J. Phys. Chem. 1992,96,6969-6973
la
lbr
IC)
Figure 9. Schematic pictures of localization of the electron density in the
closo-boranes and clmmrboranes with the trigonal bipyramidal, octahedral, and pentagonal bipyramidal skeletons. quantum chemical calculations are being performed on organoboranes, nido- and arachno-boranes, and their isomers containing bridging hydrogen atoms.
Acknowledgment. We thank Professor Suehiro Iwata of Keio University for his helpful advice on our calculations. We also thank the Computer Center, Institute for Molecular Science, Okazaki National Research Institutes, for the use of the HITAC M680H computer.
References and Notes (1) Bailer, J. C., Jr., Emeleus, H. J., Nyholm, R.,Trotman-Dickenson, A. F., Eds. Comprehensive Inorganic Chemistry; Pergamon: Oxford, U. K., 1973. (2) Stock, A. Hydrides of Boron and Silicon; Cornel1 University Press: Ithaca, NY, 1933.
6969
(3) Sidgwick, N. V. The Chemical Elements and Their Compounds;Oxford University Press: Oxford, U. K., 1950; Vol. 1, p 338. (4) (a) Bell, R. P.; Longuet-Higgins,H. C. Nature 1945, 155, 328. (b) Longuet-Higgh, H. C. J. Chim. Phys. Phys.-Chim. Biol. 1949,46,268. (c) Longuet-Higgins,H. C.; Phil, M. A. D. Q.Rev., Chem. Soc. 1957, I I. 121. (5) Lipscomb, W . N. Boron Hydrides; Benjamin: New York, 1963. (6) Ott, J. J.; Gimarc, B. M. J . Compur. Chem. 1986, 7, 673, and their related papers. (7) McKee, M. L. J. Am. Chem. SOC.1990, 112, 6753. (8) McKee, M. L. J. Phys. Chem. 1990,94,435. (9) King, R. B.; Dai, B.; Gimarc B. M. Inorg. Chim. Acta 1990,167,213. (IO) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2657. (1 1) Tatewaki, H.; Huzinaga, S.J . Comput. Chem. 1980, 1, 205. (12) Landolt-Mrnstein, New Series 11-7. Structure Data of Free Polyatomic Molecules; Springer-Verlag: Berlin, 1976. (13) Positive energies for the HOMOS and next-HOMOS suggest that each of them is unstable as a free dianion. For example, discussions on the stability of B6Hs2-anions as a free dianion and in the crystal field are given in: Fowler, P. W. J. Chem. Soc., Faraday Tram. 2 1986,82,61. (14) Iwata, S Chem. Phys. Lett. 1980,69, 305. (15) Takano, K.; Hosoya, H.; Iwata, S.J . Am. Chem. Soc. 1982, 104, 3998. (16) Takano, K.; Hosoya, H.; Iwata, S.J . Am. Chem. Soc. 1984, 106, 2787. (17) Takano, K.; Hosoya, H.; Iwata, S.J . Chem. Soc. Jpn. 1986, 1395. (18) Takano, K.; Okamoto, M.; Hosoya, H. J . Phys. Chem. 1988, 92, 4869. (19) Takano, K.; Yoshimura, R.;Okamoto. M.; Hosoya, H. J. Phys. Chem. 1990.94, 2820. (20) (a) Jemmis, E. D.; Schleyer, P. v. R. J . Am. Chem. Soc. 1982,104, 4781. (b) Jemmis, E. D. J. Am. Chem. Soc. 1982, 104, 7071. (21) Politzer, P. J. Chem. Phys. 1987, 86, 1072 and references cited therein.
Theoretical Study of the Bonding of the First- and Second-Row Transition-Metal Positive Ions to Methylene Charles W. Bauschlicher, Jr.,* Harry Partridge, J. A. Sheehy, Stephen R. Langhoff, and Marzio Rosit NASA Ames Research Center, Moffett Field, California 94035 (Received: February 18, I992)
The geometries of the molecules formed by the interaction of the fmt- and second-row transition-metal cations with methylene are optimized at the modified coupled-pair functional (MCPF) level of theory using large Gaussian basis sets, and their dissociation energies are computed employing both the MCPF and internally contracted averaged coupled-pair functional (ICACPF) methods. The compufed binding energies are generally in good agreement with the availableexperimentalresults, although the calculations indicate that the experimental values for ScCH2+, TiCH2+,and NbCH2+are probably too large. The nature of the bonding in each case and trends in the bonding patterns across the transition-metal rows are discussed.
