Theoretical study of the hydrogen-metal complex ... - ACS Publications

Jul 22, 1993 - Recently, Kemper et al.1 measured the successive binding energies of H2 to Co+. Bauschlicher et al.2 reported the computation of the fi...
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J. Phys. Chem. 1993,97, 11912-11920

11912

Theoretical Study of the Hz-ML+ Binding Energies Philippe Maitre' and Charles W. Bauschlicher, Jr.' NASA Ames Research Center, Moffett Field, California 94035 Received: July 22, 1993'

The cooperative ligand effects are studied in MLH2+ and the results are compared to the recent experiments of Kemper et al. The bonding in these compounds is principally electrostatic in origin; however, ligand to metal and metal to ligand donations are important, especially for H2. W e show that differences arise among the vanadium, cobalt, and copper complexes which are due to 3d donation to Hz. Electron correlation is required to describe the dative interaction, and we find that second order Mprller-Plesset perturbation theory (MP2) yields a good description of these systems compared with higher levels of correlation (such as the modified coupled pair functional and coupled cluster approaches) and experiment. However, obtaining quantitative results requires higher levels of theory than MP2.

I. Introduction Recently, Kemper et al.1 measured the successive binding energies of Hz to Co+. Bauschlicher et aL2 reported the computationof the first three H2 binding energies. While theory found the De of the second Hz to be larger than the first, experimentally it was found that the DOof the second Hz was smaller. Kemper et ale1attributed this differencebetween theory and experiment to the zero-point energy correction, which was neglected in the calculations. More recently, Kemper et al.3 extended their study to consider CoL+-H2 for L = CHg and HzO. They found that for L = CH4, the H2 binding energy was only 0.4 kcal/mol larger than for L = Hz but that for L = HzO, the Hz binding energy was 1.6 kcal/mol larger than for L = H2. In this work we consider the ML+-Hz binding energies for M = V, Co, and Cu and L = H2, CH4, and HzO. The small differences in the H2 binding energies can only be understood with fully optimized complex geometries and the calculation of zero-point energies at a reliable level of correlation treatment. Thus, one of the motivations of this work is to determine if secondorder Mdler-Plesset perturbation theory4 (MP2) is a suitable approach for this class of unsaturated organometallic systems. It has been shown that MP2 works well for some classes of saturated transition-metal complexes5 and also that it should satisfactorily describe the electrostatic interaction.6 However, as discussed previously,2dative bonding is important in describing the bonding in the MHz+ systems and an MP2 treatment can overestimate this effect. For example, the MP2 dissociation energy of Cr(C0)6 is 40 kcal/mol too large even after correcting for basis set superposition error.' MP2 has the advantage over other correlation methods that analyticfirst and second derivatives are available,* which dramatically simplifies the geometry optimization and the computation of zero-point energies. Thus it is worthwhile to calibrate the MP2 method for the MH2L+ systems. In section 11, we describe the methods used in this work. These methods have been chosen on the basis of several calibration calculations on the copper complexes presented in section 111. The results arediscussed and comparedwith experimentsin section IV. Section V contains a summary of our results and our conclusions. 11. Methods

The geometries are optimized and the vibrational frequencies computed at the MP2 level using the Gaussian 90 program: and all electrons have been correlated. For the open-shell systems, 0

Abstract published in Advance ACS Abstracts, November 1, 1993.

0022-3654/93/2097- 11912$04.00/0

these MP2 calculations are based on spin-unrestricted selfconsistent-field (SCF) orbitals. The 'production" basis sets used in the MP2 calculations are modified versions of the Gaussian 90 internal sets. For V, Co, and Cu atoms, we use the effective core potentials (ECPs) and valence basis sets developed by Hay and Wadt.Io In these ECPs, only the 3d and 4sp orbitals are included in the valence space. The 3d basis set is contracted to three functions instead of the default two (the two outermost Gaussians are left uncontracted). The H basis set is the scaled (4s)/ [2s] set of Dunning and Hay,ll supplemented with a diffuse s (0.07 1) and three p (1.2,0.40, and 0.13) functions. The (4s)/[2s] basis plus a single p function (a = 1.0) is used for the H atoms in H2O for the CoH20+, Co(H2)H20+, VH20+, and V ( H 2 ) H ~ 0 calculations. + Tests for CuHzO+show that employing this small H basis causes essentially no change in the geometry and only a small change in the Cu+H2O binding energy. The C basis is the (9s 5p)/[3s 2p] valence double-l (VDZ) set of Dunning and Hay.ll The 0 basis starts from the VDZ set of Dunning and Hay, uncontracting the outermost p function and adding a diffuse s function (0.095), a diffuse p function (0.059), and a 3d polarization function (0.85). The diffusefunctionson the ligand atoms are required to describe the ligand polarizability and hence the charge-induced-dipole contribution to the bonding. The 3s components of the 3d functions are not included in the calculations. As we show below the production basis set works well for all systems except CuCH4+. This exception leads to the development of an enhanced basis set for Cu where a diffuse s function (a= 0.014) is added to the production and the two p functions are replaced by three functions(a= 0.232598,0.069299,and 0.023). The two tighter p functions are taken from the all-electron basis set developed by Wachters12 (with the two diffuse p exponents multiplied by 1.5). The most diffuse p has approximately the same exponent as in the original Hay and Wadt basis set. Basis set calibrations are performed using large basis sets of either atomic natural orbital13 (ANO) contractions of large primitive sets, for the metals, or the correlation consistent basis sets of Dunning and co-workers14 for H, C, and 0. Since an A N 0 set is used on the metal, we denote these basis sets as ANO1, AN02, and AN03. These sets are described in the Appendix. We also use an all-electron Cu basis set derived from that optimized by Wachters;12 this is also described in the Appendix. Some additional basis sets, which are a subset of the production basis set, are described in the calibration section. As noted in the Introduction, it is important to calibrate the MP2 correlation treatment with higher levels of theory. This is done by comparing the MP2 results with those obtained using the 0 1993 American Chemical Society

Theoretical Study of HTML+ Binding Energies

The Journal of Physical Chemistry, Vol. 97, No. 46, I993 11913

TABLE I: Basis Set Calibration Study of CuH2+ H2 CuH2+ method re us r(Cu-H) r(H-H) WI 09 A.Default Basis ~

