J. Phys. Chem. 1991, 95, 9273-9278
9273
Heteroatom Substitution in Five- and Six-Vertex Cioso Boranes Michael L. McKee Department of Chemistry, Auburn University, Auburn, Alabama 36849 (Received: May 13, 1991)
Calculations are presented for different isomers of closo heteroboranes of the formula X,B,H,: X = N, P, CH; n 3, 4. The 1,5-isomeris strongly favored in N2B3H3and C2B3H5,while the 1,5-, 1,2-, and 2,3-isomershave similar stability in P2B3H3. The 1,S-isomer is destabilized in P2B3H3due to long P-B bonds, which causes the B-B bonds in the equatorial plane to be longer than optimal. In N2B4H4and C2B4H6,the 1,6-isomer is more stable than the 1,2-isomer, while the order is reversed in P2B4H4.The decomposition pathway has been computed for 1,2-P2B4H4in order to rationalize the experimental decomposition of I,2-P2B4CI4.The decomposition to P2 plus B4H4(Td)is inhibited by an orbital crossing while the preferred decomposition pathway to P2 plus B4H4 (Du)is orbitally allowed. Calculations on 1,2-P2B4Cl4and B4CI4have also been carried out.
Introduction A number of main-group elements are known to incorporate into closo borane cages. The most common element is carbon, which forms a class of compounds known as carboranes. Other elements known to incorporate include N , P, AI, Si, S,Ga, Ge, Sn, and Pb.' The closo boranes have a cage electron count given by Wade's rule2 as 2n 2 where n is the number of vertices. For example, in C2B3HSeach boron contributes two valence electrons to cage bonding (the third is involved in an exocyclic B-H bond) and each carbon contributes three valence electrons, for a total of 12 cage electrons, (2 X 5 ) 2. Application of Hoffmann's isolobal analogy3 indicates that a transition-metal fragment can also bring the electron count to 2n 2. Very few examples are known of nitrogen or phosphorus substituting into a closo borane. The unsubstituted N or P atom will contribute three e- to cage bonding; therefore a closo cage would be expected for molecules of the formula N2B,H, and P2B,H,. A IO-vertex closo azaborane, HNB9H9,where nitrogen is contributing 4e-, is known,4 as is a six-vertex nido azaborane, ( RN)2B4R,,'.s*6 Two theoretical studies have appeared for sixvertex closo azaboranes, a preliminary PRDD07 calculation reported by Lipscomb and co-workers* on N2B4H4and a recent comparison of B6H6*-with N2B4H4by Fehlner and c o - ~ o r k e r s . ~ The first example of phosphorus incorporating into a small closo cage is the formation of P2B3R,, R = N(iPr)2, where the cage is stabilized by the substituents on boron.1° The phosphorus atoms are in the I - and 5-positions of a trigonal bipyramid with P-B distances of 1.969 A. An example is also known of phosphorus substituting into a six-vertex closo borane cage, I,2-P2B4CI4." It is unclear whether the 1,2-isomer is thermodynamically favored over the 1,6-isomer, since, for the isoelectronic carborane C2B4H6, the 1,6-C2B4H6isomer is knownI2 to be more stable than the 1,2-isomer.
+
+
+
( I ) Adoonces in Boron ond the Borones; Liebman, J. F., Greenberg, A., Williams, R. E., Eds.; VCH: New York, 1988. (2) Jolly. W. L. Modern Inorganic Chemistry; McGraw-Hill: New York, 1984; pp 382-383. (3) Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1982, 21, 711. (4) Arafat, A.; Baer, J.; Huffman, J. C.; Todd, L. J. Inorg. Chem. 1986, 25, 3151 (5) R.; Krockert, 8.; P.aetzold, P. Chem. Ber. 1987, 120, 1913. (6) tibr, B.; Kennedy, J.; Jelinek, T. J . Chem. SOC.,Chem. Commun.
p,
1990, 1309.
(7) Halgren, T. A.; Kleier, D. A.; Hall, J. H.; Brown, L. D.: Lipscomb. W. N . J . Am. Chem. Soc. 1978, 100,6595. (8) Halgren, T. A.; Pepperberg, I. M.; Lipscomb, W. N . J . Am. Chem. SOC.1975, 97, 1248. (9) Aradi, A.; Fehlner, T. P. Adv. Orgonomet. Chem. 1990, 30, 189. (IO) Wood, G. L.; Duesler, E. N.; Narula. C. K.; Paine, R. T.; NMh, H. J . Chem. Soc. Chem. Commun. 1987, 496. ( I I ) Haubold, W.; Keller, W.; Sawitzki, G.Angew. Chem., Int. Ed. Engl. 1988, 27, 925. (!2) Takimoto, C.; Siwapinyoyos. G.; Fuller, K.; Fung, A. P.; Liauw, L.; Jarvis, W.; Millhauser, G.;Onak, T. Inorg. Chem. 1980, 19, 107.
