Energy Barriers in the Dimerization Reactions

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Energy Barriers in the Dimerization Reactions J. Phys. Chem. 1987, 91, 1857-1864 1857 Binary Association Complexes of LiH, BeH,, and BH,. Relative Isomer Stabilities and Barrier Heights for Their Interconversion: Energy Barriers in the Dimerization Reactions D. J. DeFrees,*lPKrishnan Raghavachari,*lbH. B. Schlegel,*'c J. A. Pople,*ld and P. v. R. Schleyer*" Department of Chemistry, Carnegie- Mellon University, Pittsburgh, Pennsylvania 1521 3; Molecular Research Institute, Palo Alto, California 94304; AT& T Bell Laboratories, Murray Hill, New Jersey 07974; Department of Chemistry, Wayne State University, Detroit, Michigan 48202; and Institut fur Organische Chemie, Universitat Erlangen- Niirnberg, 0-8520 Erlangen. Federal Republic of Germany (Received: November 17, 1986) Ab initio molecular orbital theory has been used to study the six compounds LizHz,LiBeH,, LiBH4, Be2H4,BeBH,, and B2H6. Geometry optimizations and vibrational analysis at the HF/6-31G* level indicate Li- -(H),--Li (DZh),Li- -(H),- -BeH (C2"),Li--(H),--BH (C3u),HBe--(H),--BeH (&), HBe--(H)3--BH (C3J, and H2B--(H),--BH2(&h) to be the most stable forms. Inclusion of electron correlation corrections at the MP4/6-3 IG** level does not alter these conclusions. Other isomers were also examined in detail, and it was found that the potential energy surfaces for the species are generally flat. Activation energies for isomer interconversion and hydrogen scrambling reactions are generally less than 10 kcal mol-'. Examination of the HF/3-21G potential surfaces indicates that there is no activation energy for the dimerization of LiH or BeH2. The same is true for the dimerization of BH3 at the correlated MP2/6-31G* level, although a small barrier is found on the HF/6-31G* surface. Enthalpies of complexation at 298 K from separate LiH, BeH,, and BH3 fragments, computed by using the HF/6-3 lG* harmonic frequencies and the MP4/6-3 lG** electronic energies are as follows: Li2H2,-45.9; LiBeH,, -43.6; LiBH4, -60.1; Be2H4,-30.5; BeBH,, -45.7; B2H6,-36.0 kcal mol-'. Introduction TABLE I: Distances (A) between Non-Hvdroeen Atoms The electron-deficient hydrides of lithium (LiH), beryllium molecule point group STO-3G 3-21G 6-31G' (BeH,), and boron (BH,) interact to form six binary association LiH- -LiH C,, 3.331 3.445 3.436 complexes which can contain a number of bridging hydrogen Li- -(H)2--Li D2h 2.222 2.364 2.343 atoms2*, Diborane, the experimentally well-established BH3 LiH- -BeH, C2" 3.122 3.123 3.104 dimer, has two such hydrogen^.^ LiH,2*3LiBeH3,4 and LiBH42 Li- -(H),- -BeH C2" 2.157 2.284 2.243 are known as crystalline solids; the atomization energy of the Li- -(H)3--Be C3" 1.842 1.977 1.940 lithium hydride dimer, (LiH)2,has been determined experimen- Li- -(H)2--BH, c2, 2.083 2.193 2.154 tally., Solid BeH2 is throught to be a polymer with two bridging Li- -(H)3--BH C3" 1.877 2.013 1.968 hydrogens between each pair of beryllium atoms.2*6 HBeH- -BeH2 c2, 3.977 3.174 3.777 ln an earlier ab initio molecular orbital.study,2 the relative HBe--(H),--BeH D2* 1.991 2.050 2.018 HBe- -(H),- -Be c3 " 1.738 1.803 1.774 energies of structures with various numbers of bridging hydrogens HBeH- -BH3 c, " 3.821 3.206 3.591 were considered, and it was concluded that the most stable forms HBe--(H)2-BH2 C2" 1.876 1.891 1.870 were Li- -(H)2--Li (&), Li- -(H)2--BeH (C2"),Li- -(H)3--BH HBe--(H),--BH C3" 1.686 1.732 1.700 (e3"),HBe- -(H),--BeH (D2h),HBe- -(H),--BH (C3J, and H,B--(H),--BH, D2h 1.805 1.785 1.778 H2B--(H)2- -BH2 ( D2h,with bridging and terminal hydrogens in perpendicular planes). Some of these complexes can be considered on non-hydrogen atoms). The results left a number of unanswered to be ionic. For example, lithium borohydride can be viewed as questions: a Li+ cation attached to the face of a BH4- tetrahedron, Li-- 1. Are the results modified if a higher level basis is used for (H),- -BH; structures with edge (Li- -(H)2--BH2) or corner geometry optimization? (Li- -H- -BH3) attachments are less stable. 