)state of Ti+, which lies 0.1 eV (2.3 kcal/mol) above the 4F(3d24sl)ground state. The binding energy in Table I1 is computed with respect to the ground state of Ti+. Alternatively, we can reference the energy to the 4F(3d3) atomic state and shift the binding energy using the well-known e ~ p e r i m e n t a l4F-4F ~ ~ separation. This approach, which minimizes the effect of errors in the computed Ti+ atomic separation, increases the binding energy by 2.2 kcal/mol. As discussed above, the d"+l occupation has a stronger interaction than the d"s' occupation. In addition, Ti+ has two 3de2 orbitals from which to donate to the A* orbitals of benzene while sc+ has only one. This results in a binding energy for TiC6H6+ that is significantly larger than for SCC6H6' and in a significantly reduced metal-benzene distance. The smaller donation to benzene is also reflected in the shorter C-C distance for SCC6H6'. The V+ ion has a 5D(3d4)ground state and a low-lying SF(3d34s1)excited state. While the MCPF state separation is in g o d agreement with experiment, the SFstate is predicted to be lower at the S C F level. Calculations at the SCF level reveal two distinct solutions for VC6H6+, one with a 3d34s1occupation for the V+ ion and the other, at shorter V-ring distances, that corresponds to 3d4. The former solution is lower at the S C F level, while the latter has lower MCPF energies at metal ion-ring distances near equilibrium. The ground state has two 3d electrons in the e2 irreducible representation to maximize metal to A*

Bauschlicher et al. donation and one in each of the a l and e, representations to minimize the metal-benzene repulsion. Since the VC6H6+ion has an occupied 3de, orbital, the V+-benzene repulsion is significantly larger than for Ti+-benzene. This leads to a 10 kcal/mol smaller binding energy for VC6H6'. The smaller metal-ring distance for V+ than Ti+ probably reflects the smaller size of the metal ion. The similar C-C distance for VC6H6' and TiC6H6+ shows that there is still significant V+ to K* donation, despite increasing the V+-benzene repulsion by occupying the 3del orbital. The ground state of CrC6H6' is 6AI derived from the %3(3d5) ground state of Cr+. The bond distance increases by about 0.1 Sa, and the De decreases by 14 kcal/mol as compared with VC&+. The bonding is weaker because the fifth 3d electron is added to the 3del orbital, which increases the repulsion with the benzene ligand. The MnC6H6+7 A ground ~ State is derived from the 7S(3d54s') state of Mn+. The metal-ring distance increases by 0 . 2 and ~~ the De value decreases by 2.3 kcal/mol as compared with crc6&+. This indicates that occupying the 4s orbital slightly increases the repulsion. Although Fe+ has a 6D(3d64s') ground state, the 4F(3d7)state of the ion is only 5.8 kcal/mol higher in energy. Because stronger bonds are formed from the 3dh1 asymptote, we optimized at the MCPF level the lowest states derived from both the 6D and 4F asymptotes. The lowest state derived from both the 3d7and 3d64s1 occupations is that expected based on the donation into the K* orbitals; namely, the doubly occupied 3d orbitals are in the e2 irreducible representation. The Fe+-benzene distance is smaller for the 4A2state derived from the 3d7occupation due to the smaller size of the ion in this configuration. The additional electron in the q orbital leads to more donation, which is visible in the slightly longer C-C distance. The 6E2state derived from the 3d64s1state of the ion lies about 6 kcal/mol higher. Thus our calculations definitively show that the ground state of FeC6H6+is the 4A2state derived from the 3d7 occupation of Fe', because further improvements in the calculations will favor the lower-spin state. The binding energy of the 4A2 ground state of FeC6H6+ is reduced by 2.2 kcal/mol when the A N 0 basis is employed in place of the DZP basis; this is comparable to the reduction found for other ions. The binding energy in Table I1 is computed with respect to the ground state of Fe+. However, an alternative (and probably more accurate) method is to compute the binding energy with respect to the 4Fexcited state of Fe+ (56.8 kcal/mol) and use the experimental 6D-4F separation to obtain the dissociation to ground state Fe+; this approach leads to a binding energy of 5 1.1 kcal/mol. The ground state of CoC&+ is the 3A2state derived from a 3d8 configuration with holes in the 3del orbitals, as expected based on the criteria of maximizing donation into the K* orbitals of benzene and of minimizing repulsion. The binding energy is larger than that for the 4A2state of FeC6H6+even considering dissociation to the 4Fstate of Fe+. This suggests that the 3da,-benzene repulsion is quite small and that this is compensated for by more metal to K* donation for CoC6H6'. The lowest state of NiC6H6+is the 'EI state derived from the 3d9 state of Ni+ with the hole in the 3de, orbital to minimize repulsion. The dissociation energy of NiC6H6+is slightly smaller than that of COC&,+, because of the increased repulsion due to having an additional electron in the 3del orbital. However, the difference is less than half that found for the Ti-V-Cr series where electrons are also being added to the 3de, orbital. The smaller effect on the right side of the row is due to reduced repulsion as a result of the contraction of the 3d orbitals with Z. Although the contraction of the 3d orbitals probably also reduces the 3de2 to A* donation, it leads to shorter metal-benzene distances and to an enhanced electrostatic interaction. Thus the reduced metal-benzene distance compensates for the increased repulsion, resulting in a binding energy for NiC6H6+that is only slightly less than CoC6H6+. At the S C F level, CuC6H,+ was found to have c6, symmetry with full optimization in both the 6-31G and 6-31G* basis sets. Electron correlation increases the binding energy by more than

