9264
J. Phys. Chem. 1992,96,9264-9268
(1 1) Partridge, H.; Bauschlicher, C. W.; Sodupe, M.;Langhoff, S. R. Chem. Phys. Lert. 1992,195, 200. (12) Chong, D. P.; Langhoff, S.R. J. Chem. Phys. 1986,84,5606. See also: Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J. Chem. Phys. 1985,82, 890. (13) Bartlett, R. J. Amu. Rev. Phys. Chem. 1981,32,359. Raghavachari, K.; Trucks, G.W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (14) Wcmer, H.-J.; Knowles, P. J. J. Chem. Phys. 1988, 89, 5803. Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1988, 145, 514. (15) Gdanitz, R. J.; Ahirid, R. Chem. Phys. Lett. 1988, 143,413. (16) Dunning, T. H. J. Chem. Phys. 1971,55,716. (17) McLean, A. D.; Chandler, G. S.J. Chem. Phys. 1980, 72, 5639. (18) Pettersson, L. G. M.; Siegbahn, P. E. M.;Ismail, S.Chem. Phys. 1983,82, 355. (19) R m , B.; Veillard, A,; Vinot, G. Theor. Chim. Acta 1971, 20, 1. (20)Moore, C. E. Atomic energy levels; US. National Bureau of Standards (US.) Circular No. 467; National Bureau of Standards: Washington, DC, 1949. (21) Huber, K. P.; Herzberg, G.Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (22) MOLECULE-SWEDEN is an electronic structure program system written by J. Almlbf, C. W. Bauphlicher, M. R. A. Blomberg, D. P. Chong, A. Heiberg, S.R. Langhoff, P.-A. Malmqvist, A. P. Rendell, B. 0. Roos, P.
E. M.Siegbahn, and P. R. Taylor. (23) TITAN is a set of electronicstructure programs written by T. J. Lee, A. P. Rendell, and J. E. Rice. (24) Scuseria, G. E. Chem. Phys. Lett. 1991, 176, 27. (25) SIRIUS is an MCSCF program written by H. J. Jenscn, H. k e n , and J. Olsen; ABACUS is an MCSCF energy derivativesprogram written by T. Helgaker, H. J. Jensen, P. Jsrgenscn, J. Olscn, and P. R. Taylor. (26) Werner, H.-J.; Knowles, P. J. J. Chem. Phys. 1985, 82, 5053. Knowles, P. J.; Wemcr, H.-J. Chem. Phys. Lerr. 1985, 115, 259. (27) Lee,T. J.; Kobayashi, R.; Handy, N. C.; Amos, R. D. J. Chem. Phys. 1992, 96, 8931. (28) Taylor, P. R. Personal communication. (29) Martin, R. L. J . Phys. Chem. 1983,87, 750. See also: Cowan, R. D.; Griffin, D. C. J . Opt. Soc. Am. 1976,66, 1010. (30) Field, R. W. J. Chem. Phys. 1974, 60, 2400. (31) Irvin, J. A.; Dagdigian, P. J. J. Chem. Phys. 1980, 73, 176. The vibrational frequency is from ref 21. (32) Partridge, H. J . Chem. Phys. 1989, 90,1043. (33) Partridge, H. J. Chem. Phys. 1987,87,6643. (34) AlmlBf, J.; Taylor, P. R. J. Chem. Phys. 1987, 86, 4070. (35) Partridge, H.; Faegri, K. Theor. Chfm.Acta 1992, 82, 207. (36) Bauschlicher, C. W.; Partridge, H.; Langhoff, S. R. Chem. Phys. 1990, 148, 57.
