J. Phys. Chem. 1083, 87,3083-3088
3083
Spectroscoplc and Theoretlcal Studies of Binuclear Molybdenum(I I ) Carboxylates Mark C. Manning, Gary F. Holland, Donald E. Ellls,' and Wllllam C. Trogler' Department of Chemlshy, Northwestern Unlverslty, Evenston, Illlnols 6020 1 (Recelved: October 25, 1982; I n Flnal Form: December 17, 1982)
Electronic absorption spectra of Mo2(02CCFJ4and Mo2(02CH),have been measured at 10 K in inert matrices. Resulta are compared with previous studies of Mo2(02CCHJ4.Raman spectra of the three carboxylate complexes have been measured and assigned. Unlike Mo2ClE4or Re2ClE2resonance enhancement of the metal-metal stretch did not occur when the lowest energy absorption band was irradiated; preresonance enhancement of a carboxylate stretching vibration did occur. Certain aspects of the SCF-Xa-DVcalculations for Mo2(02CH), agree better with previous HF calculations than with SCF-Xa-SWresults. The sensitivity of the 7 ~separation * to metal-metal distance may explain these differences. Energies of both the singlet and triplet 6 6*, 6 r*, u 6*, and 6 r* (OCO) transitions have been calculated and compared with the optical spectra.
-
- -
-
Introduction Quadruply metal-metal bonded dimeric complexes of Re(III), Mo(II), Tc(III), and W(I1) generally exhibit a moderately intense electronic absorption in the visible spectral regime.' This has been attributed to the metal-localized transition u2~4626*07r*0u*0 a27r4616*'7r*0a*0.2 Dinuclear molybdenum(I1) carboxylates display a weak highly structured absorption at ca. 430 nm (23000 cm-') whose origin has been a subject for debate.= Dubicki and Martin3 first suggested an assignment to a dipole-forbidden transition from the &bonding orbital to a a-type nonbonding level. This suggestion was based on an analogy to the initial interpretationg of the Re2Cla2-spectrum, which was later corrected.'O Single-crystal spectra of a glycinate derivative later favored assignment to a dipoleforbidden transition of some other type.4 Polarized electronic absorption spectral studies of Mo2(02CH),also led to the conclusion that the 430-nm band must arise from a dipole-forbidden transition,6 and a 6 R* (bZg eg) assignment was suggested on the basis of Xa calculations.' Spectral studiesa of a family of carboxylate complexes favored the degenerate 6 K* proposition; however, it was necessary to postulate that the low molecular site symmetry in the crystal (1in the case of Mo2(02CCH3),)split the degenerate excited state. More recently the M o ~ ( O ~ C C crystal H ~ ) ~ spectrum was reexamined5 and it was noted that a 6 6* assignment for the 430-nm absorption may be feasible if the allowed oscillator strength is weak and if vibronic intensity contributions dominate the spectrum. Recently we reported" matrix isolation studies of M o ~ ( O ~ C Cwhich H ~ ) ~reveal that at least two excited states contribute to the 23 000-cm-' absorption band. Martin and co-workers12have also de-
-
-
- -
-
(1) Trogler, w. C.; Gray, H. B. Acc. Chem. Res. 1978,ll, 232-9. (2) Cowman, C. D.; Gray, H. B. J.Am. Chem. SOC.1973,95,8177-8. (3) Dubicki, L.;Martin, R. L. Aust. J. Chem. 1969,22,1571-81. (4)Cotton, F. A,; Martin, D. S.; Webb, T. R.; Peters, T. J. Inorg. Chem. 1976,15, 1199-201. (5)Martin, D. S.;Newman, R. A,; Fanwick, P. E. Inorg. Chem. 1979, 18,2511-20. (6) Cotton, F. A.; Martin, D. S.; Fanwick, P. E.; Peters, T. J.; Webb, T. R. J.Am. Chem. SOC. 1976,98,4681-2. (7) Norman, J. G.; Kolari, H. J. J. Chem. SOC.,Chem. Commun. 1975, 648-51. Norman, J. G., Jr.; Kolari, H. J.; Gray, H. B.; Trogler, W. C. Inorg. Chem. 1977,16,987-93. (8)Trcgler, W. C.; Solomon, E. I.; Trajberg, 1.;Ballhausen,C. J.; Gray, H.B.Inorg. Chem. 1977,16,828-36. (9)Cotton, F. A,; Harris, C. B. Inorg. Chem. 1967,6, 924-9. (10)M o h l a , A. P.;Moskowitz, J. W.; Rosch, N.; Cowman, C. D.; Gray, H. B. Chem. Phys. Lett. 1975,32,283-6. Norman, J. G.; Kolari, H. J. J. Am. Chem. SOC.1975,97,33-7. (11) Manning, M. C.; Trogler, W. C. Inorg. Chem. 1982,21,2797-800.
