J . Phys. Chem. 1990, 94, 1723-1724
1723
Calculation of the Structure, Vibrational Spectra, and Polarizability of Boroxine, a Model for Boroxol Rings in Vitreous B203
H38303,
J. A. Tossell* Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742
and Paolo Lazzeretti Dipartimento di Chimica, Universita Degli Studi di Modena, Modena 41 100, Italy (Received: November 16, 1989)
Boroxine, H3B303,is a stable but reactive gas-phase molecule which is also a model for the boroxol, B3063-,rings which occur in vitreous BzO3. We have optimized the geometry of H3B303 at the RHF/3-21G* level and have calculated its vibrational energies and IR intensities. We have also calculated the polarizability of H3B303 and its polarizability derivative for the Raman-active AI’ vibrational mode involving symmetric breathing of the oxygens. Our results for H3B303 are consistent with a boroxol ring model for v-B203.
Introduction Boroxol, B3063-, rings have been postulated as important components of vitreous B203,based on evidence from NMR’ and Raman spectroscopy2 and neutron diffra~tion.~Our previous calculations on the H3B306molecule at the RHF/3-21G* level gave a B-B distance which matched well against the neutron diffraction value obtained for v-B203. The frequency for the Raman-active A,’ vibrational mode of H3B306 was calculated to be 868 cm-I if only 0 motion was allowed (all the B and H nuclei held f i ~ e d ) .This ~ value was about 10% higher than the feature at 808 cm-’ attributed to boroxol groups in v-B203,’ a direction and magnitude of error typical of 3-21G* basese5 Unfortunately H3B306was too large for a complete normal-mode analysis so we could not confirm that there was indeed an AI’mode involving purely 0 motion. We also calculated the polarizability of B3063and the derivative of its polarizability with respect to 0 motion but our basis set was limited, having only one 3d polarization function on each nucleus and no diffuse functions. To confirm the existence of an A,’ mode with (nearly) pure 0 motion by direct calculation and to examine the polarizability using a more extensive basis set we have considered the smaller model molecule boroxine, H3B303, which has been studied directly by IR spectroscopy in the gas phase? and in matrix isolation’ and by electron diffraction in the gas phase.* The experimental ED data favored a Djhstructure and the experimental bond distances and angles were R(B-0) = 1.37 A, R(B-H) = 1.1915 A, and LB-0-B = 120’. Our RHF/3-21G* values for D3hsymmetry were R(B-0) = 1.3709 A, R(B-H) = 1.1867 A, and LB-0-B = 120.6O. An optimization in C3”symmetry with a nonplanar starting geometry converged to the D3,,structure. The geometry optimization and normal-mode calculations were performed using the program G A M E S 9 Calculated vibrational energies and IR intensities for H3B303 at its optimized 3-21G* geometry are given in Table I. The ( I ) Jellison, G. E. Jr.; Panek, L. W.: Bray, P. J.: Rowse, G. B. Jr. J . Chem. Phys. 1977.66, 802. (2) (a) Galeener, F. L. Solid State Commun. 1982, 44, 1037. (b) Galeener, F. L.; Lucovsky, G.: Mikkelsen, J. C., Jr. Phys. Rea B 1980,22,3983. (3) Johnson, P. A. V.;Wright, A. C.;Sinclair, R. N. J . Noncryst. Solids 1982, 50, 281. (4) Tossell, J. A. J . Noncryst. Solids, in press. (5) Hehre, W. J.; Radom, L.: Schleyer, P. v. R.: Pople, J. A. A6 Initio Molecular Orbital Theory; Wiley: New York, 1986. (6) Grimm, F. A.; Barton, L.; Porter, R. F. Inorg. Chem. 1968, 7, 1309. (7) Kaldor, A.; Porter, R. F. Inorg. Chem. 1971, IO, 775. (8) Chang, C. H.; Porter, R. F.; Bauer, S . H. Inorg. Chem. 1969.8, 1689. (9) Schmidt, M.W.; Boatz, J. A.; Baldrige, K. K.: Koseki, S.: Gordon, M. S.: Elbert, S. T.: Lam, B. QCPE Bull. 1987, 7, 115.