I. latroductioa The transition-metal methylidene cations have been postulated as intermediates in a variety of reactions, and therefore an understanding of their bonding characteristics and a determination of the metal-CH, bond strengths are of interest. Toward this end, there have been several th~reticall-~ and experimentalg" studies of the transition-metal-cation-methylene systems. Previous theoretical results have suggested a t least two bonding mechanism~.~-'Carter and GoddardzJ have described the M+-C interaction (where M represents a transition-metal atom) in CrCH2+ and RuCH2+as a covalent double bond arising from the 3Bl state of CH2, and Harrison and co-w~rkers~,~ found the same type of bonding in M H 2 +and CrCH2+. Carter and Goddard2 pointed out that the metal-dr-carbon-pr overlap is small, leading to a poor description of the bonding at the self-consistent-field (SCF) level of theory. Planelles et al.' concluded that the bonding in CuCH2+is electrostatic in origin, resulting from the interaction of IS Cu+ with 'Al CH2. This is favored over a bonding scheme involving the 3Bl ground state of methylene, even though the latter 'Current address: Department of Chemistry, University of Perugia, I06100, Perugia, Italy.
is 9 kcal/mol lower in energy than the former," because in the complex the excited state has a pair of electrons directed toward the cation, whereas the ground state of CH, can point only a single electron at the metal ion. By contrast with the case for covalently bonded systems, an SCF calculation yields a good description of the electrostatically bonded CuCH2+. Armentrout and co-workers* recently presented experimental results for the fmt transition row MCH2+compounds. They found a linear relationship between their binding energies and the metal cation promotion-plus-exchange energies, which they defined in each case as the energy difference between the metal cation ground state and the state derived from a d 5 occupation, plus the exchange energy lost upon formation of a double bond with the ligand (see also ref 13). Armentrout et al. concluded that their plot indicated significant metal 4s contribution to the bonding, although they noted that FeCH2+deviated somewhat from the linear relationship. Carter and GoddardI3had predicted, however, that a linear relationship should exist between the binding energies and the lower of the dns and dn+' promotion-plus-exchange energies. In this work we compute the metal-ligand binding energies for the MCH2+compounds derived from the first and second transition-row atoms. We find covalent double bonds in molecules
0022-3654/92/2096-6969$03.00/00 1992 American Chemical Society
6970 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
containing metal cations from the left side of each row and significant electrostatic bonding in systems formed from metal cations on the right side of the rows. While the agreement with experiment is generally good, the calculations suggest that experimental binding energies for ScCH2+,TiCH2+,and NbCH2+are too large. The present results also show a qualitative correlation between binding energies and metal cation promotion-plus-exchange energies involving the 3d"4s asymptote, as suggested by Armentrout et al. 11. Methods
Many of the MCH2+systems are poorly described by an SCF treatment.],, As noted previously, the orbitals involved in the A bond are often too localized in SCF wave functions, leading to a poor description of the bonding and an overestimation of the ionic character. Moreover, several of the molecules have SCF energies that are above their related M+ CH2asymptotic energy, and the SCF-optimized structures of some, such as ScCH2+and YCH2+, have C, rather than the expected C2, symmetry. Therefore, we optimize the geometries at a higher level of theory, employing the SCF-based modified coupled-pair functional (MCPF) approach,I4which has been successfully applied to the MCH3+and MC2H2+s y ~ t e m s . l In ~ *the ~ ~present application of the MCPF method, the metal d and s valence electrons and all but the carbon 1s-like electrons on CH2 are correlated. We optimize both the M-C bond distance and the H-C-H angle at this level of treatment but fm the C-H distance at 2.067 ao,since selected optimizations demonstrate that it varies by less than 0.005 a. from one molecule to another. The MCPF approach yields a reasonable description of each system, as shown in the following section. Nevertheless, to compute accurate dissociation energies a level of theory is required that accounts for the significant multireference character present in many of the wave functions. Therefore, we perform complete-active-spaceSCF (CASSCF)/intemally contracted averaged CPF (ICACPF)I'S~~ calculations at the MCPF equilibrium geometries of each compound. The CASSCF active space includes the metal d and s valence orbitals as well as the carbon 2s and 2p orbitals and the hydrogen 1s orbitals. In the calculations involving metal atoms to the right of Mn and Tc, d-type orbitals with occupation numbers close to 2 are moved to the inactive space. Additionally, for NiCH2+and CuCH2+it is necessary to add an extra orbital to the a l active space to avoid having more active electrons than active orbitals in that irreducible representation. The CASSCF treatment provides much better zeroth-order descriptions of these systems than do SCF calculations; every system is bound, and ScCH2+,for example, is correctly predicted to have C,, symmetry at the CASSCF level. Any occupations which account for more than 0.04% of the CASSCF wave functions are used as reference states in the ensuing ICACPF calculations, with the same number of electrons correlated as in the MCPF calculations. For the first-row transition-metal atoms we use an [8s4p3d] contraction of the (14s9p5d) primitive sets of Wachters,19 supplemented with two diffuse p functions and one diffuse d function.20This is further augmented by a (3f)/[2fl set of polarization functions based on a three-term fit to a Slater-type orbital, with exponents varying in steps of 0.4 from 1.6 for Sc to 4.8 for Cu. The final first-row transition-metal basis set is of the form (14sl lp6d3f)/[8~6p4d2fI. For the second-row transition-metal atoms we employ the relativistic effective-core potentials (RECP) developed by Hay and Wadt.,' These include the outermost core orbitals, the 4s and 4p, in the valence shell, resulting in a node in the 5s orbital and allowing the valence electrons to be properly correlated.22 The supplemented valence basis and the (3f)/[2fl polarization sets described in ref 23 are employed, yielding a final basis set of the form (6~6~5d3f)/[5~4p4d2fl. In the MCPF calculations we use large atomic natural orbital (ANO) basis sets24on carbon and hydrogen; the C and H A N 0 basis sets are denoted (13s8p6d4f)/ [4s3p2dl fl and (8s6p4d)/ [4s2pld], respectively, and are described e l s e ~ h e r e .For ~ ~the ~~~ ICACPF calculations we employ the Dunning valence triple-{
+
w.