In a white-hot flow pyrolysis tube (T > 1370 K), the phosphaborane, 1,2-P2B4C14,extrudes a P2 molecule rather than rearrange to the 1,6-isomer.13 By contrast, the 1,2-C2B4H6carborane rearranges to 1,6-C2B4H6at 25G300 O C with an estimated activation barrier of 42-45 kcal/m01.'~*'~An approximate reaction path from reactants to products was constructed at the M N D O level where the conversion to P2 plus B4CI4 ( T d )was discussed in terms of an allowed reaction and found to have an activation barrier of 71 kcal/mol." Method All calculations have been made by using the GAUSSIAN 88 program system.I6 Geometries have been optimized at the HF/3-21G and HF/6-31G* 1e~els.I~Calculations involving phosphorus or chlorine used the HF/3-21G* basis set, which includes a set of d-functions on third-period elements and has been shown to yield reasonable geometries for compounds containing these elements.I7 Single-point calculations were made at the MP4 level of electron correlation (frozen-core approximation) with the 6-3 lG* basis set. Vibrational frequencies have been calculated to characterize the nature of the stationary points and to make zero-point corrections (scaled by 0.9). Absolute energies and zerepoint energies are given in Table I, while geometries are given in Figure 1. Unless otherwise indicated, the energy differences used in the discussion below will be at the MP4/6-31G*+ ZPC//6-31G* level of theory. A comparison of 3-21G* (d-functions on third-period elements) and 6-3 1G* (d-functions on all nonhydrogens) geometries (Figure 1) reveals that at the latter level the cages become more compact. The largest change of geometry due to the level of optimization occurs in N2B3H3and N2B4H4cages followed by C B3H5 and C2B4H6. In 2,3-N2B3H3the N-N distance is 0.12 longer at the HF/3-2lG* level than at the HF/6-31G* level, while for 1,2-N2B4H4the analogous change in the N-N distance is 0.14 A (Figure 1). Only small effects are seen in P2B3H3and P2B4H4. It would appear that d-functions on boron do not significantly change geometry predictions. In analogy with the basis set construction for phosphorus, it might be possible to improve geometry predictions in azaboranes and carboranes by adding a set of d-functions only to nitrogen and carbon. Such a basis set would
1
(13) Solouki, B.; Bock, H.; Haubold, W.; Keller, W. Angew. Chem., Int. Ed. Engl. 1990, 29, 1044. (14) Halgren, T. A.; Pepperberg, I. M.; Lipscomb, W. N. J. Am. Chem. SOC.1975, 97, 1248. (15) McKee, M. L. J . Am. Chem. Soc. 1988, 110, 5317. (16) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.;Gonzales, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J.. P.; Fluder, E. M.; Topiol. S.;Pople, J. A. GAUSSIAN 88; Gaussian, Inc.: Pittsburgh, PA. (17) For a description of basis sets, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.
