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Comparison of μ2‐scaled Hückel theory and Hartree–Fock theory of boranes and carboranes
dc.contributor.authorRousseau, Rogeren_US
dc.contributor.authorLee, Stephenen_US
dc.date.accessioned2010-05-06T22:11:20Z
dc.date.available2010-05-06T22:11:20Z
dc.date.issued1994-12-15en_US
dc.identifier.citationRousseau, Roger; Lee, Stephen (1994). "Comparison of μ2‐scaled Hückel theory and Hartree–Fock theory of boranes and carboranes." The Journal of Chemical Physics 101(12): 10753-10765. <http://hdl.handle.net/2027.42/70455>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70455
dc.description.abstractThe μ2‐scaled Hückel method is used to calculate the electronic energy surfaces of the four boranes BnH2−n (n=8–11) and the carborane C2B8H2−10. These electronic energy surfaces and their minimum energy geometries are directly compared to both the single crystal x‐ray determined structures and to Hartree–Fock optimized geometries. Bond distances differ on the average by 0.04 Å between alternate methods. It is shown that μ2‐scaled Hückel results may be directly interpreted by analysis of the highest occupied and lowest unoccupied molecular orbitals. Also studied by the μ2‐scaled Hückel and Hartree–Fock methods are the isomerization pathways of B8H2−8, B11H2−11, and C2B8H2−10. Reaction barriers and transition state geometries found by the two different calculational methods are in fair agreement with each other and known literature values. Using the μ2‐scaled Hückel method one can readily deduce that the B8H2−8 and B11H2−11 isomerizations are Woodward–Hoffmann allowed reactions. In the case of B8H2−8 this allowed mechanism is contrasted to an alternate Woodward–Hoffmann forbidden pathway. Hartree–Fock calculations on the C2B8H2−10 confirm earlier μ2‐scaled Hückel based findings, that a second less stable isomer of C2B8H2−10 exists which, in contradiction to Wade’s rules of electron deficient clusters, has a pair of open square faces in the cluster. © 1994 American Institute of Physics.en_US
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dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleComparison of μ2‐scaled Hückel theory and Hartree–Fock theory of boranes and carboranesen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Chemistry, The University of Michigan, Ann Arbor, Michigan 48109‐1055en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70455/2/JCPSA6-101-12-10753-1.pdf
dc.identifier.doi10.1063/1.467888en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
dc.identifier.citedreference(a) W. M. Hehre, L. Radom, P. V. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory (Wiley-Interscience, New York, 1986); and (b) J. Hafner, From Hamiltonians to Phase Diagrams (Springer, New York, 1987); (c) A. Szabo, and N. S. Ostlund, Modern Quantum Chemistry (McGraw-Hill, New York, 1982).en_US
dc.identifier.citedreference(a) R. Hoffmann, J. Chem. Phys. 39, 1397 (1963); (b) R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry (VCH, New York, 1970); (c) T. A. Albright, J. K. Burdett, and M. H. Whangbo, Orbital Interactions in Chemistry (Wiley, New York, 1985); (d) N. L. Allinger, Molecular Mechanics Int. Union Crystallogr. Monogr. Crystallogr. 1, 336 (1992).en_US
