12768
J . Phys. Chem. 1993,97, 12768-12772
Equilibrium Geometries, Internal Rotation Potentials, and Spectroscopic Constants in NHzOH, NHzOF, NHFOH, and NHFOF James TyrreU,'*+Wyn Lewis-Bevan,* and Donald KristiansenS Center for Environmental Health and Safety and Department of Chemistry and Biochemistry, Southern Illinois University at Carbondale, Carbondale, Illinois 62901 Received: July 8, 1993' Optimized geometries, harmonic force fields, vibrational frequencies and intensities, and molecular constants have been determined a t the MP2 level with a 6-31 1G** basis set for the molecules NH20H, NH20F, NHFOH, and NHFOF. Vibrational frequencies for several isotopically substituted species were also determined to assist in the frequency assignments. The internal rotation potentials about the N - O bond have been determined for each of the molecules.
Introduction The substitutionofisoelectronicgroupscanoften provide insight into the nature of bonding in a molecular species. During the course of a study of the peroxides HOOH, HOOF, and FOOF, it was decided to study the structural and electronic effects resulting from the substitution of one or more of the oxygens by theisoelectronicgroup,NH. In this paper we consider the species resulting from the replacement of one of the oxygens by an NH group for each of the moleculesmentioned above. This generates NH20H from HOOH, the species NH2OF and NHFOH from HOOF, and NHFOF from FOOF. In recent years it has become possible to predict geometrical parameters to a high degree of accuracy. However thevast majority of molecules for which this has been done can be well represented by a single electronic configuration. Some molecules such as FOOF clearly cannot be so represented while others may lie on the borderline. It is important to determine when either of these situations apply because it can significantly impact the predictive capability of the theoretically determined parameters. The MCSCF (multiconfigurational self-consistent field) method can provide some assistance in making this determination and was used for that purpose in this study. Experimental data on the molecular geometry are available only for NH20H.l A complete vibrational analysis for NH2OH has been reported by Gigube and Liu? though their assignment of the NH2 rocking vibration has been di~puted.~ The structure of NH2OH has been optimized at the MP2/6-31G*, MP3/631G*, and CID/6-31G* levels: and a comparison is made with the experimental structure. However the value for the ONH angle of 112.6O given as an experimental value in ref 4 does not match the value of 103.2O given for that angle in the original study of the structure of NH20H,1 and, what is surprising is that the calculated values for that angle as reported in ref 4 match the presumably incorrect experimentalangle given therein rather than the value given in ref 1. Since the calculated vibrational frequencies for NHzOH also reported in ref 4 are based on the optimized structure, it would be expected that some of the frequencies would show discrepancies from the experimental values greater than could be attributed to the use of a harmonic force field for the calculation. This is in fact observed and particularly so in the case of the torsional frequency whose calculated value of 286 cm-I at the MP2/6-31G1 level is significantly different from the experimental value of 430 cm-1. Theoretical calculations of the geometries of NH20F, NHFOH, and NHFOF have been carried out at the Hartree-Fock
* Author to whom all correspondence should be addressed.