tected a second transition in the crystal spectrum of Mo2(02CCFJ4. In this paper we report low-temperature electronic spectra of matrix-isolated Mo2(02CH),and Mo2(02CCF3), in order to further probe the two-state hypothesis. In 6* addition, since resonance Raman effects for the 6 transition are quite distinctive for Mo2X84- (X = C1, Br) and Re2Xa2-(X = F, C1, Br, 1),13-15we examined the resonance behavior of M o ~ ( O ~ C R(R ) ~=, H, CH,, CF,). As a theoretical framework for the spectroscopic analyses, we performed both spin-restricted and spin-polarized SCFXa-DV calculations in order to estimate the singlet-triplet splittings of low-lying electronic excited states. The influence of the metal-metal separation upon orbital energies (especially the u--a splitting) was also examined.
-
Experimental Section Matrix Experiments. Optical spectra were recorded with a Cary 17D spectrophotometer, whose sample compartment was modified to accommodate the matrix apparatus previously described.'l Raman Spectra. The Raman apparatus consists of a Spex 1401double monochromator, a Spectra Physics argon or krypton ion laser, and detection optics and electronics. A back-scattering geometry was adopted. Resonance and polarization studies used concentrated methanol solutions of Mo2(02CCF3),.All samples were placed in sealed 5 mm diameter tubes which were rotated to avoid local sample heating. At the laser fluence employed, sample decomposition was not observed, as evidenced by the reproducibility of measurements on the same sample (f15%). Solid samples were powdered to minimize scattering and mixed with sodium sulfate as an internal standard. Low-temperature spectra (down to -105 "C) were obtained with a quartz Dewar and a liquid-nitrogen boil-off system. Exciting wavelengths of 6764, 5145, 4965, 4880, 4765, 4658, and 4579 A were used in resonance Raman studies. The 4579-A line excited the low-energy side of the 430-nm (12) Martin, D. S.; Newman, R. A.; Fanwick, P. E. Inorg. Chem. 1982, 21,3400-6. (13)Clark, R. J. H.; Franks, M. L. J. Chem. SOC.,Chem. Commun. 1974,316-7. Clark, R.J. H.; Franks, M. L. J. Am. Chem. SOC.1975,97, 2691-7. (14)Clark, R. J. H.; D'Urso, N. R. J. Am. Chem. SOC.1978, 100, 3088-91. (15)Clark, R.J. H.; Franks, M. L. J.Am. Chem. SOC.1976,98,2763-7. Professor Clark has since extended his studies to Re2F:- and Re21,2-with similar results (personal communication). (16)Cotton, F. A.;Norman, J. G.; Stults,B. R.; Webb, J. R. J.Coord. Chem. 1976,5,217-23.
0022-3654/83/2087-3083$01.50/00 1983 American Chemical Society
3084
The Journal of Physical Chemistry, Vol. 87, No. 16, 1983
Manning et al.
TABLE 11: Comparison of Relative Energies (cm-l) of Vibronic Band Origins in Mo,(O,CCH,), and Mo,(O,CCF,), for Crystal and Ar Matrix Spectra Taken at 10 K origina
Mo 2( OZCCH3 14 crystal Ar matrix
A, BO CO
DO EO
CO
A1
61%
%
_______390
-410
._ 450nm
430
a See text for
Mo2(02CCF3)4
crystal Ar matrix
0
0
0
175 27 5 320 545 380
- 280 280 330 550 390
130 260
0 -250 270
500 370
500 370
explanation of labels.