,.. .
.
.
aauscniicner et ai. (VTZ) basis sets,26that is, the (lOs5pZdlf)/[4~3p2dlflset for C and the (5~2pld)/[3~2pld] set for H. By contrast with the A N 0 sets, the diffuse functions are uncontracted in the VTZ sets, so they are expected to more accurately describe the distortion of the ligand due to the positively charged metal ion. Calibration calculations at the MCPF level show that the VTZ basis sets yield binding energies up to about 1 kcal/mol larger than those obtained with the A N 0 sets. For the first-row metal cations, first-order perturbation theory is used to compute the mass velocity and Darwin contributions to the total energy, denoted +R. These are the same relativistic effects accounted for in the RECPs employed for compounds involving second transition row atoms. The MCPF calculations are performed using MOLECULE-SWEDEN,~' and M O L P R O ~ ' . ~is~ employed in the CASSCF/ICACPF calculations. The calculations were performed at NASA Ames using the Numerical Aerodynamic Simulation Program CRAY Y-MP and Central Computing Facility CRAY Y-MP and CONVEX C210 computers. 111. Results and Discussion
A. Description of tbe Bonding. At the MCPF level using the A N 0 basis sets described, the 'A1-3B1 separation in CH2 is 10.3 kcal/mol, which is in good accord with experiment.I2 Thus, we expect the covalent and electrostatic contributions to the bonding to be described equally well. Table I lists the geometries,d-electron Mulliken populations, and the net charges on the metal atoms for the ground and selected excited electronic states of the MCH2+ compounds, based on the MCPF calculations. The computed dissociation energies are also given, including the relativistic correction to the first-row energies. A detailed discussion of the nature of the bonding in the individual systems is presented in the following. ScCH2+and YCH2+both have ]Al ground states; double bonds polarized toward CH, are formed in both cases, yielding effective charges on the metal atoms which are greater than 1.O (see Table I). This polarization of charge toward the ligand in spite of the positive charge on the metal has been observed for other liga n d ~ . The ~ ~u-bonding , ~ ~ ~orbital ~ ~ is a mixture of metal du and s and carbon 2pz atomic orbitals, and the metal populations show that the bonding arises from a mixture of the d'sl and dZ asymptotes. For TiCH2+to CrCH2+and ZrCH2+to MoCH2+,the additional electrons occupy the nonbonding d-type al, a2, and b2 molecular orbitals. The a1 and a2 orbitals, which correspond to 6 orbitals in a linear molecule, have a smaller overlap with CHI than the d i k e b2 orbital. The ground states of TiCH2+ and ZrCH2+are both ,A1, but the ,A2 state is low lying; for ZrCH2+ it is only 2.4 kcal/mol above the ground state. The geometries of the ,Al and 2A2states of ZrCH2+are also similar-see Table I. Moving across the transition metal rows, the next electron in these compounds adds to the b2 orbital, resulting in 3B2ground states for VCH2+and NbCH2+. It is less favorable for the electron to occupy the a2 orbital since the occupation a11a21does not correspond to the metal cation ground-state asymptote. Note that the 3B1state arising from an a2b2I occupation is expected to be low lying based on the small splitting between the 2A1and 2A2 states in ZrCH2+. The ground states of CrCH2+and MoCH2+ are both 4B1,with all three nonbonding d-type orbitals singly occupied. In MnCH2+ and TcCH2+,the next electron adds to a nonbonding combination of the s and du orbitals, forming 5B, ground states; this occupation is much more favorable than doubly occupying one of the nonbonding d-type orbitals. We also considered the 'AI state of MnCH2+, where the 'Al state of CHI is electrostatically bound to Mn 'S(3d54s'), but this state was found to be more than 20 kcal/mol higher than the 5BIstate. The strength inherent in the covalent bonds of MnCH2+and TcCH2+ is indicated by their existence in spite of the large loss of metal cation exchange energy upon bond formation. RuCH2+ and RhCH2+are found to have different bonding characteristics and ground states than their first transition row