Center for Environmental Health and Safety. Department of Chemistry and Biochemistry. *Abstract published in Aduance ACS Abstracfs, November 15, 1993. t
0022-365419312091-12768SO4.00/0
level by Olsen et aL5 Internal rotation investigations of all four molecules at the Hartree-Fock level have also been conducted by Olsen et a1.,6 while similar studies have been conducted on NH2OF and NHFOH by Weinhold! and by Pople.8
Method All calculations of geometries and frequencies at the MP29 level werecarriedout usinga 6-31 1G**basisset and theGaussian 9010 or Gaussian 9211package of programs. Additional geometry optimizations on NHzOF, NHFOH, and NHFOFat the MCSCF level again using the 6-3 11G** basis set were carried out with the GAMESW package of programs to determine the extent to which a single reference configurationrepresentsthese molecules. Additional frequency calculations for isotopically substituted species were carried out using the force constant matrices determined at the MP2 level and making use of the SPECTRO theoretical spectroscopy package." In several cases artificial isotopic masses (1.2H, I3H, and 22F) were used to help clarify vibrational frequency assignmentsand to assist in following large frequency shifts observed when replacing 'Hby *H, especially when this resulted in reordering of the frequencies. Results and Discussion Molecular Geometries. Table I lists thegeometricalparameters for the molecules NHzOH, NHzOF, NHFOH, and NHFOF optimized at the MP2/6-3 llG** level. Values listed in brackets are the experimental parameters,' while the values listed in parentheses are geometries optimized at the MCSCF level using the 6-31 1G** basis set. NH20H possesses C, symmetry (this was confirmed by first optimizing its geometry without any symmetry assumptions), and there is good agreement with the parameters obtained experimentally, including the value for the HNO angle (expt = 103.2', calc = 103.9O). All of the bond lengths are consistent with single bonds as anticipated. NH2OF on the other hand is quite unusual. It is significantly distorted from C, symmetry with an unusually long 0-F bond ( 1.624 A) and a short N-O bond ( 1.268A). These are reminiscent of the bonding found in FOOF (0-F = 1.586 A and 0-0 = 1.216 A)14and suggest a structure in which the nitrogen forms a double bond with the oxygen and the fluorine is loosely bound via overlap between the N-0 U* orbital and a fluorine porbital. This is consistent with a move away from sp3 hybridization on the nitrogen toward sp2 hybridization. The degree of hybridization, spn,can be estimated using n = (cos where (Y is the angle between two hybrid orbitals. For NH20F, the HNH angle is 116O, leading to sp2.28 hybridization of the N orbitals. This leaves 0.12 of a nitrogen p-orbital to ?r bond with the oxygen atom. This move toward sp2 hybridization at the nitrogen in N H 2 0 F also explains why the ONHH dihedral angle in that molecule ( 1 4 0 ~ 9is~significantly ) larger than the corresponding 0 1993 American Chemical Society
Parameters of NHzOH, NHzOF, NHFOH, and NHFOF
The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 12769
TABLE I: Optimized Geometries of NHzOH, NHzOF, NHFOH, a d NHFOF' parameter RN-H RN-O b
H
NHzOHb 1.0168 [1.016] 1.4359 [ 1.4531 0.9578 [0.962]
NHzOF' 1.0158 (l.oo00) 1.2676 (1.3255) 1.6242 (1.6127)
RIM
RN-P
LHNH LHNF LHNO LHON LFON
105.189 [107.1]
116.112 (114.630)
103.923 [103.2] 101.138 [101.4]
115.722 (112.328) 108.460 (108.064)
LFNO
LONHH LONHF LHONH LFONH energy
108.878
140.591 (129.802)
125.096 -131.417949
70.376 (65.489) -230.442068
NHFOH' 1.0184 (1.0299) 1.3808 (1.4041) 0.9606 (0.9433)
NHFOFd 1.0221 (1.0307) 1.3311 (1.3080)
1.4248 (1.4409)
1.4527 (1.5167) 1.4124 (1.4280)
99.408 (98.813) 101.294 (100.729) 102.710 (103.637)
101.991 (101.319) 101.312 (103.223)
106.256 (105.556)
105.270 (104.997) 107.742 (107.067)
108.811 (107.974) 160.836 (161.966)
111.112 (1 10.791)
-230.487665
153.464 (152.530) -329.450779
All calculationscarried out at the MP2 level using a 6-3 1lG** basis set. Bond lengthsare in angstroms; angles are in degrees; energy is in hartrees. C MCSCF/6-3 11G**structural parameters areshown in parentheses with configurationsgenerated
* Experimentalparameters in bracketsarefrom ref 1.
from seven valence and three virtual orbitals. d MCSCF/6-311G** structural parametersare shown in parentheses with configurationsgenerated from nine valence and three virtual orbitals.