dc.identifier.citedreference(a) D. G. Pettifor and R. Podloucky, Phys. Rev. Lett. 53, 1080 (1984); (b) J. K. Burdett and S. Lee, J. Am. Chem. Soc. 107, 3063 (1985); (c) D. G. Pettifor, J. Phys. C 19, 285 (1986); (d) J. C. Cressoni and D. G. Pettifor, J. Phys. 3, 495 (1991); (e) S. Lee, J. Am. Chem. Soc. 113, 101, 8611 (1991); (f) L. M. Hoistad, S. Lee, and J. Paternak, 114, 4790 (1992); (g) L. M. Hoistad and S. Lee, 113, 8216 (1991); (h) S. Lee, Acc. Chem. Res. 24, 249 (1991); (i) Inorg. Chem. 16, 651 (1992); (j) S. Lee, R. Rousseau, and C. Wells, Phys. Rev. B 46, 12 121 (1992); (k) S. Lee and B. Foran, J. Am. Chem. Soc. 116, 154 (1994).en_US
dc.identifier.citedreference(a) K. Wade, Adv. Inorg. Chem. Radiochem. 18, 1 (1976); (b) R. W. Rudolph and W. R. Pretzer, Inorg. Chem. 11, 1974 (1972); (c) R. E. Williams, 11, 210 (1971); (d) A. J. Stone, 20, 563 (1981); (e) D. M. P. Mingos, Acc. Chem. Res. 17, 311 (1984); (f) W. N. Lipscomb, Boron Hydrides (Benjamin, New York, 1963); (g) E. L. Muetterties and W. H. Knoth, Polyhedral Boranes (Wiley, New York, 1968).en_US
dc.identifier.citedreference(a) W. Hume-Rothery and G. V. Raynor, The Structure of Metals and Alloys (Institute of Metal, London, 1962); (b) W. Hume-Rothery, in Phase Stability in Metals and Alloys, edited by P. S. Rudman, J. Stringer, and R. I. Jaffee (McGraw-Hill, New York, 1976), p. 3.en_US
dc.identifier.citedreference(a) For a description of the elemental structures see J. Donohue, The Structure of the Elements (Wiley, New York, 1974); (b) LaSe2:LaSe2: S. Bénazeth, D. Carré, and P. Laruelle, Acta Crystallogr. B 38, 33 (1982); (d) La10Se19:La10Se19:M. Grupe and W. Urland, J. Less. Common. Metals 170, 271 (1991); (e) RbDy3Se8:RbDy3Se8:B. Foran, S. Lee, and M. Aronson, Chem. Mater. 5, 974 (1993); (f) For molecular structures see references in Ref. 3(f)en_US
dc.identifier.citedreferenceFor a discussion of the effect of changes in coordination number on Hückel electronic energies see J. K. Burdett, Struct. Bond. 65, 29 (1987). The effect of this coordination number problem for the Hückel theory of boranes is well studied in (a) W. W. Porterfield, M. E. Jones, W. R. Gill and K. Wade, Inorg. Chem. 29, 2914 (1990); (b) W. W. Porterfield, M. E. Jones, and K. Wade, 29, 2919, 2923, and 2927 (1990).en_US
dc.identifier.citedreferenceG. Herzberg, Molecular Spectra and Molecular Structure: Spectra of Diatomic Molecules (Van Nostrand, Princeton, NJ, 1950).en_US
dc.identifier.citedreference(a) R. S. Mulliken, C. A. Rieke, D. Orloff, and H. Orloff, J. Chem. Phys. 17, 1278 (1949); (b) C. C. J. Roothan, 19, 1443 (1951).en_US
dc.identifier.citedreferenceM. Wolfsberg and L. Helmholz, J. Chem. Phys. 20, 83 (1957).en_US
dc.identifier.citedreferenceV. Heine, I. J. Robertson, and M. G. Payne, Philos. Trans. R. Soc. London Ser. A 334, 393 (1991).en_US
dc.identifier.citedreferenceMany important atomic parameters are used and discussed in (a) R. Hoffmann, J. Chem. Phys. 39, 1397 (1963); A. B. Anderson and R. Hoffmann, 60, 4271 (1974); (b) A. R. Rossi and R. Hoffmann, Inorg. Chem. 14, 365 (1975); (c) P. J. Hay, J. C. Thibeault, and R. Hoffmann, J. Am. Chem. Soc. 97, 4884 (1975); (d) M. Elian and R. Hoffmann, Inorg. Chem. 14, 1058 (1975); (e) R. H. Summerville and R. J. Hoffmann, J. Am. Chem. Soc. 98, 7240 (1976); (f) J. W. Lauher and R. Hoffmann, 98, 1729 (1976) (g) S. Komiya, T. A. Albright, and R. Hoffmann, Inorg. Chem. 17, 126 (1978); (h) T. Hughbanks, R. Hoffmann, M.-H. Whangbo, K. Stewart, O. Einstein, and E. Canadell, J. Am. Chem. Soc. 104, 3876 (1982); (i) D. Thorn and R. Hoffmann, Inorg. Chem. 17, 126 (1978).en_US
