J . Phys. Chem. 1992, 96, 1611-1619
1611
Geometry Optimization and Computation of the Electronic Structure of (C6H6)V, Molecules by the Local-Density-Functional LCAO Method Saba M. Mattar* and Sharon E. Brewer? Department of Chemistry, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 6E2 (Received: May 31, 1991)
The electronic structure and bonding characteristics of the arene-metal dimer complexes (C6H6)Vz that have c6,, D6h,and C2, symmetry are studied by the local-density-functionallinear combination of atomic orbitals (LDF-LCAO) method. The benzene-vanadium distance, vanadium-vanadium distance, and the angle of the hydrogen atoms with respect to the plane of the carbon atoms are optimized for all three complexes in the ground and some low-lying excited states. The ground 9eI4,4e24 which corresponds to a 'Al state. electronic configuration for the c6, molecule is found to be 2b12,lb?, The 3A2ground state of the C2, complex arises from the 13b12,8bz2,6a2', 18a11configuration. The D6h complex has two unpaired electrons in its 4e2 HOMO that formally leads to a 'A2 ground state. The structure and bonding relationships between the divanadium a n t benzene ligand are also presented. Tie binding energies of the three half-sacdwich molecules are computed. Of the three molecules the D6hcomplex is found to be metastable. The three lowest configurations for the other two molecules are stable and have positive dissociation energies. The c6, complex is slightly more stable than the corresponding C2, complex.
Introduction Arene-metal half-sandwich compounds may be considered as fractions of larger organometallic complexes and clusters. Since they might be used as building blocks for these larger molecules, it is important to study their bonding and chemical properties both theoretically and experimentally. The (q6-C6H6)v half-sandwich complex was first prepared by the wondensation of V and C6H6 in an Ar matrix at cryogenic temperatures.',2 It was characterized by electronic absorption (UV-vis), electron paramagnetic resonance (EPR), and infrared (IR) ~pectroscopies.~JIts electronic structure was first computed by the scattered-wave self-consistent-field (SW-SCF) method and the X a appro xi ma ti or^.^^^ The V
-3.00
tr C
u1 Q)
.-> +a
-m0
h
%
W
-3.25
a -2.50
21
? Q)
C
W
-3.5c Q)
.-+>
-m
I
-1 0
-3.00
I
10
Figure 4. Relative energies of the ground state (C6H6)V2molecule of c, symmetry as a function of the hydrogen angle (degrees) from the plane of the carbons. The bending angle is defined to be positive when the H atoms are bent towards the V,, and negative when they are bent away from the V2.
0)
a
-3.5c 1.55
I
0 Angle
1-65
R(V-V)
1.75
A
Figure 3. Relative energies of the three lowest states of the (C6H,)V2 molecule of C, symmetry as a function of the V-V distance. The relative energies, contraction scheme and labeling of the electronic states are the same as those of Figure 2.
(b) Donation and Back-Donation Mechanisms. To describe the donation and back-donation mechanisms in these complexes the benzene and divanadium fractions were also computed separately. Their atomic coordinates were the same as those found for the optimal geometry of the complex. The same symmetry-adapted basis sets were used when computing the fractions and the complex. The Mulliken population analyses of the complex, benzene, and divanadium were then also computed. Gross atomic and orbital population analyses of the organometallic complex are given in Tables I1 and 111. From the population analyses one can determine the amount electronic charge that is transferred from one fraction to another upon complex formation. However, because the Mulliken scheme of analysis is not unique and depends on how well balanced the basis set is, the amounts of electrons
transferred should only be regarded as qualitative.” Figure 5 shows the one-electron molecular orbital diagrams of benzene on the left, ($-C,&)V2 in the middle, and on the right. The 4el, and 4a2, molecular orbitals of the C6Hsfraction represent the filled 2p,(C) atomic orbitals that are capable of interaction with the divanadium 3d orbitals. T h e 4e,, HOMO of benzene correlates with the r gand r , orbitals of the divanadium. The 4elg and 3r, orbitals interact to form the 8el doubly degenerate orbital of the complex. The population analysis for this orbital shows that it is 21.5% vanadium in character. This is illustrated in Figure 6a by the contour diagram in the xz plane. I t shows the bonding combination between the 3d,,(V,), 2p,(C3), and 2p,(C7) that leads to the formation of the C-V q bonds. In addition, the 3 d r bond of the 8e1, formed by the in-phase combination of the 3d,,(Vl) and 3d,,(V2), is characteristic of the 3 r , orbital of the divanadium fraction. As shown in Figure 5, this interaction stabilizes the original 4e,, orbital by 0.97 eV. T h e counterpart of the 8el is
v2
(16) Dunlap, B. 1. Ado. Chem. Phys. 1987, 69, 287. (17) Szabo, A.; Ostlund, N. S. Modern Quonrum Chemistry; Macmillan: New York, 1982; pp 203-204.