angle (108.88O) in NHzOH. The weak bonding between the oxygen and fluorine and the distortion from C, is due to the combination of the r*-p bonding and the repulsion between the oxygen and fluorine lone pairs. An MCSCF geometry optimization was carried out on NHzOF using the 6-31 1G** basis set and including configurations generated from excitations from the seven highest occupied orbitals to the three lowest virtual orbitals. This produced a somewhat longer N-O bond and a smaller ONHH dihedral angle than in the MP2 optimized geometry but little change in the 0-F bond length. This indicates less N-O a bonding and a higher n value for the sp hybridization at the nitrogen. The dominant configuration contributes only about 87% to the total, which is similar to the result obtained in HOOF but considerably more than the 76% determined by us for the dominant configuration in FOOF. The latter molecule cannot be adequately represented by a single reference configuration, whereas both NHzOF and HOOF seem to be borderline cases. The difference in geometry in NHzOF as determined by the MP2 and MCSCF calculations could be due to either an inadequate choice of valence and virtual orbitals in the latter calculation or to the fact that use of a single reference configuration does not provide an adequate basis for the electron correlation study. Both of these possibilities are under current investigation. NHFOH on the other hand has a structure which is consistent with a single bond between the nitrogen and the fluorine though theN-Obond issomewhat shorterthan in NH20H. The MCSCF optimized geometry is essentially identical to the MP2 geometry, and the dominant configuration contributes over 93% to the total, indicating that this configuration is a reasonable, if somewhat imperfect, basis for a single reference correlation calculation. The MP2 result for NHFOF predicts typical 0-F and N-F single bonds, though the MCSCF calculation gives a somewhat longer 0-F bond. The N - O bond clearly has a significant amount of double bond character which is further enhanced in the MCSCF result as opposed to what was observed in NHzOF. The dominant configuration contributesalmost 89% to the total, which is similar to that found for NH20F. The considerations as to thedifferences between the MP2 and MCSCF geometries discussed above for NHlOF may also apply to NHFOF. The dihedral angle in NHFOH indicates a distorted trans structure with the distortion being due to the repulsive interaction of the lone pairs on the fluorine and oxygen atoms. A similar effect is observed in NHFOF, where a distorted trans structure is enhanced by the additional repulsion between the nitrogen lone pair and the lone pairs on the fluorine of the OF group. InternalRotatioa. Figure 1 shows the internal rotation potential
12
8
i
1
4\ 0' 0
NI-IFO-
45'
90'
135'
180-
XONH dihedral angle
Figure 1. Internal rotation potential about the XONH dihedral angle for NHzOH, NHFOH, NHzOF, and NHFOF.
as a function of the HONH dihedral angle in NHzOH and NHFOH and of the FONH dihedral angle in NH20F and NHFOF, where the geometry is optimized a t each dihedral angle. In NH20H there is a single minimum corresponding to the trans conformation of C, symmetry. NH2OF also shows a single minimum but a t a dihedral angle far removed from C, symmetry due to the nature of the bonding between the fluorine and oxygen atoms described earlier. Both NHFOH and NHFOF have qualitativelysimilar internal rotation potentials with minima at a dihedral angle of Oo and one close to 180°. The latter minimum has an equivalent conformation separated by a small maximumat 180° corresponding todifferent but equivalent orientations of the oxygen lone pairs relative to those of the fluorine in the NF group. There is a substantial difference in the stability of the Oo conformation in the two molecules relative to their global minimum. In NHFOH the 0' conformation is about 9 kcal mol-' less stable than the global minimum and is therefore unlikely to be present at room
12770 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993
Tyrrell et al.