Figure 1. Electronic absorption spectrum of Mo2(02CCF,), diluted 1:600 in a nitrogen matrix and supported on a sapphire substrate at 10 K. The rise in the lower energy pottiin of the base line is caused by interference properties of the thin sample film. Spectral resolution is 0.10 nm.
,
TABLE I : Energies (cm-l)of Band Origins for Mo,( 0,CCF3), Isolated in Matrices at 1 0 K Bo A, B, C, A,
E, C,
Bo A, 3 1
c,
A1
EO Cl
crystala
Ar
N2
Kr
22020 22060
22180 22450 22560 22720 22820 22950 23080
22170 22420 22550 22690 22790 22920 23060
22 430 22 700 22 700 22 790 22 940 23 060
Energies Relative to A, - 270 -250 0 0 110 130
0 100
c
22330 22430 22570 22690 160 0 270 370 510 630
Taken from ref 12. coincidentally with E,. a
b
270 370 500 630
270 370 500
640
Not clearly observed.
270 360 510 630
410
-
i
430
-__--_I__-
450nm
Figure 2. Electronic absorption spectrum of polycrystalline Mo,(O,CCF,), on a quartz flat at 15 K, recorded with an instrumental resolution of 0.03 nm.
-
Wl
Occurs
absorption for solid and solution samples of M O ~ ( O ~ C R ) ~ , (R = H, CH3, and CF,). I Materials. Tetrakis(~-acetato)-,~ formato-," and (triI fluoroacetato)dimolybdenum(II)l' were prepared by lit45 410 0 430 nm erature methods. Methanol (Mallinkrodt reagent grade) Figure 3. Electronic absorption spectrum of Mo2(02CH), isolated in was vacuum distilled into the sample tubes after three an argon matrix at 1:700 dilution on a sapphire substrate at 10 K. freeze-pump-thaw cycles. Spectral resolution is 0.15 nm.
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Results and Discussion Electronic Spectra. The electronic absorption spectrum of M O ~ ( O ~ C CinFan ~ )argon ~ matrix (Figure 1 and Table I) closely resembles that of M O ~ ( O ~ C C Origins H ~ ) ~ A,, Co, and E, are separated by similar energies (Table 11) as found in the acetate complex; however, origin Bo shows greater variability and a sensitivity to matrix environment (Table I and supplementary tables; see paragraph at end of the text regarding supplementary material). As for M O ~ ( O ~ C C we H ~assign ) ~ , Boto an electronic state different from that yielding the A,, Co, and Eo origins. Each origin in the trifluoroacetate complex displays a progression in the totally symmetric metal-metal stretch of -360 cm-'. This value is about 30 cm-l smaller than in the acetate complex and about 10 cm-l smaller than in crystalline Mo2(02CCF3),(Figure 2). The lower Mo-Mo progressional frequency would obscure a weak D progression (observed in the acetate com(17)Cotton, F. A,; Norman, J. G . J. Coord. Chem. 1971,I, 161-72.