0022-3654/91/2095-9273%02.50/0 0 1991 American Chemical Society
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The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
TABLE I: Absolute Energies (hartrees) and Zero-Point Energies (kcal/mol) for Various Species at Optimized 3-21G* and 6-31G* Geometries //3-21G* //6-31G* MP2/ MP4/ ZPE MP2/ ZPE H F/ F/ HF/ 6-31G* 6-31G* (NIF) 6-31G* (NIF) 6-31G' 6-31G* svmm 3-21G* -1.12683 -1.14410 -1 . I 50 82 6.64 (0) -1.144 14 6.66 (0) -1.122 96 -1.1 26 8 1 D-h 3.94 (0) 3.73 (0) -108.943 95 -1 09.248 20 -109.266 49 -108.94388 -109.24942 -1 08.300 95 D- h 1.30 (0) 1.32 (0) -681.42453 -68 1.638 75 -681.66992 -681.638 12 -68 1.424 50 -678.16980 D-h -26.464 23 -26.39001 -26.483 24 17.38 (0) -26.39001 -26.464 22 17.29 (0) -26.237 30 D3h -56.370 50 23.22 (0) -56.353 71 -56.184 36 -56.18250 -56.351 92 22.61 (0) -55.872 20 C3" -342.447 95 -342.551 52 16.48 (0) -342.447 96 -342.551 51 -342.577 86 16.43 (0) -340.81 3 99 C3" -40.332 44 -40.354 54 29.98 (0) 30.12 (0) -40.195 17 -40.195 17 -40.33242 -39.976 88 Td -100.88950 -101.171 92 30.19 (0) -100.88955 -101 .I7208 -101.22963 30.03 (0) -100.31751 DW 32.86 (0) -100.92570 -101.271 42 -101.323 28 32.58 (0) -100.92479 -101.27030 -100.33848 Td 13.35 (0) -1927.823 17 -1936.71 199 -1937.51944 D2d 14.22 (0) -1927.854 76 -1936.745 50 -1937.62264 Td 31.72 (0) -1 84.7 16 95 -185.27489 -185.323 19 32.32 (0) -184.70684 -185.26703 -183.63048 D3h -184.59746 -185.178 14 -185.22962 30.75 (0) no minimum cs c2, -183.501 49 -184.565 90 -185.18250 28.99 ( I ) -184.577 28 -185.181 43 -185.227 88 29.90 ( I ) -209.895 33 -2 10.590 53 38.69 (3) -209.904 98 -210.59239 -2 10.645 68 40.52 ( I ) -208.67072 D4h -209.885 60 -2 10.569 04 39.97 (0) -209.899 16 -210.57504 -210.63367 41.08 (0) -208.683 23 c2u -757.226 56 -757.699 22 27.54 (0) -757.22699 -757.702 94 -757.764 74 27.09 (0) -753.533 73 D3h -757.201 42 -757.689 29 27.46 (0) -757.20202 -757.691 62 -757.753 04 27.18 (0) -753.505 98 cs -757.191 06 -757.68794 27.07 (0) -757.191 48 -757.689 12 -757.74902 26.61 ( I ) -753.494 50 c, -782.508 49 -783.094 95 37.06 (0) -782.508 82 -783.095 61 -783.16297 37.32 (0) -778.66361 D4h -782.514 I O -783.09777 37.37 (0) -782.51454 -783.098 66 -783.16726 37.51 (0) -778.668 64 C2" -782.31047 -782.81376 3 1.92 (2) -782.3 10 07 -782.81755 -782.904 80 32.10 (2) -778.486 27 C2" -782.328 56 -782.896 27 34.81 (3) -782.330 13 -782.898 70 -782.978 43 34.33 (0) -778.501 48 C2a -782.29963 -782.827 04 32.83 (3) -782.299 78 -782.83 1 30 -782.917 17 32.65 (3) -778.482 54 C2" -782.343 43 -782.897 98 33.31 (3) -782.343 96 -782.899 20 -782.980 33 33.13 (2) -778.504 27 C2" -2606.1 19 49 -2618.27267 -2619.388 05 16.90 (0) D4h c2c -2606.134 19 -2618.28664 -2619.40321 17.16 (0) 47.71 (0) -1 52.686 57 -1 53.1 82 46 -1 53.239 36 47.32 (0) -152.683 78 -153.17681 -1 51.81903 D3h -152.61058 -153.1 I828 46.53 (0) -152.61431 -1 53.1 24 59 -153.181 52 46.33 (0) -1 5 1.74064 cs -1 52.561 60 -1 53.079 88 44.96 ( I ) -1 52.565 81 -153.087 16 -1 53.143 03 44.26 (2) -1 51.69053 c 2 v -177.943 16 -178.55896 56.88 (0) -1 77.946 22 -178.56202 -178.623 75 57.37 (0) -176.91762 D4h -I 77.932 70 -1 78.542 98 57.08 (0) -177.936 21 -178.54692 -178.610 I O 57.44 (0) -1 76.909 65 c2u TABLE 11: Relative Energies (kcal/mol) for Various Species at Optimized 3-21G* and 6-31G* Geometries 1G* . /3-21G* . .116-3 . HF/ HE/ MP2/ H F/ MP2/ MP4/ svmm 3-21G* 6-31G* 6-31G* +ZPE 6-31G* 6-31G* 6-31G* 0.0 0.0 0.0 0.0 0.0 0.0 0.0 75.0 60.7 58.7 no minimum 59.8 88.4 53.0 50.6 87.6 58.6 80.