TABLE II: Vibrational Frequencies and Intensities of NHzOH, N b O H , NH20D, NDzOD, 15NH20H,and NH2WH* mode NH20H exptb ND2OH NHzOD NDzOD I5NH2OH NH2'80H a' 0-H str 3920.58(44.6) 3656 3920.52 2856.99 2856.92 3920.58 3907.34 N-H(s) str 3508.99( 1.0) 3297 25 35.98 3509.08 2535.92 3504.08 3508.99 NH2 sciss 1677.79(16.9) 1605 1412.24 1670.92 1217.00 1676.01 1676.83 NOH bend 1428.68(29.5) 1357 1214.26 1258.94 1088.75 1423.35 1425.22 NHz wag 1177.81(133.7) 1120 995.58 991.05 977.76 1175.61 1171.73 N-O str 979.34(11.2) 895 888.98 976.93 863.15 961.84 955.90 a" N-H (a) str 3599.92(0.2) 3350 2654.62 3599.90 2654.60 3589.64 3599.92 NHz rock 1344.12(0.01) 998.24 1342.18 992.76 1341.13 1341.87 torsion 429.91( 192.5) 430 396.09 353.79 312.50 429.81 428.71 Frequencies are in cm-I; intensities are in km mol-'. All frequencies were calculated using MP2/6-311GS*. Giguere, P. A,; Liu, 1. D. Can. J . (I
Chem. 1952,30,948.
TABLE III: Vibrational Frequencies and Intensities of NHIOF. NDtOF, WH20F. and NHt'WF' NH2OH ND2OF 15NH20F NH2I80F mode N-H (asym) str 3633.70(62.0) 2694.33 3621.99 3633.70 3495.34( 16.1) 2513.83 3491 -79 3495.30 N-H (sym)str 1717.81(24.9) 1395.29 1713.38 1717.65 NH2 sciss N-O str 1395.01(62.0) 1223.11 1375.71 1356.38 1354.85(0.004) 1040.92 1349.01 1350.21 NH2 rock 791.04 798.78 NOF bend 799.35(245.6) 677.43 651.23 649.16 485.25 651.73(13.4) NH2 wag 543.97 527.43 544.23 547.21(97.1) 0-F str 351.96 torsion (NH2 twist) 354.57(223.7) 313.39 353.26 0 Frequencies are in cm-1; intensities are in km mol-'. All frequencies were calculated using MP2/6-311G**. ~
temperature, whereas in NHFOF the energy difference is only 2 kcal mol-' and a mixture of conformers should be observable. In essence, NHFOF has two energetically almost equivalent conformationsin which the two fluorinesminimize their repulsive interaction. Vibrational Frequencies. Tables 11-V list the vibrational frequenciesand intensities of the molecules, NHzOH, NHzOH, NHFOH, and NHFOF, respectively, along with the frequencies of various isotopically substituted forms. The vibrational frequencies and intensities of the most abundant species were determined with the Gaussian program at the MP2 level using a 6-311G** basis set and using the optimized geometries. The frequencies of the isotopically substituted forms were obtained using the Cartesian coordinates and force constants from the MP2 calculation as input to the SPECTRO theoretical spectroscopic program. Because of the very large frequency shifts resulting from substitution of deuterium for hydrogen causing, in some cases, reordering of the frequencies and because there is only one naturally occurring isotope. of fluorine, pseudoisotopic masses such as 1.2H,l.SH, and 22F were used to aid in assignments. Figure 2 illustrates the application of this procedure to the four fundamental vibrations of NHFOH lying in the range 950-1600 cm-1 when the N H hydrogen is replaced by deuterium. The method of isotopicinterpolationhas significant advantages, especially for molecules with low symmetry (Cl,C,, Ci), over conventional isotopicsubstitution. In the present case, where the vibrations involving the fluorine atoms were to be identified, the inclusion of a pseudoisotopic mass (22F) was especially helpful in the assignment. Isotopic substitution with 2H for lH can have dramatic effects on the relative frequencies of the closely lying fundamentals, especially if more than one vibrational band is dependent upon the isotopic substitution. This effect can be seen in Figure 2, where the three lower bands come into close proximity with one another upon substitution of the N H hydrogen with deuterium. Extrapolation from the IH mass through two intermediate isotopic masses (I.ZH, l3H) leads to a clear assignment of the fundamentals in the deuterated isotopomer. NHzOH is the onlyone of the molecules studied which possesses a plane of symmetry and also has available an almost complete assignment of its experimental spectrum. The fundamental correspondingto the NHz rock was initially assigned by GiguBre