The Journal of Physical Chemistry, Vol. 96, No. 8, 1992 3277

Transition-Metal Ions Bound to Benzene

TABLE IV StNCtUres (A and deg) and Binding Energies (kcal/mol) for Selected Second-Row Transition-Metal Ions Bound to Benzene (Values in Parentheses Are Not Optimized)

metal

Y Y Y Y Nb Nb Ru Ru h3

state

level MCPF AN0 MCPF AN0 MCPF DZP MCPF DZP SCF 6-31G' MCPF DZP MCPF DZP MCPF AN0 SCF 6-31G' MCPF AN0 MCPF DZP

r(M-ring) 2.426 2.604 (2.426) (2.604)

r(C-C) 1.416 1.407

r(C-H) (1.074) (1.074)

H bend

(1.416) (1.407)

(1.074) (1.074)

40.8 39.7

2.129

1.421

(1.074)

29.4 52.1

2.068

1.421

(1.074)

48.7

(2.068)

(1.421)

(1.074)

46.6 27.9 34.6 36.5

0.6

37.6 37.5

see text

see text 1.410 1.083 (1.410) (1.083)

2.353 Ag (2.353) Ag "The MCPF calculations are carried out in C, symmetry. As discussed in the text, the actual symmetry of the SCF geometry may be lower. bThe dissociation energies are computed relative to the ground state of the metal ion. CTheSCF optimized structure has C, symmetrysee Figure 1. Distortion from-C6, symmetiy lowers the energy 6y 0.23 kcal/mol. 10 kcal/mol, as was observed for ScC&6+. Associated with this increase in binding energy is a large reduction in the Cu-ring distance at the MCPF level. However, the binding energy is about 9 kcal/mol smaller and the metal-benzene distance 0.1 A longer than found for Ni. Thus adding the fourth electron to the 3de, orbital seems to adversely affect the bonding by more than adding the third. However, the stability of the closed d shell in Cu+ reduces the metal to A* donation (visible in the shorter C-C bond in CUc6H6') and therefore also contributes to the reduction in binding energy between NiC6H6+and CuC6H6'. Thus we find a larger difference between the binding energies of Cu+ and Ni+ with C6H6 than with either H@'O or NH3I1but not as large as the difference in the experimental binding energiese3v4 The stability of the Cu+closed shell is perhaps even more clearly seen from a comparison of Cu+ with Co+. They have similar metal-ring distances and therefore similar charge-induced dipole contributions to the bonding. However, the Co+ binding energy is 12 kcal/mol larger than that of Cu+. This difference in binding energy is another indication of the importance of the metal to A* donation, because the electrostatic contributions of the bonding are expected to be similar. We note that a plot (not shown) of the binding energy with 1/ P is not linear, as would be expected for electrostatic binding, but shows significant variation, much of which we attribute to changes in the metal to T* donation. Calculations were also carried out for selected transition-metal ions in the second row for comparison with the results in the first row; they are summarized in Table IV. For YC6H6' we considered the IAl and 3E2states derived from the 'S(5s2) and 'D(4dl5sl) states of Y+, respectively. We find these two states to be very close in energy. The results in the A N 0 basis set suggest that BSSE is larger for the 3E2state because of the shorter Ybenzene distance. However, the MCPF 1S-3Dseparation in Y+ is 1.8 kcal/mol too large, so that improvements in the treatment of Y+ will favor the triplet state. Because we are probably underestimating the 4d to A* donation, which is larger for the triplet state, the ground state is probably the 3E2state (in the absence of Jahn-Teller distortion). The experimental binding energy of Y