A theoretical study of internal rotation in H2BOBH2and H2BNBH2-

摘要

Mendeleev Communications Electronic Version, Issue 2. 1997 (pp. 47ndash;86) A theoretical study of internal rotation in H2BOBH2 and H2BNBH2 ndash; Ruslan M. Minyaev* and Evgenii A. Lepin Institute of Physical and Organic Chemistry, Rostov State University, 344090 Rostov-on-Don, Russian Federation. Fax: +7 863 228 5667 It has been shown by using MP2(fc)/6-31G** and MP2(fc)/6-311+ +G** methods that the internal rotation of H2BNBH2 ndash; and H2BOBH2 allene structures occurs through the corresponding angle structures with a very small energy barrier.Boron anhydrides 1, according to experimental data,1ndash;3 have a stable angular structure with bond angle BOB varying in a wide range depending on R1, R2. The BOB fragment in anhydrides 2 appears3,4 to have a linear structure. The angle form of the BOB fragment (BOB 180deg;) has been observed in pyroborate ions 3 of various metal salts.3 The planar structure (D2h) has been established for 1 (R1 = R2 = F).5 At the same time, according to X-ray data,6,7 lsquo;isoelectronic (relative to BOB fragment) analoguesrsquo; 4 and 5 have the allene structure.Bond BO is considered to be stronger than BC and BN bonds and to have higher p-bond order.3 Hence these facts should lead to more favourable stable form of the allene type for 1ndash;4.To elucidate the thermodynamic difference between allene and angle forms of the BOB and BNB fragments in 1ndash;5 here we report ab initio MP2(fc)/6-31G** and MP2(fc)/6-311+ +G**8,9 calculations on the thermodynamic stability of allene 6 and angle 7 structures and their rearrangements (internal rotation) for model compounds H2BYBH2 (Y = Nndash;, O).Allene structure (7, Y = Nndash;), according to ab initio calculations, corresponds to a minimum on the H2BNBH2 potential energy surface (PES) whereas the angle form (6, Y = Nndash;) corresponds to a saddle point (hessian has one negative eigenvalue) and is the transition state structure for simultaneous internal rotation of the both BH2 groups around BN bonds (Scheme 1).Bond BN predicted by ab initio calculations (Figure 1) in 7 is very close to the similar bond in 5 where it equals 1.38(2) Aring;.7 Planar structure (8, Y = Nndash;) with D2h symmetry corresponds to the top of a hill (hessian has two negative eigenvalues). Geometry and energy for 6ndash;8 are presented in Figure 1 and Table 1. Thus, anion (H2B)2Nndash; is stable only in the allene form (7, Y = Nndash;) and internal rotation in 7 occurs, according to Scheme 1, by two equivalent pathways 7a 6a 7b and 7a 6b 7b, with overcoming of the energy barrier of 15.5 and 12.8 kcal molndash;1dagger; predicted by MP2(fc)/6-31G** and MP2(fc)/6-311+ +G** methods, respectively.In contrast to anion (H2B)2Nndash;, boran (H2B)2O has two stable structures, angle 6 and allene 7, the energy difference of which is very dagger; 1 cal=4.184 J.small. The ab initio MP2(fc)/6-31G** method predicts that allene form 7 is more favourable by 0.43 kcal molndash;1 than angle structure 6. Increasing the level of calculation to MP2(fc)/6-311+ +G** changes the energetic stability of 6 and 7: angle structure 6 becomes 1.3 kcal molndash;1 more favourable than 7. Both structures 6 and 7 can convert into each other via transition state structure 9 by overcoming energy barrier of 1 and 0.2 kcal molndash;1 calculated by MP2(fc)/6-31G** and MP2(fc)/6-311+ +G** methods, respectively (see Table 1).Geometric and energetic characteristics of 6ndash;9 