MP2

QCISD MP2

QCISD MP2

SCF

~~~

w1

D.

~

0.739 4531 0.747 4365

1.973 0.758 564 744 4200 7.55 1.968 0.767 585 772 4050 7.88 B.Recontract Cu to 3d and Add One p (1 .O) to H 0.735 4622 1.922 0.758 586 845 4230 8.80 0.739 4517 1.936 0.761 600 840 4168 8.89 C.Cu from B and Add Two p’s (1.2 and 0.4) to H 0.737 4575 1.825 0.767 650 828 4101 10.82

D.Cu from B and Add One s and Three p’s to H (This Is the Production Basis Set)

QCISD

487 799 4346 6.77 737 894 4047 12.85 744 828 3991 13.14 E.H from D.For Cu Add Diffuse s and Replace

MP2

0.739 4524

MP2

0.736 4588 0.739 4524 0.744 4414

2.053 1.769 1.787

0.751 0.771 0.774

p’s (This Is the Enhanced Basis Set) 1.781

0.772

824

950 4021 14.77

F.AN03 Set CCSD(T) 0.741

1.729

0.779

14.15

G.ANOI Set MCPF

0.742 4393

1.764

0.779

14.55

CCSD(T) 0.742 4393 1.746 0.780 818 1128 3882 15.65b ‘Bond Lengths are in A, Harmonic Frequencies in cm-I, and dissociation energies in kcal/mol. b The CCSD De at this geometry is 13.85 kcal/mol. modified coupled-pair functionalls (MCPF) method, thecoupledcluster singles and doubles approach16including a perturbational estimate of the triple excitations17[denoted CCSD(T)], and the quadratic configuration interaction method,’* QCISD(T). Note that unlike the MP2 and QCISD calculations, the MCPF and CCSD treatments are spin-restricted. In order to treat the second root of the same symmetry on equal footing with the ground state, we perform state-averagedcomplete-active-spaceSCF (SACASSCF) calculations followed by multireference configuration interaction (MRCI) calculations. All electrons are correlated in the MP2 calculationsas this facilitatesthecalculation of gradients. In the other calculations,only thevalence electronsare correlated, that is, the metal 1s to 3p and the carbon and oxygen 1s electrons are not correlated. The MCPF and CASSCF/MRCI calculations are carried out using the SWEDEN packageIginterfaced into SEWARD,Mwhile the CCSD(T) calculations are performed using TITAN21 for the closed shell systems and the program developed by Scuseria22for the open-shell systems. 111. Calibration Calculations

A. Cu(H2),,+,II = 1,2. The results of CuH2+ are summarized in Table I. The final row in the table, the CCSD(T) results using the ANOl basis set, is the highest level of theory used and so the other entries are compared with it. For all basis sets, the MP2 and QCISD results are very similar; for example, the maximum difference in bond length is 0.018 A and the maximum difference in De is 0.33 kcal/mol. Therefore we first focus on the basis set effects. The first entry is for the default “LANLlDZ” basis set from Gaussian 90. The binding energies in this basis set are about half of the best value. This is a result of the small H basis which yields a polarizability of H2 that is significantly too small. Recontracting the Cu to three d functions and adding one p function to H improves the results slightly. Adding a second p function to H increases the binding energy even more. Adding a diffuse s and expanding the p space to three functions gives a QCISD result that is in good agreement with the CCSD(T) result in the larger basis sets. Because the QCISD and CCSD methods are very similar, the binding energies, which differ by only 0.71 kcal/mol, suggest that basis set D (the

production basis) is quite reasonable and this basis set is used for most calculations. Improving the Cu basis set (basis set E, the enhanced basis) yields an MP2 binding energy that is even larger and agrees with the best calculation to within 0.88 kcal/mol. The A N 0 3 basis set yields a De that is about 90%of the ANOl. This indicates that very large basis sets are required to obtain quantitative results. Nevertheless, these results show that the A N 0 3 basis set yields a quite reasonable value for the binding energy relative to the larger ANOl basis set. Therefore, the A N 0 3 basis set has been used for the open-shell complexes in order to keep the calculations tractable. The error in the geometries, especially the Cu-H distance, follows the error in the binding energy. (A note of caution; in this work we report the Cu-H distance while in the past we commonly reported the metal-Hz bond midpoint distance.) The MP2 results using the production or enhanced basis sets are in good agreement with the CCSD(T)/ANOl results. Using these basis sets, the H2 vibrational frequency is too high at the MP2 level, while the QCISD and CCSD(T) frequencies are in good agreement with experiment.23 For CuH2+,the MP2 and QCISD results are in reasonable agreement with those from the CCSD(T) level of theory. The H-H stretch frequency is too large at the MP2 and QCISD levels but the MP2 accurately reproduces the CCSD(T) change in the H-H stretching frequency rerative to free H2 better than the QCISD. While the agreement between the three methods for the symmetric Cu-H stretch is reasonable, both MP2 and QCISD yield an antisymmetric stretch that is significantly too small. The enhanced basis set, which yields a larger binding energy, yields smaller errors for the vibrational frequencies than the production basis set. While the agreement between the MP2 (or QCISD) vibrational frequencies and those obtained at the more accurate CCSD(T) level is not perfect, the MP2 results are significantly better than those obtained at the SCF level-see Table I. The SCF yields too small a shift in the H2 frequency between free Hz and CuH2+. In addition, both the symmetric and antisymmetric Cu-H stretching frequencies are significantly too small. The errors in the SCF vibrational frequenciesare consistent with the very small binding energy and long Cu-H distance at this level of theory. Because of the SCF and MP2 frequencies of the metal-Hz modes are too small and the H2 mode is too large, there is no simple scaling that would improve either set of frequencies. This is also true of the other ML+ systems. The errors in the ligand modes in L and ML+ will partially cancel. Hence, there is expected to be some cancellation of errors in computing the zero-point contribution to the binding energy. Thus, the vibrational frequencies at the MP2 level in the production basis set should yield a very reasonable estimate of the zero-point energies and are clearly a major improvement over the SCF. This is very fortunate, because the MP2 is the highest levelof treatment where it is practical to compute vibrational frequencies for large molecules. The results for C U ( H ~ )are ~ +summarized in Table 11. As for CuHz+, the MP2 results in the production and enhanced basis sets are in good agreement with the CCSD(T)/ANOl . The MP2 second ligand binding energies are 2.46 and 2.17 kcal/mol larger than the first for the production and enhanced basis sets, respectively, which are in good agreement with the CCSD(T) difference of 2.32 kcal/mol. Therefore MP2 in the production basis set appears to give good relative ligand binding energies. B. CuHJI20+. The CuH2H20+ results are summarized in TableII. For theH20geometry, the CCSD(T) resultsarealmost identical for the ANOl and A N 0 2 basis sets. The MP2 results using the production basis set are also very similar. (Remember that the H and 0 basis sets are the same in the production and enhanced basis sets). Similar geometries are also found for CuH20+at the four levels of theory. While the geometries are similar, the binding energies are somewhat different. Reducing