0022-36S4/90/2094-1723$02.50/0
TABLE I: Calculated Vibrational Energies (in cm-I) for H3B3OJ from RHF/3-21G* Calculation Compared with Gas-Phase Experimental Data6 for E’ and from Matrix Isolation Data’ for Other Symmetries“ E
E
calculated IR intensity IR Active Only
E
X 0.9
A;
1001 399
901 359
E‘
2803 1532 1325 1072 567
2523 1379 1193 965 510
2823 1060 884 990 231
2523 954 796 891 208
1273 1224
1146 1102
6.13 0.013
experimental IR intensitv
910 (380)
S
IR and Raman Active 6.98
2613 1403 1200 998 530
20.95 2.32 0.25 0.40
S
vs S W W
Raman Active Only Ai‘
E”
(2616) 906 (800) 1050 343
Inactive A{
1471 1197
” Values in parentheses are estimated. TABLE 11: Cartesian Displacements of Symmetry Unique B, 0, and H Atoms in 884-cm-I A,’ Normal Mode B x 0.01573 H x 0.01666 0
y z x
y z
-0.00096 -0.00005 0.14371 -0.00038 -0.000 13
y z
-0.00017 0.000 02
calculated values scaled down by 10% (a typical overestimate at this level of approximations) are in reasonable agreement with experiment for the 1R-active modes (A; and E‘ symmetry). Although integrated intensities were not given for the experimental IR spectra, it is clear from the published spectra and the qualitative intensities reported (i.e., s (strong) vs w (weak)) that the 1403-cm-I E’ band is the most intense and that the 2613-cm-I E’ band, the 1200-cm-’ E’ band, and the 910-cm-l A; band all have significant intensity, in agreement with the calculations. The high intensity of the E’ mode observed at 1403 cm-’ results from the motion of the three 0 atoms in the same direction, as determined from the empirical force field analysis of ref 6 (see 0 1990 American Chemical Society
Letters
1724 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
TABLE 111: Calculated Polarizabilities (A3) for H3B303at the 3-21G* ODtimized Geometrv [5S4P/3SI [5s4pld/3slpJ [5s4p2d/3slp] [6s5pld/3slpld
3.337 4.071 4.196 4.352
6.002 6.313 6.404 6.482
5.114 5.556 5.668 5.772
0.52 0.40 0.39 0.37
is along the C, axis. * ? p (al- all)/aav. [5s4p/3s] signifies five s and four p contracted Gaussians on both B and 0 and three s contracted Gaussians on H. ”The outermost s and p Gaussians on B and 0 are diffuse primitives with exponents of 0.0315 for B and 0.0845 for
0.
Figure 5 of ref 6) and confirmed by our a b initio calculations. For the Raman-active-only modes AI’ and E” the agreement of calculation and experiment is much poorer, but the Raman spectrum was not actually observed experimentally. Instead, the Raman energies for A,’ and E” symmetries are estimated from the energies of weak combination bands in the IR spectra, a procedure which may be the source of the discrepancy. The energy of 800 cm-l estimated from experiment for the lowest energy A,’ mode is in good agreement with our scaled theoretical value of 796 cm-’ and the experimental value of 808 cm-l in v - B ~ O ~In. Table I1 we give this A,’ normal mode in terms of displacements of symmetry equivalent B, 0, and H atoms lying along the x axis. The normal-mode displacement of 0 is almost 10 times as large as that for B and H, in agreement with qualitative argumentsh and with the normal-mode analysis based on empirical force constanb6 According to the ab initio normal-mode calculation this is the only vibration of H3B30) dominated by 0 motion. When the motion of -BH is completely neglected and the energy of this mode determined by point calculations allowing only 0 motion the energy obtained is 874 cm-’ (unscaled), only I O cm-l different from the result of the full normal-mode analysis. Studies of the Raman spectrum of v - B ~ O using ~ both B and 0 isotopic substitution have also established that the 808-cm-, peak corresponds almost entirely to 0 motion.I0 The other Raman modes corresponding to predominant 0 motion in v-B203occur from 400 to 650 cm-I. The only energetically possible counterpart of these features in H3B303 is the 530-cm-’ E’ peak but the normal-mode calculations show it to involve significant B motion. Thus the 400-600-cm-’ Raman features in v - B ~ O probably ~ do not arise from boroxol rings. The experimental depolarization ratio, pn, is also much smaller for the 808-cm-’ band (Fig. 8 of ref 10) than for the other Raman features in v-B203 supporting its assignment to a localized and totally symmetric vibration.” To determine the intensity of this mode we have calculated the polarizability of the molecule using the coupled Hartree-Fock proceduret2incorporated in the program SYSM0.I3 We have used (9s5p) bases for B and 0 and (5s) for H from van D~ijneveldt,’~ contracted to [5s4p] and [3s], respectively, and have added either one or two polarization functions on each nucleus. We have also determined the effect of adding diffuse s and p functionst5on the B and 0 nuclei. Calculated polarizabilities at the 3-21G* equilibrium geometry are given in Table 111. Clearly the largest change takes place when single polarization functions are added on all the nuclei. The use of two 3d polarization functions on B and 0 and the addition of the diffuse s and p functions on B and (IO) Windisch, C. F., Jr.; Risen, W. M. Jr. J . Noncryst. Solids 1982, 48, 307. (11) Ebsworth, E. A. V.; Rankin, D. W. H.; Cradock, S . Structural Methods in Inorganic Chemistry; Blackwell: Oxford U.K., 1987; pp 190-192. (12) (a) Lipscomb, W. N. Adu. Mag. Reson. 1966,2, 137. (b) Ditchfield, R. Mol. Phys. 19’14, 27, 789. (1 3) Lazzeretti, P.; Zanasi, R. J . Chem. Phys. 1980, 72, 6768. (14) Van Duijneveldt, F. B. IBM Res. Rep. 1971, RJ 945. (1 5 ) Clark, T.; Chandrasekhar, J., Spitznagel, G. W.; Schleyer, P. v. R. J . Comput. Chem. 1983, 4, 294.
