J. Phys. Chem. 1986,90, 5661-5665 a
,
i\
I
I
1130
180
a
JL-----
2080
Conclusions When NO is two photon (1 1) ionized through the u = 0 level of its A 2 2 excited electronic state, both Franck-Condon-allowed u = 0 ions and unexpected u = 6 ions are produced. Our measurement of this vibrational state distribution corroborates the recent work of Miller and Compton” which was performed on the same molecular system but with a different type of electron energy analyzer. Since these (1 + 1) studies could not possibly be exciting states in the ”three photon region” (near 66000 cm-’), the latter need not be involved in the production of slow electrons. Particularly interesting are the strong wavelength dependence and isotropic angular distribution of the slow electrons which suggest that a resonant autoionizing state in the continuum is involved. The fact that just a single slow electron peak is observed suggests that vibrational autoionization is occurring, but the exact electronic state involved cannot be established a t this time. One issue remains unresolved: Kimman et al. and White et al. report distributions of peaks from u = 1 to u = 6 in addition to the Franck-Condon-allowed Au = 0 transition. However, in the spectra of Miller and Compton several of these peaks are substantially weaker and they suggested that this might be due to different angular dependence^.^ Certainly the spectra that we observe with the laser polarized parallel and perpendicular to the electron flight direction are simpler than those of ref 6 and 7. This implies that in experiments using the (2 2) ionization scheme, resonances in the third photon region also affect the observed distribution.
+
* n 2080
5661
1130
180
Photoelectron Energy (meV)
Figure 6. Photoelectron spectra obtained by tuning to the P2 head (2268 A) of the A-X transition. No acceleration field was employed and the grids were retracted from the ionization region; (a) laser polarized perpendicular and (b) laser polarized parallel to the electron flight direction.
-
Together with our wavelength scan referred to earlier, this clearly points to the fact that, near the region of the 2X+ 2113,2band head, no vibrationally excited NO+ ions are seen. This result is different from that of Kimman et a1.6 suggesting that their ion vibrational distribution was strongly affected by the three photon resonances (near 66000 cm-I), and supports the hypothesis that different mechanism(s) may be dominant depending on whether a (2 + 2) or (1 + 1) ionization scheme is employed. It is possible that in a (2 + 2) scheme, both the three photon region (66000 cm-’) and the four photon region (in the ionization continuum) may be involved in the production of slow electrons. In our (1 + 1) scheme only the ionization continuum can be involved.
Force Fields for SIF, and H,SiO,:
+
Acknowledgment. This work has been supported by the National Science Foundation and by the Environmental Protection Agency. Registry No. NO, 10102-43-9.
Ab Initlo Molecular Orbital Calculations
Anthony C. H~ss,*Paul F. McMillan, and Michael O’Keeffe Department of Chemistry, Arizona State University, Tempe, Arizona 85287 (Received: May 12, 1986)
Harmonic force constants and frequencies have been calculated for the molecules H4Si04and SiF4 by using STO-3G, 3-21G, 6-31G, and 6-31G* basis sets at the SCF level. Results for SiF4 are compared with experimental values from the literature corrected for anharmonicity. Internal symmetry force constants for SiF4 at the 6-31G* basis level are F , , = 806.0, FZ2= 28.02, F3, = 722.5, F34= 24.67, and Fez = 48.1 1 N m-’,in good agreement with experiment. The minimum energy geometry of H4Si04has previously been suggested to be a conformation with DZdsymmetry. The present study indicates that the Dzd structure is unstable with respect to rotation of the H atoms about the Si-0 bonds and is the geometry of a transition state rather than that adopted at the global minimum. Internal symmetry force constants and harmonic frequencies for H4Si04are compared as a function of basis set. Selected internal force constants have been extracted for comparison with previous estimates from empirical force constant calculations for silicates. The present work suggests that Hartree-Fock calculations can provide realistic force constants for silicate molecules and clusters.