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 6971
Bonding of Transition Metal Ions to Methylene
TABLE I: Calculated M C Bond Distances (in a@),H-C-HBond Angles (in deg), d-Orbital Mulliken Populations, Net Charges on the Metal Atom, JXssociitioa Eaerpics (in kcal/nml), and Relativiatidy Corrected Dissociation Energies for the Ground and Selected Excited Electronic States of the MCH,+ Compounds, Computed at the MCPF Level MCPF ICACPF ~~
system ScCH2' TiCH? VCH2' CrCH2+ MnCH2+ FeCH2+ CoCH2' NiCH2+ CUCH~' YCH2+ ZrCH2+ NbCH2' MoCH~' TcCH2' RuCH2' RhCH2' PdCH2+ AgCH2'
state
04-C)
angle
dpoP
3.129 3.646 3.502 3.407 3.471 3.434 3.418 3.386 3.408 3.383 3.559 3.880 3.734 3.731 3.669 3.567 3.564 3.409 3.41 1 3.430 3.357 3.529 4.101
109.4 111.1 110.3 115.2 112.2 111.9 112.0 111.4 111.4 111.9 110.1 110.2 112.8 112.7 113.2 116.8 115.1 119.6 119.3 122.3 122.0 116.0 109.2
1.40 2.52 3.51 4.58 5.27 6.40 6.76 7.83 7.84 8.61 9.67 1.44 2.41 2.57 3.62 4.73 5.25 6.88 6.87 6.88 8.09 8.76 9.90
net 1.42 1.35 1.35 1.31 1.24 1.10 1.01 0.94 0.93 0.94 0.83 1.36 1.32 1.35 1.28 1.21 1.09 1.05 1.os 1.04 0.90 0.85 0.86
De 77.5 77.4 67.2 39.6 45.9 63.4 63.3 68.3 67.7 66.4 52.8 81.9 95.0 92.6 83.0 62.2 72.7 71.9 71.4 60.2 77.2 67.5 36.1
De
+R
77.3 76.8 71.5 44.4 45.0 61.1 60.9 74.2 73.4 72.4 58.5
0," 82.3 80.7 71.2 47.9 57.0 71.5 71.2 72.3
69.5 54.6 86.7 98.3 86.4 67.2 75.5 79.6 69.6 36.1
Dissociation energy obtained with the CASSCF/ICACPF method. analogues, FeCH2+ and CoCH2+. RuCH2+and RhCH2+ both form covalent bonds to CH2 from the 4d"+' metal cation occupationthe metal d-electron populations in Table I. This leads to a 'Al ground state for RhCH2+,whereas the ground state of RuCH2+is determined to be 2Az. The 2Al state of RuCH2+, by analogy with the ZrCH2+ calculations, is nearly degenerate with the ground state, consistent with the small overlap of the a, and a2 &like orbitals with CH2. While the b2 orbital has a larger overlap with the ligand, singly occupying this orbital is unfavorable, since such an occupation is derived from an excited-stateasymptote of Ru+. Quartet states of RuCH2+are not considered in this work since the thorough study by Carter and Goddard3 found the lowest-lying quartet states (4AI,4B,, and 4B2)to all lie about 12.9 kcal/mol above the ground state. The ground state of FeCH2+is found to be 4BI,although the 4B2state is virtually degeneratewith the ground state. Both states are derived from a mixture of the 3d64s' and 3d7 electronic configurations of the metal cation. The 4Bl and 4B2states in this doubly bonded system are derived from different occupations of the four nonbonding orbitals: the 4Bl state has the nonbonding al(4s3da)),a2,and bz orbitals singly occupied, whereas the 4B2state is derived from moving an electron from the a, Mike orbital to the a2 orbital. Based on the results for ZrCH2+and RuCH2+, it is not surprising that the 4Bl and 4B2states are so close in energy. The 2A2state is more than 20 kcal/mol above the 4B1state at the ICACPF level (at the 4B, MCPF equilibrium geometry). While formation of a doublet state for FeCH2+requires an Fe+ 3d64s' 3d7 promotion energy of 5.8 kcal/m~l,'~ the difference in the ground states of FeCHz+ (4Bl) and RuCH2+ (2A2) is probably due more to the smaller exchange energy for Ru+ and the stronger 4d bonds formed by the second transition row atoms as compared with the 3d bonds of the first transition row atoms. The M-C interaction in CoCH2+is a mixture of electrostatic bonding from the 3d8 asymptote and covalent bonding from the 3d74s1asymptote. In order to maximize electrostatic bonding, the 3da orbital is singly occupied, thereby reducing metal-ligand repulsion, and the second hole is in a 3dMike orbital, since this occupation is derived from 100%ground-state Co+. As expected the 'A, and 'A2 states are nearly degenerate, and as with the other systems considered, it is more favorable to doubly occupy the a, in preference to the az orbital. By analogy with FeCH2+ and RuCH2+, we attribute the difference between CoCH2+ and RhCH2' to the smaller exchange energy and stronger d bonds