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.1 13.5 14.7 3.6 10.9 7.5 -7.8 93.8 101.9 38.9 106.2 44.8 108.0 32.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.3 15.8 6.2 6.1 15.7 7.1 17.4 9.9 7.1 22.3 6.7 22.3 8.7 24.6 2.7 1.9 1.5 3.6 3.5 1.8 3.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 164.7 128.3 176.4 114.4 127.8 178.2 173.3 118.5 124.1 115.7 125.5 116.4 126.4 104.9 156.9 134.8 167.8 134.6 169.9 116.8 165.8 117.3 125.2 121.8 107.0 107.1 125.4 103.1 168.0 175.3 125.8 180.6 125.6 180.6 1 1 3.8 109.2 118.3 103.4 118.8 1 1 5.9 103.1 100.6 9.2 8.8 9.5 9.3 0.0 0.0 0.0 0.0 88.6 94.2 154.I 151.9 73.2 89.4 68.8 88.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 36.3 45.9 36.1 35.7 45.3 36.3 49.2 60.4 59.8 76.7 60.8 58.3 75.8 80.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 8.6 6.6 10.0 10.2 6.3 9.5 5.0
be much less expensive than the 6-31G* basis set, which includes d-functions on all boron atoms as well. To test this hypothesis, the geometries of 2,3-N2B3H3and l,2-N2B4H4were reoptimized with the 3-21G basis set supplemented by a set of d-functions (exponent = 0.8) on nitrogen. The N-N distances shortened considerably. If one takes the difference in the bond length at the HF/3-21G and HF/6-31G* levels as a reference, the intermediate basis set, which includes a set of d-functions on nitrogens, decreases the N-N distance by 80% of
+ZPE 0.0 57.3 57.6 0.0 8.0 87.9 0.0 7.4 9.5 2.5 0.0 159.8 1 15.6 152.5 113.4 162.4 105.9
0.0 35.4 57.6 0.0 8.7
the reference and decreases the B-B and B-N distances by 50-60% of the reference. Results and Discussion
It has been found that heats of formation can be estimated by calculating the exothermicities of eq 1 combined with the exxBH3 yH2 boron hydride (1)
+
-
perimental heat of formation of H, and the adjusted heat of
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9275
Heteroatom Substitution in Boranes nS
i m (la)
P,
1.m
(im)
H
H Bfld
B...B 64 BCI
B&I.
2350 1.731 1.738
B-B
1.712 [1.71]*' MI 1.726 11.701
2-P-Z-PBdH4 TS
2-P-2-PB4H4
Benzvalene-like
l,S-P2B&
TS
Figure 1. Selected geometric parameters are given at the HF/3-21G and HF/6-31G* levels (in parentheses). Hydrogens on carbons are shown explicitly, while each boron has one implicit hydrogen. Values in brackets are experimental X-ray values for the indicated molecule or a closely related one. The X-ray structures for the carboranes are from ref 19. formation of BH3.I8 The adjustment is necessary due to the systematic underestimation at the MP2/6-31G*//3-21G level of the nonclassical boron hydride relative to BH3 and H2. With an adjustment of the heat of formation of BH3 downward by 2 kcal/mol, heats of formation of the boron hydrides can be predicted with an accuracy of 3-4 kcal/mol. In the present work, heats of formation of C2B3H5and C2B4H6 can be estimated from the calculated exothermicities of eqs 2 and 3 (Table I l l ) . It is expected that the stabilities of nonclassical C2B3HS 2CH4 + 3BH3 - 6H2 (2)
--
C2B4H6
2CH4
+ 4BH3 - 7H2
(18) McKee, M. L.J . Phys. Chem. 1989, 93, 1265.