plex) of 330 cm-l, either by direct overlap or by stronger coupling between al,(M+Mo) and ( M A ) vibrations. By analogy to the acetate complex, the Ao-Co and Ao-Eo spacings are assigned to a nontotally symmetric molybdenum-oxygen stretch and to a carboxylate bend or rock, respectively. On the other hand, the absorption spectrum of Moz(02CH), is markedly different from the acetate and trifluoroacetate spectra (see Figure 3). It exhibits a single, broad progression of 380 cm-l in the matrix. Even the single-crystal spectrum displays much less fine structure than the corresponding acetate and trifluoroacetate compounds.6*8As in the other carboxylate cases, a low-energy feature, Bo,is still present; however, here it is spaced -390 cm-' below &, almost exactly the progressional frequency (see Table 111). We surmise that the &-Bl separation is therefore quite small (-20-30 cm-l), which facilitates strong vibronic coupling between the two electronic states. This mixing may be sufficient to prohibit the &-Bo spacing to vary as widely as in the previously mentioned
The Journal of Physical Chemistty, Vol. 87, No. 16, 1983 3085
Binuclear Molybdenum(II ) Carboxylates
TABLE 111: Vibronic Details for the Lowest Energy (cm-') Electronic Absorption Band of Mo,(O,CH), in Argon and Nitrogen Matrices at 10 K and in the Solid State" argon nitrogen crystal peak energy AE energy AE peak energy AE 22 720 -390 22 550 0 22 940 23 110 23 490 380 23 320 AI 23 710 23 880 (390) A2 24 100 A3 24 240 (360) 24 480 24 630 (390) A4 24 880 25 010 (380) A, " Energies in parentheses are spacings from the previous member
- 390
Bo
21 868 21 892 21 995 22 231 22 259
A0
0
A0
A,' BO
380 (390) (390) (380) (400)
62:.
0 24 127 (363) (367)
in the progression. Otherwise they are relative to A,.
A
1 *
I
i,
I
u & # M w Q , l IS**
$0.'.
Ils.'I
186')
Sad8 """CW"
111'1
0.03) and is also alg in symmetry as is the strong car~~
(18) Bratton, W. K.;Cotton, F. A,; DeBeau, W.; Walton, R. A. J. Coord. Chem. 1971, I, 121-31. (19) Heyns, A. M. J. Mol. Struct. 1972,11,93-103.
~~
(20) Herzberg, G. "Molecular Spectra and Molecular Structure. 11. Infrared and Raman Spectra of Polyatomic Molecules";Van NostrandReinhold Co.: New York, 1945; pp 269-71.
The Journal of Physical Chemistry, Vol. 87, No. 16, 1983
3086
Manning et al.
, I
~
--_I
I
5:'
I
1
\
h
n-,
I
--LtbMLd lL%wvk * - udw e*', ' w'bw -
t w t
sm.
/.z
* l o 6
I*'*
LIS
cas*
% a * ' ,*
C Y "i
t,,
16.
L e *
~ I * (
> P I C
I
S
L I I
1 1
Figure 6. Raman spectrum of a concentrated methanol solution of Mo,(O,CCF,),, taken with polarizers parallel and perpendicular to the polarizatlon of the laser. Excltatlon was at 4880 A and instrumental resolution was 2 cm-'.
boxylate vibration at 1460 cm-' ( p = 0.40). Previous work on Mo2Xs4-(X = C1, Br) and Re2X2- (X = F, C1, Br, 1)13-15 demonstrated that excitation into the lowest energy transition, assigned as dipole-allowed 6 6*,2 results in distinctive resonance Raman effects. The metal-metal stretch displays numerous overtone vibrations upon resonance excitation with more than a 10-fold increase in intensity of the fundamental. Since the effect is so dramatic, we examined the resonance Raman behavior of M o ~ ( O ~ C C HM~O ) ~~,( O ~ C Hand ) ~ ,Mo2(02CCFJ4. Initial studies of the aforementioned carboxylates in the solid state revealed a slight decrease in Raman intensity on resonance excitation. Due to potential problems of differential scattering by the colored complexes and the transparent internal standard (Na2S04),we examined Mo2(02CCFJ4in methanol solution. No (f15%) resonance enhancement of any low-energy Mo-Mo or Mo-0 modes was found; however, there was an approximately fivefold intensity increase of the 1450-cm-' Raman band. As mentioned above this is the symmetric carboxylate stretching vibration. Although this behavior is inconsistent 6* assignment for the lowest energy with a simple 6 transition in molybdenum(I1) carboxylates, a number of factors complicate the interpretation. The presence of a second electronic state may lead to interference effectsz1-= which fortuitously cancel resonance enhancement. In addition, the weak oscillator strength of the 430-nm absorption, relative to the 6 6* absorption in the halide compounds, may serve to attenuate resonance enhancement of the metal-metal stretch to the point where it cannot be detected. The origin of the resonance enhancement of the carboxylate modes is not clear, but preresonance effects associated with the intense ultraviolet
-
+
-
(21) Albrecht, A. C. J. Chem. Phys. 1961,34, 1476-84. (22) Friedman, J.; Hochstrasser, R. M. Chem. Phys. Lett. 1975, 32, 414-9. (23) Spiro, T. G.; Stein, P. Annu. Reu. Phys. Chem. 1977,28, 501-21.