Introduction The nature of the force field in silicates has been, and still remains, a subject of considerable discussion.’ In the present work we have determined the force field of the prototype molecule H4Si04 in order to model the tetrahedral silicate unit which is a basic building block of silicate structures. Since there has not yet been an experimental determination of the force field of H4Si04, we have carried out calculations on the isoelectronic tetrahedral molecule SiF4 to allow comparison of calculated force (1) Bell, R. J.; Dean,P. Discuss. Faraday SOC.1970, 50, 55. Elcombe, M.M.Proc. R. Soc. (London)1967,91,947. Iishi, K. Am. Mineral. 1978,
63, 1190. Newton, M. D.; O’Keeffe, M.; Gibbs, G. V. Phys. Chem. Mineruls 1980, 6, 305.
0022-3654/86/2090-5661$01 SO10
constants and frequencies with experimental values.2 It is now well established that ab initio molecular orbital calculations at the Hartree-Fock level for suitably chosen molecular fragments closely model local geometries in condensed silicate^,^ and that such calculations can provide accurate force fields for a variety of molecules.4 The calculations reported here were carried out with a number of standard basis sets, including the minimal STO-3G, the split-valence 3-21G and 6-31G, and the split-valence 6-31G* with d-type polarization functions on Si, (2) McDowcll, R. S.; Reisfeld, M. J.; Patterson, C. W.; Krohn, B. J.; Vasquez, M. C.; Laguna, G. A. J . Chem. Phys. 1982, 77,4337. ( 3 ) Gibbs, G. V. Am. Mineral. 1982, 67, 421. (4) Pulay, P. In The Force Concept in Chemistry, Deb, B. M.,Ed.; Van Nostrand New York, 1981; pp 449-480.
0 1986 American Chemical Society
5662 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 TABLE I: Calculated Geometry, Energy, and Vibrational Parameters for SiF," r(Si-F), E(RHF), basis A hartrees STO-3G 1.585 -677.8470 3-21G 1.584 -683.2721 6-31G 1.625 -686.7337 6-31G* 1.557 -686.9498 expt 1.552 Harmonic Vibrational Frequencies, cm-I STO-3G 3-21G 6-31G 6-31G* exptb exptc
E 263.21 (-1.4)d 269.73 (1 .O) 233.20 (-12.7) 274.05 (2.6) 267.0 264.2
F2 370.1 1 (-5.1) 391.53 (0.4) 356.08 (-8.7) 406.41 (4.3) 389.8 388.4
F2 1099.4 (5.3) 1156.1 (10.7) 1036.6 (-0.7) 1107.5 (6.1) 1044.2 1031.4
AI 761.23 (-5.7) 844.49 (4.6) 756.64 (-6.3) 848.55 (5.1) 807.2 800.6
Internal Symmetry Force Constants
RI STO-3G 3-21G 6-31G 6-31G* expt
F,, 26.00 27.15 20.29 28.02 26.6
648.6 798.3 640.8 806.0 729.2
F?? 695.0 784.9 628.4 722.5 637.4
FU 12.42 21.74 16.76 24.67 20.4
CoordinatesC / 2 k l + r2 + 73 + r4) s )' = 12-1/2(2a12- a 1 3 - a 1 4 - Cy23 - CY24 s ) = 1/2(aI3- a 2 3 - a 1 4 + 0124) s 2) = 1/2(r1 - r2 + r3 - r4) s '2) = l/2(-r1 + r2 + r3 - r4) s '2) = 1/2(rl r2- r3 - r4) s 6 2 ) = 1/21/2(a1, - CYz4) s#*)= 1/2 1/2(a23- a14) $2) = 1/21/2(a,, -
i
SA')
=
FM 40.62 44.60 36.99 48.11 44.5
+ 2CY34)
+
Force Constants = f r - 3f, F 2 2 = f a - 2fao + Yo, Fl1
F33 F44
TABLE II: Calculated Geometry and Energy Parameters and Harmonic Vibrational Freauencies for HSiO. Geometry and Energy Parameters STO-3G R(Si-0)' 1.655 r(O-H) 0.983 L(OSiO)b 112.42 L(OSi0) 103.73 L(Si0H) 109.08 E(RHF)C -583.3724
=A-L
= 1/21/2cf,e -YrJ = fa-
sm
OThe experimental values are taken from ref 2. bEstimated harmonic frequencies. Observed (anharmonic) frequencies. "Percent differences between experimental harmonic and calculated values. Internal symmetry force constants following the coordinate conventions of Pulay and co-workers.20 All force constatns expressed in N m-l: terms in b2E/6a2 multiplied by l/$; terms in 62E/6r 6a multiplied by l / r ; where r is the calculated Si-F bond length at that basis.