0 have smaller but still noticeable effects. We have also calculated the intensity and degree of depolarization for Raman light scattered at right angles to the direction of incidence, given byI6 1 I , = const X -[45(n’)2 + 1 3 ( ~ ’ ) ~ ] 45 Pn
=
6(r’I2 45(a’)2 7(y’)2
+
where a’ = da/dQ, y’ = dy/dQ, y = cyL - all, Q is the normal coordinate, and const = (64r2/3$)(v0 A v ) ~ We . have evaluated a and y at three different values of the 0 coordinate around the equilibrium value using the [5s4pld/3slp] basis. We obtained average values of 0.651 A2 for a’ and 0.557 A2 for y’ giving I,/const. = 0.513 and pn = 0.0876. We have also evaluated average values of a’,, = dYy = 2.51 A2 and a’,, = 0.84 A2 for this mode. Experimental values of pn for this mode in v-B203 are in the range we have calculated with Walrafen et al.17agiving an average value of 0.14 f 0.03 and Ramos et giving values from about 0.05 to 0.08 for temperatures from 150 to 300 K increasing to about 0.30 for very low temperatures. Our values for a’,, and dZz, however, do not satisfy the criterion a’,* > O.l5a’,, assumed by Windisch and To utilize our calculated A,’ intensity of H$303 to interpret the Raman intensity distribution of v-B203we would need to assign at least some of the other features in the spectrum. In the experimental Raman spectrum of borazine, B3N3H6,there is an intense peak at about 940 cm-I, assigned to an Al’ peak.7 Isotopic substitution studies1*establish that this peak corresponds primarily to motion of the B atoms. Our normal-coordinate analysis indicates that the At’ peak calculated at 1060 cm-’ in H3B303 and observed (in IR combination) at 906 cm-l also involves mainly B motion. No such feature is expected to appear in the spectrum of v-B203since such a B motion would couple with other lattice modes. We have calculated the normal modes of (BH2)20 (for assumed dihedral angle of both Oo and 180°), another species with a bridging oxygen, at the 3-21G* level but we find that there are no modes calculated to occur between 400 and 1000 cm-’ so no features in the v-B203 spectrum can be attributed to such a model, in contradiction to the suggestion of Soppe et Unfortunately, the only Raman feature of v-B203interpretable within a molecular model seems to be the A,’ mode of the boroxol ring at 808 cm-I. Therefore, we presently have no way to relate the relative intensity of this feature to other peaks in the Raman spectrum. It is worth remembering that our present results for H$@3 are similar to those obtained for H3B306and B3063 in ref 4. The calculated energy of the At’ 0 symmetric stretch was 868 cm-l in H3B306compared to 874 cm-’ for H3B303from the same procedure, and the depolarization ratio calculated for B3063-by using the H3B3O6geometry and a [4s3pld] basis was 0.075. A further discussion of our coupled Hartree-Fock calculations on H3B303 and the other “inorganic benzenes”, H6B3N3,H6B3P3, and H6A13P3,will be reported later.
+
Acknowledgment. This work was supported by the Experimental and Theoretical Geochemistry Program of N S F under Grant EAR-8603499. (16) Woodward, L. A. In Roman Spectroscopy: Theory and Practice; Szymanski, H., Ed.; Plenum: New York, 1967; Vol. 1, p 32. (17) (a) Walrafen, G. E.; Samanta, S. R.;Krishnan, P. N. J . Chem. Phys. 1980, 72, 113. (b) Windisch, C. F., Jr.; Risen, W. M. Jr. J . Noncryst. Solids 1982, 48, 325. (c) Ramos, M. A,; Vieira, S . ; Calleja, J. M. Solid State Commun. 1987, 64, 455. (18) Niedenzu, K.; Sawaodny, W.; Watanabe, H.; Dawson, J. W.; Totani, T.; Weber, W. Inorg. Chem. 1967, 6, 1453. (19) Soppe, W.; van der Marel, C.; van Gunsteren, W. F.; den Hartog, H. W. J . Noncryst. Solids 1988, 103, 201.