A
B
C
D
E
Figure 7. Energy-level diagram for the ground state of Mo,(O,CH), (idealized D,,, symmetry) as calculated by the Xa-DV method: (A) SCC-Xa-DV; (B) I = 0 least-squares potentlal; (C) I = 0 least-squares potential plus parabolic correction functions; (D) I d 1 least-squares potential plus correction functions; (E) i < 2 least-squares potential plus correctlon functions.
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bands may be responsible. In this context, we note that an assignment of 6 carboxylate x* has been proposed' for the transition observed at 300 nm. Theoretical Considerations. Matrix isolation experiments have established that two distinct electronic transitions contribute to the 430-nm band system in the three binuclear molybdenum(I1) carboxylates. The spectra are consistent with the previous assignments that & is a pure electronic origin? Do is alg molybdenum oxygen in character, and Co and Eoare nontotally symmetric vibronic c ~ m p o n e n t s . Origin ~ ~ ~ Bo is derived from a different electronic state, which may be a triplet, based upon the matrix-dependent intensity variation found in the acetate complex." A t this point a reliable, quantitative energy diagram based upon theory would be most useful. Unfortunately, none exists despite great computational eff ~ r t . ~For ~ example, ' ~ ~ ~ the magnitude of the n-x orbital splitting continues to be contr~versial.~~ Higher order perturbations such as configuration interaction, multiplet, and relativisitic effects are yet to be fully included. These factors appear to be of appreciable magnitude.26 We performed SCF-Xa-DV calculations to address one of these problems, primarily that concerning multiplet splittings. First, however, a consistent ground-state picture (24) (a) Benard, M. J. Chem. Phys. 1979, 71, 2546-56. (b) Norman, J. G., Jr.; Ryan, P. B. J. Comput. Chem. 1980,1,59-63. (c) Benard, M. J. Am. Chem. SOC.1978,100, 2354-62. (d) Guest, M. F.; Hillier, I. H.; Gamer, C. D. Chem. Phys. Lett. 1977,48,587-9. (e) Benard, M.; Veillard, Dick, B.; Hohlneicher, A. N o w . J.Chim. 1977,1,97-9. (0Freund, H.-J.; G. Theor. Chim. Acta 1980,57,181-207. (g) Guest, M. F.; Garner, C. D.; Hillier, I. H.; Walton, I. B. J. Chem. Soc., Faraday Trans. 2 1979, 75, 2092-8. (25) Cotton, F. A.; Walton, R. A. "Multiple Bonds Between Metal Atoms"; Wiley: New York, 1982. (26) Hay, P. J. J. Am. Chem. SOC.1978, 100, 2897-8.