F, and O5and ptype polarization functions on H. All calculations were performed with the Gaussian-82 set of programs.6 The Cartesian force constant matrices output by GAUSSIAN-82 were transformed to internal symmetry force constants to avoid the problem of angular redundancy inherent among members of an internal valence coordinate set on atom centers with a connectivity of four.'
SiF,. Geometry and energy parameters calculated for SiF, as a function of basis set are shown in Table I. Also given are the calculated harmonic frequencies and symmetry force constants, compared with experimental values.2 All force constants were calculated as analytical second derivatives of the S C F energy (5) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. Franci, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordan, M. S.; Defrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (6) Binkley, J. S.; Frisch, M.; Raghavachari, K.;Defrees, D.; Schlegel, H. B.; Whiteside, R.; Fluder, E.; Seeger, R.; Pople, J. A. GAUSSIAN 82, Release A, Carnegie-Mellon University. (7) Wilson, E. B., Jr.; Decius, J. C., Cross, P. C. Molecular Vibrations; Dover: New York, 1955.
3-21G
6-31G
6-31G*
1.642 0.957 111.50 105.49 128.41 -587.7205
1.662 0.941 111.88 104.75 134.63 -590.6995
1.629 0.947 112.63 103.32 117.24 -590.8864
Harmonic Frequencies, cm-l mode A2 B1
E AI Bl B2
E A1 E B2 AI
E B2 E AI
B2
STO-3G 48.6 206.5 274.5 282.8 352.8 356.8 370.2 769.7 980.5 1058 1254 1271 1272 4278 428 1 4282
'Bond lengths in hartrees.
I
F34
Hess et al.
A.
3-21G (219)i 218.3 246.8 293.1 389.1 398.5 410.5 712.7 690.4 756.7 88 1.3 1139 1072 4025 4028 4022
6-31G
(229)i 208.3 265.7 268.1 358.1 366.9 366.0 604.0 573.8 656.7 823.0 1059 985.4 4197 4201 4194
6-31G* (1OO)i 198.1 316.0 290.9 429.1 378.4 413.9 815.9 881.2 920.5 929.2 1042 1047 4142 4145 4140
bAngles in degrees. e R H F S C F energies in
surface with respect to nuclear coordinates* at the calculated equilibrium geometries. All of the calculated frequencies and force constants are comparable in magnitude to the experimental values, showing that the vibrational properties of SiF4 may be realistically modeled at the S C F level. The frequencies calculated at all basis levels are in agreement with the harmonic frequencies estimated by McDowell and co-workers2 to within approximately 12%. The highest level calculation using the 6-31G* basis set exhibits the smallest range of deviations, giving frequencies 2.6 to 6.1% higher than the experimental values. These residual errors can be attributed to inadequacies in the basis set (see below) and neglect of electron correlation in the c a l c ~ l a t i o n . ~ Some interesting trends may be observed within the calculated force constants. At the STO-3G level, the calculated value of FIl is less than that for F33:the reverse of the experimental values. This suggests that the sign of the stretchstretch interaction term f, is not calculated correctly with the STO-3G basis. At the 3-21G level, the calculated F,, and F,, force constants are approximately equal, to give thef,, term as 3 N m-l, compared with the experimental value of 23 N m-'. The 6-31G results are surprisingly different to the 6-31G* force constants,illustrating the large effect of basis set polarization functions in vibrational calculations on Si-F, and presumably Si-0, containing molecules. In all cases the 6-31G force constants are smaller than either the experimental or the 6-3 1G* values, resulting in lowered vibrational frequencies. We consider t h a t , of t h e four basis sets considered, t h e 6-31G* basis yields the most realistic