Borinine (Borabenzene): Its Structure and Vibrational Spectrum. A Quantumchemical Study Gerhard Raabe, Wolfgang Schleker, Eberhard Heyne, and Jörg Fleischhauer Lehr- und Forschungsgebiet Theoretische Chemie der Rheinisch-Westfälischen Technischen Hochschule Aachen Z. Naturforsch. 42a, 352-360 (1987); received December 31, 1986 Recently we reported the results of some semiempirical and ab initio studies in which we compared the electronic structure of the hitherto unknown borinine with those of benzene and pyridine. The results of our calculations led us to the conclusion that the elusive nature of borabenzene is caused by its high reactivity, which might at least in part be due to the pronounced a acceptor properties of a low-lying er* molecular orbital. We now present the results of further ab initio and semiempirical (MNDO) investigations in which we performed full geometry optimizations for the molecule using two different basis sets (STO-3G, 4-31G) and also calculated the vibrational spectra of the 10B and "B isotopomeric borabenzene molecules at the 4-31 G level of ab initio theory and with the semiempirical MNDO method. The calculated vibrational spectrum might be helpful to the experimentalist in identifying the molecule, for example trapped in a rare gas matrix among the side products. The calculated orbital energies can be useful in identifying the molecule by means of its photoelectron spectrum. 1. Introduction Further it was found, that among its doubly occu- pied orbitals there are three of n symmetry. This Although a lot of borabenzene complexes are last result was confirmed by an STO-3G single known [1], and even though it was possible to trap point calculation using the MNDO optimized struc- the molecule with pyridine [2, 3] to our knowledge ture [4], If we accept three doubly occupied molec- no preparation and characterization of the unsub- ular orbitals of n symmetry in a planar perimeter as stituted neutral borinine* has been reported until a criterion for aromaticity, we have to consider the today. The problems which obviously occur during closed shell singlet of borinine as an aromatic. This the preparation of this elusive molecule may have aromatic however, in contrast with e.g. pyridine two reasons: and phosphabenzene, should be destabilized by its 1. In contrast to the substituted borinine deriva- pronounced acceptor properties, which are due to a tives, which serve as ligands in the complexes men- low-lying er* orbital [4], The reason for the hitherto tioned above, and different from the situation in its fruitless attempts to prepare and characterize the trapping product with pyridine, the unsubstituted borabenzene molecule [3] may therefore lie in its and unstabilized sixmembered ring might be no high reactivity which might cause reactions even with relatively inert matrix and carrier gases, not to longer a minimum on the C5H5B hypersurface. speak of those possible reactions with molecules of 2. The high reactivity of the target molecule is the reactants and of side products. reason for its elusive character. The results of our preceeding study are further In a previous study [4] we found that at least at supported by the calculations presented here, which the semiempirical MNDO level the C hexagon is 2v not only prove that the planar sixmembered ring of a stationary point on the C5H5B hypersurface. C2v symmetry is a real minimum at the MNDO level, but that similar minima exist at the STO-3G Reprint requests to Prof. Dr. Jörg Fleischhauer; Lehr- und and 4-31 G level of ab initio theory, too. Forschungsgebiet Theoretische Chemie der Rheinisch- The identification of the molecule, for example Westfälischen Technischen Hochschule Aachen, D-5100 Aachen. West Germany. trapped in a matrix, will be facilitated if one knows * For nomenclature see [1], something about its spectroscopic properties in 0340-4811 / 87 / 366-0310 S 01.30/0. - Please order a reprint rather than making your own copy. G. Raabe et al. • Borinine (Borabenzene): Its Structure and Vibrational Spectrum 353 advance. We therefore calculated the vibrational spectra of both isotopomers, containing either 10B or "B atoms. These calculations were performed using a 4-31 G basis set [5], as well as the semi- empirical MNDO method [6], 2. Computational method All calculations were performed on the CDC Cyber 175 of the Rechenzentrum der RWTH Aachen. For the ab initio calculations we used the HONDO 5 Fig. 1. Choice of coordinate system in symmetry analysis program package [7], Geometry optimization at the of