The Journal of Physical Chemistry, Vol. 87, No. 16, 1983 3087
Binuclear Molybdenum(1I) Carboxylates
TABLE IV Atomic Populations for the Mo,(02CH), Calculation ( I < 2) Mo 4 s Z 0 2 4p5.59 4d4.49 t&0.31 5p0.18 5dO.08 0 ~2~1.74~2~4.54L&-O,O2 CJp-O.03 c 2si.i7 2 p a ~ 3so.05 ~ 3p0.~ H is13 Volume Charges Mol.73 t
00.70 -
0
Be,
-
6e0
-n*
2a
6p0.W
esO.W
-1
29
6eg
-n*
2b
-6+
29
2b l u - s *
-2
TABLE V: Atomic Character of t h e Frontier Orbitals from t h e SCF-Xu-DV Calculation of Mo,(O,CH), That Included Terms through 1 = 2 in the Least-Squares Expansion of the Electron Density
-
2a
H0.47 -
Cl.00'
6eu
:U
-3
~~
orbital 2 a19
energy, eV
Mo 44 %
-0.702 -1.107 -1.134 92 6eg(r*) -2.128 80 2 blu(6*) -4.543 77 2 b,g(6) -5.518 70 7 a,g(a)a 7 eu(.) -5.763 72 1 a1u -6.563 -6.741 2 5 eg -7.028 4 eg -7.121 1 5 a1u 3 b2u -7.139 6 6 eu -7.426b 16 a Also a 10% Mo 5s contribution. contribution. 8 eu
Mo 5p, %
-4
0 ZP, %
47 48 3 20
C 2p, %
-5
21
-I
7alq-
10
7eu
23
e p , l a lU
100
7a1.,-7e;
-n
-
2a
:
5e
96 99 2 92 90 3 58 Also a 15% H 1s
(27)Ellis, D. E.; Rosen, A.; Adachi, H.; Averill, F. W. J.Chem. Phys. 1976,65, 3629-34. (28)Delley, B.;Ellis, D. E. J. Chem. Phys. 1982, 76, 1949-60. (29)Green, J. C.; Hayes, A. J. Chem. Phys. Lett. 1976, 31, 306-8. (30)Coleman, A. W.; Green, J. C.; Hayes, A. J.; Seddon, E. A.; Lloyd, D. R.; Niwa, Y. J. Chem. SOC.,Dalton Trans. 1979, 1057-64.
29
2b 29- 6
53 48
had to be achieved. Five separate calculations were generated, each introducing further improvements upon the previous model (see Figure 7). Result A is for a SCCXa-DV calculation which uses numerical atomic-like wave functions as variational basis functions and approximates the charge density as a sum of overlapping atomic charge d e n s i t i e ~ . ~A~Mulliken population analysis is used to determine the expansion coefficients. An improvement upon this approximate potential is to perform a leastsquares expansion of the electron density with 1 = 0 (s), 1 4 1 (p or dipolar corrections included), 1 < 2 (d or quadrupolm corrections included) (see Figure 7). Parabolic functions not centered on the nuclei can be added to provide more accuracy in the potential fit. The numerical atomic orbital basis set was optimized for the atomic charges found in the complex (Table IV). Details of the computational procedure are found elsewhere.28 Figure 7 demonstrates the influence of these refinements on the energy-level scheme. While the calculated IP for the 6(2bz,) orbital is overestimated by 2.0 eV by the SCC calculation, the calculated I P of 7.25 eV from l < l and l < 2 results agrees quite well with experiment (7.6 eV). Below the 6 level, the DV-Xa scheme predicts the u (7alg)and H (7eJ orbitals to be almost isoenergetic (spacing 0.05-0.20 eV), and about -1.5 eV more stable than the 6(2b,) orbital (Table V). This calculated ~ - u , Hsplitting is consistent with the 1.7-eV gap between the first two bands in the photoelectron spectrum. Whether the higher energy band (B) is due to both the u and T orbitals or just the H electrons has been a point of contention. Early work by Green et al.29930leads to the formulation that band B
6-2b
2b - 6
2
l a ? =,
-7
-I
1.99 A
2.09 A
2.19 A
-I
Flgure 8. Energy-level diagram (I 6 1 least-squares potential plus correction functions) for Mo,(O,CH), at the equilibrium metal-metal distance (2.09 A), at an expanded dlstance (2.19 A), and at a compressed distance (1.99 A). Ligand geometry was held constant.