vibrational properties for SiF4. The symmetry force constants F l l ,FZ2,F33, and F44calculated with the 6-31G" basis are 5-13% larger than the experimental values corrected for anharmonicity.2 The direction and magnitude of these errors are typical of vibrational calculations using Hartree-Fcck wave f ~ n c t i o n s .The ~ calculated value of F3,is approximately 20% larger than the experimental harmonic value. This was an unexpected result since interaction terms, like diagonal force constants, are normally calculated to within 10% of the (8) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J . Quantum Chem., Quantum Chem. Symp. 1979, 13, 225. (9) Pulay, P.; Lee, J.; Boggs, J. J. Chem. Phys. 1983, 79, 3382. Hout, R. F., Jr.; Levi, B. A.; Hehre, W. J. J . Comp. Chem. 1982, 3, 234.
Force Fields for SiF4 and H4Si04
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5663
TABLE III: Definition for Internal Symmetry Coordinates and Force Constants for HSiO, with DU Symmetrya
r
a
B
Y
r/
r7
ffY
Br a7
BT
77
‘Internal coordinates (R, r, a, @, y, 7) are defined in Figure 1. In the definition of the force constants involving the internal coordinates (a,0) a single prime represents adjacent/adjacent interactions, a double prime represents opposite/oppositeinteractions. In the force constants involving (R, r, y , 7 ) a single prime represents an interaction across an a angle, a double prime represents an interaction across a 0 angle. experimental values: In the case of SiF,, however, the magnitude and even the sign of the interaction constant F3, has been the subject of some controversy.2 The value of F34is critically deand is strongly pendent on the Coriolis coupling terms i3and i4 For excoupled to the diagonal force constants F33and ample, Heicklen and Knight,” Clark and Rippon,l0 and McDowell et al.z all calculated FU to be 44 N m-l, but F33was calculated at 636,618, and 637 N m-l, and F34at -27, 19, and 20 N m-l, respectively. W e suggest ’that, even after the careful force field analysis of McDowell and co-workers? there may be some remaining error in the experimental determination of F33,F-, and especially F3,. HJiO,. The H4Si04molecule was constrained to have DU symmetry with the hydrogen atoms in an eclipsed conformation (Figure 1). This was suggested to be the most stable conformation in a previous calculation,12 using a smaller basis set (6-31G* with d-type polarization functions on silicon only). Calculated geometry and energy parameters as a function of basis set are shown in Table 11. The bond lengths and angles found in the present calculation (10) (11) (12) 2304.
Clark, R. J. H.; Rippon, D. M . J. Mol. Specfrosc., 1979, 44, 479. Heicklen, J. H.; Knight, V . Specirochim. Acia 1964, 20, 295. OKeeffe, M.; Domenges, B.; Gibbs, G. V . J. Phys. Chem. 1985,89,
n
n
Y Figure 1. Definition of internal coordinates for H4Si04. R and rare the Si-0 and 0-H bond lengths, respectively, and y is the SiOH angle. 6 forms the set of four larger OSiO angles, and a forms the set of two (opposite) smaller O S 0 angles. The torsional coordinate T is defined
as the change in dihedral angle between the planes described by the HOSI and OSiO angles (for example, 77312 is the change in dihedral angle between the H703Siland 0 3 S i 1 0 2planes). at our 6-31G* basis level are similar to those found by O’Keeffe and co-workers.12 The two calculations did show a significant difference in the total SCF energy. The energy found in the present study is lower, indicating the importance of d-type functions on oxygen. The present study also indicates that the
5664
Hess et al.