and Liu2to a bandat 765 cm-I, but that assignment wasquestioned by Tamagake et al.3 Our results indicate that this fundamental is the weakest band by more than an order of magnitude and its value, even allowing for anharmonicitycorrections,is far removed from the value assigned by Gigube and Liue2 The ratio of the observed to calculated frequencies in NHzOH ranges from 0.91 to 0.95 except for the torsional frequency. Choosing a correction factor of 0.95 for the NHz rocking mode would indicate that the band corresponding to that vibration should be located around 1277 cm-1. The frequency shifts on isotopic substitution provide excellent confirmationof the assignmentsand also clearly indicate those frequencieswhich correspondto highly localized vibrations ascompared to those whosevibrationalactivityismoredelocaliied. The NH2 rocking mode is an example of the former while the NHz wag represents the latter case. In NHzOF the NHz rocking mode is again by far the weakest vibration. The frequency of the N-O stretch lies at 1395 cm-1, considerably higher than the value of 979 cm-I in NHzOH, primarily due to the much stronger N-O bond in NHzOF. The 0-F stretch in NHzOF is unusually low at 547 cm-I (compare this with the value of 677 cm-I in NHFOF), which is also due to the very weak bond between the oxygen and fluorine. Selectiveisotopicsubstitution in NHFOH was of considerable assistance in assigningthevibrations. Figure 2 shows the change in vibrational frequency for four bands in the range 95G1600 cm-l as the mass of the N H hydrogen is changed from 1 to 2. One fundamental, the N-O stretch, is completely unaffected, while the remaining three show varying degrees of adjustment. In the region indicated there are two bending modes representing the in-phase and out-of-phasebending modes associated with the ONH and HON angles. The higher of the two bending modes, at 1567 cm-I, is only moderatelyaffected by replacementof either hydrogen by deuterium, but when both hydrogens are replaced a much larger reduction in frequency is observed. The other, lower frequency at 1235 cm-l is much more modified by replacement of either hydrogen by deuterium and having both hydrogens replaced only produces a relatively small additional reduction. The frequencies and assignments for NHFOF are in accord with the results of isotopic substitution and comparison with the other species studied. Molecular Constants. The equilibrium molecular geometries and quartic force fields of each molecular species were used to predict the rotational and quartic centrifugal distortion constants of the four normal species. The results are listed in Table VI. The rotational constants have been adjusted to include the effects of centrifugal distortion and should correspond more closely to experimentally derived results. Because all of the molecules are near prolate asymmetric rotors, the F representation has been used throughout. In addition, the magnitude of the asymmetry parameter, K , for NHzOH was calculated to be 4.9999,leading us to choose the more appropriate S-reduced Hamiltonian of Watson's when reporting the spectroscopicconstants for all four molecules. Unfortunately, we were unable to obtain any higher order spectroscopic constants because of the present restrictions on
Parameters of NHzOH, NHzOF, NHFOH, and NHFOF
The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 12771
TABLE I V Vibrational Frequencies and Intensities of NHFOH, NDFOH, NHFOD, NDFOD, 15NHFOH, and NHWH'
0
mode
NHFOH
NDFOH
NHFOD
0-H str N-H str HONH (s) bend HNF bend HONH (a) bend N - O str N-F str ONF bend torsion
3887.05(70.1) 3528.72(3.3) 1567.13(1.0) 143 1.89(32.3) 1234.60(105.0) 1058.64(45.8) 891.33(144.8) 537.96(29.7) 484.01(93.0)
3886.92 2584.20 1460.62 1082.15 977.15 1057.41 888.81 533.22 482.53
2831.95 3528.91 1510.88 1343.41 1009.97 1058.13 888.47 531.84 363.04
NDFOD 283 1.93 2583.98 1169.38 1066.78 924.29 1051.65 879.76 527.19 361.18
IsNHFOH 3887.05 3520.56 1564.73 1428.31 1232.39 1038.77 872.50 536.37 482.80
NHFl*OH 3874.05 3528.71 1562.28 1430.62 1232.58 1034.85 888.21 524.78 483.1 1
Frequencies are in cm-1; intensities are in km mol-I. All frequencies were calculated using MP2/6-311G**.