1614 The Journal ofphysical Chemistry, Vol. 96, No. 4, 1992 0.0 %I
=
-1 .o
Mattar and Brewer X -
I
-2.0 -3.0
2
-4.0
P
-5.0
\
4
-8.0
-7.0 -8.0
-9.0
-10.0
Figure 5. The spin-restricted one-electron molecular orbital energy diagram for the C6H6, c6, (C6H6)V2,and V, molecules. The spin-restricted results are only used for illustrativepurposes. Spin-polarized results are used for all the population analyses of the (C&)V,, C6H6,and V, molecules.
the gel. It is 89% vanadium in character and the antibonding combinations between the 3d,,(V1), 2p,(C3), and 2p,(C,) destabilize it slightly with respect to the original 3s,(V,). The benzene 4a2, orbital can only interact with the divanadium u, or u, orbitals. The 14al orbital is essentially the 4a2, orbital that has gained 0.2 electrons from a g-type spd hybrid orbital of the divanadium fraction. This interaction is weak and only stabilizes the original 4a2, orbital by 0.32 eV. Just as the benzene ring gives up some of its 2p,(C) a electrons to form the V-C bonds, the V2 molecule must also give up some of its 10 V-V bond electrons to form the new C-V 7 bonds. The main back-donation pathway arises from the interaction of the filled 16, and the empty 4e2, orbitals of the vz and C6H6 components. Figure 5 and the population analysis show that the 4e2 orbital, that was originally 100% 16,(V2), has now gained 18.33% 2p,(C) character from the empty 4e2, orbital. The 4ez contour diagram in the xz plane (Figure 6b), illustrates the in-phase combinations of the 2p,(C3) and 2p,(C7) orbitals with the 3d,2-,,2(Vl) to form two of the C-V q bonds. The plot also shows the 6 bond formed between the 3d+2 vanadium orbitals. In Figure 5 the 4e2 orbital of the (s6-C6H6)V2molecule is totally filled while the 16al is empty. Thus, upon complex formation, the V2 fraction of the complex gains some &bond character at the expense of the u bonds. The population analysis shows that the molecule has 3.26 electrons that are 3d(V) and transform according to the e, irreducible representation. If one assumes that the original V2 fraction had a 32; ground state7 then this implies that approximately 1.26 electrons have been transferred from the u orbitals to the 6 orbitals during formation of the complex. The population analysis also shows that that total amount of 4s(V) electrons is only 0.66, indicating that most of the lost electronic charge originates from the 4s vanadium electrons. The small V-V distance (1.67 A) in the (q6-C6H6)V2complex is adequately explained as the result of the electron rearrangement during complex formation. The electrons that were in the original divanadium u, orbital, and possessed significant 4s(V) character, are moved to molecular orbitals and are predominantly 3d,(V) and the 3d+,z(V) in character. These orbitals are far more compact when compared with the diffuse 4s(V) resulting in a shorter V-V bond distance upon complex formation. Such a situation also occurs in the gas phase for V,. It was found experimentally that the bond length of the V, 311uexcited state is actually shorter by 0.07 A than the corresponding 3Z; ground
Figure 6. Wave function contour diagrams of c6, (C6H6)V2in the xz plane. Positive contours are indicated by a solid line and negative contours have dashed lines. Contour values are (1) 0.025, (2) 0.05, (3) 0.075, (4) 0.1 and (5) 0.125 (electrons/ao3)1/2.(a, top) The 8e,t molecular orbital. (b, bottom) The 4e2' molecular orbital.