arises from only the H ionizations, and the u orbital could be placed -1.5 eV higher. This was supported by SCFXa-SW calculation^.'^^^ The Manchester group has performed ab initio calculation^,^^-^^ generating an orbital framework similar to ours, with the u orbital lying just barely above H. Other Hartree-Fock calculations also suggest a small u-H splitting.24 Ordering of the virtual states remains constant in all the calculations. We calculate that the lowest unoccupied MO is the 2bl, (a*) level, being -2.5 eV above the HOMO. SCF-Xa-SW methods gave a less reasonable estimation of the 6 6* gap at 1.0-1.5 eV.7v31Next lowest among the calculated excited electronic states are 6 to metal H* (6e ) and 6 to carboxylate A* (8e,). The 6(2b,) 8e, (lA, 4E,) charge-transfer transition is fully allowed and probably accounts for the fEst intense UV band at 300 nm. Overlap considerations were deemed by us to be crucial in understanding the complicated electronic structure of quadruply bonded compounds. To this end calculations were performed to investigate the sensitive relationship between metal-metal distance and ground-state orbital energies. Employing a fixed ligand geometry, separate calculations (at 1 4 1) were done for molybdenum-mo-
-
-
-
-
(31)Cotton, F. A.; Stanley, G. G. Inorg. Chem. 1977, 16, 2668-71. (32)Hillier, I. H.; Garner, C. D.; Mitcheson, G. R.; Guest, M. F. J. Chem. Soc., Chem. Commun. 1978, 204-5. (33)Guest, M. F.;Garner, C. D.; Hillier, I. H.; Walton, I. B. J. Chem. SOC.,Faraday, Trans. 2 1978, 74, 2092-8. (34)Hillier, I. H. Pure Appl. Chem. 1979, 51, 2183-95. (35)Berry, M.; Garner, C. D.; Hillier, I. H.; MacDowell, A. A.; Walton, I. B. Chem. Phys. Lett. 1980, 70, 35C-2.
3088
The Journal of Physical Chemistry, Vol. 87,No. 16, 1983
TABLE VI: Transition-State Energies and Corresponding Multiplet Splitting5 as Calculated by the SCF-Xa-DV Method for Mo,(O,CH), transition 6 +6*(2bZg+2b,,) 6 -+ II* (2b,, + 6eg) u 6* (7atg+ 2b,,) +
6 a
+
~*0~0(2+ b ,8e,) ~
singlet, cm-'
triplet, cm-I A , cm-' ~
21900 28400 34000 29 500
17700 23900 29000 28 200
4200 4500 5000 1300
A = Esinglet - Etriplet.
Manning et al.
ference between HF and X a theory in that the latter approach is based on the electron density and not the LCAO wave function. As Slater has pointed H2 will correctly dissociate to two neutral H atoms in the Xa description. It is possible that part of the underestimation of the 6 6* transition energy by SCF-Xa-SW theory may arise from deficiencies in the truncated Muffin Tin potential rather than from correlation effects. In this context, we note that SCF-Xa-SW calculations do predict3' the correct ground state for Cr2(02CH)4.2H20 while the ionic-covalent correlation problem in the HF approach is so severe as to lead to an entirely incorrect description of the ground ~ t a t e . ~ " Further ,~~ Xa calculations which incorporate both an accurate potential and electron correlation would be necessary to test this point. What are the possible assignments for the second weaker B progression? It is clear from the spin-polarized calculations (Table VI) that it cannot be the triplet component41 of 6 6*. The next logical candidates on energetic grounds are 6 7r* or a 6*. Both excited states are of identical symmetry (E,) and should be spectroscopically indistinguishable. Our calculations suggest that 6 a* lies slightly lower (2000 cm-') in energy than a 6*. One possible assignment would attribute B to the dipole-fora* (IA1, 'E,) transition. A second weak bidden 6 absorption feature near 360-370 nm (27 000-27 800 cm-') may be the corresponding a 6* (lA1, 'E ) feature. An alterriative assignment would ascribe B to t i e triplet 6 a* excitation and the 360-370-nm component to the singlet 6 a* process. Both of the above possibilities are energetically reasonable; however, it should be noted that triplet 6 a* is both spin and dipole forbidden. The oscillator strength of the main 6 6* absorption in M o ~ ( O ~ C C has F ~ )been ~ found8 to be Therefore, component B will have an oscillator strength in the 10-4-10-5range, perhaps too intense to be triplet 6 a*. The singlet 6 A* (OCO) charge-transfer transition ('Alg IEJ is calculated to occur at 340 nm (29500 cm-'). An intense charge-transfer absorption is actually observed7in the spectrum of Mo2(02CH),at slightly higher energy 300 nm (33500 cm-'). Because the singlet-triplet splitting we calculate for this transition is small, this triplet component is not a reasonable candidate for feature B.