dc.identifier.citedreference(a) E. Clementi and C. Roetti, At. Data Nucl. Data Tables 14, 177 (1974); (b)J. B. Mann, Atomic Structures Calculations, 1: Hartree-Fock Energy Results for Elements Hydrogen to Lawrencium (Clearinghouse for Tech. Lit. Springfield. 1967).en_US
dc.identifier.citedreference(a) B8H82−:B8H82−:L. Guggenberger, J. Inorg. Chem. 8, 2771 (1969); (b) B9H9−:B9H9−:7, 2261 (1968); (c) B10H102−:B10H102−:J. T. Gill and S. Lippard, 14, 751 (1975).en_US
dc.identifier.citedreferenceRecent ab initio calculations on borohydrides include: (a) M. Buehl and P. Von R. Schleyer. In Electron Deficient Boron and Carbon Clusters, edited by G. A, Olah. K. Wade, and R. E. Williams (Wiley, New York, 1991), p. 113; (b) M. L. McKee, J. Am. Chem. Soc. 114, 879 (1992); (c) M. Bühl and P. v. R. Schleyer, 114, 477 (1992); (d) M. L. McKee, 113, 9448 (1991); (e) A. M. Mebel, O. P. Charkin, M. Bühl, and P. v. R. Schleyer, Inorg. Chem. 32, 463 (1993); (f) M. L. McKee, M. Buhl, and P. v. R. Schleyer, 32, 1712 (1993); (g) A. M. Mebel, O. P. Charkin, and P. v. R. Schleyer, 32, 469 (1993).en_US
dc.identifier.citedreferenceIn this article all the reported Hartree-Fock calculations used the Gaussian 90 molecular orbital package (Gaussian 90 Revision 1; M. J. Frisch, M. Head-Gordon, G. W. Tucks, J. B. Foresman, H. B. Schelegel, K. Raghavachari, M. Robb. J. S. Binkley, C. Gonzalez, D. J. Fox, R. A. Whiteside, R. Seager, C. F. Melius, J. Baker, R. L. Martin, L. R. Kahn, S. Topoil, and J. A. Pople. Gaussian Inc. Pittsburgh, PA, 1990).en_US
dc.identifier.citedreferenceWe have studied the effect of point group symmetry on the electronic energy of borohydride clusters in Ref. 3(f).en_US
dc.identifier.citedreferenceCharacterization of all stationary points on the potential energy surface was conducted by calculation of theoretical vibrational spectra. For the μ2-μ2- Hückel surface, a Hessian matrix was calculated numerically for the 3N mass weighed Cartesian coordinates of the N skeletal boron or carbon atoms of the clusters. Rotational, translational and one coordinate corresponding to size expansion (not a variable in second moment scaled Hückel theory) were subtracted from the vibrational spectrum prior to stationary point characterization. Thus, in μ2-μ2- Hückel theory there are 3N−73N−7 relevant of internal motion for clusters of this type. This compares to the 3n−63n−6 (where n is the total number of atoms in the cluster) degrees associated with the ab initio calculations. Note that in closo-systems n equals; 2Nnequals;2N as there are equal numbers of hydrogen and boron atoms. Thus we see that frequencies derived from μ2-μ2- Hückel theory cannot be quantitatively compared to Hartree-Fock calculations. We therefore cannot use μ2‐Hückelμ2‐Hückel theory for vibrational analysis studies.en_US
dc.identifier.citedreferenceThe parameters used for Hückel calculations correspond to those compiled in Ref. 12. For carbon the parameters are Hii(2s)  =  −21.4 eV,Hii(2s)=−21.4eV, Hii(2p)  =  −11.4 eV,Hii(2p)=−11.4eV, ξ(2s)  =  1.625,ξ(2s)=1.625, and ξ(2p)  =  1.625.ξ(2p)=1.625. For hydrogen the parameters are Hii(1s)  =  13.6 eVHii(1s)=13.6eV and ξ(ls)  =  1.30.ξ(ls)=1.30. Boron parameters are given in the text.en_US
dc.identifier.citedreferenceFor this detailed analysis using the Walsh diagram approach see R. Rousseau, and S. Lee, in Graph Theory Approaches to Chemical Reactivity, edited by D. Bonchev (Kluwer, Dordrecht, in press).en_US
