. I . Phys. Chem. 1994, 98, 13243-13248
13243
Singlet- Triplet Splittings in Carboranylcarbenes and Carboranylnitrenes. A Theoretical Study Michael L. McKee Department of Chemistry, Aubum University, Auburn, Alabama 36849 Received: August 9, 1994@
Ab initio calculations have been carried out on the o-carborane cage (1,2-C2B10H1~)with a carbene (-CH) or nitrene (-N) substituent at the 1-,3-, or 9-position. When the carbene or nitrene is attached to the 1-position (carbon vertex), the singlet carbene is stabilized relative to the triplet. In contrast, when attached to the 3or 9-position (boron vertex), the triplet is stabilized. Except for l-CH-l,2-C2Bl,& (where the singlettriplet splitting is small), all carboranylcarbenes and carboranylnitrenes considered have triplet ground states. The lowest-energy singlet state of the carboranylnitrene is the open-shell singlet when nitrogen is attached to the 3- or 9-position and closed-shell singlet when attached to the 1-position. All carboranylcarbenes are predicted to be bent (singlets, 108-1 14";triplets, 129-140"). However, the triplet inversion stationary structure is nearly linear (179-180") and, for substitution at the 3- or 9-position, only 1.0 kcal/mol higher than the triplet minimum.
Introduction In contrast to phenyl~arbenel-~ and phenylnitrene?-1° which have been extensively studied, the related species with carboranyl replacing phenyl, ~arboranylcarbene~,' and carboranylnitrene,z2 have received much less attention. Phenyl and carboranyl groups are both aromatic and share similar chemical and physical properties.19 Jones19 and others23have noted the similarity of benzene to o-carborane as well as 1,2-dehydrobenzene to 1,2-dehydro-o-carborane. The ground state of phenylcarbene is a triplet," but addition to olefins is stereospecific,' indicating that reactivity is dominated by the singlet state. Carboranylcarbene (1-CH-1,2C2B10H11) is also known to have a triplet ground state," but as Jones and co-workers have shown in a number of s t u d i e ~ , ' ~ - ' ~ J ~ the singlet state is much more reactive. Recently, Jones and co-workers16-18have synthesized a carboranylcarbene with the carbene center attached to a boron vertex (3-CH- 1,2-C2B10Hll) rather than to carbon (1-position). For these carbenes, the triplet states show enhanced reactivity as judged by an increase of products due to hydrogen abstraction. The authors reasoned18 that the triplet would be stabilized by attachment to a boron vertex compared to a carbon vertex. The singlet state is stabilized by substituents that can donate electrons into the empty p orbital or accept electrons from the filled p orbital on the carbene carbon. On the other hand, electropositive substituents should stabilize the triplet state through electron donation into the u system.24 Thus, in HCBHz, the singlet state is stabilized by conjugation with the empty orbital on boron while the triplet state is stabilized by the electropositive nature of boron. Theoretical calculations predict the singlet to be the ground state by about 6 kcal/m01,~~ which emphasizes the importance of conjugation with the empty p orbital on boron. When a carbene is attached to a carborane cage, there is no clear orientation of the carbene which will allow conjugation with a filled or empty orbital since the cage is bound by a network of multicenter interactions. However, the site of attachment, carbon or boron, should have a direct effect on the singlet-triplet splitting through the u bond. In a recent ESR study of ~ - C H - ~ , ~ - C ~ B Jones I O H Iand ~ , cow o r k e r ~ ' ~photolyzed .'~ the corresponding o-carboranyl diazo ea Abstract published in
Advance ACS Abstracts, November 15, 1994.