11914 The Journal of Physical Chemistry, Vol. 97, No. 46, 1993

TABLE 11: Comparison of the MP2 Results Obtained Using the Production or Enhanced Basis Sets with the CCSD(T) and MCPF Levels of Theory in the ANOo Basis Sets. Cu(H2)2+ method basis r(Cu-H) r(H-H) De(both) De(one) MP2 production 1.752 0.772 28.16 15.31 1.758 0.774 MP2 enhanced 31.71 16.94 MCPF

ANOl

CCSD(T) ANOl

1.750 1.731

0.777 0.781

31.05 33.62

16.50 17.97

HzO r(0-H) L(HOH) production CCSD(T) ANOl CCSD(T) A N 0 2 MP2

0.965 0.960 0.959

CuH20+ r(Cu-0) r(0-H) MP2 MP2

CCSD(T) CCSD(T)

production enhanced ANOl AN02

1.993 1.978 1.935 1.949

0.968 0.969 0.963 0.962

H&uH20+ r(Cu-0) r(Cu-H) MPZC MP2C

production enhanced

1.953 1.946 1.882

1.671 1.652 1.665

103.8 104.4 104.3

L(H0H)

De

106.5 106.6 107.3 107.2

35.52 37.37 39.726 38.56

r(H-H)

De

0.781 0.779 0.832

17.70 18.76 19.83

CCSD(T)d AN02 I, Bond lengths are in A, bond angles in degrees, and binding energies in kcal/mol. D,(one) is the binding energy to remove one ligand from Cu(H2)2+. Using the CCSD(T) geometriesfrom ANOl, theCCSD(T) binding energy in AN03 is 37.87 kcal/mol. (0-H) = 0.968 A and the L(HOH) = 107.3'. dr(O-H) and L(HOH) are taken from CuH20+, 0.963 A and 107.3', respectively. the size of the A N 0 sets from ANOl to A N 0 3 reduces the binding energy by about 2 kcal/mol, with the A N 0 2 results being intermediate. Thus this quantity is sensitive to basis set enhancement. In spite of this, the MP2 binding energies in the small basis sets are in reasonable agreement with the CCSD(T) result using the ANOl basis set. While the absolute error is somewhat larger than found for Cu(Hz),,+, an MP2 calculation in a moderate basis set yields about 90% of the binding energy. At the MP2 level it iseasy tooptimize theCuH2Hz0+geometry. The summary of our results for the staggered conformation is reported in Table 11. Because of the size of the problem, on the basis of the MP2 calculations, we constrain the r ( 0 H ) and L(H0H) parameters in the CCSD(T) calculations to be the same as in CuH20+ and optimize the remaining three parameters. The increase in the H2-Cu binding energy in CuHzH20+ relative to CuH2+ is 4.85 or 3.99 kcal/mol at the MP2 level of theory using the production and enhanced basis sets, respectively,in reasonable agreement with the CCSD(T) result of 4.18 kcal/mol. Overall the agreement between MP2 and CCSD(T) for CuHzH20+ is similar to that for CuH2+ and therefore provides support for using the MP2 level of theory with the production or enhanced basis sets. C. CuC&+. The CuCH4+ results are summarized in Table 111. While it is straightforward to optimize the geometry at the MP2 level of theory, the calculations are expensive at the CCSD(T) level using large A N 0 basis sets. Thus we optimize only CH4 at the CCSD(T) level and use the MP2 geometry for CuCH4+. This should result in a binding energy that is only slightly smaller than if all parameters were optimized. Because the MP2 binding energy in the production basis set was about 20% smaller than the CCSD(T) result in the ANOl set, several additional basis set tests were performed. The CH4 and CuCH4+ geometries were optimized at the MP2 level of theory for each basis set. As can be seen from Table 111, each C and H basis set improvement slightly increases the MP2 binding energy, that is,

Maitre and Bauschlicher

TABLE III: Basis Set Calibration for the Binding Energy of Cu+-c)4. Geometries Are Optimized at the Mp2 Level of Theory for Each Basis Set unless Otherwise Noted De

method (kcal/mol) A. MP2 with production basis 16.82 B. MP2 add 3d to carbon 17.15 C. MP2 B plus contract carbon (5p)/[3p] 17.47 D. MP2 C plus diffuse p 17.72 E. MP2 D replace the carbon one 3d with 18.26 two 3d functions F. QCISD(T) in basis E at MP2(E) geometry 18.56 G. MP2 CH4 production and Cu Wachters basis 21.05 H. MP2 with enhanced basis set 20.13 I. MP2 with H plus diffuse d on Cu 21.39 J. MP2 the production basis, except Cu p 20.45 functions are replaced K. CCSD(T) with ANOl basis set at MP2(E) 21.43 geometry CH4 geometry is optimized at CCSD(T) level, so the De is a lower bound.

there is no single seriousdeficiency in the C or H production basis set. The low binding energy is not a failure of the MP2 level of correlation treatment as it agrees with the QCISD(T) binding energy. Using the production C and H basis sets, but replacing the Cu basis set with the all-electron basis set derived from that optimized by Wachterslz (see Appendix), the error in the binding energy is dramatically reduced, indicatingthat there is a deficiency in the production Cu basis set when ligand donation into the Cu 4p orbital occurs. Switching to the enhanced basis set removed this problem. Adding a diffused to the metal improves the results further. We should note that while all basis sets yield an q2 structure to be the most stable at the MP2 level, the Wachtersderived basis set and the enhanced basis set also yield an qz structure at the SCF level, but at the SCF level the production basis set incorrectlyyields a structure that is intermediate between the q2 and q3 conformations. In retrospect, rather than retain the diffuse p functions and add a tight p function and a diffuses function in the same region as the diffuse p, the p basis set should have been replaced with two tighter p functions with exponents similar to those commonly used in all-electron calculations. This was tested by replacing the two p functions in the production basis set with functions with exponents of 0.232 598 and 0.069 299. This basis set is of the same size as the production basis set, but the results are much better-see Table 111. The two Hay and Wadtlo p functions are even more diffuse than those optimized by Wachters,12 and the Wachters functions are normally multiplied by 1.25 or 1.5 to make them more suitable for molecular calculations. Therefore we conclude that the p functions given by Hay and Wadt for the first transition row Ar core atoms should not be used, but rather replaced with tighter exponents, such as the scaled exponents optimized by Wachters.12

IV. Results and Discussion On the basis of the calibration calculations involving CuHzL+, it is clear that the MP2 level of theory can be used to determine the geometry and zero-point energy. The MP2 vibrational frequencies also confirm that the structures correspond to a minima. We also use the MP2 to study the relative separations between the differential low-lying states. Our best binding energies are then determined using either the CCSD(T) or MCPF level of theory in one of the A N 0 basis sets. The bonding in the systemsstudied herein is largely electrostatic in origin. However, as noted previouslyZdonations make an important contribution to the bonding. For V+ 5D(3d4)and Co+ 3F(3d8),the occupation of the 3d orbitals plays an important role in determining the ground state. The four factors that are critical in the systems studied here are the following. (1) The ligand to