state. This was also explained as a result of the increased 3d character in the metal-metal bond at the expense of its 4s character. Examination of Figure 5 shows that there is a possibility of donation of charge from the 3e?, orbitals of free benzene to the 16, orbitals of V2. However, an inspection of that orbital indicates that it is mainly s(C) and s(H) in character and has too little 2p,(C) character to be an efficient electron donor. Andrews and Ozin have computed the electronic structure of this molecule using the spin-restricted X a and scattered wave approximation^.^ The ground state was found to be a quintet state, which contains four holes and does not obey Fermi-Dirac statistics.I6 The authors suggested that a variation in the V-V and V-C bond lengths or the atomic sphere sizes might help unravel the cause of the high spin multiplicity of this m o l e c ~ l e . ~ This high-spin state could be partially due to the use of the Xa approximation. It is known that this approximation predicts metal-metal bonds are too weak and long when compared to those computed using correlated potentials6 and those observed experimentally.*5~'8In this study, this problem has been avoided by considering the electron-electron exchange and correlation according to the method of Perdew and Zunger." In the present work the geometry of the (q6-C6H6)V2 of c , symmetry was optimized for the ground and two low-lying excited states using the spin-unrestricted version of the LDF-LCAO method. The optimization shows that this molecule, in its ground state, has relatively short V-V and long V-C bond distances when compared with those assumed by Andrews and Ozias The earlier V-V distance of 2.0 ASmay favor the V-C interactions at the expense of the V-V interactions. (18) Michalopulos, D. L.; Geusic, M. E.; Hansen, S.G.;Powers, D. E.; Smalley, R. E. J . Phys. Chem. 1982, 86,3914.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1615
Structure of (C6H6)V2Molecules
TABLE IV: Selected Vertical Excitation Energies and Corresponding Wavelengths for the molecular sym type polarizn transition x, Y u-0 c 6 u 9el l6a, 0-0 z 15a, l6a, z c6~ 4e2 5e2 8 8* forbidden c6" 9el 5e2 u 8* forbidden 15al 5e2 a-8' forbidden C2" 16al 6a2 u 8* c2u 8b2 18al Y u-u X c2u 8b2 6a2 u 8* c2u 6a2 15bl Y MLCT X cl8 l8al 15bl MLCT z c2u 15al l8al 77-u
---
----C
--
The vertical excitation energies using the Slater transition state methodlg are listed in Table IV. There are five transitions that occur in the visible region of the spectrum. All the orbitals involved in these transitions are a t least 85% vanadium in character. Consequently, they may be qualitatively classified as 3d(V)-3d(V) transitions. Our matrix isolation experiments involving the condensation of other ligands such as 1,4-difluorobenzene, 1,3,5trifluorobenzene, or 1,2,4,5-tetrafluorobenzenewith vanadium all produce (arene)V, complexes that have the same broad electronic absorption band around 700 nm.,O This strongly suggests that this band must be due to 3d(V)-3d(V) transition(s). Table IV shows that three of the d-d vanadium transitions span the range between 740 and 860 nm. Consequently all these transitions are possible candidates for the 700-nm band. However, without the explicit computation of oscillator strengths and Franck-Condon factors the assignment of the 700-nm band to a particular transition in Table IV should only be tentative. The (C6H6)V2Molecule Possessing C b Symmetry. (a) Geometry Oplimizationprocedure. The optimization of