The Journal of Physical Chemistry, Vol. 90, No. 22, I986
62
i
i
A
4140.
E t 920.5
A, Ai
329.2
Figure 2. Calculated normal-mode displacements for H4Si04at the 6-31G*level. The molecule is shown projected on the yr (left) and xz (right) planes. Dotted lines indicate the displacements of "hidden" atoms. X marks the position of H atoms projected on the S i 4 bond line. These are only shown when the H atoms have an observable displacement.
D, geometry is not the lowest energy structure, since a negative eigenvalue was present in the force constant matrix giving rise to one imaginary frequency (Tables I1 and 111). This strongly suggests that the D 2 d structure is a geometry found at a saddle point rather than that adopted at the global minimum. Calculated harmonic frequencies as a function of basis set are also shown in Table 11. It can be seen that the relative ordering of the frequency values changes with the basis set used in the calculation. In view of the results for SiF,, and previous discussions in the l i t e r a t ~ r e , we ~ . ~consider that the frequencies and force constants calculated at the 6-31G* level are the most realistic. The displacement vectors for selected normal modes calculated with the 6-31G* basis set are illustrated in Figure 2. The symmetric stretching motion of the SiO, tetrahedron may be recognized in the A, mode at 8 15 cm-', where the H atoms track the breathing displacements of the oxygens. This corresponds well with the frequency found for the symmetric stretching of SiO, groups in silicate glasses and ~rysta1s.I~This mode appears to be decoupled from the Si-OH deformation modes at 920 (B2) and 929 (A,) cm-'. This may be of interest for the interpretation of the vibrational spectra of hydrous silicate glasses and crystals, where the Si-OH stretching and SiOH deformation modes have not yet been explicitly identified.14 The E pair at 1042 cm-'along with the B2 mode at 1047 cm-' resemble the asymmetric stretching vibrations of a tetrahedral S i 0 4group,15 but in H4Si04,these are strongly coupled with SiOH deformation motions. The A, mode at 290 cm-' and the E modes near 400 cm-' may be described as OSiO bending motions, but these do not correspond simply to B.; McMillan, P. F. Am. Mineral. 1983, 68, 426. (14) Hartwig, C. M.; Rahn, L. A. J . Chem. Phyf. 1977,67,4260. Stolper, E. Contrib. Mineral. Petrol. 1982, 81, 1. McMillan, P. F.; Jakobssen, S.; Holloway, J. R.; Silver, L. A. Geochim. Cosmochim Acta 1983, 47, 1937.
the bending modes expected for a tetrahedral SiO, group.I5 Internal symmetry force constants for H4Si04at the STO-3G and 6-31G* basis levels are shown in Table IV. Most of the diagonal terms are comparable in magnitude, with differences on the order of 5-10% between the basis sets. The largest differences arise in the off-diagonal terms. For example, the Si-O/O-H stretchstretch interaction terms F5,,, F6,*, and F7,3are calculated to be large and negative at the STO-3G level (-50 to -43 N m-l), but are much smaller in magnitude (-9.5 to +2.5 N m-l), and two (F6,2and F7,J are even positive at the 6-31G* basis level. The SiO/OSiO stretch-bend interaction term Fl is calculated to be 34% larger with the 6-3 l G * basis, while the other stretch-bend interaction F9,, changes sign between calculations, although both bases find this term to be small in magnitude. These observations suggest that Si-0 vs. 0-H bond length correlations, or OSiO angle/angle correlations, may be unreliable in calculations at the STO-3G basis level. As noted above, we consider that the eclipsed conformation of H4Si04 (D2d symmetry) does not represent the most stable equilibrium configuration, due to the presence of a mode with an imaginary frequency. The mode in question was found to belong to an A2 representation by the symmetry analysis performed by the program (Table 11). This representation does not correspond to a true vibrational degree of freedom within the D, point group, but to a rotation. This inconsistency is due to the instability of the mode with respect to a hydrogen "pseudo-rotation" about the S i 4 bond axis (Figure 2). Due to the instability, the associated torsional force constants are suspect in this calculation. The actual magnitudes of these terms, however, are quite small and should
(13) Piriou,
(15) Herzberg, G. Infrared and Ramon Spectra; Van Nostrand: New York, 1945.