Theoretical Study of H r M L + Binding Energies

The Journal of Physical Chemistry, Vol. 97, No. 46, 1993 11915

TABLE I V Summary of the MHs+ Results. The Low-Lying States Are Studied at the MP2 Level of Theory. MCPF and CCSD(T) Results Using the AN03 Basis Set Are Also Reported for the Ground State state method r(M-H) r( H-H) Wl WZ u3 De DO Hz MP2-production 0.739 4522 VH2+ 'Bz MP2-production 2.537 0.746 91 462 4417 3.20 2.56 'BI MP2-production 2.378 0.750 256 626 4361 4.01 2.97 'A2 MP2-production 2.184 0.752 4.72 'Ai MP2-production 2.176 0.752 49 1 833 4318 7.12 5.51 MCPF-AN03 2.058 0.759 8.17 CCSD(T)b-AN03 10.78 CoH2+ 'Bz MP2-production 1.998 0.757 346 486 4252 5.88 5.07 3B~ MP2-production 1.881 0.768 535 856 4087 10.13 8.76 'Ai MP2-production 1.770 0.773 757 1133 3985 14.51 12.57 MP2-production 1.768 0.774 753 1125 3975 14.49 12.58 1.731 0.776 813 1278 3908 14.41 MCPF-AN03 17.05 CCSD(T)b-AN03 . . CuHz+ 'A, MP2-oroduction 1.769 0.771 737 894 4047 12.85 11.36 MP2-k1hanced 1.781 0.772 824 950 402 1 14.77 12.95 MCPF-AN01 1.764 0.779 14.55 CCSD(T)-AN03 1.729 0.779 14.15 818 1128 3882 15.65 CCSD(T)-AN01 1.746 0.780 a Bond Lengths are in A, harmonic frequencies in cm-l, and dissociation energies in kcal/mol. Single-point calculation using the MP2 geometry. metal donation that arises from electron transfer into the metal 3du and 4s orbitals; thus the minimization of the 3da and 4s orbital occupations increases the donation and also minimizes the metal-ligand repulsion. (2) The metal to ligand donation should be maximized. For example, in MH2+ it is favorable to maximize the occupation in the in-plane 3 d r orbital to maximize donation into the H2 u* orbital. (3) The remaining 3d electrons should be distributed to minimize the metal-ligand repulsion. (4) The atomic parentage of each metal 3d occupation must be considered, that is, an occupation that is very favorable based on the three first factors might be a mixture of the ground and high-lying atomic asymptotes and, hence, not lead to the molecular ground state. In this section we consider the interaction of the metal with each ligand first, and then consider the H r M L + systems to investigate the cooperative effects. In the last subsection, we compare our results with experiment and discuss the trends. A. MH2+. The H2 bonds side-on to the metal ion, because of the charge-quadrupole contribution to the bonding. With a 3di0 occupation for Cu+, the ground state of CuH2+ is clearly 'AI. For both CoH2+and VH2+, the open 3d shell results in several states and we consider a few to illustrate how the 3d occupation affects that dativecontribution to the bonding. We first consider CoH2+. As noted above, we should maximize the metal to H2 a* and ligand to metal donations, and this requires that the in-plane 3dr(b2) orbital be doubly occupied and the 3du(al) be singly occupied. The second 3d hole could be in the 6(az), 6(a1), and x(b1) orbitals, leading to 3A2,3A1,and 3B1 states, respectively. Since the two 3d6 orbitals have very small overlap with H2, the geometries and frequencies are very similar for the nearly degenerate 3A2and SAl states (see Table IV). The 3B1state lies and 3AI about 4 kcal/mol above these two states. While the states are well described by a single configuration, the 3B1state is not. The Mulliken populationanalysis of the MP2 wave function indicates that this state is a mixture of two configurations. In the minor one (25%) the metal cation occupation (3dui3dx(bl)l) is the one that minimizes the c 0 - H ~repulsion, while the dominant configuration has a metal occupationof 3d6(ai)i3dx(bl)i. While the former occupation has the desirable feature of having the 3da orbital singly occupied, it is derived from an atomic asymptote that is 40% 3F ground state and 60% 3P excited state. The latter configuration is derived from 80% 3F but has the undesirable feature that the 3da orbital is doubly occupied. The longer CoHz bond length is probably due to the reduced donation and

increased repulsion associated with the 3da orbital being doubly occupied. These factors lead to the 'B1 state being less strongly bound than the 'Al and 3A2states, which are derived from 100% 3F, As discussed by Perry et this mixing of configurations can be viewed as a rotation of the metal atom axis by 90°, so that the a axis no longer points directly at the ligand. This allows the metal "a" and "6" orbitals to interact with the ligand, while the metal atom retains the 3F coupling. The final state that we consider is the 3B2state of CoH2+ where the 3dr(b2) orbital is singly occupied, leading to a small 3d to u* donation. This can be seen in the shorter H2 bond length, the longer Co+-H2 distance, and higher H-H stretch frequency. As in the case of the 3B1state, the 3B2is a mixture of two configurations, 3da13dr(bz)l and 3d6(a1)i3dx(b2)i,the former is derived from 40% 3F and 60% 3P while the latter is derived from 80% 3F. Given the small 3d to us donation for this state and that the component with the 3da orbital singly occupied is 60% 3P,it is not surprising to find this state to be weakly bound. V+ has a 3d4 occupation that gives rise to five low-lying states for VH2+, all of which are derived from 100% V+ 5D. Thus the repulsion and dative bonding effects associated with each occupation are the most important factors that affect the bonding. The most stable state is clearly the where the 3du orbital is empty. The 5A2state, which has the 3d6 empty, is a higher lying state. We cannot consider the @)SA1state at the MP2 level, which is also derived from an empty 3d6 orbital. However in a SA-CASSCF/MRCI calculation,which included three5Al states in the averaging procedure, the (2)5A1state was found to be 2.1 kcal/mol above theground state. As expected,this isvery similar to the SA2-( l)5A1 separation. The 5B2 state, where the 3dr(b2) orbital is empty, is the highest lying state as there are no electrons to donate into the u* orbital. The reduced donation is visible in the shorter H2 bond length and higher H2 frequency. However, the energy differences between the states are much smaller than for CoHz+,that is, the dative interactions are weaker for V+ with only singly occupied 3d orbitals than for Co+ where the 3dr(b2) orbital can be doubly occupied. This weaker dative bonding coupled with the reduced electrostatic bonding (due to the larger size of V+ than Co+) results in the ground state of VHz+ being bound by 7.1 kcal/mol, which is about half of the CoH2+ binding energy. We should recall at this point that the 3B2state of CoH2+, where the metal to ligand donation only involves one electron as in the VH2+ground state, also has a small H2 binding energy (5.9 kcal/mol). These results clearly show that for the first transition

Maitre and Bauschlicher

11916 The Journal of Physical Chemistry, Vol. 97, No. 46, 1993