-
associated with the second transition row cation. NiCH2+and PdCH2+are found to have ZAlground states with the open-shell electron in the du orbital to maximize the electrostatic bonding. The electrostatic contribution to the bonding can be estimated by computing the binding energy for a model system where the metal cation is replaced by a point charge; the metal-ligand repulsion will naturally reduce this value. The d populations (Table I) show that there is some mixing of higher asymptotes to allow for sda hybridization, reducing the metalligand repulsion, and they also indicate a covalent component to the bonding. For both NiCH2+and PdCH2+these enhancements to the bonding lead to binding energies (72.4 and 67.5 kcal/mol, respectively) that are slightly larger than the related point-charge binding energies (71.9 and 64.0 kcal/mol). The bonding in the 'Al ground states of CuCH2+and AgCH2+ is predominantly electrostatic. Because the electrostatic component of the bonding varies inversely with ?, Ag', with the largest radial extent of the metal atoms considered in this work, has the longest M - C bond length and smallest M-CH2 binding energy. The binding energies of CuCH2+and AgCH2+are enhanced somewhat by sdu hybridization, which reduces the metal-ligand repulsion. As can be seen from the Mulliken d populations in Table I, the effect of sda hybridization is much smaller for Ag+ than for Cu+, because of its much larger d'0-d9s1separation. For both AgCH2+ and CuCH2+,the binding energies calculated for the relevant point-charge model systems are 4-5 kcal/mole larger than the directly computed values. This is in contrast to NiCH2' and PdCHz+,where the computed binding energies are slightly larger than the point-charge results, and at variance with the covalently bonded ScCH2+,where the computed value (77.3 kcal/mol) is significantly larger than the point-charge result (55.2 kcal/mol). The larger binding energy in the point-charge calculation for CuCH2+and AgCH2+shows that the covalent contribution to the binding is small, and gives an indication of the magnitude of the metal-ligand repulsion. Thus the significantly larger binding energy for CuCH2+as compared with AgCH2+is primarily due to the smaller size of Cu+, which enhances the electrostatic contribution, and the greater importance of sda hybridization, which reduces metal-ligand repulsion. The ground states determined in this work show a systematic filling of the nonbonding orbitals in the order a1(6), bZ,a2, and a,(sdu), and the a'(&) and a2 orbitals are similar in energy for all systems. The ground states found in this work are consistent
6972 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
with those determined by Harrison and c o - w o r k e r ~for ~ ~ScCH2+ ~ and CrCH2+,Carter and Goddard2v3for CrCH2+and RuCH2+, and Planelles et al.' for CuCH2+. B. Dimciation Eoergies. Previous work has shown that MCPF calculations can give accurate De values for electrostatic bonding and single bonds between transition metals and various ligands.15316929 However, it has also been shown that the MCPF level of theory underestimates double-bond energies3' For MCH2+ systems, where an SCF wave function is often a poor zeroth-order reference state, the MCPF calculations may significantly underestimate the binding energy. Therefore, we perform CASSCF/ICACPF calculations to obtain accurate De values; these results are reported in Table I. The differences between the MCPF and ICACPF results are small for the electrostatically bound systems; for example, the CuCH2+binding energy computed employing the ICACPF approach is less than 2.0kcal/mol larger than the MCPF value. However, the ICACPF result for the covalently bonded MnCH2+ is 12.0 kcal/mol larger than the MCPF binding energy. Thus, as expected, levels of theory higher than MCPF are required to accurately describe the transitionmetal-ligand covalent double bonds. The improvement of the CASSCF treatment over SCF is clearly seen in the dissociation energies of the zeroth-order reference wave functions; by contrast