are presented in Table 1 and Figure 2. The length of the BO bond predicted by ab initio calculations is in the range of experimentally-known lengths (1.30ndash;1.40 Aring;) of similar bonds.1ndash;5,10 The PES topology of (H2B)2Y (Y = Nndash;, O) in the region of the internal rotation, according to ab initio calculations, is very complicated and internal rotation in (H2B)2Y which occurs due to Scheme 1 differs from the usual one-valley pathway.To R1 B O B R1 R2 R2 O B O B O O O B O C C B C C 1 2 3 C B C C C SiMe3 SiMe3 B N Ar Ar C Ph Ph 4 5 ndash; B Y H H B H H H B Y B H H H 6, C2v 7, D2d B Y H H B H H H B Y B H H H H B Y B H H H B Y H H B H H B Y B H H H H 6a (Y = Nndash;), C2v 7a (Y = Nndash;), D2d 8 (Y=Nndash;), D2h 7b (Y = Nndash;), D2d 6b (Y=Nndash;), C2v Scheme 1 Figure 1 Geometric parameters of stable structure 7, transition state structure 6 and the configuration 8 corresponding to stationary point with index two for (H2B)2Nndash; calculated by ab initio MP2(fc)/6-31G** and MP2(fc)/6-311+ +G** (number in parenthesis).Bond lengths are given in angstrom, bond angle in degrees. (1.400) 1.403 (121.3) 121.9 114.5 (113 .5) 117.3 (117.1) 1.224 (1.226) (1.230) 1.224 B N B 6, C2v B N B (1.359) 1.362 (1 .216 ) 1 .222 116.5 (115.9) 7, D2d B N B 111.1 (111.4) (1.370) 1.368 (1.243) 1.235 8, D2hMendeleev Communications Electronic Version, Issue 2. 1997 (pp. 47ndash;86) show that the reaction pathway in (H2B)2Y consists of two equivalent gradient lines we calculated all gradient lines (orthogonal trajectories) for analytic function V(a,b) (where a is a rotational angle and b an inversion angle) approximating the (H2B)2O PES in the region of the internal rotation (a = ndash;90 to 90deg;, b = ndash;90 to +90deg;). A two-dimensional map of V(a,b) and its field of the orthogonal trajectories are presented in Figure 3.As one can see from Figure 3, all gradient lines are originated or terminated only stationary points (DE = 0) or comes to infinity.11 Gradient lines cannot bifurcate or disappear in regular points (DE � 0). Only two gradient lines connect minima 7a and 7b passing through saddle points 9andash;d and lsquo;intermediatesrsquo; 6a and 6b, respectively.These two equivalent gradient lines make up the gradient reaction path of the internal rotation.11 Thus, the internal rotation in boranes (H2B)2Nndash; and (H2B)2O occurs according to Scheme 1. Small energy difference between the two structures 6 (Y = O) and 7 (Y = O) and the negligible energy barrier separating these forms appears to be crucial in hampering the experimental observation of the separate allene and angle structures.The authors thank INTAS (grant no. 94-0427) and Russian State Committee on the High Education (grant no. 95-0-9.1-70) for financial support of the present work. References 1 A. Pelter and K. Smith, in Comprehensive Organic Chemistry. The Synthesis and Reactions of Organic Compounds, eds.D. Barton and W. D. Ollis, Pergamon Press, New York, 1979, vol.3. 2 N. N. Greenwood, in Comprehensive Inorganic Chemistry, eds. J. S. Bailard, H. J. Emeleus, R. Nyholm and A. F. Trotman-Dickenson, Pergamon Press, New York, 1973, p.665. 3 A. F. Wells, Structural Inorganic Chemistry (5th edition), Claredon Press, Oxford, 1986. 4 M. F. Lappert, Chem. Rev., 1956, 56, 959. 5 K. S. Krasnov, N. V. Filipenko, V. A. Bobkova, N. L. Lebedeva, U. V. Morozov, E. I. Ustinova and G. A. Romanova, Moleculyarnye postoyannye neorganicheskikh soedinenii (Molecular constants of inorganic compounds), Khimiya, Leningrad, 1979, p. 446 (in Russian). 