TABLE V: Vibrational Frequencies and Intensities of NHFOF. NDFOF. NHFWF. and lSNHFOF' mode N-H str HNF bend ONH bend N - O str N-F str 0-F str FONF (s) bend FONF (a) bend torsion
NHFOF 3502.16(28.9) 1467.87(3.4) 1219.69(55.0) 987.92(2.0) 9 19.6 1 (109.43) 677.05(73.8) 589.60(0.8) 506.85(7.3) 194.1g(3.0)
NDFOF NHF'*OF "NHFOF 3494.30 2562.34 3502.15 1086.73 1466.20 1466.56 1 209.9 1 1026.88 1212.75 964.58 974.09 959.33 916.48 914.89 899.70 658.92 643.36 615.37 576.92 577.45 583.23 500.55 482.33 503.69 192.53 191.20 193.41
0 Frequencies are in cm-I; intensities are in km mol-l. All frequencies were calculated using MP2/6-311G**.
1.o
1.2
1.4 1.6 1.8 Isotopic mass of NH hydrogen
2.0
Figure 2. Selected vibrational frequencies in NHFOH as a function of the mass of the N H hydrogen: (0)HONH (s) bend; (e) HNF bend; (m) HONH (a) bend: (X) N - O stretch.
TABLE VI: Rotational and Centrifugal Distortion Constants of NH20H, NHzOF, NHFOH, and NHFOF' parameter A(fi Bcfi
Ofi DjX lo6 DJKX 103 DKX lo3 dl X lo7 dzX lo*
NHzOH 6.424178 0.856608 0.855953 0.2495 0.2556 0.4719 0.357 0.64
NHzOF 1.675102 0.326952 0.287608 -0.1078 0.0450 -0.0058
-0.080 -7.55
NHFOH 2.071099 0.856441 0.681641 2.9721 0.0575 -0.0082 0.271 -23.70
NHFOF 1.970672 0.168767 0.154762 0.1600 0.0035 -0.0021 -0,158 0.53
0 All constants are in units of cm-I. Rotational constants include distortion due to quartic centrifugal distortion constants. Rotational constants are in the S-reduced Hamiltonian.
obtaining the higher order energy derivatives at the MP2 level. Among others, the higher order derivatives would have allowed us to determine the anharmonic corrections to the vibrational frequencies and higher order centrifugal distortion constants. A t this point, due in part to the lack of experimental results, Coriolis coupling constants have not been reported.