this molecule was done in a similar manner to that described earlier for the C,, molecule. A schematic diagram of the geometry and orientation of the molecule is shown in Figure lb. The initial V-V bond distance was chosen to be 2.00 A. Assuming a planar geometry for benzene, the V-V, C-C, and C-H distances were kept fixed, and the optimal distance between the Vz and the benzene plane was determined. This was followed by the optimization of the V-V distance, leaving the benzene-vanadium distance fixed at its determined optimum value. This whole process of optimization was repeated several times. The same procedure was also used to optimize the geometries of the low-lying excited states. The ground-state configuration was found to be 13b12,8b2, 6a2', 18al' and corresponds to a 3A2state. A plot of the total energy as a function of benzene-vanadium distance is given in Figure 7 while that of the corresponding vanadium-vanadium distance is given in Figure 8. Next the optimum angle of the hydrogen atoms with respect to the carbon plane was determined. The angle of the hydrogens of the first type, HI (numbered 4 and 11 in Figure lb) with respect to the carbon plane, was varied while all other parameters were kept fixed. Once an optimum angle was found, the angle of the second type of hydrogen atoms, H2 (numbered 5,12,13, and 14), was varied. The two types of hydrogen angles were further interactively optimized. The [4333/43/311] contraction scheme resulted in an H1 angle of -10 deg and an H2 angle of -4.5 deg. The optimum final ground-state geometry is given in Table I. Plots of the total energy as a function of the H1, H2 angles and the spin unrestricted molecular orbital diagram are given in Figures 9 and 10, respectively. (b) Donation and Back-Donation Mechanisms. For the C, case the correlation between the bonds of V2 and the (C6&,)V, complex is complicated by the fact that the V-V direction lies along the x instead of the z axis. In this orientation the ru(Vz)and 6 (V,) orbitals both split into a , and b2 pairs. Similarly the r,(Vzk and (19) Slater, J. C. Ado. Quantum Chem. 1970, 6, 1. (20) Mattar, S.;Howarth, D.; Unger, I. Manuscript in preparation. (21) Dunlap, B. I. Phys. Rev. A 1984, 29, 2902.
(C6H6)V1Complexes in Their Ground States E,, eV E,, cm-I wavelength, nm 11 601 862 1.44 1.54 12422 805 1.68 13510 740 2.86 23 036 434 3.04 24 643 406 1.13 9113 1097 1.29 10 404 96 1 1.43 11 533 867 1.54 12421 805 1.68 13549 738 2.01 16210 617
*
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al
.->
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1
- 2.75 ' 1.8
2.0 R(Bz-V)
2.2
2.4
A
Figure 7. Relative energies of the three lowest states of the (C&)V2 molecule of C, symmetry as a function of the benzene-V distance using the vanadium [4333/43/311] contraction scheme, and the carbon 621-G basis set. The energies are relative to -57 462 eV. Curves a, b, and c represent the (8b2, 13bl,6aZ1, 18a11),(8b2, 13b1,6a2, 18a10),and (8b2, 13bl, 6aZ0, 18a12)electronic configurations, respectively. In the region of 2.03-2.12 A the avoided crossing between states b and c has been drawn manually. The exact energies of these two states in this region may be obtained by solving a 2 X 2 eigenvalue problem.21
1.65
1.75
1.85
R(V-V)
1.95
A
Figure 8. Relative energies of the three lowest states of the (C6H6),v2 molecule of ClUsymmetry as a function of V-V distance. The relative energies, contraction scheme, and labeling of the electronic states are the same as those of Figure 7.