with the very large (more than 80 kcal/mol in some cases) difference in binding energies between SCF and MCPF, the largest difference in the CASSCF and ICACPF binding energies is 29.4 kcal/mol. Those systems for which the ICACPF binding energy is more than 10 kcal/mol larger than the CASSCF value are CrCH2+(12.0),MnCH2+(25.3),FeCH2+(29.4),MoCH2+(1 1.6), TcCH2+ (22.0),RuCH2+ (13.7),and RhCH2+ (16.8). In these cases, we suspect that even the ICACPF calculations are underestimating the differential correlation contributions to the binding energies. Therefore, we make an empirical correction for these systems: 2.0 f 2.0 kcal/mol is added to the ICACPF binding energies of MnCH2+,FeCH2+,and TcCH2+,while the 0, values of the other four systems are increased by 1.0 f 1.0 kcal/mol. We should also note that for ScCH2+,YCH2+,and CuCH2+we have performed coupled-clustersingle- and doubleexcitation calculation^^^ with a perturbational estimate of the contribution from triple excitations [CCSD(T)],33)34 employing the same basis sets and geometries as in the MCPF calculations. The CCSD(T) binding energies agree with the ICACPF results to within approximately 1 kcal/mol for all three compounds, which include both covalently (ScCH2+and YCH2+)and electrostatically bonded (CuCH2+)systems. In the future we plan to test more systematically the single-reference-basedCCSD(T) method for a variety of transition-metal-ligand systems. The ICACPF De values of the fmt-row compounds are adjusted using the relativistic correction from the MCPF calculations. While we use the full correction for all systems, its magnitude is larger than 5.0 kcal/mol in three instances, and consequently we increase the uncertainties for these cases by f l . O kcal/mol. Moreover, an adjustment for the incompleteness of the Gaussian basis sets must be included. For example, MCPF calculations for FeCH2+using [7~6p4d2flg]/[6~5p4d3f2g]/[4~3p2d] AN0 basis sets for Fe/C/H yield a binding energy that is 2.9 kcal/mol larger than that reported in Table I. Therefore, we estimate conservatively that the basis-set incompleteness error for the covalently bound systems is 5.0 f 3.0 kcal/mol. As has been shown in previous work,16 the error in electrostatically bonded compounds is generally about half that found in covalently bonded system, or 3.0f 3.0kcal/mol for the present molecules. Lastly, the zero-point effect is computed to be 2.0 kcal/mol for ScCH2+ and 2.3 kcal/mol for CuCH2+. Since the Vibrational frequencie~~.~ for CrCH2+and RuCH2+are similar to those found for ScCH2+ and CuCH2+,we conclude that the zero-point correction will be approximately 2.0kcal/mol for all systems considered in this work. Our best estimate for Docomes from correcting the ICACPF value for zero-point motion, relativistic effects, limitations in the correlation treatment, and basis-set incompleteness as described in the foregoing discussion. These values are summarized in Table I1 along with theoretical and experimental binding energies from
Bauschlicher et al.
TABLE Ik C
Oof the XBcrt ~ EstimteS of the Mssocitioa Energies (in kal/md) of the MCHz+ Colapollads from the Preseat Work with hevim Theoretical and Experiment Values
theory system ScCH2' TiCH2+ VCH2' CrCH2' MnCH2+ FeCH2' CoCH2+ NiCH2+ CUCH~' YCH2+ ZrCH2' NbCH2' MoCH2' TcCH~' RuCH2+ RhCH2' PdCH2+ AgCH2'
best estimate 85 f 3 83 f 3 79 f 3 57 f 4 61 f 5 74 f 5 79 f 4 77 f 4 61 f 4 90 f 3 101 f 3 89 f 3 71 f 4 83 f 5 80 i 4 84 f 4 70 f 3 31 f 3
previous 68.0b 38.7: 49.6d 58.4' 69.2c
experiment' 96.9 f 5.3 91.9 f 3.5 78.5 3.2 52.3 f 1.9 69.3 f 3.0 81.5 f 4.0, 82 f 5, 76.0 f 2.3, 84 f 9 ' 73.7 f 1.8 62.4 f 1.6 93 f 3' 107 f 7h
68.0 (73.2)' 89 f 5h
Experimental values have been adjusted to 0 K, as described in the The values are taken from ref 8, unless otherwise noted. bAlvarado-Swaisgood et al., ref 5. 'Alvarado-Swaisgood et al., ref 6. dCarter and Goddard, ref 2. 'Brusich and Goddard, ref 4. fHettich and Freiser, ref 10. SSunderlin and Armentrout, ref 9. hHettich and Freiser, ref 11. 'Carter and Goddard, ref 3. The value in parentheses is their best estimate. text.