Rigorous Interpretation of Electronic Wave Functions. 1. Electronic Structures of BH,, B,Hd, B9H7, and B& Jerzy Cioslowski* Department of Chemistry and Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306- 3006
and Michael L,McKee Chemistry Department, Auburn University, Auburn, Alabama 36849 (Received: June 8, 1992)
Electronic structures of the simplest boron hydrides, BH3, B2H6, B3H7,and B3H9,were investigated at the MP2/6-3lG(2d,p) level of theory using rigorous interpretive tools. The computed topological properties of electron density, localized natural orbitals, atomic charges, and covalent bond orders make it possible to unequivocally describe bonding in these molecules. In the BH3 and B2H6molecules, the bonding patterns are in agreement with the widely accepted notions of the B-H bonds and the B-H-B bridges. The 2102 isomer (in the styx terminology) of the B3H7molecule is best described as possessing an open B-B-B tricentric bond in addition to seven B-H bonds. There are no B-H-B bridges present in B3H7,although the atomic occupancies of the strongly occupied localized natural orbitals suggest a substantial degree of delocalization for two of the B-H bonds. In contrast, the 3003 isomer of the B3H9species has three B-H-B bridges together with six B-H bonds. In all of the systems under study, large ionicities of both the B-H and B-H-B bridges indicate that the hydrogen atoms have a strongly hydridic character.
Boron hydrides, also known as boranes, constitute a classical example of electrondeficientmolecules, Le., species in which there are fewer electrons than required to explain bonding with only conventional two-center bonds. Although the presence of the tricenter B-H-B bonds in molecules such as B2H6 has been postulated since the seminal work of Longuet-Higgins’ and is presently widely accepted by the chemical community, it can be uncovered only if localized molecular orbitals (LMOs) are used in the description of the electronic structures of boranes. In a series of Lipscomb and co-workers employed the Edmiston-Ruedenbergs and Foster-Boys6 localization produm to m e to the conclusion that only a few elementary types of LMOs are necessary to adequately account for chemical bonding in most boranes. These LMOs correspond to the conventional B-H and B-B bonds and the tricentric B-H-B and B-B-B bonds. The aforementioned calculations have been performed at the Hartrce-Fock (HF) level, and many of them used a semiempirical scheme for computation of the necessary twoelectron integrals. Therefore, the electron-correlation effects, which are well-known to be important (at least from the energetics point of view) in boranes? have not been included in the ensuing picture of the localized bonding. With the aim of alleviating this 0022-3654/92/2096-9264$03.00/0
deficiency, a new interpretation of the localized bonding in B2H6 has been recently put forward by Gerratt et a1.8 In contrast to the previous calculations, which involved a posteriori analysis of the computed wave functions, the new approach was based on an approximate spin-coupled electron-correlation theory in which minimization of the electronic energy results in one-electron wave functions (spin-orbitals) that spontaneously break the symmetry of a molecule under study. Such a theory, which is capable of recovering a substantial fraction of the correlation energy, affords LMOs directly. However, since the symmetry breaking at the oneelectron level is an obvious consequence of the projection of the Hamiltonian onto the Hilbert space of the allowed manyelectron Slater determinants (note that an unprojected Hamiltonian in the full CI method would not favor any particular form of spin-orbitals), it remains unclear whether the resulting LMOs indeed reflect the electronic structures of molecules rather than the underlying structure of the spin-coupling approximation. Among others, the controversial description of bonding in benzene that is obtained from the spin-coupled theory9raises more questions of this kind. Building upon the extensive body of work published previously by other researChers,lo recently we have proposed a set of rigorous interpretivetools for analysis of electronicwave functions.11J2The 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9265
Rigorous Interpretation of Electronic Wave Functions TABLE I: Atomic Charges ia the Molecdesaunder Study BH3
B3H7
B2H6
B3H9
atom
charge
atom
charge
atom
charge
atom
charge
B
2.041 -0.680
1.949 -0.659 -0.645
B, B; HI
1.159 1.635 -0.600 -0.630 -0.651 -0,649
B
H
B HI
1.845 -0.653 -0,627 -0.565
H2
H2
H3 H,
HI H 2
H3
"See Figures 1 4 for atom numbering.