6,(V2) correlate with the a, and bl. Finally the u,(V,) becomes an a, while the u,(V2) becomes a b,. The one-electron molecular orbital diagram in Figure 11, in conjunction with the population analysis (Tables V and VI) and
Mattar and Brewer
1616 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 TABLE V Gross Atomic Orbital Populations for the C L (C6H6)V2Complex irreducible remesentation a2 b2 b, orbital UD down UD down UD down 0.500 0.500 0.500 0.500 0.495 0.496 0.035 0.034 1 .ooo 0.500 0.500 0.500 1.000 0.500 0.999 0.999 0.499 0.499 0.500 0.500 0.024 0.025 0.005 0.005 0.034 0.006 0.032 0.550 0.546 0.228 0.499 0.499 0.372 0.367 0.573 0.562 0.225 0.205 0.209 0.228 0.250 0.250 0.250 0.250 0.250 0.250 0.128 0.125 0.127 0.212 0.210 0.129 0.183 0.188 0.558 0.148 0.558 0.28 1 0.187 0.187 0.099 0.101 0.1 12 0.091 0.093 0.110 ~~~~~
~
-6 3
z
a,
total
UD
down
UD
0.500 0.500 0.492 0.453 1.000 0.988 0.128 1.332 0.499 0.340 0.496 0.250 0.199 0.506 0.197 0.083
0.500 0.500 0.492 0.129 1.000 0.988 0.045 1.246 0.499 0.344 0.510 0.250 0.199 0.494 0.197 0.085
1.ooo 1 .ooo 0.987 0.488 3.000 2.986 0.157 2.144 0.998 0.707 1.491 1.000 0.668 1.533 0.384 0.383
.
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I
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-
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.
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Figure 9. Relative energies of the ground state C , (C,H,)V, molecule as a function of the H angles from the plane of the carbons. A negative angle is defined as bent away from the divanadium. (a, top) Bending of the H4 and H I 1 atoms. (b, bottom) Bending of the H5, H12, H13, and H 15 atoms. ~~~. .. . ~
contour diagrams, shows that the benzene 4el, orbitals interact with those of the divanadium to form the 13bl and 7b2 orbitals of the complex. The resulting orbitals are stabilized by approx-
-10.0
*
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- Spin
-
0 Spin
4a = lsb, 14, Bb, 184 17a, 1%
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-
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down 1.000 1.ooo 0.988 0.163 3.000 2.986 0.075 1.830 0.998 0.716 1.517 1.000 0.661 1.383 0.384 0.391
154
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-
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-
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‘C6H6’ ‘C6HS’”* Ca v2 Figure 11. The spin-restricted molecular orbital energy diagram for the C6H6,(C,H,)V, with C2, symmetry, and V2 molecules.
Structure of (C6H6)V, Molecules
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1617
4
7 1 -0
/I
X -
I
P
I
I
x-
Figure 12. Wave function contour diagrams for the C, (C6H6)V,complex. The contours for plots a and c are in the xz plane, while those of plots b and d are defined by the origins of the V6, CBand C9 atoms. All contour values are the same as those in Figure 6. (a, left top) The 13bl' molecular orbital. (b, left middle) The 7b2fmolecular orbital. (c, left bottom) The 15alt molecular orbital. (d, right top) The 6a2t molecular orbital. (e, right bottom) Contour plot of the same orbital in an xy plane situated 0.5 au above the V-V moiety. It illustrates the 6, character of the V-V interactions.