the literature. Note that the experimental results have been adjusted to 0 K assuming an ideal gas and no vibrational contributions to the heat capacity; this correction reduces the experimental values by 1.5 kcal/mol. Our computed binding energies for ScCH2+and CrCH2+are significantly larger than those of Harrison and ~ e w o r k e r s(Table ~*~ 11). We attribute our increased binding energies to larger basis sets and a more extensive treatment of electron correlation. The agreement between our results and those of Goddard and coworker~?-~ by contrast, is fairly good (Table 11). Our directly computed ICACPF values for CrCH2+and FeCH2+are slightly larger than their computed results, and our best estimates of the Dovalues are somewhat larger still. For RuCH2+both our directly computed binding energy and our best estimate are approximately 7 kcal/mol larger than the values of Carter and G ~ d d a r d . ~ Nevertheless, we are confident in our results since they are derived from a higher level of correlation treatment and we have more systems upon which to base our corrections. Our best estimates of the binding energies agree with the experimental values to within the stated uncertainties for all systems except ScCH2+,TiCH2+,and NbCH2+(Table 11). In previous we concluded that the NbCH2+binding energy must be near the lower limit of the experimental range; the uncertainty in our new value is smaller, suggesting that the correct result is significantly smaller than the experimental result." We have performed additional calculations for ScCH2+but are unable to find any significant missing contributions to the binding energy. For example, correlating the Sc 3s and 3p electrons increases DO by less than 1 kcal/mol. We conclude, therefore, that the experimental values for ScCH2+and TiCH2+ are also too large. Figure 1 depicts a plot of our best estimates for the binding energies of the MCH2+systems (from Table 11) versus the metal cation promotion-plus-exchange energies for the dns asymptote, as tabulated by Carter and G0ddardl3and Armentrout et a1.8 This is analogous to the plot presented by Armentrout et al. for the first transition row compounds. Because the second-row transition-metal systems generally form stronger bonds than their f i t transition row analogues, the two sets of data are fit separately. All of the binding energies, except those of YCH2+and RhCH2+ correlate well with the model of Amentrout et al.; therefore, these two systems were omitted from the least-squares tit for the sccond transition row. With a 4d population of 1.44electrons out of a
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 6973
Bonding of Transition Metal Ions to Methylene 110 1
I
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the first transition row systems as for their second-row analogues, except in the pairs FeCH2+,RuCH2+ and CoCH2+,RhCH2+. Evidently, the covalent component of the bonding is more important in compounds containing cations from the right side of the second transition row than in those comprised of the first transition row cations. The computed binding energies are generally in good agreement with experiment, and they appear to follow qualitatively the correlation with metal cation promotion-plus-exchangeenergies suggested by Armentrout et a1.' Based on the level of the calculations performed in this work, there appears to be no apparent way to account computationally for the comparatively large discrepancies between theory and experiment for Sd3H2+,TiCH2+, and NbCH2+,suggesting that the experimental binding energies reported for these systems are too large. The differences between experiment and theory for FeCH2+and NiCH2+are more modest, and it is possible they would be accounted for by more intensive computational efforts.
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F g u e 1. Correlation of the calculated best estimates of the binding energies for MCH2+ compounds, from Table 11, with the metal cation promotion-plus-exchange energies involving the d 5 occupation, as tabulated by Carter and Gcddard (ref 13) and Armentrout et al. (ref 8). The solid tine represents a linear least-squares fit to the points for the first-row compounds. The dashed line is the analogous fit to the points for the second-row compounds, with the exception of YCH2+ and RhCH2+, as discussed in the text.
total valence population of 1.64 electrons, the Mulliken populations show that YCH2+contains more 4d2 than 4d15s1character and consequently the promotion energy is significantly larger than that used in the model. Similarly, the binding energy of RhCH2+is larger than expected because it bonds almost entirely from a 4d8 configuration, instead of the 4d75s1 excited state, implying a promotion energy that is significantly smaller than that used in the model. It is important to note that some caution must be used in such arguments, as the d-electron Mulliken populations of Table I show that the bonding in most of the systems is derived from a mixture of both the d"s and ddl asymptotes, but we nevertheless obtain linear relationships between the binding energies and the promotion-plus-exchange energies for the d"s asymptote for both the first- and the second-row transition-metal compounds. The fits suggest that the s contribution to the bonding is extremely important, even if the bond is derived predominantly from a d"+l rather than a d"s occupation. A more quantitative model would have to account correctly for the mixed character of the bonding and use a promotion energy that lies somewhere between the two limiting cases.I3 Moreover, variations in the covalent and electrostatic contributions to the bonding would need to be considered in some manner. The differences between the experimental and theoretical binding energies for FeCH2+and NiCH2+ (Table 11) are somewhat larger than might have been expected. Since the bonding is electrostatic in NiCH2+, it is surprising that our value is 4 kcal/mol larger than the experimental result, although spin-orbit splitting has been neglected in this study. For example, accounting for the Ni+ 2Dterm valuesmdecreases the NiCH2+binding energy by 1.7 kcal/mol. The remaining discrepancies in our values for FeCH2+and NiCH2+,if not due to experimental considerations, are most likely the result of underestimating the residual errors in the present level of correlation treatment.