TABLE V: Summary of the MH,O+ Results. The Low-Lying States Are Studied at the MP2 Level of Theory. MCPF and CCSD(T) Results Using the AN0 Basis Sets Are Also Reported for the Ground State. state method W-O) r(O-H) L(H0H) De Do VH20+ 'Bi 'Ai

MP2-production MCPF-AN03 MP2-production MCPF-AN03 CCSD(T)-AN03

2.215 2.043 2.259 2.156 2.146

0.969

106.0

0.968

105.9

MP2-production MP2-production MCPF-AN03 MP2-production MCPF-AN03 MP2-production MCPF-AN03

2.007 2.072 2.005 2.070 2.006 2.064 1.974

0.970 0.969

106.9 106.5

0.969

106.5

0.969

106.4

MP2-production MP2-xhanced CCSD(T)-AN0 1

1.993 1.978 1.935

0.968 0.969 0.963

106.5 106.6 107.3

28.65 30.02 30.40 32.43 32.67

28.78

COH~O+ IB2 3A1 IA2 IBI

27.83 34.65 36.55 34.70 36.60 33.83 37.15

33.02 33.05 32.14

CuH20+ 'Ai

35.52 37.37 39.72b

33.91 35.70

0 Bond lengths are in A, bond angles in degrees, and dissociation energies in kcal/mol. At the MCPF and CCSD(T) levels, only the M-O bond length has been reoptimized. Using the CCSD(T) geometries from ANOl, the CCSD(T) binding energy in A N 0 3 is 37.87.

row, metal to ligand donation from a singly occupied d orbital makes a negligiblecontribution to the binding energy as previously found by Carter and Goodard.25 We suspect that this arises because of the large 3d-3d exchange energy for V+. Metal to H2donation results in a spreading out of the 3d orbital and hence some loss of exchange energy. Thus donation is less favorable for singly occupied 3d orbitals than for doubly occupied 3d orbitals. As discussed below, this small binding energy for V+ is consistent with experiment. The VH2+ binding energy is quite small. At the MP2 level, we find that the basis set superposition error (BSSE) is 0.5 kcal/ mol. We expect that the BSSE will be smaller in the A N 0 3 basis set. Because the binding energy in the A N 0 3 set is larger than in the production set, we expect that the basis set incompletenessis larger than the BSSE even for the weakly bound VH2+. Therefore, we conclude that our computed values are lower bounds. The ground states of CoH2+ and VH2+ have also been treated at the MCPF and CCSD(T) levels in the A N 0 3 basis set. As shown in Table IV, the MCPF and MP2 geometries and binding energies are in good agreement. As for CuH2+, the largest discrepancy between the MP2 and MCPF frequencies is found for the antisymmetric stretch, but the MP2 frequencies are still quite reasonable for this open-shell complex. The CCSD(T) binding energy was found to be 2.6 and 3.7 kcal/mol larger than the MP2 value for CoH2+ and VH2+, respectively. As shown by the work of Handy and co-workers,26 perturbation theory does not always work as well for open-shell systems as closed-shell ones. However, the agreement between the CCSD(T) and MP2 levels of theory shows that this is not the case for these systems, where the MP2 level of theory using the production basis set works about as well for the open-shell complexes as for the closed shell CuH2+. As has been disc~ssed2~ for covalent bonding, mixing of different atomic asymptotes leads to an energy stabilization. This is also true for electrostatic bonding. The SA1 state of VH2+ involves the mixing of three electronic configurations, one deriving from the 3d34s1asymptote, the two others from the 3d4 asymptote and differing by the location of the hole in the 3d shell (3dB and 3d6(a1)O). This extra flexibility allows the rotation of the V u axis to help reduce the metal-H repulsion. This mixing appears to be enhanced at the MCPF level and is probably the origin of the decrease in the V+-H2 bond length at the MCPF level compared with the MP2 value (see Table IV). We wish to note one technical problem encountered in these calculations. In the A N 0 3 basis set, the spin-restricted SCF calculations converged to a 3d6(a1)0 occupation for the ( 1)5A1

state of VH2+. In this state, the 3du orbital mixes with the 4s orbital to polarizeaway from theHZ. This solutionoccursbecause the SCF treatment is biased toward the 3d34s1 occupation in this basis set. With the addition of correlation, at the SA-CASSCF/ MRCI level, the ground 5AI state has a large 3 d B character, with 3d6(a1)0and 3d34s1making only a small contribution to the wave function. Thus, we forced the spin-restricted SCF to convergeto the 3dB solutionbecause it is the appropriate reference wave function for the correlated calculations. B. MH20+.The charge-dipole contribution to the M+-H20 bonding leads to a CzVstructure with the oxygen pointing at the metal ion. This bonding is significantly stronger than that for H2 or CH4. Previous work28 has shown that while the dative bonding is small, the occupation of the 3d orbitals is important in determining the ground state. Namely, it is important to minimize the metal 3d repulsion with the H2O orbitals. The overlap clearly varies as 3du > 3d?r(bl) > 3dr(b2) > 3d6(al or az), where the 3d?r(bl) overlaps with the T H20 lone pair. With a 3d1° occupation, the ground state of CuH20+ is clearly 'Al. Our best De in the present work is 0.7 kcal/mol larger than that reported previously.28 This is consistent with use of the CCSD(T) and a very large basis set in the present work. For CoH20+the occupation that minimized the metal-HzO repulsion is 3du13d?r(bl)1,leading to a 3B1state. However as noted above, this occupation is derived from 40% 3F and 60% 3P. As in the case of CoH2+,this state becomes a mixture of two configurations, the one just noted and the more important 3d6(al)13dr(bl)1 configuration, which is derived from 80% 3F. As noted above, this mixing has been discussed24in terms of rotating the metal u axis as a mechanism of reducing the metal-ligand repulsion, while retaining the3Fatomic coupling. The importance of mixing in the 3du13d~(b1)loccupation is apparent from the fact that the 3B2 state which is derived from the other component of the 3d?r(b1)13d6' occupation is about 7 kcal/mol above the 3B1state. The 3A1 and 3Az states are both derived from 100% 3F with an occupation of 3du13d61and are almost degenerate. At the MP2 level of theory these states are below the 3B1,but at the MCPF level the ground state is 3B1. This is the same result as found previously2*(after accounting for the differentsymmetry labeling.) The stabilization of the 3BI state relative to the others at the MCPF level is probably due to a greater mixing of the 3 d d 3d?r(bl)l occupation and to the better description of the sdu hybridization. On the basis of the metal 3d-H20 overlaps, we consider only two states for VH20+, the 5A1(3dd)where the 3du repulsion has been minimized and the 5B1(3d?r(bl)o)where the a(bJ repulsion has been minimized (Table V). The latter state might appear

Theoretical Study of Hz-ML+ Binding Energies

The Journal of Physical Chemistry, Vol. 97, No. 46, 1993 11917