Force Fields for SiF4 and H4Si04 TABLE I V Internal Symmetry Force Constants for H S i 0 4 Calculated at the S T O - X and 6-31C* Basis Levels” STO-3G 6-31G* 618.43 667.55 FI.1 625.31 573.75 F2.2 618.76 574.14 F3,3 1023.2 960.34 F4,4 1023.7 958.29 F5,S 1021.5 959.85 F6,6 45.783 47.638 F7,7 41.637 47.059 F8.8 21.260 22.115 F9,9 37.245 45.956 Fl0,lO 51.718 43.702 F11.11 51.935 43.968 FI2.12 48.016 40.909 F13,13 2.5858 3.1302 F14.14 0.0535 -0.2398 F15,15 2.3416 2.9156 F16,16 -50.124 -9.5596 F5,1 -44.1 45 2.5386 F6.2 -43.400 0.6298 F7.3 1.6126 -1.3370 F9, I 22.363 33.822 F11.2 -1 1.329 -18.587 F12.3 37.898 18.235 F14.1 39.336 20.618 F15.2 35.134 28.337 F16,3 0.0 0.0 F18,1 0.0 0.0 F19,2 2.2381 1.8268 F20.3 17.383 6.1511 F9,5 15.156 2.3788 F11,6 10.917 8.3465 F12,7 39.133 25.257 F14,5 39.964 22.186 F15.6 37.618 23.299 F16.7 0.0 0.0 F18.5 0.0 0.0 F19.6 0.6433 0.0305 F20,7 14.247 7.3870 F14.9 10.802 16.020 F15,11 6.5204 10.802 F16.1Z 0.0 0.0 F18,9 0.0 0.0 F19.11 0.7235 2.7861 F20,12 0.0 0.0 F18,14 0.0 0.0 F20,15 0.1699 0.4549 F20,16
‘Force constants and coordinates are defined in Table 111. All force constants expressed in N m-l: terms in 62E/M2 where = a and j3 multiplied by 1/R2; where R is the calculated Si-0 bond length; terms in a2E/6y2 multiplied by l/$; where r is the calculated 0-H bond length; terms in h2E/6r2multiplied by 1/rR where rand R are defined as above; terms in 62E/6a 6j3 multiplied by 1/R2; terms in 62E/6a 6y multiplied by l/rR; terms in 62E/6y 67 multiplied by l/r2; all bond/ angle interaction terms divided by the calculated bond length of the bonding coordinate involved in the term. have a minimal effect on the other calculated force constants and frequencies. Since most empirical force constant refinements for silicates have been performed in internal valence coordinates, it is instructive to express the force constants for the silicate portion of our H4Si04cluster in internal coordinates for comparison with values previously estimated for silicates. This is possible for the diagonal S i 4 stretching force constants and the associated interaction terms, but not all of the individual internal force constants involving OSiO angle bending terms may be specified uniquely due to the problem of angular r e d ~ n d a n c y . For ~ example, the Si-0 stretching force constant f R and the stretch-stretch interaction termsyR andf;, may be obtained from the symmetry force constants F l l , Fz2, and Fj3 (Table 111). However, the angle bending force constantsfs,y@,andf”,, as well as the stretch-bend interaction terms fk,and yRC may not be uniquely determined (the chosen angular redundancy condition is defined in Table 111). Those internal force constants which can be expressed uniquely
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5665 TABLE V Comparison of Internal Valence Force Constants from This Study (6-31C* Level) and Previous Empirical Studies on Crystalline SiO2# fR
f’k fh fa fa” f8
-ffl
fs’-f{ fku fR$
f R i -fRE
this work
Etchepare et aLb
BatesC
597 23.2 23.4 47.4 0.3 46.0 11.9 12.5 -11.4 -13.2
594.3 71.1
490.5 79.1
28.5 -6.5
42.8
-16.4 0.0 -16.4
-59.2