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COllC~USiOM
In the MCH2+compounds containing cations from the left side of both transition-metal rows, a metal-carbon double bond is formed, whereas the bonding is mainly electrostatic in the molecules formed from metal cations on the right side of the rows. The symmetries of the ground electronic states are the same for
Acknowledgment. J.A.S. gratefully acknowledges a research associateship from the National Research Council and the National Aeronautics and Space Administration.
References and Notes (1) Vincent, M. A,; Yoshioka, Y.; Schaefer 111, H. F. J. Phys. Chem. 1982, 86, 3905. (2) Carter, E. A.; Goddard 111, W. A. J. Phys. Chem. 1984, 88, 1485. (3) Carter, E. A.; Goddard 111, W. A. J. Am. Chem. Soc. 1986,108,2180. (4) Brusich, M. J.; Goddard 111, W. A. Cited in ref 13. (5) Alvarado-Swaisgood, A. E.; Harrison, J. F. J. Phys. Chem. 1988,92, 2757. (6) Alvarado-Swaisgood,A. E.; Allison, J.; Harrison, J. F. J. Phys. Chem. 1985.89, 2517. (7) Planelles, J.; Merchln, M.; Nebot-Gil, I.; Tomis, F. J . Phys. Chem. 1989, 93, 6596. ( 8 ) Armentrout, P. B.; Sunderfin, L. S.;Fisher, E. R. Inorg. Chem. 1989, 28, 4436, and references therein. (9) Sunderlin, L. S.; Armentrout, P. B. J. Am. Chem. SOC.1989, 1 1 1 , 3845. (10) Hettich, R. L.; Freiser, B. S. J. Am. Chem. SOC.1986, 108, 2537. (11) Hettich, R. L.; Freiser, B. S. J. Am. Chem. SOC.1987, 109, 3543. (12) (a) Leopold, D. G.; Murray, K. K.; Miller, A. E. S.; Lineberger, W. C. J. Chem. Phys. 1985,83, 4849. (b) Bunker, P. R.; Jensen, P.; Kraemer, W. P.; Breadsworth, R. J. Chem. Phys. 1986.85, 3724. (13) Carter, E. A.; Goddard 111, W. A. J. Phys. Chem. 1988, 92, 5679. (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) Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H.; Barnes, L. A. J. Chem. Phys. 1989, 91, 2399. (16) Sodupe, M.; Bauschlicher, C. W. J. Phys. Chem. 1991, 95, 8640. (17) (a) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1988,89,5803. (b) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514. (18) Gdanitz, R. J.; Ahlrichs, R. Chem. Phys. Lett. 1988, 143, 413. (19) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (20) Hay, P. J. J. Chem. Phys. 1977,66, 4377. (21) Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985,82, 299. (22) Rohlfing, C. M.; Hay, P. J.; Martin, R. L. J. Chem. Phys. 1986,85, 1447. (23) Langhoff, S. R.; Pettenson, L. G. M.; Bauschlicher, C. W.; Partridge, H. J. Chem. Phys. 1987,86, 268. (24) Almliif, J.; Taylor, P. R. J. Chem. Phys. 1987, 86, 4070. (25) Bauschlicher, C. W.; Langhoff, S.R.; Taylor, P. R. J. Chem. Phys. 1987. 87. 387. (26) Dunning, T. H. J . Chem. Phys. 1989, 90, 1007. (27) MOLECULE-SWEDEN is an electronic structure program system written
by J. AlmlBf, C. W. Bauschlicher, 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. (28) (a) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985,82, 5053. (b) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 115, 259. (29) Pettersson, L. G. M.; Bauschlicher,C. W.; Langhoff, S.R.; Partridge, H. J. Chem. Phys. 1987,87,481. (30) Moore, C. E. Atomic Energy Leuels; Natl. Bur. Stand. (US.) Circ. no. 461, 1949. (31) Langhoff, S. R.; Bauschlicher, C. W.; Taylor, P. R. Chem. Phys. Lett. 1991, 180, 88. (32) Bartlett, R. J. Annu. Rev. Phys. Chem. 1981, 32, 359. (33) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (34) The CCSD(T) calculations were performed using TITAN,a set of
electronic structure programs written by T. J. Lee, A. P. Rendell, and J. E. Rice.