the vibrational spectra and the molecular orbitals. STO-3G level [8] was started from a planar hexagon with the following bond distances and angles* (for accomplished by numerical differentiation of numbering of atoms see Figure 1): B[-C : 1.53 A, 2 analytical gradients [13]. In the case of the semi- C -C : 1.40 A, C -C : 1.41 A, C-H: 1.10 A, 2 3 3 4 empirical method, this matrix was calculated com- £C2-B,-C6: 113.8°, £B,-C2-C3: 119.8°, pletely numerically, using a standard MNDO pro- <C2-C3-C4: 124.9°, * C3-C4-C5: 116.8°, gram [14], modified by us. In the calculation of the £B,-C2-H: 121.1°, <C2-C3-H: 118.4°. The STO-3G optimized structure was then used as a second derivatives we used a step width of 0.01 A. starting point for optimization at the 4-31 G level [5], If not mentioned otherwise, no symmetry con- straints have been imposed during the optimization 3. Results and Discussion procedure. However, symmetry constraints turned out to be indispensable in the calculation of the The total energies of the optimized structures vibrational spectra. Otherwise, the HONDO 5 pro- are given in Table 1. To get an idea of the quality of gram did not "recognize" the symmetry of the the MNDO optimized geometry, the total energies molecule. of the MNDO structure at the STO-3G (STO-3G/ MNDO)* and the 4-31 G level (4-31 G/MNDO) are The natural abundances of the two stable boron listed there, too. In addition Table 1 contains the isotopes are 80.22% "B and 19.78% ,0B [10], leading 4-31G energy of the STO-3G optimized structure to an average atomic mass of 10.811. Due to the (4-31 G/STO-3G). high percentage of l0B, the vibrational spectrum of The structures of the molecule optimized at the C H 10B should be observed beside that of C H5nB 5 5 5 different levels of theory employed here are shown in a sample containing borabenzene, prepared from in Figure 2**. With all methods the molecule precursors containing boron in its natural isotopic turned out to be planar. Checking the eigenvalues composition. Because the electronic structures, and of the force constant matrices confirmed that all therefore the force constant matrices of isotopic structures are true minima. molecules are the same to a high level of approxi- mation [11], we calculated the isotopic shifts by Alternation of the bond lengths in the ring massweighting the cartesian force constant matrix is only weak. According to both ab initio meth- once using 10 and once 11 for the atomic mass of ods the bond lengths decrease in the order boron. B,-C2 > C2-C3 > C3-C4, whereas MNDO gives the order B, -C = C -C < C -C . Different In the HONDO 5 program the force constant 2 3 4 2 3 matrix was calculated by the force method [12], in which the calculation of the second derivatives is * The symbol (method 2/method 1) means that the geometry has been optimized with method 1, while a single point calculation using that structure has been * Bond lengths and the angle at boron were taken from performed with method 2. the boratabenzene part of the ligand in tricarbonyl(l- ** Our STO-3G minimum is completely different from phenylborinato)manganese [9]. the one given in [15]. 354 G. Raabe et al. • Borinine (Borabenzene): Its Structure and Vibrational Spectrum 354 Table 1. Total energies (in a. u.). Table 2a. Eigenvalues of the borinine Table 2 b. Eigenvalues of the borinine molecule according to STO-3G/STO- molecule according to 4-31G/4-31G Method Total energy 3G (all values in a. u.). (all values in a. u.). STO-3G/MNDO -214.197667 No. e Type No. £ Type 4-31 G/MNDO -216.554189 21 0.23616 Ha, (cr) 21 0.10219 11 a,(a) STO-3G/STO-3G -214.200641 LUMO LUMO 4-31 G/STO-3G -216.557482 4-31G/4-31G -216.558625 20 -0.23696 2b2(;r) 20 -0.29264 2b2(7T) HOMO HOMO 19 -0.27888 U (Tx) 2 19 -0.33634 1 a2 (TT) 18 -0.41753 7b, 18 -0.47559 7b, 17 -0.44064 lb 2(B) 17 -0.48314 lb2(7t) 16 -0.45171 10a, 16 -0.50792 10a, 15 -0.51069 6b, 15 -0.57198 9a, 14 -0.51664 9a, 14 -0.57391 6b, 13 -0.55312 5b, 13 -0.60707 5b, 12 -0.63016 8a, 12 -0.67986 8a, 11 -0.68037 7a, 11 -0.73408 7a, 10 -0.74689 4b, 10 -0.80390 4b, 9 -0.87105 6a, 9 -0.93039 6a, 8 -0.95361 3b, 8 -1.01324 3b, 7 -1.06011 5 a, 7 -1.11995 5a, 6 -7.39108 4a, 6 -7.60082 4a, 5 -10.98787 2b, 5 -11.18998 2b, 4 -10.98793 3 a, 4 -11.19002 3a, 3 -10.99609 2a, 3 -11.19138 2a, 2 -11.03136 la, 2 -11.22433 la, 1 -11.03140 lb, 1 -11.22436 lb, MNDO from the case of pyridine [16] some of the bond angles significantly deviate from 120°. Com- M Hs mon feature of the optimized structures is, beside C^ '22.3 their planarity, the wide C2-B,-C6 angle.