TABLE VI: Summary of the MP2 Results for M a + and MH2C)4+ Using the Production or Enhanced Basis Sets, Which Are is $ Bonded to the Cu. H Atoms in C)4 That Are Directed at the Cu Are Labeled Ha, Labeled P and E, Respectively. Are Labeled W While the Other H Atoms in basis r(Cu-Ha) r(C-Ha)' r(C-Hb) LHaCHa LHbCHb r(Cu-H) r(H-H) De Do CuCH4+ 16.82 16.82 1.080 117.8 112.7 P 1.944 1.108 118.1 112.7 20.13 19.57 1.110 1.080 E 1.911 CuH2CH4+(eclipsed) P 1.924 1.109 1.080 118.5 112.5 1.697 0.777 16.38 13.36 E 1.889 1.112 1.080 118.7 112.7 1.727 0.777 17.48 14.71 a Bond lengths are in A, bond angles in degrees, and dissociation energies in kcal/mol. For comparison the C-H distance in free CH4 at the same level of theory is 1.085 A.

a

to be very unfavorable, but it must be remembered that sdu hybridization is very efficient at reducing the metal-ligand repulsion in the u space. At both the MP2 and MCPF levels we find the two states to be close in energy, but the ground state is SAl as expected. There is sizable V-0 bond length contraction a t the MCPF level relative to the MP2 results. This is especially true for the 5Bl state and is probably due to a better description of sdu hybridization a t the MCPF level. For the SAl state, this is due to mixing in of the other occupations (3d6(a1)0 and 3d34s'). However, as expected, the MCPF natural orbitals show that this state is derived mostly from the 3d4 occupation with an empty 3du orbital. We should note that as for VH2+, we did find the SAl state with a 3d34s' occupation but it was significantly higher in energy and did not lead to any problems. Our best computed H2O Devalues for V+ and Co+ in this work are 32.7 and 37.2 kcal/mol, respectively, which are obtained a t the CCSD(T) level using the A N 0 3 basis set. As noted above, we expect that these values would increase by 2 kcal/mol if the ANOl basis set was used. Thus our best estimates from the present work are 34.7 and 39.2 kcal/mol for V+ and Co+, respectively. These values are in reasonable agreement with the values of 36.4 and 39.9 kcal/mol reported previously2* and consistent with the estimated uncertainty of between 3 to 5 kcal/ mol for the M+-H20 bond energies. C. Cuc)4+. CuCH4+is the only example of a methane complex studied in this work. We found that the optimal MP2 geometry for CuCH4+ is an 72 configuration, which is 0.3 and 1.2 kcal/mol below the 73 configuration using the production and the enhanced basis set, respectively. At the SCF level using the production basis set, the optimal geometry is between 72 and 73. In addition, the 7 3 structure was found to be the ground Thus it appears that both basis set improvements and electron correlation favor the 7 2 structure over the 73. We should also note that the present Devalueis significantly larger than that found previ0usly,2~ which was significantly too small, mostly because of the very small basis set. Our best result, that obtained a t CCSD(T) level in the ANOl basis set, is expected to be accurate to f 3 kcal/mol and should definitely be accurate to kt5 kcal/mol. Perry, Ohanessian, and G ~ d d a r found d ~ ~ that the v2 geometry was favored for CoCH4+. They find essentially the same difference (1.3 kcal/mol) between the 72 and 73 as we find 'for Cu. They suggested that C-H u donation in both the a1 and bl symmetries favored the 72 structure over the 7 3 configuration. For Cu this involves donation into the 4p orbital. While the binding energy is similar to that in the MH2+ systems, ligand to metal donation rather than metal to ligand donation appears to be the most important effect. We should note that for MgCH4+, where the occupied 3s orbital leads to a long bond length, the q3 geometry is the lowest a t both the S C F and MP2 levels of theory.3' CH4 to Mg donation also appears to be smaller than in CuCH4+.Thus it appears that electrostatics favor the 7 3 structure, while the dative interaction favors the 72 structures for Cu+. Our best binding energy (see Table 111) is slightly smaller than that found for CoCH4+. Consistent with the weak bonding, the CH4is only slightly distorted from that in free CH4 (see Table VI).

TABLE W: Summary of Results for M(H2)2+. The Difference between the Eclipsed and Staggered Geometries Is Considered at the MP2 level. The Energy To Remove the First H2 Is That Computed at Higher Levels of Theory' state method r(M-H) r(H-H) De DO V(H2)2+ 2.176 0.752 7.45 5.09 Dzd 5 A ~ MP2-production 2.171 0.752 7.56 5.15 D2h '4 MP2-production MCPF-AN03 2.074 0.761 9.51 CCSD(T)'-AN03 11.10 Co(H2)2+ 0.213Ag MP2-production 1.792 0.771 15.12 MP2-production 1.779 0.772 15.67 DM'B1 Dzd MP2-production 1.777 0.773 15.80 12.07 MCPF-AN03 1.767 0.778 16.64 17.81 CCSD(T)'-AN03 Cu(H2)2+ 0 2 1 'Ag MP2-production 1.762 0.771 14.93 MP2-enhanc-A 1.762 0.773 16.65 Dtd 'Ai MP2-production 1.752 0.772 15.31 12.14 MP2-enhanc-A 1.758 0.774 16.94 14.35 MCPF-AN01 1.750 0.777 16.50 CCSD(T)-AN01 1.731 0.781 17.97 a Bond lengthsare in A and dissociationenergiesin kcal/mol. b Singlepoint calculation using the MP2 geometry. D. M(H2)2+. On the basis of the MH2+ systems discussed above, the 3d occupation in the M(H2)2+ is straightforward to assign. For V(H2)2+ the 3du orbital is empty and for Co(H2)2+ the 3du and 3db orbitals are singly occupied as for the ground states of the corresponding MH2+ complexes. Thus, the only question is whether the geometry of M(H2)2+ is eclipsed ( 0 2 3 or staggered (DZd), and we have considered both. The staggered configuration is the most stable for both Co(H2)2+ and Cu(H&+ (see Table VII). As pointed out previously2 for Co(H2)2+, the staggered is preferred because the H2 antibonding orbitals interact with two different doubly occupied 3d orbitals, resulting in a more efficient M-L donation. The same is true for Cu(H2)2+. The eclipsed structure is the transition state and is only slightly above the minimum, indicating that the extra donation associated with two different 3d orbitals is small. Without zero-point energy, for both Cu(H2)2+and Co(H2)2+the second ligand is more strongly bound than the first. We attribute this to sdu hybridization which reduces the repulsion on both sides of the metal. Thus the two ligands share the cost of this hybridization and the second ligand binding energy is larger than the first. This effect is sufficiently small that after including the zero-point energy the second DOfor Co(H2)2+ is smaller than the first. The calculations confirm the suggestion of Kemper et al.1 as to the origin of the difference between the experimental Dovaluesand the theoretical Devalues. For C U ( H ~ )the ~ + second ligand binding energy is still larger than the first even after the zero-point correction is added. In the case of vanadium, the minimum on the potential energy surface is the eclipsed conformation with the staggered transition state only slightly higher in energy. While the energy difference is small, it is a significant difference between the V+ and the Co+ or Cu+ complexes. Because the bonding is so weak, it is difficult to definitely determine the origin af this effect, but we suspect that the difference arises because of the large 3d-3d exchange

11918 The Journal of Physical Chemistry, Vol. 97, No. 46, 1993

Maitre and Bauschlicher