analysisbegins with calculation of the oneelectron density matrix, which either can originate from the correlated or HF wave function or can be calculated from the energy deri~atives.'~The oneelectron density matrix is diagonalid to provide canonical natural orbitals, whereas its diagonal part (electron density) is used in determination of atomic properties with the help of Bader's topological theory of atoms in moIccules.'O8 In particular, the atomic overlap matrical4 are calculated and employed in a localization crikrion15J6that yields LMOs through isopyCnic of the canonical natural orbitals. Unlike its older this orbital localization has the desirable property of preserving the u / r orbital separation in planar molecules. It also provides atomic occupancies of the LMOs, together with localization indices and covalent bond orders.I6 The table of the atomic occupancies for LMOs, which in most cases can be limited to strongly occupied (Le., those with occupation number close to 2) orbitals, is usually sufficimt to discem and characterize all bonding feature8 pertinent to the electronic structure of the molecule in question. Since nowhere in the above procedure is reference made to basis functions, the resulting atomic occupancies and covalent bond orders are true observabla.ll Therefore, these interpretive tools are equally applicable to wave functions obtained with the conventional nuclei-centered basis sets, floating and bond-centered basis functions, 'ghost orbitals", one-center expansions, or finite-element numerical orbitals. The fact that all the necessary information concerning LMOs is contained in the table of atomic occupancies renders plotting of LMOs unnecessary. Prompted by the success of the aforedescribed methodology in providing a clear descriptions of bonding in the so-called "hypervalent" molecules of sulfur, phosphorus, and chlorine,"J2 we report here on the rigorous analysis of the electronic structures of the four simplest boron hydrides, namely BH3, B2H6, B3H7, and B3H9.
Computational Metbods All one-electron density matrices were computed at the MP2/6-3 1G(2dIp) approximation (unless stated otherwise) for molecular geometries optimized at the MP2/6-31G(d) level of theory. The calculations were performed with the GAUSSIAN 90 suite of programs.'* The analyses of electron densities were carried out with the program SADDLE,14 whereas program VECAIMI9was used to calculate the atomic charges and atomic overlap matrices. The determination of localized natural orbitals and covalent bond orders was accomplished with the program Both VECAIM and LOSSES are available from one of the authors (J.C.) upon request.
Bonding in Simple Boron Hydrides In all of the boranes under study, the boron-hydrogen bonds are quite ionic, resulting in large negative charges on the hydrogen a t o m and positive charges on the borons (Table I). The charges on the hydrogens do not change significantly from one molecule to another, as they span a narrow range between -0.565 and 4.680. The hydridic character of the hydrogens in boranes easily explains the well-known reactivity of these species toward even weakly acidic molecules, such as water. According to the topological theory of atoms in molecules,'OB the presence of a bond critical in sterically noncrowded ~ystems,2~ point associated with an attractor interaction tine connecting two nuclei is a necessary and sufficient condition for the existence of a chemical bond between these nuclei. Keeping this definition
Figure 1. Nuclei and the electron-density critical points in the BH3 molecule. The bond critical points are denoted by heavy dots. The
overall symmetry is D3*.
R 0
Figure 2. Nuclei and the electron-density critical points in the B2H6 molecule. The bond critical points are denoted by heavy dots, and the ring critical point is marked by a diamond. The overall symmetry is Dm