2. Does inclusion of polarization functions on hydrogen (p The previous study was carried out entirely at the Hartree-Fock functions) change the relative energies of structures with different (HF) leveL2 Geometries were optimized with the minimal numbers of bridging atoms? STO-3G7 basis set, and single-point computations were performed 3. Do the stationary points found on the potential surface all using the 6-3 1 G* basis8 (split-valence with polarization functions correspond to local minima (separate isomers) or are some of them saddle points (transition structures connecting distinct isomers or connecting equivalent isomers) leading to scrambling of the (1) (a) Carnegie-Mellon University and Molecular Research Institute. bridging and terminal hydrogens? Current address: Molecular Research Institute. (b) Carnegie-Mellon University and AT&T Bell Laboratories. Current address: AT&T Bell 4. Are the relative isomer energies and binding energies (for Laboratories. (c) Carnegie-Mellon University and Wayne State University. dissociation to separate LiH, BeH2, and BH, fragments) altered Current address: Wayne State University. (d) Carnegie-Mellon University. significantly if electron correlation is included in the theoretical (e) Universitat Erlangen-Nilrnberg. model? (2) Dill, J. D.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. A. J. Am. Chem. SOC.1977, 99, 6159 and references cited therein. 5. What is the nature of the association reactions; are there (3) (a) Wiberg, E.; Amberger, E. Hydrides of the Elements of Main activation barriers? Groups I-IK Elsevier: Amsterdam, 1971. (b) Wade, K. Electron DeJicient Since only partial answers to some of these questions can be Compounds; Nelson: 197 1. found in the literature, much of which was cited in our previous (4) Ashby, E. C.; Prasad, H. S. Inorg. Chem. 1975, 14, 2869. (5) Ihle, H. R.; Wu, C. H. Adu. Mass Spectrom. 1978, 7A, 636. paper,* or in recent studies (cited below), a comprehensive (6) Marynick, D. S. J. Am. Chem. Soc. 1981, 103, 1328 and references reexamination of these six compounds at a uniform level oftheory cited therein. (7) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657. (8) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. 0022-3654/87/2091-1857$01.50/0 0 1987 American Chemical Society 1858 The Journal of Physical Chemistry, Vol. 91, No. 7, I987 DeFrees et al. TABLE 11: Optimized Total Energies (hartrees) and Number of Imaginary Frequencies“ molecule point group STO-3G 3-21G 6-31G* LiH -7.863 38 (0) -7.92984 (0) -7.98087 (0) BeH, -15.561 35 (oj -15.673 78 (oj -15.76593 (oj BH3 -26.070 70 (0) -26.237 30 (0) -26.39001 (0) LiH- -LiH -15.765 10 (2) -15.902 19 (0) -16.00331 (0) Li- -(H)2--Li -15.79681 (0) -15.933 25 (0) -16.035 59 (0) LiH- -BeH2 -23.44246 (2) -23.634 38 (2) -23.777 67 (2) Li- -(H)2--BeH -23.481 86 (0) -23.66447 (0) -23.81 100 (0) Li- -(H)3--Be -23.458 04 (0) -23.641 45 (0) -23.788 85 (0) Li- -(H)2--BH2 -33.99207 (1) -34.23807 (1) -34.441 92 (1) Li- -(H)3--BH -34.00247 (0) -34.243 84 (0) -34.449 98 (0) HBeH- -BeH2 -31.12357 (0) -31.34944 (1) -31.53314 (1) HBe- -(H)2--BeH -31.15400 (0) -31.378 05 (0) -31.570 19 (0) HBe- -(H)3--Be -31.10896 (0) -31.334 10 (0) -31.52786 (0) HBeH- -BH3 -41.63303 (2) -41.91566 (0) -42.15791 (2) HBe- -(H)2--BH2 -41.667 59 (0) -41.949 45 (0) -42.20074 (0) HBe--(H)3--BH -41.669 87 (0) -41.948 31 (0) -42.205 28 (0) H2B- -(H)2--BH2 -52.166 10 (0) -52.497 81 (0) -52.81240 (0) a In parentheses following the total energy. is appropriate. The objective of this paper is to examine these TABLE III: Harmonic Vibrational Frequencies (cm-’) and molecules by using newer theoretical methods in an attempt to Zero-Point Vibrational Ehergies (kcal mol-’) Evaluated at the answer the questions posed above. HF/6-31G* Level Theoretical Methods and Results point molecule group harmonic frequencies ZPE The most favorable HF/STO-3G structures, reported previ- LiH C,, 1416(a) 2.0 ously,2 were optimized by gradient minimizationg within the in- BeH2 D..h 761(~,),2107(~,), 2323(~,) 8.5 dicated symmetry constraints using the split-valence 3-21G basislo BH3 Djh 1225(a?), 1305(e’), 2693(a,’), 17.4 and the polarization 6-31G* basis set.8 Table I gives the distances 28 13(e’) between non-hydrogen atoms; full structures are published sep- Li- -(H),- -Li D2h 516(a,), 609(b3,), 851(b3,), 1.4 arately.” Addition of p polarization functions to the basis set 952(b1,), 1056(b2d, 1164(a,) used for geometry optimization (HF/6-31G** geometries) does Li- -(H)2--BeH C2, 346(bl), 589(al), 602(b2), 899(b,), 14.4 not significantly alter the result. For exam le, the HF/6-31G* 1137(b2), 1259(a,), 1517(b2), eometry for diborane is r(B-B) = 1.778 , r(B-Hb) = 1.316 1663(al), 2085(a1) w Li- -(H)3--BH C,, 491(e), 683(a,), 1225(e), 1338(al), 25.3 r(B-H) = 1.185 and L(H-B-H) = 122.1’ (Hb indicates 1, A, 1365(e), 2240(e), 2323(a,), the bridging hydrogen); this is virtually identical with the HF/ 6-31G** geometry of r(B-B) = 1.778 A, r(B-Hb) = 1.317 A, r(B-H) = 1.185 A, and L(H-B-H) = 122.0’.
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