TABLE VIII: Summary of Results for MH,H20+. The Difference between the Eclipsed and Staggered Geometries Is Considered at the MP2 Level. The First Ligand Binding Energy Is That Computed at Higher Levels of Theoryo state method r(M-H) r(H-H) r(M-0) r(0-H) L(H0H) 4 DO VHzH20+ s A staggered ~ SAI eclipsed CoHzHzO+ 3 B eclipsed ~

'B1 staggered 'A1 eclipsed 'Al staggered 'Az eclipsed 'Az staggered CuHzHzO+ IAl eclipsed 'A1 staggered

MP2-production MP2-production MCPF-AN03

2.104 2.087 2.014

0.753 0.754 0.767

2.260 2.254 2.155

0.968 0.968

105.8 106.0

7.40 7.61 9.74

5.28

MP2-production MCPF-AN03 MP2-production MCPF-AN03 MP2-production MP2-production MCPF-AN03 MP2-production MCPF-AN03 MP2-production MCPF-AN03

1.709 1.721 1.832 1.708 1.634 1.624 1.643 1.629 1.648 1.622 1.642

0.781 0.785 0.760 0.785 0.786 0.789 0.796 0.788 0.792 0.791 0.797

2.030 1.953 2.031 1.983 2.052 2.043 1.978 2.050 1.985 2.043 1.971

0.970

106.7

0.970

106.6

0.969 0.970

106.7 106.8

15.78

0.969

106.8

0.970

106.8

14.47 15.24 11-01 13.61 18.67 19.19 17.88 18.82 17.50 19.18 17.95

MP2-production MPZ-enhanced MP2-production MPZ-enhanced CCSD(T)-AN02

1.683 1.652 1.671 1.691 1.665

0.778 0.779 0.781 0.780 0.832

1.959 1.946 1.953 1.941 1.882

0.968 0.986 0.968 0.986

107.2 107.3 107.3 107.3

17.22 18.67 17.70 19.06 19.83

15.78

14.39 15.83

a Bond lengths are in A, bond angles in degrees, and ML+-Hz dissociation energies in kcal/mol. At the MCPF or CCSD(T) levels, only the M-O, M-H, and H-H bond lengths have been optimized.

energy for V+ resulting in a very small donation as noted above for VH2+, that is, conserving metal 3d-3d exchange energy is more important than any increased dative interaction associated with metal to u* donation from two different singly occupied 3d orbitals. This is clearly very different from Co+ and Cu+, where the 3d orbitals are doubly occupied. The second H2 is more strongly bound than the first for the V(H2),,+ system. This is probably due to increased mixing in of the other asymptotes, as described above for VH2+, because the promotion costs are shared by both ligands. E. MHJ-I20+. The MH2H20+results are summarized in Table VIII. For CoH2H20+ we compute the Hz binding energy with respect to the computed ground state of CoH20+ at the same level of theory. Thus the MP2 is computed with respect to the 3A2state of CoH20+, while the MCPF is with respect to the 3B1 state. For CuH2H20+ the ground state is IA1. The staggered configuration is slightly more stable than the eclipsed transition state. Considering the similarity in the bonding for the two CoH20+ 3da13d6 states, it is not surprising that the 3A1and 3Az states of CoH2H20+ are essentially identical. For both systems the staggered configuration is slightly below the eclipsed transition state. While this configuration is favored for Co+ and Cu+ for both M(H2)2+ and MH2H20+, the origin of the effect that favors this configuration must be different as no metal to HzO donation is expected. The preference for the staggered configurations in MHzH20+ can be explained by the water-metal r repulsion that causes the 3d?r orbitals to polarize away from the water. This effect is larger for the bl orbital than the b2 orbital because the r lone pair has a larger overlap with the metal. This polarization of the 3d orbital away from the H2O enhances the bonding with the Hz by promoting more 3d to a* donation. This leads to a staggered minimum and a larger H2 binding energy in MH2H20+ than M(H2)z+or MH2+. The H2O-metal interaction in the u space should lead to better sda hybridization than in M(H2),,+ which should also increase the H2 binding in MH2H20+ relative to the other systems. As the ground state of CoH20+ is 3B1, we also consider this state. For this state, the eclipsed structure is strongly favored over the staggered because it is very unfavorable for the H2 to interact with the singly occupied 3d(bl) orbital. However, even the eclipsed configuration is significantly less strongly bound than for the 3A1and 3A2states. This is consistent with CoH2+, where it was found that doubly occupying the 3da orbital reduced the binding energy by about 4 kcal/mol (see Table IV).

For VHzH20+ the ground state is 5 A where ~ the 3da is empty. As noted for V(H2)2+, conserving the metal 3d-3d exchange appears to be more important for V+ than the dative bonding. Therefore it is not surprising to find the eclipsed configuration to be the most stable. These calculations, along with those for MH20+, illustrate the weakness of only using the MP2 level of theory; it predicts the incorrect ground state for CoH20+ and predicts the Hz binding energy in CoH2H20+ to be significantly larger than in CoHz+, whereas the MCPF level predicts a smaller enhancement in the H2 binding energy by the addition of water. For V+, the MP2 yields a small HzOenhancement in the Hz binding energy, while the MP2 predicts a much larger enhancement. On the other hand, the MP2 results are more consistent with the MCPF (or CCSD(T)) for the Cu complexes. Thus, while MP2 is an excellent starting point, higher levels of correlation treatment are clearly required for quantitative results. F. CuH2CH4+.The CuH2CH4+calculations are summarized in Table VI. We find the eclipsed structure (where by eclipsed we are comparing the H2 with the two H atoms in CH4 that are pointing at the Cu) to be 0.14 kcal/mol below the staggered at the MP2 level using the enhanced basis set. CH4 donation to the metal and metal polarization away from the C-H bonds favor the eclipsed geometry. These effects yield an increase of the H2 binding energy compared with CuH2+ or Cu(H2)2+, but smaller than found for CuH2H20+, where the stronger Cu+-H20 leads to more 3d polarization and sdu hybridization and hence to a larger enhancement in the Hz binding energy. G. Trends and Comparison with Experiment. We derive our best estimate for the binding energies as follows. For Cu(Hz),,+, CuH20+,CuH2H20+, and CuCH4+ we correct the CCSD(T) D, values (using either the A N 0 1 or A N 0 2 basis sets) with the MP2 (in the production basis set) zero-point energy. For CuH2CH4+ we add the change in the MP2 (in the enhanced basis set) binding energy between CuH2+and CuHzCH4+ to the CCSD(T) binding energy for CuH2+. For VHzL+ and CoHzL+ we correct the CCSD(T) result using the A N 0 3 basis set with the MP2 zero-point energy. For VHzHzO+ and CoH2H20+ we do not have CCSD(T) results, so we correct the MCPF results with the difference between the MCPF and CCSD(T) results for MH2+. We then make a basis set correction based on the difference between the A N 0 1 and A N 0 3 basis sets based on the CuHzL+ calibration calculations. Namely we add 1 kcal/mol to M-Hz binding energies and 2 kcal/mol to M-H2O bond energies for V

Theoretical Study of H r M L + Binding Energies

TABLE I X Summary of the Best Estimates for the Binding Energies, in kcal/mol, Compared with Experiment best estimate expt 14.2 14.8 38.1 16.5 21.4 15.6 16.9 15.1 37.5 18.2 10.2 9.7 33.1 11.0

37.6 f 1,' 35.0 f 3b

18.2 f 1.W 17.0 f 0.4c 37.1 f 3,b 40.1 f 4," 37.7 f 1.2' 19.8 f 0.6e 10.25 f 0.3' 10.74 0.3' 36.2 f 3,b 35.1 f 4,d 34.1 f 1.2'