6 M. Pilz, J. Allwohn, P. Willershausen, W. Massa and A. Berndt, Angew. Chem., Int. Ed. Engl., 1990, 29, 1030. 7 G. J. Bullen, J.Chem. Soc., Dalton Trans., 1973, 8, 858. 8 W. J. Hehre, L. Radom, P. v. R. Schleyer and J. A. Pople, Ab initio molecular orbital theory, J. Wiley amp; Sons, New York, 1986. 9 M. J. Frish, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. A. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Allaham, V. G. Zakrzewski, J. V.Ortiz, J. B. Foresman, C. Y. Peng, P. Y. 117.1 (117.3) 1.186 ( 1. 190 ) 1.189 (1.194) 123.6 (122.9) (1.378) 1.379 122 .9 (122.8) B O B 6, C2v B O B (1.344) 1.345 1. 188 (1.192) 123.0 (123.2) 7, D2d B O B 122.5 (122.8) 136.3 (144.4) (1.357) 1.366 (a) 1.186 (1.181) B O B (107.5) 99.5 (b) 9, C2 B O B 121.3 (121.4) (1.358) 1.358 1.1 91 (1.197) 8, D2h Figure 2 Geometric parameters of stable structures 6 and 7, transition state structure 9 in two projections, (a) face view and (b) side view and the form 8 corresponding to stationary point with index two for borane (H2B)2O calculated by ab initio MP2(fc)/6-31G** and MP2(fc)/ 6-311++G** (numbein parenthesis). Bond lengths are given in angstrom, bond angle in degrees.a 1hartree=627.5095 kcalmolndash;1. Table 1 Total energy (Etot in hartree), relative energy (DE in kcal molndash;1),a the number of the negative hessian eigenvalues (l), zero point energy (ZPE in hartree), relative energy with including ZPE (DEZPE in kcal molndash;1),a the imaginary or the smallest positive frequency (in/n1 in cmndash;1) predicted by MP2(fc)/6-31G** and MP2(fc)/6-311+ +G** (in parenthesis) methods for structures 6ndash;9 of H2BYBH2 ( Y = N ndash;, O).Structure Etot DE l ZPE DEZPE in/n1 6 ( Y = N ndash;), C2v ndash;106.51136 (ndash;106.57030) 16.5 (12.6) 1 (1) 0.04507 (0.04357) 15.4 (11.8) i136.5 (i87.8) 7 ( Y = N ndash;), D2d ndash;106.53765 (ndash;106.59043) 0 (0) 0 (0) 0.04674 (0.04492) 0 (0) 257.0 (224.3) 8 ( Y = N ndash;), D2h ndash;106.49421 (ndash;106.54802) 27.2 (26.6) 2 (2) 0.04393 (0.04182) 25.5 (24.6) i988.3; i262.8 (i964.2; i309.1) 6 (Y=O), C2v ndash;126.97325 (ndash;127.02904) 0.43 (ndash;1.3) 0 (0) 0.04834 (0.04714) 0.5 (ndash;1.2) 206.4 (214.9) 7 (Y=O), D2d ndash;126.97394 (ndash;127.02690) 0 (0) 0 (0) 0.04823 (0.04688) 0 (0) 121.3 (92.9) 8 (Y=O), D2h ndash;126.95743 (ndash;127.01048) 10.4 (10.3) 2 (2) 0.04671 (0.04531) 9.4 (9.3) i495.7; i284.4 (i492.6; i306.3) 9 (Y=O), C2 ndash;126.97169 (ndash;127.02651) 1.4 (0.2) 1 (1) 0.04783 (0.04660) 1.2 (0.1) i180.1 (i95.1) 30deg; 0deg; ndash;30deg; ndash;90deg; 0deg; 90deg; a b 6a 7b 6b 7a a b Figure 3 Two-dimensional map and orthogonal trajectories of V(a,b).Thin close lines designate contour lines, thin lines being orthogonal to contour lines are gradient lines (orthogonal trajectories). Gradient line reaction path of the internal rotation consists of two equivalent gradient lines a and b. Angles a denote the rotation angle around OB bond (zero value corresponds to planar structure 8), b ndash; inversion angle BOB (zero value corresponds to BOB=180deg;), respectively.Mendeleev Communications Electronic Version, Issue 2. 1997 (pp. 47ndash;86) Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, Gaussian-94, Revision B.3, Gaussian Inc., Pittsburgh PA, USA, 1995. 10 F. H. Allen, O. Kennard and D. G. Watson, J. Chem. Soc., Perkin Trans. 2, 1987, S1. 11 R. M. Minyaev, Int. J. Quant. Chem., 1994, 49, 105. Received: Moscow, 18th November 1996 Cambridge, 15th January 1997; Com. 6/08038C