(3)
carboranes will also be underestimated with respect to reactants in eqs 2 and 3. For that reason, the estimated heats of formation will be decreased 2 kcal/mol per boron, Le., 6 kcal/mol for C2B3HS and 8 kcal/mol for C2B4Hb(last column, Table 111). A comparison of stabilities of the heterosubstituted cages can be made by using eqs 4-7. From the estimated heats of formation P2B3H3+ 2CH4 P2B4H4+ 2CH4
+
N2B3H3 2CH4 N2B4H4+ 2CH4
--
+
C2B3HS 2PH3
(4)
C2B4H6+ 2PH3
(5)
C2B3HS+ 2NH3
(6)
+
C2B4Hs 2NH3
(7)
of C2B3HSand C2B4H6,heats of formation of heteroboranes can
9276
McKee
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
TABLE 111: Calculated Reaction Energies (kcal/mol) and Estimated Heats of Formation for Various Species //3-21G* //6-3 1G* HF/ HF/ MP2/ HF/ MP2/ MP4/ reaction 3-21G* 6-31G* 6-31G* +ZPE 6-31G* 6-31G* 6-31G* -6.4 -9.1 12.1 -70.8 195-C2B3HS 2CH4 3BH3 - 6H2 -68.3 -72.6 -9.9 23.5 -73.0 30.7 -75.0 29.0 52.3 I,6-C2B4H6 2CH4 4BH3 - 7H2 -78.2 51.7 49.4 21.9 23.4 52.8 46.4 I,5-P2B,H, I,5-C2B3Hs 2PH3 - 2CH4 25.4 59.9 58.1 61.4 54.7 35.8 1,6-P2B4H4 I.6-C2B4H6 + 2PH3 - 2CH4 45.0 37.5 I,5-N2B3H3 1,5-C2B3Hs 2NH3 - 2CH4 13.0 30.4 32.1 33.0 32.6 31.3 32.6 1,6-N2B4H4 1,6-C2B4H, + 2NH3 - 2CH4 -23.6 -14.1 -4.7 -1.9 -12.3 -7.6 -6.3
--
---
+ +
+ +
+ZPE 13.2 46.6 43.2 51.8 33.9 -3.3
AHdO K)"*6 28.0 19.0 31.6 14.0 7.5 29.1
"The experimental heats of formation of BH, (26.4 kcal/mol), NH3 (-9.3 kcal/mol), CH4 (-16.0 kcal/mol), and PH3 (7.4 kcal/mol) at 0 K are taken from: Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. J . Phys. Chem. Ref. Data 1985, 14, Suppl. 1; JANAF Thermochemical Tables, 3rd ed. bThe heat of formation of the reactant heterocage is estimated from the calculated exothermicity of the given reaction and the experimental heats of formation of BH,, NH3, CH4, and PH,. The estimated heat of formation of 1,5C2BJHS and 1 ,6-C2B4H6are decreased by 2 kcal/mol per boron (to compensate for underestimation of the stability of nonclassical cage relative to CH4, BH3, and H2) and used in the calculation of the nitrogen and phosphorus heterocages that follow. For example, AHr(l,5-C2B,HS, 28.0) = 2AHr(CH4, -16.0) + 3AHr(BH3, 26.4) - AHrxn(13.2)-. 6 kcal/mol.
then be calculated from the calculated exothermicity of eqs 4-7 (last column, Table 111). The heats of formation of the other isomers can be obtained by adding the relative energies of the 1,2or 2.3-isomers in Table 11 to the heat of formation of the 1,5- or 1,6-isomer in Table 111. In the absence of experimental values, the calculated values can be used in thermodynamic calculations. The accuracy is estimated to be f 5 kcal/mol. If one considers the last four chemical equations in Table 111, it can be concluded that nitrogen and phosphorus are stabilized when surrounded by a cage relative to three hydrogens, since three of the four reactions are endothermic. One possible reason is that the heterocages allow the electron density on nitrogen and phosphorus to be delocalized over the cage. Relative to the Mulliken population in NH3, PH3, and CH4, the heteroatoms in 1,5-X2B3H3,X = N, P, CH, transfer 0.45e-, 0.10e-, or 0.21e- to other cage atoms, respectively (6-3 1G*).In the 1,6-X2B4H4cages, the analogous charge transfers are 0.44e-, 0.23e-, and 0.23e-. Thus, while 1 ,5-N2B3H3and 1 ,6-N2B4H4have a similar amount of charge transfer (0.45e- and 0.44e-), the five-vertex cage is more stable and the six-vertex cage is less stable than the isostructural carboranes (Table 111). The 1,6-N2B4H4cage may be destabilized due to compressed B-B bonds in the equatorial plane (Fi ure 1, 1.647 A), which are shorter than optimal19 (1.72-1.85 ). The site preference for the heteroatom within the cage can also be addressed. Grimac has developed20 the rule of topological charge stabilization which can be used to predict the stability order of the carboranes. The charge distribution is calculated for an isoelectronic isostructural closo reference and the stability order is given by assuming an electronegative atom will be most stable at the site of greatest negative