in mind, one finds without much surprise that the only bonds present in the BH, molecule are three B-H ones (Figure l), whereas in the B2H6 species there are four terminal B-H bond together with two B-H-B bridges (Figure 2). There is no evidence for a direct B-B bond. As revealed in Table I1 and Figures 1 and 2, the terminal B-H bond paths (B-Hd are almost perfectly straight, whereas those connected with the bridging hydrogens (B-HI) exhibit large curvatures as measured by the differences between the bond line arc lengths and the respective B-H distances (A1in Table 11). The B3H7molecule is believed to be a key transient intermediate in the pyrolysis of B2He22 There is mass-spectral evidence that B3H7is a well-defined chemical spec5es.D According to ab initio calculations, the most stable isomer of B3H7has the 2102 structure (in the styx Figure 3), although the 1103 species is The picture of bonding in only 4.4 kcal/mol higher in the 2102 isomer of B3H7(denoted in the following as simply B3H,) is slightly more complicated than that in either BH, or B2&. The middle boron atom (BJ is linked directly through two bonds to its terminal counterparts (B2). Two straight B-H bond paths (B2-H3 and B2-H,) terminate at each of the terminal borons. In addition, there are three more B-H bond paths, all asaiated with the central boron atom. One of them (Bl-H2) is almost straight, whereas the two remaining paths (B,-HI) are highly curved, There is, however, reminiscent of the B-H-B bridge in
9266 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
Cioslowski and McKee
TABLE II: Properties of Boads in the Molecules under Study“ molecule BHI
bond B-H
B2H6
B-H I B-H2 B-B’ B1-W B2-Hl
P V2P 0.1858 -0.3573 (0.1853) (-0.2998) 0.1266 0.0523 (0.1243) (0.1319) 0.1850 -0.3434 (0.1852) (-0.2852) bond path absent (bond path absent) 0.1447 -0.0654 (0.1436) (0.0210) bond path absent (bond-path absent) 0.1894 -0.3268 (0.1900) (-0.2680) 0.1876 -0.3360 (-0.2824) (0.1885) 0.1855 -0.3269 (0.1861) (-0.271 1 ) 0.1241 -0.1506 (0.1252) (-0.1996) bond path absent (bond path absent) 0.1212 0.0791 (0.1196) (0.1562) 0.1868 -0.3334 (0.1874) (-0.2744) 0.1769 -0.3052 (0.1776) (-0.2453) bond path absent (bond path absent)
c
A1
P
0.2807 (0.2711) 0.6700 (0.6558) 0.0786 (0.0790)
O.oo00
0.524 (0.491) 0.298 (0.272) 0.519 (0.479) 0.075 (0.056) 0.458 (0.468) 0.288 (0.265) 0.604 (0.578) 0.555 (0.522) 0.560 (0.519) 0.410 (0.402) 0.199 (0.148) 0.324 (0.296) 0.539 (0.499) 0.491 (0.453) 0.058 (0.042)
(O.oo00) 0.1000 (0.1007) 0.0003 (0.0003)
1.1211 (1.2042)
0.0691 (0.0690)
0.0126 (0.0119) 0.1210 (0.1239) 0.1631 (0.1623) 2.5484 (1.7769)
0.0003 (0.0003) 0.0003 (0.0003) 0.0005 (0.0005) 0.03 15 (0.2182)
0.68 18 (0.6453) 0.0762 (0.0806) 0.0008 (0.0067)
0.0386 (0.0470) 0.0008 (0.0009) O.OOO9
(0.0006)
‘The HF/6-31G(2d,p) values in parentheses. All values in atomic units. See Figures 1-4 for atom numbering.
0
d
b
Figure 3, Nuclei and the electron-density critical points in the B3H7 molecule. The bond critical points are denoted by heavy dots. The overall symmetry is C,.
no evidence of the Bz-Hl bonds that would complete the bridge. The other borane with three boron atoms, B3H9, is also a Its lowest energyZJ6isomer (3003 in the styx transient ~pecies.2~ notating,24Figure 4) possesses a simple system of bonds. The boron atoms are bridged through six highly curved B-H bond paths (B-H,). Due to the resulting ring formation, the set of critical points in the electron density of B3H9includes a ring point (Figure 4). The remaining six hydrogens are linked through two families (B-H2 and B-H3) of straight B-H paths. The electron densities at the B-H and B-B bond critical points ( p in Table 11) exhibit characteristic patterns. The values of p for the terminal B-H bonds fall within the range between 0.1769 and 0.1894. The corresponding numbers for the bridging B-H bonds are 0.1212 and 0.1266. The “terminal” (see below) B,-HI bond in the B3H7molecule is the only exception, with its p of 0.1447. The values of Laplacians of the electron density at the critical point (Vzpin Table 11) exhibit a similar bimodal distribution, being negative for the terminal bonds and close to zero for the bridging ones. Again, the Bl-HI bond in B3H7 is an exception. The negative values of v2pindicate the presence of shared (in this case polarized covalent) interactions between the atoms in que~tion.~’
F i p e 4. Nuclei and the electron-density critical points in the B3H9 molecule. The bond critical points are denoted by heavy dots, and the ring critical point is marked by a diamond. The overall symmetry is C3”.