dc.identifier.citedreferenceAt θ  =  51°θ=51° the bond lengths are a  =  1.46 ,a=1.46Å, b  =  2.13 ,b=2.13Å, and c  =  2.32 c=2.32Å as compared to θ  =  60°,θ=60°, a  =  1.68 ,a=1.68Å, b  =  1.79 ,b=1.79Å, c  =  1.87 .c=1.87Å.en_US
dc.identifier.citedreference(a) E. L. Muetterties, R. J. Wiersema, and M. F. Hawthorne, J. Am. Chem. Soc. 95, 7520 (1973); (b) E. L. Muetterties, Tetrahedron 30, 1595 (1974).en_US
dc.identifier.citedreference(a) W. N. Lipscomb, Science 153, 373 (1966); (b) D. P. M. Mingos and D. J. Wales, in Electron Deficient Boron and Carbon Clusters, edited by G. A. Olah, K. Wade, and R. E. Williams (Wiley, New York, 1991); (c) A. Rodgers and B. F. G. Johnson, Polyhedron 7, 1107 (1988); (d) R. B. King, Inorg. Chim. Acta 49, 237 (1981); Theor. Chem. Acta 64, 439 (1984); (e) D. J. Wales, D. M. P. Mingos, and Z. Lin, Inorg. Chem. 28, 2754 (1989).en_US
dc.identifier.citedreference(a) D. A. Kleier and W. N. Lipscomb, Inorg. Chem. 18, 1312 (1979); (b) D. J. Wales and R. G. A. Bone, J. Am. Chem. Soc. 114, 5394 (1992); (c) J. W. Bausch, G. K. Surga Prakash, and R. E. Williams, Inorg. Chem. 31, 3763 (1992); (d) M. Buhl, A. M. Mebel, O. P. Charkin, and P. v. R. Schleyer, 31, 3769 (1992); (e) D. J. Wales, J. Am. Chem. Soc. 115, 11 191 (1993); (f) D. J. Wales and A. J. Stone, Inorg. Chem. 26, 3845 (1987).en_US
dc.identifier.citedreference(a) K. Müller and L. D. Brown, Theor. Chem. Acta 53, 77 (1979); (b) M. J. S. Dewar, E. F. Healey, and J. P. Stewart, J. Chem. Soc. Faraday Trans. 2 80, 272 (1989).en_US
dc.identifier.citedreferenceA detailed analysis of other diamond to square to diamond rearrangements for closo BnHn2−BnHn2− clusters exists in the literature. It is known that B8H82−B8H82− and B11H112−B11H112− are Woodward-Hoffmann allowed processes and that they are fluxional. By contrast in B5H52−B5H52− and B9H92−B9H92− the diamond to square to diamond rearrangements are symmetry disallowed processes and the molecules are not fluxional. See B. M. Gimarc and J. J. Ott, Inorg. Chem. 25, 83, 2708 (1986).en_US
dc.identifier.citedreference(a) E. I. Tolpin and W. N. Lipscomb, J. Am. Chem. Soc. 95, 2384 (1973); (b) E. L. Muetteries, E. L. Hoel, C. G. Salentine, and M. F. Hawthorne, Inorg. Chem. 14, 950 (1975).en_US
dc.identifier.citedreference(a) D. A. Kleier, D. A. Dixon, and W. N. Lipscomb, Inorg. Chem. 17, 166 (1978); (b) B. M. Gimarc, B. Dai, D. S. Warren, and J. J. Ott, J. Am. Chem. Soc. 112, 2597 (1990).en_US
dc.identifier.citedreferenceB. Stibr, Z. Janousek, K. Base, S. Hermanek, J. Plesek, and I. Zakharova, Collect. Czech. Chem. Commun. 49, 1891 (1984).en_US
dc.identifier.citedreferenceR. E. Williams, in Electron Deficient Boron and Carbon Clusters, edited by G. A. Olah, K. E. Wade, and R. E. Williams (Wiley, New York, 1991).en_US
dc.identifier.citedreferenceC. Scott, B. W. Eichhorn, and S. G. Bott, J. Am. Chem. Soc. 115, 5837 (1993).en_US
dc.identifier.citedreferenceIt is important to note that the isoelectronic homoatomic Hiickel calculation neglects any effects of the overall increase in the total net charge of the system. It is clear that in a −4−4 cluster, this net charge should have an important consequence. At the ab initio 3-21G∗ level for instance, calculations show that neither B10H104−B10H104− nor Li2[B10H104−]Li2[B10H104−] have a stable nido-10 (iv+iv)(iv+iv) isomer.en_US
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