charge. However, geometry relaxation effects are not taken into account, which are also important in determining relative energies among the different cage isomer. In Table IV the stability of the cage with heteroatoms in axial positions (1 ,5- or 1,6-isomers) is compared to the 1,2isomer. For all but one of heterocage systems studied, the isomer with heteroatoms in axial positions is more stable than the 1,2isomer, in agreement with the topological charge stabilization rule.20 However, the relative energies vary by almost 50 kcal/mol. If one uses the I ,2-isomer as the reference, the relative energies of 1,5-X2B3H3,X = N, P, CH, are -57.3, -7.4, and -35.4 kcal/mol, respectively (Table IV). In other words, the 1,5-P2B3H3 isomer appears to be destabilized and the 1,5-N2N3H3isomer appears to be stabilized relative to 1 ,5-C2B3H5.The cause of the variation can be understood from the predicted average B-B bond lengths (Table IV). In 1 ,5-P2B3H3,the B-B bonds are longer than optimal19 as a result of the bond length and bond angle requirements around the axial phosphorus atoms. In the 1,2-isomer, the phosphorus is in a position less favored by charge stabilization
TABLE IV: Comparison of the 1,s- or 1,dIsomer with the 1,2-lsomer X N P CH X2-B3H3
energy" ( 1.5- - 1,2-isomer) av B-B in 1,5-isomer, A av B-B in 1,2-isomer, A
-57.3 1.775 1.747
-7.4 1.973 1.748
-35.4 1.886 1.772
-8.0 1.647 1.754
2.5 1.794 1.742
-8.7 1.709 1.731
X2-B4H4
energy6 (1,6- and 1,2-isomer) av B-B in 1,6-isomer, av B-B in 1,2-isomer, A
a Energy difference (kcal/mol) between the 1,5-isomer and 1,240mer. Energy difference (kcal/mol) between the 1,6-isomer and 1,2isomer. D
1
(19) Range of B-B bonds (1-72-1.85 A) in experimental structures of several carboranes. See: Beaudet, R. A. In Advances in Boron and the Boranes; Liebman, J . F., Greenberg, A., Williams, R. E., Eds.; VCH: New York, 1988; pp 417-473. (20) (a) Gimarc, B. M.J. Am. Chem. SOC.1983, 105, 1979. (b) Ott, J. J.; Gimarc, B. M . J. Am. Chem. SOC.1986, 108,4303.
Figure 2. Known structure of P2B3R3, R = N(iPr)2, indicating the back-donation of charge from the amine substituent into the empty orbital on boron. The 1J-isomer is better suited for back-donation than the 1,2- or 2,3-isomer.
but the B-B bonds can assume more optimal values. In 1 3 N2B3H3,the nitrogen is in a position favored by charge stabilization and, due to shorter N-B bonds, the B-B distances in the equatorial plane can assume more optimal values. The B-B distances in 1,5-C2B3H5are intermediate to the nitrogen and phosphorus heterocages and the stability of the 1,5-isomer is also between the two heterocages. One might ask why only the 1,Sisomer is known with phosphorus substitution since the energy preference is small. The known X-ray structureloof P2B3R3,R = N(iPr)2, shows the amine to be planar, indicating strong ?r-donation into the underutilized orbitals on boron. The 1,5-isomer may be favored because it is the only isomer that can be described by two-center two-electron bonding with a vacant orbital on each boron which is available for accepting electron density from the amine (see Figure 2). In the six-vertex heterocages, the N2B4H4and C2B4H61,6isomers have nearly equal stability (relative to the 1,2-isomer), while in the P2B4H4cages, the 1,6-isomer is destabilized to the extent that the 1,2-isomer is lower in energy. Again, the bond length and bond angle requirements around phosphorus cause the equatorial B-B bond distances to be longer than optimal in the 1,6-isomer (Table IV). Intramolecular Reactions of 1,2-P2B4H4. Calculations were carried out to determine the mechanism of P2 elimination to form
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9277
Heteroatom Substitution in Boranes
a)
176.3 (162.4)
p2+B4&
@&I)
\
HOMOLUMO croaping
H
H
I
H b2
nP2
bl
X*
P2
Figure 3. Diagram indicating the favorable interaction of P2 with the DM symmetry isomer of B4H4. (a) The A orbital of P2 can donate charge into the empty b2 orbital of B4H4(DM), while the T* orbital of P2 can accept charge from the occupied b, orbital of B4H4 ( D Z d ) .
