1265
J. Phys. Chem. 1989, 93, 1265-1266
Theoretical Study of the Classical and Nonclassical Forms of C,B,H8 Michael L. McKee Department of Chemistry, Auburn University, Auburn, Alabama 36849 (Received: May 9, 1988)
Ab initio calculations have been carried out on the nonclassical and classical forms of C2B4H8. At the MP2/6-31G* + ZPC//3-21G (zero-point corrections using the 3-21G basis) level, the classical form, whichis a six-membered ring in a chair conformation, is 56.5 kcal/mol higher in energy than nido-2,3-C2B4H8.Calculations using the 3-21G basis indicate the chair form to be 7.8 kcal/mol lower in energy than the nido form. Despite the obvious shortcomings of the double-{ basis, geometries and vibrational frequencies are reasonably reproduced.
It is now recognized that a number of nonclassical carborane parents also have classical derivatives that can be stabilized and made isolable with the proper choice of substituents. Recently, a classical structure was Characterized’ for a derivative of the CZB4H8carborane that is well-known in a nonclassical nido structure.*-’ The structure, a chair conformation, is stabilized by dimethylamino groups on each boron. The mode of stabilization is undoubtedly A donation into the “empty” p orbital on boron. Since the proposal that boranes and carboranes may rearrange through classical transition states,8 there has been interest in determining the geometries and relative energies of classical structures with respect to their better known nonclassical counterparts. Also, understanding factors that stabilize classical structures may lead to new isolable compounds. In theoretical studies of organic compounds, the double-{ basis set (such as 3-21G, 4-31G, 6-31G, etc.) is often adequate for qualitative estimation of barrier heights, rotational barrier, conformational preference, and many other proper tie^.^ Large basis sets and inclusion of correlation (such as MP2/6-31G*) are necessary when quantitative predictions are required or when choosing between alternative reaction pathways. However, when the relative energies of classical and nonclassical isomers of electron deficient molecules are compared, a large basis plus inclusion of electron correlation is absolutely necessary for even qualitative predictions.1° In the present study the HF/3-31G and MP2/ 6-31G* relative energies differ by over 70 kcal/mol! Although relative energies require more sophisticated methods, geometries appear to be adequately reproduced by a small basis set (i.e., 3-21G). All calculations were carried out by using the GAUSSIAN 86 program package.11v12 Energies were determined at 3-21G optimized geometries (Figure l), and single-point calculations were carried out a t the MP2/3-31G* level. Absolute and relative
TABLE I: Total Energies (hartrees) and Relative Energies (kcal/mol) of Species on the C2B4H8Potential Energy Surface
Total Energies molecule
3-21G 6-31G* 1, nido C, -178.06064 -179.08640 2, planar D2* -178.04589 -179.041 86 3, chair C2, -178.073 16 -179.06798 Relative Energies molecule 3-21G 6-31G* 1, nido 0.0 0.0 2, planar 9.2 28.0 3, chair -7.8 11.6 sym
MP2/6ZPE 31G* (NEV)“ -179.70640 71.07 (0) -179.57421 66.71 (3) -179.61230 68.45 (0) MP2/6-31GS
+ZPCb
0.0
0.0
83.0
78.6 56.5
59.1
