J . Phys. Chem. 1990, 94, 6969-6973 program.18 The geometries for methylenes were taken from HF/GVB( 1 /2) geometry optimizations for the ]A'13Aff states of CHCI (using TZ2P basis sets) by Scuseria et aL2' and the HF/GVB(1/2) calculations for 1AI/3BIstates of CC12 (using DZp basis sets) by Bauschlicher et aL4 C . DCCI Calculations. The GVB-DCCI approach is based on the GVB wave function in which the carbene lone pair and the two bond pairs are correlated ( 2 GVB orbitals per pair), followed by a small CI based on the GVB orbitals.6.16For calculation of an accurate bond energy for a halogen-substituted double-bonded molecule, XYC = CZW, the DCCI prescription is to solve first for the GVB-PP(6/12) wave function in which the double bond and the four carbon-ligand bonds are correlated. Then, to relax the perfect spin-pairing restriction of the GVB-PP wavefunction, we allow a full C1 restricted so that each correlated pair has two electrons distributed among the two orbitals (this is referred to as GVB-RCI). Then all quadruple excitations are allowed out of the double bond [leading to the RCI*SDTQ(ar) wave function]. This wave function dissociates smoothly to the RCI*SD(mr) wave function on each carbene fragment, leading to a consistent description for dissociation of the double bond. For the halogen-substituted systems, it has been previously shown6 that to obtain accurate AEsr for carbenes, one must include the r-lone pair orbitals in the RCI. Hence, we would consider the RCI*[IICI + SDTQ(ar)] wave function for XYC=CZW, which dissociates to RCI*[lTCI S D ( a r ) ] on each carbene
+
6969
product. This was designated CCCI by Carter and Goddard.6 If calculated self-consistently, these wave functions should lead to accurate bond energies. However, for computational convenience we calculated the orbitals at the GVB-PP level. Hence to include such orbital readjustment we must also include all single excitations from the GVB-RCI wave function (Sva,). Thus the final wave function is RCI*[lTCI S,, SDTQ(or)] for X Y C = CZW and RCI*[IICI ,S , SD(ar)] for the carbenes. This choice of the wave function for CXY ensures that the double bond in XYC=CXY is calculated at an equivalent level as the bond length is increased to R = m. Hence, we refer to this as dissociation-consistent CI.'6-32 The DCCI description (RCI*[IICI SvaI S D ( a r ) ] ) differs from the previous CCCI description (RCI*(IICI SD(ur)]), only by inclusion of all single excitations from the GVB-RCI wave function (SV8J. We find that inclusions of Svalis important to balance the relative stabilities of the singlet and triplet states.I6
+
+
+
+
+
+
+
Acknowledgment. We acknowledge the support of the National Science Foundation under Grant Nos. CHE87-11567 (J.L.B.) and CHE83- 18041 (W.A.G.). Registry No. CHCI, 2108-20-5; CC12, 1605-72-7; SiHCI, 1393 1-97-0; SiCI,, 13569-32-9. (32) Bair, R. A,; Goddard, W. A,, 111. Unpublished. See: Bair, R. A. Ph.D. Thesis, California Institute of Technology, 1981.
Bonding of Intact Molecular Hydrogen to Cr+ and CrH+ Mildred Rivera, James F. Harrison,* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824- 1322
and Aileen Alvarado-Swaisgood Amoco Oil, Amoco Research Center, Naperville, Illinois 60566 (Received: October 3, 1989; In Final Form: February 12, 1990)
We argue that the electrostatically bound complexes of H, with Cr+ and CrH+ in which the H2 molecules are intact are the lowest energy structures on the OH,+ ( n = 2, 3, 4, and 5 ) potential surfaces. Similar results are expected for other first-row transition-element cations. It is suggested that, in more complex systems, substituents on the transition metal will result in the metal being cationic and thus opening the electrostatic channel as a viable bonding mode.
Introduction When a transition-metal ion reacts with H2to form a dihydride
transition-metal ions will, however, bind electrostatically with H2, and the reaction
H
M+ +
H2
4
Mt
M+'
\
H
in which the hydrogens are bound to the metal center the reaction will be exothermic if the sum of the metal-H bond energies is greater than the H2 bond strength. Since the H, bond strength] is 104 kcal/mol, the average M-H bond energy must be greater than 52 kcal/mol for the reaction to be exothermic. While this might be for some transition-metal ions ( e g , Sc+ and Fe+) it will not be possible for othersSv6(e.g., Cr+ and Cu'). All ( I ) Benson, S. W. Thermochemical Kinetics; 2nd ed.; Wiley: New York,
+
H2
.-c
H Mt***I H
in which the transition metal does not change its spin will always be exothermic.' The lowest energy state for many transition-metal cations and H2 will be the electrostatically bound complex in which the H2 is essentially intact. Similar arguments obtain for M+-H. The choices are M+-H
+
H~
4
H \ M+-H H'
or
1976.
(2) Alvarado-Swaisgood, A. E.; Harrison, J. F. J. Phys. Chem. 1985,89, 5 198. ( 3 ) Rappe, A. K.; Upton, T. H . J . Chem. Phys. 1986, 85, 4400. (4) Mavridis, A.; Harrison, J. F. J . Chem. SOC.,Faraday Trans. 2 1989, 85. 1391. ( 5 ) Schilling, J. B.;Gcddard, 111, W. A,; Beauchamp. J. J . Phys. Chem. 1987, 91, 4470. (6) Alvarado-Swaisgood, A. E.; Harrison, J. F. Unpublished results.