0022-3654/94/2098-13243$04.50/0
compound at 10 K in an ESR cavity and measured the zerofield splitting parameters, IDlhcl and IElhcl.26 The IDlhcl values showed that the electrons were largely localized on carbene, while the zero-field splitting parameter, IElhcl, was near zero, indicating that the B-C-H angle was near 180". MNDO calculations17 seemed to support the quasi-linear B-C-H geometry with a calculated value of 173". In contrast, the measured IElhcl value for l-CH-1,2-C2BloH11 was nonzero, indicative of a bent C-C-H geometry. Carboranylnitrenes have only recently been reportedz2so the similarities between phenylnitrene and carboranylnitrene are unknown. Jones and co-workers2zphotolyzed the o-carboranyl azide at 5-10 K in an ESR cavity and measured the zero-field splitting parameters, IDlhcl and IElhcl, for l-N-2-Me-1,2C2B1OH10 and 9-N-1,2-C2B10Hll. The ESR spectrum is likely to be that of the triplet since the ground state of phenylnitrene is a triplet.2bJ0 Yet to be determined is the nature of the lowestenergy singlet state of carboranylnitrene. In phenylnitrene, the lowest-energy singlet state is the open-shell 'A2 state which is more stable than the closed-shell singlet ('AI) because the unpaired n electron on nitrogen can delocalize onto the phenyl ring, thereby reducing Coulombic repulsion.lo For triplet . is not as phenylnitrene (3Az), delocalization of the ~ telectron extensive as the 'A2 state because Coulombic respulsion is already reduced through the Pauli exclusion principle. The calculated ((8/8)MCSCF/3-21G) N-C bond distance in the open-shell singlet (1.288 A) is much shorter than in the closedshell singlet (1.402 A) or triplet (1.374 A), which is a consequence of spin delocalization.1° The ESR results for triplet carboranylnitrene'* indicate even less spin delocalization than calculated in triplet phenylnitrene.lo The purpose of this study is to calculate properties of several carboranylcarbenes and nitrenes. Of the five chemically unique sites of attachment in o-carborane (1, 3, 4, 8, 9), carbene or nitrene substitution has been achieved at three positions (1, 3, 9).16-18,22Calculations will be limited to these three positions because substitution at the 4- and 8-positions are expected to be very similar to the 3- and 9-positions. Several questions come to mind, including the following. Does the carboranyl group stabilize carbenes and nitrenes relative to hydrogen? What is the singlet-triplet (S-T) splitting? Are the unpaired electrons
0 1994 American Chemical Society
13244 J. Phys. Chem., Vol. 98, No. 50, 1994
McKee
TABLE 1: Absolute Energies (hartrees) and Zero-Point Energies (kcavmol) of Substituted o-Carboranes (X-1, 2-C81&1, X = H, CH. N) X state HF/3-21G ZPC(NEV)” HF/6-31G(d) PMP2/6-3 1G(d) PMP2/6-31G(2d,p) 1-H‘Ai -327.744 66 116.85 (0) -329.618 31 -330.825 72 -330.973 34 1-CH-trans ‘A’ -365.267 22 117.42 (0) -367.352 98 -368.662 19 -368.821 45 1-CH-cis ’A’ -365.262 32 117.13 (0) -367.347 82 -368.657 48 1-CH-trans 3Atf -365.305 94 117.12 (1) -367.386 30 -368.675 63 -368.829 08 1-CH-cis 3A” -365.304 54 117.06(1) -367.384 77 -368.673 81 1-CH-linear 3A” -365.289 36 115.61 (2) -367.369 07 -368.663 06 -368.818 96 ‘A’ -365.273 03 118.31 (0) -367.353 42 -368.658 64 -368.813 04 3-CH- trans -367.346 16 -368.651 38 3-CH- cis ‘A‘ -365.266 91 117.99(0) 3A” -365.330 93 117.98 (0) -367.405 71 -368.692 67 -368.849 20 3-CH- trans 3-CH- cis 3Att -365.329 42 117.84(1) -367.403 79 -368.690 47 3-CH- linear 3A’* -365.326 27 116.94(2) -367.400 08 -368.689 18 -368.845 97 ‘A’ -365.267 88 117.88 (1) -367.349 20 -368.653 54 -368.813 19 9-CH- trans 117.86 (1) -367.347 78 -368.652 39 9-CH- cis ’A‘ -365.266 55 9-CH- trans 3A” -365.328 32 118.21 (0) -367.403 55 -368.690 48 -368.846 96 -367.403 06 -368.690 01 9-CH- cis 3A“ -365.327 90 118.08 (0) 9-CH- linear 3A’t -365.323 49 117.06 (2) -367.397 98 -368.687 11 -384.843 66 l-N-b ‘A‘ -381.163 79 108.79(1) -383.336 19 -384.675 93 -384.829 55 -384.833 65 1-N-381.210 60 110.24(0) -383.388 65 -384.680 44 1-N3A” -381.247 86 110.25(0) -383.419 82 -384.726 41 -384.877 35 -383.349 51 -384.671 20 -384.823 07 3-N‘A’ -381.190 39 111.58 (0) 3-N1AP* -381.248 16 112.14 (0) -383.414 24 -384.699 27 -384.852 45 -383.444 38 -384.746 43 -384.897 57 3-NSAf8 -381.283 67 112.15 (0) -383.350 86 -384.676 46 -384.828 55 9-N‘A’ -381.193 44 111.53 (0) 9-NIA” -381.247 09 112.00 (0) -383.413 12 -384.698 07 -384.851 50 9-N3A” -381.282 56 112.02 (0) -383.443 31 -384.745 57 -384.896 95 I
I
_
Zero-point energy (kcdmol) and number of imaginary frequencies in parentheses. The C-N bond was fixed at 1.315 8, during optimization at the HF/3-21G level to avoid disruption of the carborane cage.