B4H4,since experimental work on 1 ,2-P2B4CI4in a pyrolysis tube indicates that the elimination of P2 is favored in that system.13 mbar) and high temThe reaction occurs at low pressure ( perature (1 370 K), and the products observed are P2 and BC13, where the latter is the decomposition product of B4C14 under pyrolysis conditions. Using simple assumptions, a rough estimate of the free energy barrier could be as high as 100 kcal/mol.2' Symmetric stationary points were located as candidates for intermediates or transitions states on the P2 elimination and rearrangement pathways. The term transition state will be used loosely in the following discussion as the structures located were often characterized by more than one imaginary frequency at the HF/3-21 G*and HF/6-31G* levels. The distinction is not critical since single-point calculations including electron correlation indicated that the "transition state" for P2 elimination is lower in energy than that of the products. With no reverse barrier, the forward activation barrier can be calculated as the difference between reactants and products. A study of the rearrangement pathway of 1,2-C2B4H6 1,6C2B4H6has suggested' that a benzvalene-like structure can serve as the transition state or high-energy intermediate for the rearrangement.22 The energy of the structure was 39 kcal/mol above that of the 1 ,2-C2B4H6structure, which is in good agreement with the estimated barrier of the experimental rearrangement (42-45 kcal/mol).14 A similar benzvalene-like structure was calculated on the P2B4H4surface to give a rough indication of the size of the rearrangement barrier. At the MP4/6-31G*+ZPC level the benzvalene-like structure is 1 13.4 kcal/mol higher than 1,2P2B4H4.Since there may also be a barrier leading to and from the benzvalene-like structure, the 113.4 kcal/mol value may be considered a lower limit for the activation barrier. The overall reaction 1 ,2-P2B4H6 1,6-P2B4H6is nearly thermoneutral (endothermic by 2.5 kcal/mol). In contrast to the previous MNDO results,13which suggest that 1 ,2-P2B4CI4can form P2 and B4CI4( Td)in an allowed reaction, the current results at a much higher level of theory find the pathway 1,2-P2B4H4 P2 + B4H4 (Td) to be blocked by a HOMO/LUMO crossing, proceeding instead to P2 and B4H4 (Dzd). Two pathways were considered for the elimination of P2, a concerted sideways elimination from 1 ,2-P2B4H4and an end-on elimination form 2-P-2-PB4H4,a trigonal-bipyramidal intermediate with an exocyclic P-P bond, 115.6 kcal/mol less stable than 1,2-P2B4H4. The transition state for elimination of P2 by this pathway is 36.9 kcal/mol higher than the intermediate but 7.3 kcal/mol lower than the sideways elimination of P2 from 1,2P2B4H4.However, at the MP4/6-3 lG*+ZPC level both transition states are lower in energy than P2 + B4H4( D 2 J , and therefore, on the correlated surface, it is likely that the reverse pathway P2
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(21) With an assumed preexponential factor of 10I2 (unimolecular decomposition) and an activation barrier of 100 kcal/mol, the rate constant would be about IO4. (22) For a recent X-ray structure of a benzvalene-like structure on the (CH)*B4R4 surface, see: Krimer, A.; Pritzkow, H.;Siebert, W. Angew. Chem., Int. Ed. Engl. 1990, 29, 292.
b)
I ao [0.0]
19=94Q
MP2/&31G*+ZPC//3-21G* FIP.YSSlG*+ZPC//f3-31G*]
Figure 4. Potential energy profile of (a) 1,2-P2B4H4and (b) 1,2-P2B4C14. The activation barrier for P2 elimination is calculated as the energy difference between the reactant and P2 + B4H4 (D2d)(or B4C14). The barrier to rearrangement to the 1,6-isomer is only a "rough" estimate. The energy is for a benzvalene-like model, which should be similar in energy to a species on the actual rearrangement pathway.