“ Zero-point energies (kcal/mol) and number of negative frequencies in parentheses. bRelative energies at the MP2/6-31G* level plus zero-point correction at the HF/3-21G level. TABLE II: Geometric Parameters for the Nido and Chair Form of C2B4H8
nido-2,3-C2B4H8 parameter 3-21G“ EDb C2C3 1.417 1.460 1.521 1.544 C2B6 B4B5 1.819 1.758 C2BI 1.848 1.832 BIB4 1.819 1.761 BIBS 1.730 1.687 B4Hb 1.323 B5Hb 1.325
chair C2B4H8 X-raf parameter 3-21G X-ray“ 1.432 C1B2 1.602 1.590 1.520 B2B3 1.699 1.711 1.778 a 104.4 105.5 1.762 /3 114.3 113.3 1.768 132.1 130 1.705
“The 3-21G nido geometry has been reported previously: McKee, M. L. J. Am. Chem Soc. 1988, 110, 4208-4212. bElectrondiffraction study of 2-[(CH3),Si]-2,3-C2B4H76cX-ray diffraction study of parent
~ompound.~ “X-ray diffraction study of (RB),(CH,),, where R = dimethylamino.’ (1) Fisch, H.; Pritzkow, H.; Siebert, W. Angew. Chem., Int. Ed. Engl. 1984, 23, 608-613. (2) Onak, T. In Boron Hydride Chemistry; Muetterties, E. L., Ed.; Academic Press: New York, 1975; pp 349-382. (3) Onak, T. In Comprehensive Organometallic Chemistry; Wilkinson, G., Stone, F. G. A,, Abel, E., Eds.; Pergamon: Oxford, England 1982; Vol. 1, pp 41 1-457. (4) Hosmane, N. S.; Islam, M. S.; Burns, E. G. Inorg. Chem. 1987, 26,
3231-3239. (5) Lipscomb, W. N.; Marynick, D. S. J . Am. Chem. SOC. 1972, 94, 8699-8106. (6) Hosmane, N. S.; Maldar, N. N.; Potts, S. B.; Rankin, D. W. H. Inorg. Chem. 1986, 25, 1561-1565. (7) Boer, F. P.; Streib, W. E.; Lipscomb, W. N. Inorg. Chem. 1964, 3, 1666. (8) Camp, R. N.; Marynick, D. S.; Graham, G. D.; Lipscomb, W. N. J . Am. Chem. SOC. 1978, 100, 6781-6783. (9) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley: New York, 1986. (IO) McKee, M.L.; Lipscomb, W. N. Inorg. Chem. 1985, 24, 765-767. ( 1 1 ) GAUSSIAN 86, Frisch, M. et al., Carnegie-Mellon Quantum Chemistry Publishing Unit, Carnegie-Mellon University, Pittsburgh, PA 15213. (1 2) For a description of basis sets see ref 9.
0022-3654/89/2093-1265$01.50/0
energies are given in Table I, a comparison of calculated and experimental geometric parameters is made in Table 11, and vibrational frequencies at the HF/3-21G level are listed in Table 111. At the HF/3-21G level the chair form of C2B4H8is predicted to be 7.8 kcal/mol more stable than the nido form. Unless there is a high kinetic barrier separating the chair form from the nido form, this is in contradiction with experimental results, which show 2,3-C2B,H8 to be nonfluxional at room t e r n p e r a t ~ r e .As ~ mentioned above, polarization functions and electron correlation both strongly favor the nido form of 2,3-C2B4H8. In contrast with 3-21G results, calculations at the HF/6-31G* level favors the nido form over the chair form by 19.4 kcal/mol; at the MP2/6-31G* level the nido form gains 47.5 kcal/mol of further stabilization. Including zero-point correction, the chair form (3) is predicted to be 56.5 kcal/mol above the nido form (1). A planar six-membered ring was calculated (2) to determine the rigidity of the chair form. At the HF/3-21G level 2 is 17.0 0 1989 American Chemical Society
1266 The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 B.
1
Figure 1. Numbering scheme for CzB4H8structures 1-3. Geometric parameters for 1 and 3 are given in Table 11.