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lybdenum distances uniformly compressed and expanded by 0.1 A. These are compared to the equilibrium (Mo-Mo: 2.09 A) situation in Figure 8. One result is most striking: the placement of the metal localized a orbitals, both bonding and antibonding, is extremely sensitive to distance. As the metal-metal distance increases, the a bonding weakens rapidly, as shown by the destabilization of the bonding level and the severely decreased a-a* energy gap. The 6 bond suffers the same fate, but to a much smaller extent. Metal-metal u bonding appears to get stronger at the longer distance (7algbecomes -0.2 eV more stable). This sensitivity of orbital energies to relatively small perturbations may partially explain the discrepancy among the various theoretical predictions of the photoelectron spectra. A reason for the dependence of the u-a splitting on calculation type may be inferred from computations shown in Figure 8. As the Mo-Mo distance decreases, there is a marked increase in the *-a* separation. It is possible that u overlap between the two metals may be near maximum such that a further decrease in bond length leads to destructive interference%between the u-d2 orbitals. At this point A overlap has not yet maximized and should increase dramatically as the bond length decreases. The 6 overlap, which is very weak, should not vary as sharply (see Figure 4 of ref 36). Transition-state calculations (both spin restricted and spin polarized) were conducted on four one-electron transitions: 6 6*, 6 a*,6 a*oco,and u 6* (Table VI). The first three are predicted to be the lowest oneelectron excitations, while u 6* was considered since it might exhibit large relaxation effects. One clear feature Acknowledgment. We thank the National Science is the larger singlet-triplet splitting (4000-5000 cm-') exFoundation for financial support of the Chemistry Depected for metal-localized transitions compared to the partment's computer facility (CHE-8108990). metal to ligand charge-transfer process (1300 cm-'). The calculated 6 6* singlet energy is very close to the Registry No. Mo2(O2CCF3),, 36608-07-8; Mo2(02CH),, experimental value. This offers further support for the 51329-49-8;M02(02CCH3)4, 14221-06-8. tentative assignmentgof the main absorption band to 6 Supplementary Material Available: Figures of the 6* ('Al, 'Aa). There has been speculation'J' concerning room-temperature Raman spectra of M o ~ ( O ~ C C F ~ ) ~ , the underestimation of the 6 6* transition energy. For M O ~ ( O ~ C H and ) ~ , M o ~ ( O ~ C C and H ~ )tables ~ of vibronic calculations of weakly coupled systems, it is well-known details in the electronic absorption spectra of Mo2(02CCthat an MO wave function overestimates the ionic charF3)4in methyl bromide, krypton, argon, and nitrogen acter of the ground state and underestimates the ionic matrices at 10 K (7 pages). Ordering information is given character of the antibonding excited state. Thus, on any current masthead page. ground-state H2 dissociates to H+ and H-in the HartreeFock description. While it has been suggested that SCFJ. C. 'The Self-Consistent-Field for Molecules and Solids: Xa-SW calculations suffer from a similar d e f i ~ i e n c y , ' . ~ ~ , ~Quantum ~ (39) Slater, Theory of Molecules and Solids"; McGraw-Hill: New York, this may be only partly true. There is an essential dif1974; p 83.
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(36) Trogler, W. C. J. Chem. Educ. 1980,57, 424-7. (37) Cotton, F. A. Pure Appl. Chem. 1980,52, 2321-37. (38) Noodleman, L.; Norman, J. G., Jr. J . Chem. Phys. 1979, 70, 4903-7.
(40) Garner, C. D.; Hillier, I. H.; Guest, M. F.; Green, J. C.; Coleman, A. W. Chem. Phys. Lett. 1976,41, 91-3. (41) Incorporation of configuration interaction for 6 61 would lead to a lower triplet energy and higher singlet energy (see ref 26). Therefore, our results rule out the triplet 6 6* assignment with a fair degree of certainty.
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