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+ B4H4(DM) 1,2-P2B4H4proceeds without activation. As soon as the P2 departs, the B4H4(D2J can form the more stable B4H4 ( Td) by a reaction that is orbitally forbidden but yet has a low activation barrier.23 Also, the precursor of BC13 in the observed reaction could be the DZdisomer of B4CI4 rather than the T d isomer, since only BCI3 is detected as a reaction product in the decomposition of 1,2-P2B4CI4.l3 The P2 fragment has favorable donor/acceptor interactions with the B4H4(DJ structure. The ?r orbital of P2 can donate charge into the empty b2 orbital of B4H4(DM)(Figure 3a), while the ?r* orbital of P2 can accept charge from the occupied b, orbital of B4H4 (D2J (Figure 3b). A similar interaction of the occupied lone pair orbital and empty ?r* orbital at one end of P2 is also possible as the P2 molecule departs in the end-on elimination pathway. The interactions would be unfavorable on the B4H4(Td) surface where the b2 orbital is filled and the b, orbital is empty (assigned in DZdsymmetry). The potential energy profile is given in Figure 4. The barrier to rearrangement is "roughly" 1 13.4 kcal/mol plus possible activation to/from the intermediate, compared to 162.4 kcal/mol for the P2 elimination pathway. Even with a more favorable entropy of activation for elimination, the rearrangement pathway is probably more likely. However, the rearrangement will favor the thermodynamically more stable 1,2-isomer and at equilibrium the 1,6-isomer may not be formed in sufficient quantity to be observed. Since the system actually studied was 1,2-P2B4CI4,optimizations (3-21G*) were carried out for the reactant, 1,6-P2B4C14and B4CI4 (D2d, Td). Single-point calculations were carried out at the MP2/6-31G* level, and the effect of higher orders of electron correlation was estimated from calculations on the parent system. The activation barrier is assumed to be the energy difference between 1,2-P2B4C14and P2 B4CI4 (D2d), which is 151.9 kcal/mol a t the MP2/6-3lG*//3-21G*+ZPC level (Table 11). A correction of 12.6 kcal/mol is made, which is the energy lowering found in the parent system (1,2-P2B4H4 P2 + B4H4 (&)) when the level of theory is increased from MP2/6-31G*//6-31G* to MP4/6-31G*//6-31G*. The corrected barrier (139.3 kcal/ mol) is still higher than the barrier estimated from experimental conditions (100 kcal/mol).21 The energy difference between the 1,2- and 1,6-isomers increases from 1.5 kcal/mol in P2B4H4to 9.3 kcal/mol in P2B4CI4
+
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(23) McKee, M. L.; Lipscomb, W. N. Inorg. Chem. 1981, 20, 4148.
J . Phys. Chem. 1991, 95, 9278-9288
9278
at the MP2/6-31G*+ZPC//3-21G* level. This strongly supports the suggestion that the thermodynamic instability of the 1,6-isomer is the reason that it is not observed, not a high rearrangement barrier. The B4CI4isomers themselves are interesting, as several papers have calculated the electronic structure of the T d Swanton and Ahlrichs have recently calculatedz6 the structure of B4H4and B4C14 in Td and Dlh geometries. Using the C P F method and DZP optimized geometries, they calculated a difference of 83.3 kcal/mol. In the present work, a difference of 56.5 kcal/mol between the Tdand Dzd isomers is calculated, which is lower due to the DOh DZdrelaxation. For B4C14,the authors calculate the D4,,to Tddifference as 24.2 kcal/mol at the HF/DZP level (their highest level), which can be compared to the DZdto T d difference of 21.0 kcal/mol at a comparable level or 63.9 kcal/mol when electron correlation and zero-point correction are included (Table 11). The authors suggest that the D4,, Td
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(24) Morrison, J. A. In Advances in Boron and the Boranes: Liebman, J . F., Greenberg, A., Williams, R. E., Us.; VCH: New York, 1988; pp 151-189. (25) Morrison, J . A. Chem. Reu. 1991, 91, 35. (26) Swanton, D. J.; Ahlrichs, R. Theor. Chim. Acta 1989, 75, 163.
rearrangement is likely; however, the D4hstructure will relax to a D2dstructure, not Td. While the D2disomer of B&14 is much less stable than the Td isomer (63.9 kcal/mol higher), it could have kinetic stability. Unfortunately, the second isomer has not been observed, probably because the temperature for decomposition of B4CI4is low (-200 0C).25 Conclusions
Heterosubstitution in five-vertex cages is strongly preferred in the axial position by nitrogen and carbon and less strongly by phosphorus. In the six-vertex cages, axial substitution is slightly preferred by nitrogen and carbon and slightly disfavored by phosphorus. The present calculations predict that the concerted extrusion of P2 to form B4H4 (Td) is symmetry forbidden. An alternate allowed pathway is via formation of the higher energy D,, isomer of B4H4.
Acknowledgment. We thank the donors of the Petroleum Research Fund, administered by the American Chemical Society, for financial support. Computer time for this study was made available by the Alabama Supercomputer Network and the YSF-supported Pittsburgh Supercomputer Center.
Theoretical Study of the Interactions of Be and Mg Atoms with Acetylene Jestis R. Flares? and Antonio Largo*,$ Departamento de Quimica Fisica, Facultad