The covalent bond orders,’ (P in Table 11) show distinct r e g ularities in boron hydrides. The terminal B-H bonds have values of P between 0.458 and 0.604. The fact that the covalent bond orders are much smaller than one is directly related to the large ionicities of the B-H bonds. The magnitudes of the covalent bond orders for the bridging B-H bonds (0.298 in B& and 0.324 in B3H9) are roughly half of those pertinent to their terminal counterparts. In general, the trends in bond orders follow the presence/absence of bond paths between the pairs of atoms. In particular, the absence of direct B-B bonds in BzH6 and B3H9 is confirmed by the low values of the corresponding bond orders (0.075 and 0.058). On the other hand, the BI-Bz bond order in B3H7is quite large, as expected from the presence of the respective bond path. In contrast, the Bz-B’2 bond order of 0.199 is apparently too small to precipitate the corresponding bond point. The same is true about the Bz-Hl pair of nuclei. By comparing the MP2/6-31(2d,p) values with the HF/631(2d,p) ones (given in Table I1 in parentheses), one concludes that the electron-correlation effects tend to reduce the ionicities of all bonds in boranes, resulting in increased covalent bond orders. This is in agreement with observations concerning similar effects in other molecules.12*28In general, corrections to the HF bond properties due to correlation effects are rather small, with the
Rigorous Interpretation of Electronic Wave Functions TABLE Ilk Strongly Occupied I.ocdized Natural Orbitals of the BHI Mokeuk” kinetic orbital principal orbital(s) occ no. energy, au descriptn atomic occ 1 2.000 10.986 B (core) 0.998 (B) 2-4 1.976 0.733 B-H 0.799 (H), 0.159 (B) ”See Figure 1 for atom numbering.
exception of the B1-B2 bond in the B3H7species, in which the inclusion of electron correlation dramatically straightens the bond path and increases the bond ellipticity (e in Table 11) by almost 50%. As pointed out in the Introduction, a detailed picture of bonding in molecules is provided by the tables of atomic occupancies of the strongly occupied localized natural orbitals. Inspection of Table I11 does not reveal any surprising features in the electronic structure of the BH3 species. As one may easily conclude from its large kinetic energy, the first localized orbital describes the core electrons, The remaining three LMOs correspond to three equivalent strongly polarized B-H bonds. The localized description of the B2Hsmolecule is equally simple (Table IV). The first two LMOs of core electrons are followed by two equivalent localized orbitals describing the B-H-B bridges. Each of these LMOs is only 90.4% localized on the B-H-B bridge, indicating a substantial degree of electron delocalization (a typical well-localized LMO is > 94% localized within its constituting centers).12 The localization is better (93.5%) for the four LMOs describing the terminal B-H bonds. The strongly occupied localized orbitals of B3H7,which are listed in Table V, clearly describe bonding in this molecule. The first three LMOs with the largest kinetic energies correspond to the core electrons. The tricentric B-B-B bond is represented by the fourth LMO. The atomic occupancies of this orbital on the terminal boron atoms are much smaller than the occupancy on the middle boron. This fact explains the relatively low value of the B2-B‘2 covalent bond order and the absence of the corresponding bond path. In other words, the direct boron-boron bonding in B3H7is provided by an open tricentric B-B-B bond. The LMOs 5-9 correspond to ordinary B-H bonds. Finally, the last two strongly occupied localized natural orbitals describe two strongly asymmetric B-H-B bridges that extend between the
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9267 middle boron and each of its terminal counterparts. The asymmetry is pronounced enough to result in the absence of the B2-Hl bond paths (see above) and make the BI-Hl bonds appear to be the ordinary two-center ones. On the other hand, the orbital occupancy on each of the B2 atoms is sufficiently large to make the Bl-Hl bonds strongly curved and possess unusually small values of p and v2p(see Table 11). There are only four distinct types of LMOs in the B3Hg molecule (Table VI). One of them (LMOs 1-3) corresponds to the core electrons. Two others (LMOs 4-6 and 10-12) describe the two-center B-H bonds. The remaining three LMOs (7-9) extend over symmetrical B-H-B bridges. In summary, the LMOs of B3Hgare in full agreement with the pattern of bond paths in this molecule.