kcal/mol higher than the chair form (3), and at the MP2/6-31G* ZPC level the difference increases to 22.1 kcal/mol. Relative to 1, the planar form (2) is 9.2 kcal/mol less stable at the HF/3-21G level. This increases to 83.0 kcal/mol when relative energies are compared at the MP2/6-31G* level, a difference of 7 3.8 kcal/mol! A comparison of the predicted and experimental geometry of the parent 2,3-C2B4H8is made in Table 11 as well as a comparison of the predicted chair form of C2B4H8and a known structure of a CZB4H8derivative in the chair form. The agreement is reasonable especially between the crystallographic data and the calculated structure in the chair form. A detailed assignment of the vibrational spectrum of nido2,3-CzB4H8has appeared.” To make vibrational assignments of 2,3-C2B4H8, we used IR and Raman spectra of mono- and dimethyl-substituted 2,3-C2B4H8as well as IR spectra of deuteriated 2,3-C2B4H8. A comparison with vibrational frequencies calculated at the HF/3-21G level is made in Table 111. Except where assignments are marked with an asterisk, the dominant character of the normal mode is in agreement with the experimental assignment. The assignments have been reversed for the 1451 and 1233 cm-’ pair of frequencies of a’ symmetry and the 1122 and 954 cm-l pair of frequencies of a’’ symmetry. If the lowest mode of a’ and a” symmetry is disregarded, the calculated frequencies are an average of 11% higher than the experimental ones. Earlier work using a large number of molecules has found that the 3-2 1G basis overestimates the experimental frequencies
+
by the same percentage.14
It is thus reassuring that despite
(13) Jotham, R. W.; McAvoy, J. S.; Reynolds, D. J. J. Chem. SOC.,Dalton Trans. 1912,413-419. (14) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.;Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; hehre, W. Int. J. Quantum Chem. Symp. 1981, 15, 269.
McKee TABLE 111: Comparison of Calculated (3-21C) and Experimental Vibrational Frequencies for nido -2,3-C,B,H8 nido-2,3-CzB4Hs chair C2B4Hs species 3-21G exptl‘ A, % assngtb species 3-21G a’ 3376 3042 11 CH stre 3255 2903 2624 11 BH ap stre 3073 2871 2592 11 BH eq stre 2722 2850 2592 10 BH ax stre 1592 2052 1936 6 Hb stre (s) 1268 1852 1882 -2 Hb stre (s) 1056 1451 1348 8 CH def* 906 1233 1106 11 CC def* 760 1204 1112 8 CH def 697 1135 1034 10 BC stre 352 1053 1069 -1 282 BH eq def 950 854 11 BH ap def 944 9 BH eq def 8 66 2712 vs 93 1 958 -3 1343 cage stre 889 -3 858 1138 vs BB stre 780 784 0 BH ax def 1081 637 8 cage def 687 976 662 586 13 Hb def 753 443 25 cage def 552 722 408 127 cage def 215 (180) a’’ 3358 3032 11 CH stre 2699 9 BH eq stre 2851 2610 1306 1992 1590 25 Hb stre (as) 1138 1694 1510 12 Hb stre (as) 996 1531 1323 16 CH def 922 1179 1052 12 BC stre 650 1146 1033 11 CH def 290 1122 1022 10 BH ax def* -1 972 986 BB stre 3254 6 BB eq def* 3070 954 902 13 BH ap def 946 837 2072 vs 4 BH eq def 1595 765 734 18 Hb def 1189 714 606 2 cage def 951 668 656 -2 600 588 889 cage def 21 cage def 847 484 (400) 326 142
Reference 13. * ap = apical BH; eq = equivalent basal BH; ax = unique basal boron (axial); stre = stretch; def = deformation; s = symmetric; as = antisymmetric. An asterisk indicates that the given assignment is different from the experimental assignment in ref 13.
overestimating the stability of the classical surface relative to the nonclassical surface, the 3-21G basis reproduces the shape of the potential energy well Vibrational frequencies for the chair form are also given in Table I11 to aid possible IR studies. The three vibrational frequenices marked vs have large predicted IR intensities.
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 also donated by the Auburn University Computer Center. Drs. U. Peter and T. Webb are thanked for a careful reading of the manuscript. Registry No. 1, 18972-20-8; 2, 3, 91996-05-3 (15) In contrast, the errors predicted by MNDO for cage compounds are much less systematic: Dewar, M. J. S.; McKee, M. L. J . Mol. Srruct. 1980, 68, 105-118.