TABLE VI: Gross Atomic Populations and Net Charge for the Ck (CJIAV, ComDlex ~
atom V c1 c2 H1 H2
UP
11.75 3.197 3.200 0.384 0.383
down 11.02 3.231 3.041 0.384 0.390
total
net charge
22.78 6.428 6.241 0.768 0.774
0.2244 -0.4280 -0.2408 0.3230 0.2265
imately 1.6 eV when compared to the original 4el,. The contour plot in Figure 12a represents the 13bl which has approximately 8% V2 character. It shows V-C bonds formed by the overlap of
the 2p,(C2) and 2p,(C7) with a V2 orbital that is a mixture of the original ng(V2),6,(V2), and u,(VJ bonds. The plot also illustrates the antibonding nature of the two vanadium centers with respect to one another. The V-C bonds of the 7b2 orbital are formed by interaction of the 2p, atomic orbitals of the carbon atoms numbered 3,8,9, and 10 to the vanadium 3d orbitals. This is best illustrated by the contour plot in the plane of the C8, C9, and v6 atoms (Figure 12b). The amount of vanadium character in the 13bl and 7b2 is the same. The benzene 4a2, orbital interacts with a vanadium spd hybrid and gains 13% vanadium character when forming the 13al molecular orbital. This is about 1.20 eV more stable than
Mattar and Brewer
1618 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
TABLE VII: Binding and Bond Dissociation Energies for (C6H6)V2 of C,,,.C6,.and D,* Svmmetries electronic bond dissocn' configurn sym De, eV Te, cm-I energy, eV 0.0 5.7091 4e,4 C, 73.6346 1.383 4e2, 16al' c6, 73.4610 5.5376 5.399 4e?, 16aI2 C, 72.9639 5.0390 C2a 73.1111 18a,', I6az1 0 5.1866 4.170 6a12 C2, 72.5941 4.6696 8.230 ]Sal2 C2, 72.0913 4.1662 0.0 -0.0246 4elp2 D6h 67.9005 (-1.0300) The bond dissociation energy represents the energy required to separate the molecule into V, and C6H6. In the case of the D,,+complex the value in parentheses is the energy required to separate the molecule into a benzene fragment and two vanadium atoms. (i
-7.0 4.0
.S.O
.
-10.0
-
-
%IS*
3e1,
H= %o*
%a*
ea,+
8a,+
the original 4a2,. The population analysis reveals that for the 13a,, 13bl, and 7b2 there is less than 1.0% difference in character between their CY and 0 spin components. The back-donation occurs from the filled V, orbitals and the empty r*-type orbitals of benzene. In the case of the 15al the 3d,,(V) orbitals, that form an already strong V-V a bond, are properly oriented to overlap with the 2p,(C) orbitals of 4e2,. This results in the back-donation of approximately 0.28 electrons. Two of the V-C bonds formed are shown in Figure 12c. The second component of the divanadium 3r, lies in the xy plane and its lobes are not well positioned to overlap with the 2p,(C) orbitals of the benzene. Consequently the 8b2 of (C&)V2 is predominantly vanadium in character and does not contribute to the bonding of the complex. The 16al, 17al, and 18al have approximately 9.0%, 4.0%, and 4.5% ligand character, respectively. The 16al represents a a bond formed by the interaction of the vanadium 3d,2+ while the 17a, is a 6 bond formed by the overlap of the 3d,2. The 18alt is mainly an in-phase combination of the 4s(V) orbitals that results in a V-V a-type bond. The contribution of these three orbitals to the ligand-metal bonding is very small. The 6a2' stems from the strong interaction of the divanadium 16, orbital and the empty 4e2, benzene orbital. Almost 50% of this orbital is metal in character. The resulting V-C bonds are apparent in Figure 12d. The 6, character of the V-V region can also be seen when this orbital is plotted in the xy plane, 0.5 au above the V-V moiety, shown in Figure 12e. The spin-allowed vertical excitation energies of this molecule in the region 1-2 eV have also been computed. They are listed in Table IV. The D 6 h (C&,)V2 Molecule. Due to the high D6h Symmetry of this complex the two vanadium atoms are always equidistant from the center of the C6H6 moiety. In addition, the hydrogen atoms always lie in the plane of the carbon ring. Thus only the distance between the vanadium atoms and the center of the benzene ring is optimized. This was found to be 1.67 A and the resulting optimal coordinates of the complex are listed in Table I. The ground-state electronic configuration of this complex is 3e,: 5elu42bIu2lb2,, 4e22. Both electrons 7a2,2 9alp' occupying the doubly degenerate 4e2, orbital are unpaired leading to the totally antisymmetric 3A2 state. The one-electron molecular orbital diagram for this compfex is depicted in Figure 13. As described in the next section, the bond dissociation energies between the benzene and the two vanadium atoms for this com-