0022-3654/90/2094-6969$02.50/0
(7) For other examples of electrostatic effects in transition-metal bonding see: Allison, J.; Mavridis, A,; Harrison, J. F. Polyhedron 1988, 7 , 1559. Mavridis, A,; Harrison, J. F.; Allison, J. J. Am. Chem. SOC.1989, 1 1 1 , 2482.
0 1990 American Chemical Society
6970
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990
Rivera et al.
41
TABLE I . Comparison of Calculated and Experimental Properties of HIa
Re, A De, kcal/mol
0.741 104 4400 0.468 6.30 4.85
o,,cm-' 9. au all. a u
el,au
2l
GVB 0.767 94 4180 0.421 6.35 5.29
expb
i
R, is the internuclear distance, D, is the dissociation energy, we is the vibrational frequency at equilibrium, 8 is the quadrupole moment, a,, is the parallel polarizability, and a,, is the perpendicular polarizability. Reference 16.
HGVB
3*
For many transition-metal hydrides the oxidative addition reaction will be endothermic while the electrostatic complex will always be formed exothermically. Clearly these ideas are applicable to reactants other than H2. For example, CH4 could react as
-4i
L,';'A'r'!'
-6 0
H
Mt
-k
CH,
-D
M" 'CH,
or
depending on the bond strengths involved.* In what follows, these ideas are developed computationally for Cr+ and CrH+. In particular, we argue that the exothermic product of the reaction Cr+
+ nH2
-
[CrH,,]'
contains n intact H 2 molecules and the product of the reaction Cr+-H
+ nH2
[CrH2,+,]+
contains one covalently bonded H and n discrete H 2 molecules. Calculations The basis set on Cr+ is the standard Wachters set9 contracted to 5s,4p,3d and the basis on H is the HuzinagalO 4s contracted to 2s and augmented with a diffuse s (a = 0.03). In addition, three uncontracted p functions (a = 1 .O, 0.33,O.ll) were added to H. A 2 X 2 generalized valence bond" (GVB) calculation on the H2 molecule in the basis results in the properties shown in Table I . Cr+ + H 2 . A GVB calculation on the 6Al state of CrH2+ (Cb symmetry) in which the H2 bond was correlated results in the solid potential curve shown in Figure I . The curve was calculated with the H2 separation fixed at 0.767 A. The H2 separation was optimized at each Cr-H2 distance and varied from 0.767 A at infinite separation to 0.773 A at equilibrium. The Cr+-H2 separation is 2.34 A with a bond energy of 3.6 kcal/mol. The dashed curve shown in Figure 1 was calculated by using the charge-induced dipole, charge-quadrupole, and an ad hoc term to describe the Pauli repulsion. This electrostatic calculation used the free H2 parameters a and 8 (Table I) and is described in detail in the Appendix. The agreement between the ab initio and electrostatic interaction is excellent. Further confirmation of the electrostatic character of the interaction is found in the electron density contours shown in Figure 2. When the Cr+ and H2 densities are subtracted from the O H 2 + molecular density, the resulting difference density is very small, reflecting only the mutual polarization of H2 and Cr+. The relative energies of the linear and sideways bonded O H 2 + are shown in Figure 3 as a function of the Cr+-H2 separation. (8) Armentrout, P. 9.; Georgiadis, R. Polyhedron 1988, 7, 1573, and references therein. (9) Wachters, A. J. H. J . Chem. Phys. 1970, 52, 1033. (10)Dunning, T.H.J . Chem. Phys. 1971, 55, 716.
Electrostatic
2
10
8
R (Cr+-H2)
12
(i)
Figure 1. Comparison of GVB and electrostatic perpendicular interaction of Cr+ and H1.
The sideways bonded (C2,) geometry is the more stable by approximately 2.5 kcal/mol. We estimated the basis set superposition error by calculating the GVB energy of H 2 in the presence of the Cr basis functions. The resulting energy of H2 was 0.1 1 kcal/mol lower than the energy in the absence of the Cr functions, suggesting that the basis set superposition error is negligible. CrH+(?2+)+ H2. A GVB calculation on the SAlstate of CrH3+ in which the CrH and H2 bonds are correlated results in the solid potential curve shown in Figure 4. Once again the H2 separation is fixed at the free H2 value for this curve, but optimization results in a slight enlargement of 0.012 A at the equilibrium Cr+.-H2 separation. The equilibrium Cr+-H2 separation is 2.32 A, and the HCr+-.H2 bond energy is 5.7 kcal/mol. Superimposed on this plot is an electrostatic interaction energy which is calculated by using the dipole moment of CrH+ (relative to the Cr nucleus) as well as a,0, and an ad hoc Pauli repulsion term. The agreement is excellent. Details of this electrostatic calculation are in the Appendix. The density difference map shown in Figure 5 reflects the mutual polarization of CrH+ and H2 and substantiates the electrostatic interpretation. Cr' + 2H2 and CrH+ + 2H2. Similar calculations were carried out on
and
H
with the results summarized in Table 11. Discussion Are the electrostatic complexes described above the ground states for the CrH,+ systems? There is no doubt they are the ground states on the high-spin, sextet surface for n even and on the quintet surface for n odd. It is likely they are also the global minima. For example, the reaction H-Cr'...
H
H
I
H
-c
H-Crt