Conclusions The molecular geometries, internal rotation potentials, and spectroscopic constants for the four species NHzOH, NHzOF, NHFOH, and NHFOF have been determined from ab initio calculations at the MP2 level. Additional geometry calculations
were also run at the MCSCF level to determine the quality of the single configuration model. For the fluorine containing molecules the contribution of the reference configuration decreased in the order NHFOH (93%), NHFOF (89%), and NH2O F (87%). It should also be noted that the agreement between the MP2 and MCSCF optimized geometries became worse as the contribution of the reference configuration decreased. The optimized equilibriummolecular geometry for NH20H was found to be in excellent agreement with the experimental results. In NHFOF and more particularly in NHzOF there is a significant amount of N-0 P bonding, and this seems to correlate with the length of the 0-F bond. The internal rotation potentials for NHzOH and NHzOF clearly show that only one possible conformer exists. However, those for NHFOH and NHFOF show that two minima exist, and, in the latter molecule, both conformers should be observable at room temperature. The calculated harmonic vibrational frequencies of NHzOH were compared with the experimental values and found to be in good agreement. The rotational constants were also found to agree well with experiment for NHzOH. No experimental data were available for comparison of the centrifugal distortion constants. While the structures and properties of HOOH, HOOF, and FOOF follow a consistent pattern in that the replacement of hydrogen by fluorine produces enhanced bonding between the oxygens and weaker bonding between the oxygen and fluorine, this pattern is only partially observed when one of the oxygens is replaced by an NH group. In NHzOH unlike HOOH there are two possible distinct sites for replacement of hydrogen by fluorine. Replacement of the OH hydrogen leads to a result similar to that observed in going from HOOH to HOOF; the N-0 bond becomes stronger while the 0-F bond weakens considerably. On the other hand when the N H hydrogen is replaced by fluorine, there is only a modest shortening of the N-0 bond and the N-F bond is essentially a normal single bond. When two of the hydrogens of NH2OH are replaced by fluorine, one on the nitrogen and one on the oxygen, the resulting structure follows the NHFOH pattern rather than the NHzOF one. The N-0 bond length does shorten relative to that in NHFOH, but both the N-F and 0-F bond lengths are consistent with single bonds.
Acknowledgment. The research was partially supported by a supercomputergrant from the National ScienceFoundation, grant number CHE93000n. References and Notes ( 1 ) Tsunekawa, S. J . Phys. Soc. Jpn. 1972, 33, 167. (2) Gigubre, P. A.; Liu, I. D.Can. J. Chem. 1952, 30, 948. (3) Tamagake,K.; Hamada,Y.;Yamaguchi,J.; Hirakawa, A. Y.;Tsuboi,
M. J. Mol. Spectrosc. 1974, 49, 232. (4) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory;John Wiley &Sons: New York, 1986; Tables 6.7
and 6.41. (5) Olsen, J. F.; Howell, J. M. J . Fluorine Chem. 1978, 12, 123. (6) Olsen, J. F.; OConnor, D.; Howell, J. M. J. Fluorine Chem. 1978, 12, 179. (7) Brunck, T. K.; Weinhold,
F.J . Am. Chem. Soc. 1979, 101, 1700.
12772 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 (8) Radom, L.;Hehre, W. J.; Pople, J. A. J. Am. Chem. Soc. 1972,94, 2371. (9) M~ller,C.; Pleaset, M. S. Phys. Rev. 1934.16, 618. (10) Frisch, M. J.; Head-Gordon, M.;Trucks, G. W.; Foresman. J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.;Binkley, J. S.; Gonzalez, C.;
Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople. J. A. Guussiun 90,Revision J; Gaussian, Inc.: Pittsburgh, PA, 1990. (11) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M.W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Rcplogle, E. S.;Gomperts, R.; Andres, J. L.; Raghavachari, K.;Binkley. J.S.;Gonzalez,C.;Martin,R.L.;Fox,D. J.;Defrees,D.J.;Baker, J.;Stewart,
Tyrrell et al. J. J. P.; Poplc, J. A. Gaussiun92, Revision B Gaussian, Inc.: Pittsburgh, PA,
1992. (12) Schmidt,M.W.;Baldridge,K.K.;Boatz,J.A.;Jensen,J.H.;Koscki, S.; Gordon, M. S.; Nguyen, K. A.; Windus, T. L.; Elbert, S.T. QCPE Bull. 1990, 10, 52. (13) Gaw, J. F.; Willetts, A.; Green, W. H.; Handy, N. C. In Advunces in Molecular Vibrations and Collision Dynumics; Bowman, J. M.,Ed.; JAI Press: Greenwich, CT, 1990. (14) Hedberg, L.; Hedberg, K.;Eller, P. G.; Ryan, R. R. Inorg. Chem. 1988, 27,232. (15) Watson, J. K.G. In VibrurionulSpectruundStrucrure;Durig, J. R., Ed.; Elsevier: Amsterdam, 1976; Vol. 6, pp 1-80.