pound is slightly negative. This implies that, in the gas phase, it would spontaneously breakdown into two V atoms and a benzene fragment. Bond Dissociation Energies and Binding Energies. One of the main goals of this work is to determine if the (C&)V, of c,,, D6,,, and c6, symmetries are stable molecules. These complexes might be stable thermodynamically but due to their high reactivity are very short lived. Although the total energies of the molecules as a function of their geometrical parameters all display energy minima some complexes might be metastable. In order to verify this their binding energies must be calculated. First, the total energies for the carbon, hydrogen, and vanadium atoms were computed using the same basis sets used in the computation of the (C6Hs)V2complexes. The binding energies of these molecules take the form
D, = Et0t[(C6~6)~21 - 6(Etot[C,1s2,2s2,2P21-tEtot[H,lsllJ 2Etot [Vp4F1 (1 ) The terms E,,, [C, ls2,2s2,2p2],E,,,[H, Is'], and E,,,(V,4F) denote the total energies of the C, H, and V atoms in their ground states. The E,,,(V,4F) term is estimated by the approximation method of Baykara and Salahub.' First the E,,,(V,6S), of the spherical 6S state with the 3dS configuration, is computed. E,,t(V,4F) is then estimated to be lower than E,,,(V,%) by the experimental value (2.498 eV) of the energy separation between the two states.22 This method, although approximate, avoids any inadequate correlation of the 4s2 shell in the 3d34s2atomic configuration or other complications arising from non-spherical atomic states.' The binding energy of the individual benzene and divanadium fractions were also computed separately. For benzene the binding energy is given by De = Etot[C6H6] - 6(Et,,[C,l~~,2~~,2p'] iE,,,[H,ls']J (2)
which gives 68.95 eV. If one considers the bond enthalpies of the aromatic C-C bond and C-H bonds to be 5 18 and 469 kJ/mol, re~pectively,~~ then the binding energy of benzene is estimated to be at least 61.39 eV. This indicates that the LDF-LCAO method overestimates the binding energy of benzene by approximately 10.9%. This is a reasonable result considering that the compact 6-21G basis set for carbon was used in the computation. The binding energy of divanadium was found to be 3.17 eV. The electronic configuration of the ground and low-lying excited states of the half-sandwich complexes are listed in Table VI1 along with the binding energies. The total energies were obtained by a separate set of S C F computations for each configuration. Table VI1 shows that for the C .and C, molecules all the lowest six configurations are stable and have positive dissociation energies. The benzeneV2 (Bz-V,) dissociation energies in this table are defined as (22) Moore, C. E. Atomic Energy Levels; Natl. Bur. Stand. (US.)Circular 467; 1949, Vol. I; 1952, Vol. 11. (23) Atkins, P. W . Physical Chemistry, 4th ed.; Freeman: New York, 1990; Table 2.7, p 938.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1619
Structure Of (c6H6)V~Molecules D,(Bz-V,) = Et0t[(C6H6)~21- (Elot[(C6H6);'Algl
+ E101[V~;3Z~1~ (3)
where Et,J(C6H6);1AI,] and E,[V,;'Z,] denote the total energy of the benzene and divanadium molecules in the ground electronic states, respectively. The Bz-V2 dissociation energies give a semiquantitative measure of the V-C bond strengths. Since these values range from 5.71 to 4.17 eV, we expect the V-C bonds to be strong and comparable to other arenevanadium organometallic complexes! Thus the main reason for the short lifetime of these complexes, when not isolated, is the reactivity of their V, moiety. In addition, the stability of the (C6H6)Vz isolated in argon matrices5 is not due to the matrix where V2 and benzene moieties are being held together by a matrix trapping site. In contrast the bond dissociation energy (V-Bz-V) for the DM (C&)V2 complex, defined as DJV-Bz-V) = Eiot[(C6H6)Vz] - { E ~ O ~ [ ( C ~ H ~ ) ; ~2Etot[V,4FII AI,] (4) is -1.03 eV. This indicates that the molecule is metastable and fragments into two vanadium atoms and a benzene molecule. The depth of the metastable potential well is 1.943 eV while the V-ring equilibrium distance is 1.67 A.