ConclusiolM Rigorous interpretive tools based on the topological theory of atoms in molecules afford a clear and simple picture of electroncorrelated bondw in simple boron hydrides. The BH3, B2&, and B3Hgspecies are best described by combinations of an a p propriate number of the strongly occupied localized natural orbitals describing boron core electrons, B-H bonds, and symmetrical B-H-B bridges. The bonding in B3H7is more complicated. The three boron atoms are directly linked through an open B-B-B bridge, whereas all of the hydrogen atoms participate in the ordinary two-center B-H bonds. Two of the LMOs describing these bonds exhibit substantial atomic occupancies on the boron atoms adjacent to the B-H bonds, indicating the presence of strongly asymmetric B-H-B bridges. However, the residual B-H interactions are not strong enough to precipitate the respective B-H bond paths, resulting in a bonding pattern of seven B-H two-center bonds in addition to an open B-B-B bridge. The bonding pattern could possibly be different if the energy-minimum geometry of B3H7 corresponded to a more symmetrical arrangement of the B-H-B triads. Like in the other molecules under study, all of the hydrogen atoms in the B3H7molecule are strongly hydridic. The above description is the result of a posteriori analysis of high-quality one-electron density matrices and therefore is not subject to any bias that could passibly arise from the assumptions concerning the nature of the approximations used in the present electronic structure calculations. It is almost certain that neither
TABLE I V Strongly Occupied h l i z e d Natural Orbitals of the B2H, Molecule“ kinetic orbital orbital@) occ no. energy, au description 1, 2 1.999 10.973 B (core) 3, 4 1.967 0.746 B-H 1-B’ 5-8 1.973 0.738 B-H2
principal atomic occupancies 0.998 (B) 0.718 (HI), 0.093 (B), 0.093 (B’) 0.771 (Hz), 0.164 (B)
“See Figure 2 for atom numbering. TABLE V Strongly Occupied Locrllzed Natural Orbitals of the Bd,Moleculeu kinetic orbital orbital(s) occ no. energy, au descriution 1, 2 1.999 10.961 B2 (core) 3 1.999 10.956 BI ( a r e ) 4 5 6, 7 8, 9 10,11
1.953 1.971 1.972 1.972 1.964
0.899 0.755 0.748 0.741 0.735
B2-BI-B’z B1-H2 2-H
3
B2-H4
BI-HI-BI
principal atomic occuuancies 0.999 (B2) 0.999 (Bl) 0.409 (Bl), 0.219 (BZ), 0.219 (B’2) 0.762 (H2), 0.189 (Bl) 0.765 (H3), 0.175 (B2) 0.769 (Hd), 0.176 (B2) 0.701 (HI), 0.140 (BI), 0.087 (B2)
“SeeFigure 3 for atom numbering. TABLE VI: Strongly Occupied Localized N8tud Orbitals of tbe B&. kinetic orbital(s) occ no. energy, au 1-3 4-6 7-9 10-12
1.999 1.971 1.964 1.968
“See Figure 4 for atom numbering.
10.965 0.744 0.747 0.733
Molecule” orbital description B (core) B-HZ B-Hl-B’ B-H3
principal atomic occupancies 0.998 (B) 0.757 (Hz), 0.175 (B) 0.688 (HI), 0.106 (B), 0.106 (B’) 0.724 (H3), 0.164 (B)
9268
J. Phys. Chem. 1992,96,9268-9272
the qualitative nor the quantitative conclusions reached in this study wodd change upon further improvement in either the quality of the oneelectron basis sets or inclusion of electron correlation through more accurate level of approximations.
Acknowledgment. This work was partially supported by the National Science Foundation under Contract CHE-9015566, the Camille and Henry Dreyfus Foundation New Faculty Award Program, the Florida State University through time granted on its Cray Y-MPWtal computer, and the donors of the Petroleum Research Fund, administered by the American Chemical Society.