“All values expressed in N m-I. bReference 17. cReference 18. or can be expressed as suitable linear combinations of terms are given in Table V, compared with values assumed or refined in previous empirical force field studies. The f’6 term (opposite/ opposite interaction of the two smaller OSiO angles) is extremely small (Table V). If this is also true for t h e y @term then the magnitude of t h e y , (adjacent/adjacent interaction term of the four larger OSiO angles) would be approximately 12.0 N m-l. Simple empirical vibrational calculations of silicate molecules, crystals, and glasses often ignore interaction terms.16 From the stretch-bend VR,, observed magnitudes of stretch-stretch VR), fllRa), and bend-bend Cf”,,f’, -f”,)interactions (Table V), this appears to be a rather poor approximation. Etchepare et al.17 and Bated8 have refined empirical valence force fields to experimental data for several crystalline polymorphs of SOz. Our calculated value of the S i 0 stretching force constant is (we believe fortuitously) close to that found by Etchepare et al., but is some 100 N m-I larger than Bates’ value. Our OSiO angle bending terms (near 47 N m-l) are close to the values refined by Bates (42.8 and 30.4 N m-l for the two OSiO angles in &quartz) but are significantly larger than those constants refined by Etchepare. The Si-0 stretch-stretch interactions found in both empirical studies are similar but are more than three times the magnitude found here. It is of interest to note that a previous ab initio force field calculation for H6SiZO7found an f R R interaction constant within the SiOSi linkage of approximately 30 N m-’.19 Finally, there are major differences in the values found for the SiO/OSiO stretch-bend interaction terms. Etchepare set the opposite stretch-bend termYR, to zero and found -16.4 N m-l for the corresponding adjacent term. Bates refined values of -59.2 and 33 N m-I respectively for these terms, while the present calculation found values of +12.5 and -1 1.4 N m-l for the same two interaction constants. In conclusion, it should be noted that although both empiricalI7J8force fields are quite different, each reproduces the observed spectra equally well. This illustrates the fact that, due to the underdetermined nature of the vibrational problem in complex systems, correspondence of observed and calculated vibrational frequencies is not a sufficient constraint for a unique or even a correct force field. We consider that, if the force fields calculated for small silicate molecules are transferable to larger systems, ab initio calculations of force constants for suitably chosen silicate clusters will provide a first step in establishing reliable force fields for complex condensed silicates.
Acknowledgment. The present work was supported by NSF Grant EAR-8407105. W e thank P. Pulay of the University of Arkansas for many valuable discussions, and H. Rhodes of the ASU Computing Center for technical advice during the computations. Registry No. SiF4, 7783-61-1; H4SiO4,10193-36-9. (16) Furukawa, T.; Fox, K. E.; White, W. B. J. Chem. Phys. 1981, 75, 3226. Gaskel, P. H. Phys. Chem. Glasses 1969, 8, 69. (17) Etchepare, J.; Merian, M.; Smetankine, L. J . Chem. Phys. 1974,60, 1873. (18) Bates, J. B.; J . Chem. Phys. 1972, 56, 1910. (19) OKeeffe, M.; Mcmillan, P. F. J. Phys. Chem. 1986, 90, 541. (20) Pulay, P.; Meyer, W.; Boggs, J. E. J . Chem. Phys. 1978, 68, 5077.