Conclusions In summary, the spin-polarized version of the LDF-LCAO method has been used to determine the electronic structure, op timal geometries, and ground states of the (C6H6)V2complexes of c6,, D6h, and C, symmetry. In all these complexes the orbitals of free benzene that share their electrons with the divanadium 3d orbitals are the 4el, and the 4az,. In the case of the C, complex, a major component of the stabilization energy stems from the interaction of the divanadium 16, with the empty benzene 4eh to form 4ez molecular orbital. The divanadium fraction in its 'Z - ground state has the electronic configuration 717 3r,4 l S x j l 6 , y ' . The Mulliken population analysis of C, (&H6)V2 complex in conjunction with its wave function contour plots suggest that the 16, orbital gains approximately 1.26 electrons a t the expense of the 7ug orbital. Thus some of the electrons that possessed significant 4s vanadium character have been transferred to the 16, orbital that is predominantly 3d, and 3d+ These 3d orbitals are quite contracted as compared with the diduse 4s(V) which lead to a shorter V-V bond. The C, (C&)V2 molecule is predicted to have a 'Az ground state. For complex formation, the benzene 4el, orbital interacts with a divanadium orbital that is a hybrid of the original antibonding 3r,, 16,, and 617, to form the 13bl and 7b2 molecular
.
orbitals. The benzene 4a2, orbital also gains some divanadium character when forming the 13al molecular orbital. The backdonation in this complex arises from two different pathways. The first is from one component of the filled divanadium 3*, to the empty benzene 4e2, resulting in the 15al orbital of the complex. The second is due to the interaction of the partially filled 16, with the benzene 4ez, to form the partially filled 6az. The lowest three configurations of each of the C,, and c6, complexes are stable and have positive dissociation energies. They range from 5.71 to 4.17 eV, indicating that the V-C bonds are strong and comparable to other arene-vanadium organometallic c ~ m p l e x e s . ~In contrast, the D6h complex is predicted to be metastable. Undoubtedly, the most reactive moieties of the three halfsandwich complexes studied are their vanadium centers. The terminal V atom of c6, complex and the other v centers of the C, and D6h complexes have 3d orbitals that are available for bond formation with other ligands. However, in the case of the D6h molecule its unstability indicates that the benzene ring cannot act as six C-H bridges between its two V atoms. This study has shown that the LDF-LCAO method provides a useful and reasonable molecular orbital picture for the bonding of the (C&)V, complexes. It would be interesting to see if this method could also be successful in clarifying the structure-bonding relationships of the larger (C6H6)zVz molecules. To get a better picture of the structure and bonding of organometallic fractions it is essential to optimize their geometry. The geometry optimization procedure used here, although accurate, is very tedious. Recent LDF-LCAO programs that have automatic geometry optimization procedure^^^^^^ will prove very useful in this respect.
Acknowledgment. We are very grateful to Dr.B. I. Dunlap for his help and for providing the original version of the LDFLCAO program. We would also like to thank Professor D. R. Salahub for his comments on the manuscript. We acknowledge and appreciate the constant interest and discussions of Professors G. A. Ozin and M. A. Andrews regarding this project. This work was made possible by the allocation of computer time by the University of New Brunswick Computer Center. S.M.M. thanks the Natural Sciences and Engineering Research Council and the University of New Brunswick Research Fund for their continued financial support. S.E.B. acknowledges the University of New Brunswick for a graduate research and teaching assistantship. Registry NO. (C6H6)Vzr 9961 7-97-7. (24) St-Amant, A.; Salahub, D.R. Chem. Phys. Lett. 1990, 169, 387. (25) Mintmire, J. W. Int. J . Quantum Chem. (Quantum Chem. Symp.) 1990, 24, 857.