a Reference 33. Reference 34. Reference 1. Reference 35. Reference 2. /Reference 32.

and Co. Note that even these estimates are expected to be smaller than the true values, probably by about 1-2 kcal/mol. These estimates along with experimentlJ-32-35 are given in Table IX. Overall there is good agreement between our best estimates and experiment. For CoH2L+ our trends are reasonably consistent with experiment.'^^ We find the second H2 to be less strongly bound than the first, as found in experiment. The difference between this and previous work2 is the inclusion of zero-point energy. We find that water enhances the H2 binding relative to an H2, in agreement with experiment. However, the magnitude of this effect is difficult to predict reliably. For V(H2)2+, our computed binding energies are in reasonable agreement with experiment,32 but we find the second ligand to be slightly less strongly bound than the first. We predict that H20 will slightly increase the H2 bond strength for V+, while the experimental results suggest a slight decrease.32 The results for CuH2L+ are somewhat different than for Co+. The H2 and CHI binding energies to Cu+ are slightly smaller than for Co+,consistent with theextra stability of the Cu+ because of the closed 3d shell. The second H2 is more strongly bound than the first for Cu+ even after accounting for zero-point energy. Unfortunately, the difference is so small that it might be difficult to observe experimentally. We find that both CH4 and H2O enhance the bonding of an H2 relative to a second H2. The CH4 enhancement is probably an upper bound as it was computed at the MP2 level, which yields an HzO enhancement that is 0.7 kcal/mol larger than the MCPF. It is also of interest to compare the bonding of the same ligand to the different metal ions. As Z increases the size of the metal ions decrease, thus the electrostatic bonding increases with Z the expectation values of r and for the 3d orbital are 1.46, 1.10, and 0.98 a0 for V+, Co+,and Cu+,respectively. However, the bonding is enhanced by sda hybridization and the orientation of the 3d holes. These effects results in the H2O binding energy to Co+ being only 0.6 kcal/mol smaller than that to Cu+, in spite of the smaller size of Cu+ than Co+. For V+, the much larger size leads to a smaller H20 binding energy despite the fact that the 3da orbital is empty. For H2, dative interactions are important; the donation is smaller for Cu+ than Co+ because of the stability of the closed 3d shell for Cu+.Thus leading to a Co+-H2 binding energy that is larger than that for Cu+. Metal to ligand donation from a singly occupied d orbital is found to be ineffective at enhancing the metal-ligand bond strength, a t least for the first transition row. This, coupled with the larger size of V+, leads to a V+-H2 binding energy that is smaller than for Cu+ or Co+. Because the 3da is doubly occupied for Cu+, sda hybridization is a more important mechanism for reducing the metal-ligand repulsion for Cu+ than Co+ or V+. The cost of this hybridization can be shared by a second ligand; therefore it is not surprising

The Journal of Physical Chemistry, Vol. 97, No. 46, 1993

11919

to find that the H2 binding energy is enhanced by more with the addition of H2 or H2O for Cu+ than for V+ or Cot. The trends for a given ligand with metal ion are clearly related to the size and the specific 3d occupation of the metal ion. The larger differences for H2 than H20 reflect that datiye contribution to the bonding for H2 are important. VI. Conclusions The MH2L+ binding energies have been computed for M = V, Co, and Cu and L = H2 and H20. CuH2CH4+ has also been studied. Overall our best estimates for the binding energies are in good agreement with the experimental results. In particular, we confirm the experimentally observed increaseof the H2 binding energy in CoLH2+ when L goes from H2 to H2O. We show that when L is a 7r-donor ligand like H20, there is a polarization of the 3d7r orbital of the metal toward H2 which permits an enhancement of the 3d7r donation to the a* orbital of H2. This effect is also observed in the case of Cu+ for both H20 and CH4 *-donor ligands. We should note that the enhancement of the 3d7r donation to the u* orbital of H2 is weaker with CH4 than with H2O in the case of Cu+, in agreement with the experimental results for CO+.~ We are therefore confident in making several predictions about the trends for CuH2L+. Metal to ligand donation from a singly occupied 3d orbital is found to be ineffective at enhancing the metal-ligand bond strength, because it is preferable for the metal to conserve the large 3d-3d exchange energy instead of increasing the 3d metal to ligand donation. This leads to H2 binding energies to V+ that are smaller than those to Cu+ or Co+ (two-electron donation). Donation from singly occupied 4d or 5d orbitals is probably larger than that of 3d orbitals as the d-d exchange energy is smaller for the second and third transition row atoms. The MP2 approach has been shown to yield reasonable geometries and binding energies for the metal-ligand systems. For each complex, MP2 leads to the proper relative energy ordering of the conformers and states compared to the higher level of correlation. The only exception is CoH20+, for which MP2 assigns the wrong ground state (3A2instead of 3B1), but we should note that these states are very close in energy whatever level of correlation is used. Overall, MP2 underestimates the ligand binding energy by 1-6 kcal/mol, and we show that a higher level of correlation must be used to compute accurate binding energies. We also recommend that the p functions from the first transition row (Ar core) valence basis sets of Hay and Wadt be replaced with tighter functions.

Acknowledgment. These authors would like to thank Paul Kemper and John Bushnell for helpful discussions and making the results of their experiments available to us before publication. P.M. would like to thank the CNRS for financial support. Appendix A. ANO1. The Cu basis set and H basis sets for H2 are A N 0 contractions, (20s 15p 10d 6f 4g)/[6 + 1s 5 + l p 4d 2f lg] and (8s 6p 4d)/[4 + 2s 2 + 2p 1 + Id], respectively. The large primitive set of Partridge36 is used for Cu and the polarization functions and contraction are described in detail in ref 37. The H basis set is the same as used in our previous study2 and is described in detail in that work. We note that this H basis set yields an excellent polarizability and quadrupole moment for H2 (see ref 2), which are important in describing the electrostatic bonding. The H and 0 basis set used for H2O are the augmented correlation-consistent polarized valence quadrupole (aug-ccpVQZ) sets of Dunning and co-workers;14 these basis sets are of the form (7s 4p 3d 2f)/[5s 4p 3d 2fl and (13s 7p 4d 3f 2g)/[6s 5p 4d 3f 2g], respectively. The H and C basis sets in CH4 are derived aug-cc-pVQZ basis set; the diffuse f and g functions on C and the diffuse d and f functions on H are deleted, thus yielding basis sets of the form (7s 4p 2d If)/[% 4p 2d lfl and (13s 7p 4d 2f lg)/[6s 5p 4d 2f lg], respectively.