Referenccs rad Notea (1) Longuet-Higgins, H. C. J. Chim. Phys. 1949, 46, 275. (2) Switkes, E.; Lipscomb, W. N.; Newton, M. D. J . Am. Chem. SOC. 1970, 92, 3847. (3) Eptein, I. R.; Marynick, D. S.;Lipscomb, W. N. J . Am. Chem. Soc. 1973,95, 1760. (4) Kleier, D. A,; Halgren, T. A,; Hall, J. H., Jr.; Lipscomb, W. N. J . Chem. Phys. 1974,61, 3905. (5) Edmiston, C.; Ruedenberg, K. J . Chem. Phys. 1965, 43, S97. (6) Foster, J. M.;Boys, S.F. Rev. Mod. Phys. 1960, 32, 300. (7) McKce, M. L. J. Am. Chem. Soc. 1990,112,6753 and references cited
therein. (8) Sironi, M.; Raimondi, M.; Cooper, D. L.; Gerratt, J. J . Phys. Chem.
1991, 95, 10617. (9) Cooper, D. L.; Gerratt, J.; Raimondi, M. Nafure 1986, 323, 699. (10) (a) Bader, R. F. W.A?oms in Molecules: A Quantum Theory; Clarendon Press: Oxford, 1990. (b) See,for example: Boyd, R. J.; Edge-
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An Electron-Rich, Three-Coordinated Sulfur Atom: A Correlated ab InRio Study of 1,6-Dioxa-6a-thiapentalene Svein Saeb~,* Department of Chemistry, Mississippi State University, Mississippi State, Mississippi 39762
James E. Boggs, and Kangnian Fant Department of Chemistry, The University of Texas, Austin, Texas 78712 (Received: June 8, 1992)
Ab initio calculations on 1,6-dioxa-6a-thiapentalene(DOTP) and 1,6,6a-trithiapentalene(TTP) have provided insight into the symmetry and structureof these unusual molecules which contain threecoordinatedsulfur atoms. HartreFock geometry optimizations using a 421G basis set for carbon and 3-3-216 for sulfur give bond lengths agreeing with results of a gas-phase electron diffraction study within the experimental errors of the latter. They do, however, incorrectly predict a classically bonded, asymmetric ground-state structure rather than the C, form with extensive electron delocalization, suspected from experimental evidence to be the ground state. In the case of DOTP,a t the Hartree-Fock level, the transition bamer a t the symmetrical configuration is 0.9 kcal/mol, increasing to 3.8 kcal/mol with the 6-31G** basis set and further increasing to 4.8 kcal/mol with the 6-311G** basis set. For TTP, the barrier at the symmetrical transition state is predicted considerably higher with the 4-21G calculation, approximately 6 kcal/mol. Our newly developed technique for doing electron correlation treatments of larger molecules using localized orbitals made it possible to study DOTP with calculations as large as MW(SDQ) with 6-311G** basis set, although without full geometry optimization. With the inclusion of electron correlation, the correct symmetric minimum is predicted with an energy about 1 kcal/mol lower than the classically bonded asymmetric form.
Introduction The compounds 1,6-dioxa-6a-thiapentalene(DOTP),the related trithiapcntalene (TTP), and various derivatives of them have been the subject of a large number of experimental investigations because of the unusual threacoordinatedstructure around the sulfur atom in the 6a position (see Figure la,b). When the first structural determination by X-ray diffraction' revealed the correct order of attachment of the atoms, the bonding was explained in terms of single bond-no bond resonance structures as in Figure 'Permanent address: Department of Chemistry, Fudan University, Shanghai, People's Republic of China.
IC. Alternative structures with a double bond from Sb to C3a were also proposed but are not in accord with presently available information about the relative bond lengthsS2 Later discussion was based on the concept of three-electron, single-center bonds. A number of reviews of the subject are The quantitative structural data provide interesting insight into the description of the bonding, although a number of puzzles remain. To begin with, a question of much interest for structural chemists, and one difficult to resolve by electron diffraction, was whether the molecules have C, symmetry with a single minimum electronic ground state or whether they exist as equilibrium mixtures of two interconvertingvalence tautomers (see F w e IC).
0022-3654/92/2096-9268$03.00/00 1992 American Chemical Society