TABLE 2: Calculated Singlet-Triplet Splitting (kcal/mol) of HCH, HC-CH3, HC-BH2, N-CH3, and N-BHz at the PMP/ 6-31G(2d,p) ZPC and 6 2 Levels relative S-T separation state G2” PMP2/6-3 1G(2d,p)+ZPC G2 Ab correction‘ 0.0 0.0 HCH ‘AI -39.058 40‘ -18.6 -6.6 12.0 8.0 HCH 3B1 -39.069 OW HC-CH3 LA’ -78.297 54 0.0 0.0 -12.3 -0.7 11.6 7.6 HC-CH3 3A” -78.298 73 HC-BH2 ‘AI -64.474 15 0.0 0.0 HC-BH2 3A” -64.452 03 1.o 13.9 12.9 8.9 N-CHs‘ ‘E -94.314 58 0.0 0.0 -53.5 -37.9 15.6 11.6 N-CH3 ’A2 -94.375 05 N-BH, ‘Ai -80.536 65 0.0 0.0 N-BH2 3A~ -80.516 89 -2.9 12.4 15.3 11.3
+
In units of hartrees. Calculated lowering of the closed-shell singlet state relative to the triplet state at the G2 level compared to the PMP2/ 6-31G(2d,p) ZPC level. G2 theory overestimates the stability of the closed-shell singlet relative to the triplet. The A (S-T) splitting minus 4 kcdmol will constitute a correction to be applied to the calculated singlet-triplet separations of substituted o-carboranes (Table 3). Reference 28. e A closed-shellcalculation was made with imposed C3” symmetry. The geometry is not a stationary state, and the zero-point correction was taken from the triplet calculation.
+
in the triplet localized? What effect does the site of attachment have on carbene or nitrene properties?
Method All calculations have been made by using the GAUSSIAN 92 program systems?’ Geometries have been fully optimized at the HF/3-21G level within the appropriate point group unless stated otherwise. Analytical frequencies have been calculated to determine the nature of the stationary point as well as to make zero-point corrections (0.9 weighting factor). Single-point calculations have been made at the MP2/6-31G(d) and MP2/ 6-3 1G(2d,p) levels. The effect of spin contamination in openshell species has been projected out of the MP energies (PMP) by the spin-projection method developed by Schlegel and coworkers.28 Optimizations have also been carried out for the singlet and triplet states of l-CH-1,2-C2B10Hll at the HF/6-31G(d) level where it was found that the singlet-triplet splitting at the PMP2/ 6-31G(d)//6-31G(d) level was the same as that calculated at the
PMP2/6-3 lG(d)//3-21G level. For the remainder of this paper, unless otherwise stated, standard calculations are at PMP2/63 lG(2d,p)//3-21G+ZPC. Absolute energies in hartrees and zero-point energies in kcal/mol are given in Table 1 for the substituted o-carborane cages. For four species, HC-CH3, HC-BH2, N-CH3, and N-BH2, G2 energies29were calculated for the singlet and triplet states. As the G2 method has been shown to give energetics (heats of formation, relative energies, etc.) to chemical accuracy ( f 2 kcaY our standard computationalmethod (PMp2/6-31G(2d,p)/ /3-21G+ZPC) can be compared with G2 theory to assess its accuracy (Table 2). It is well-known that the stability of the carbene closed-shell singlet state is underestimated with respect to the triplet state unless quite extensive electron correlation is used with large basis sets. The difference between the splitting predicted by the two methods (G2 and PMP2/6-3 1G(2d,p)//321G-tZPC) might be used to “correct” the less sophisticated method, assuming that the G2 level gives the correct splitting and that the correction is transferable.
Carboranylcarbenes and Carboranylnitrenes Numerous calculations have been reported for methylcarbene, HC-CH3.30-32 In this work, only the C, form is calculated for the singlet, even though it is known that a C1 structure is more stable.32 At the G2 level, the triplet is predicted to be lower than the singlet by 0.7 kcdmol. Gallo and S ~ h a e f e rin , ~ a~ much more exhaustive study, found that the triplet was more stable by 5.2 kcaYmo1. Since the S-T splitting in methylene is also too small with G2 theory (6.6 kcaYmo1 cal~ulated,2~ 9 kcal/ mol e~perimental~~), it seems likely that singlet stability is slightly overestimated by G2 theory. At our standard level, the singlet-triplet splitting in methylcarbene is 12.3 kcaYmol favoring the triplet, which represents an underestimation of the singlet stability by 11.6 kcaYmol with respect to G2 theory and 7.1 kcaYmo1 with respect to Gallo and Schaefer. When a carbene is attached to BH2, the singlet is greatly stabilized by conjugation with the carbene lone pair. With G2 theory, the singlet is more stable than the triplet by 13.9 kcaY mol, which can be compared to 1.0 kcaYmol at our standard level. While a BH2 group does not closely resemble the o-carboranyl group, the HC-BHz model compound will show the inductive effect of attaching a carbene center to a boron vertex. The H-C-B angle is 180” in the singlet and 141.1’ in the triplet. Methylnitrene is another molecule which has received much a t t e n t i ~ n . ~The ~ - ~G2 ~ calculations on the singlet and triplet states were carried out in C3” symmetry. Only a single configuration (closed shell) was used to describe the ‘E singlet state rather than the three configurations required. While the ‘E state will Jahn-Teller distort to a lower symmetry, recent results by Schaefer and c o - ~ o r k e r sindicate ~~ that the true classical Jahn-Teller splitting is very small (
