Scaled quantum mechanical force fields for trifluoromethyl selenium derivatives. II. The [(C[F.sub.3]).sub.2] Se and [(C[F.sub.3]Se).sub.2] molecules.

Introduction

Theoretical studies on the vibrational properties of the selenium compounds, C[F.sub.3]SeX (X = H, D, Cl, or Br) and two simple C[F.sub.3]Se derivatives, i.e., C[F.sub.3]SeCN and C[F.sub.3]SeC[H.sub.3], were recently performed in our laboratory. 1,2 Now, we turn our attention to the vibrational studies of other two selenium compounds, i.e., [(C[F.sub.3]).sub.2]Se and [(C[F.sub.3]Se).sub.2].

These molecules were prepared by Dale, Emeleus, and Haszeldine (3) and by Emeleus and Dunn. (4) The molecular structures were obtained by Marsden and Sheldrick by means of electron diffraction techniques. (5,6) The vibrational spectra and assignments were reported for these two molecules by Marsden (7) and Clase et al. (8)

In the present work, the vibrational characteristics of the above-mentioned molecules were calculated using the methods of quantum chemistry to check the published normal mode frequencies and their assignments and to obtain the corresponding force constants, which were scaled to reproduce the experimental frequencies. Such adjustment was made using the formalism of the scaled quantum mechanical (SQM) force field, as defined by Pulay et al. (9)

Calculation procedure

Optimized structures, force constants, and vibrational frequencies for the [(C[F.sub.3]).sub.2]Se and [([CF.sub.3]Se).sub.2] molecules were obtained with density functional theory (DFT) methods using the B3LYP functional (10,11) together with the 6-311G* basis set. These theoretical data allowed a good reproduction of the experimental frequencies and facilitated the comparison of the results with those obtained in previous studies (1,2) in which the same combination of functional and basis set was used. All calculations were made for the isolated molecules using the Gaussian 03 set of programs. (12)

The harmonic force field in Cartesian coordinates given by the theoretical calculation was transformed to natural (local symmetry) coordinates (13) through the corresponding B matrix, (14) calculated with a standard program. The resulting force field was subsequently scaled using the scheme of Pulay et al., (9) in which the diagonal force constants are multiplied by scale factors [f.sub.i], [f.sub.j], and so forth, and the corresponding interaction constants are multiplied by [([f.sub.i] [f.sub.j]).sup.1/2], adjusting the scaled factors by a least-squares procedure to reproduce as well as possible the experimental frequencies. No anharmonicity corrections of these frequencies were made because of the lack of the necessary experimental data. The potential-energy distribution (PED), which gives the participation of each defined coordinate to each normal mode of vibration, was calculated with the resulting SQM force field.

The force field transformation, scaling, and PED calculation were performed with the program FCARTP. (15)

Structural results

The molecular conformations of [(C[F.sub.3]).sub.2]Se were investigated starting with an initial, staggered structure having FCSeC dihedral angles of 180[degrees] ([C.sub.2v] symmetry). The C[F.sub.3] groups were both rotated around the Se-C bonds in opposite directions, so that the [C.sub.2] symmetry was preserved. The twist angles were varied from 0[degrees] to 60[degrees], in steps of 5[degrees], and the structure was optimized with that dihedral angle frozen. These calculations showed that only a single conformer exists for this molecule for a twist angle of ~5[degrees]. This structure was fully optimized at the B3LYP/6-311G * level to obtain the real position of the minimum, which was located for a twist angle of 6[degrees] and FCSeC dihedral angles of 174[degrees]. The starting [C.sub.2v] conformation turned out to be a transition state characterized by an imaginary frequency associated with the C[F.sub.3] torsion, as expected. However, the difference in energy between both conformations (0.067 kJ [mol.sup.-1] at B3LYP/6311G * level) is very small. The relative energies of the two forms are listed in Table 1 at various levels of theory; at all investigated approximations, the [C.sub.2] conformation was the most stable, always very close in energy to [C.sub.2v]. These theoretical results do not agree completely with the electron diffraction data; in fact, Marsden and Sheldrick (5) found two possible structures in good agreement with the data having C[F.sub.3] twist angles of 4[degrees] and 33[degrees], respectively.

A similar analysis was performed for the [(C[F.sub.3]Se).sub.2] molecule starting with an initial structure in which the C[F.sub.3] groups are in an exactly staggered position in relation to the Se-Se bond. This conformation has CSeSeC and FCSeSe dihedral angles of 91[degrees] and 180[degrees], respectively. The C[F.sub.3] groups were rotated simultaneously in steps of 5[degrees], preserving always the [C.sub.2] symmetry and the mentioned CSeSeC angle. A single minimum in the potential energy curve was found, corresponding to the conformation in which the twist angle was equal to 10[degrees] for both C[F.sub.3] groups. Subsequently, this structure was fully optimized to a dihedral angle of 9.2[degrees]. On the other hand, the potential energy curve was also explored varying the CSeSeC dihedral angle in steps of 5[degrees]. These calculations confirmed the existence of only one minimum in the potential energy surface for this molecule. The optimized molecular structure for [(C[F.sub.3]Se).sub.2] agrees with the electron diffraction study. (6)

[FIGURE 1 OMITTED]

The structures of the most stable conformations predicted for [(C[F.sub.3]).sub.2]Se and [(C[F.sub.3]Se).sub.2] molecules are shown in Fig. 1. The corresponding calculated geometric parameters and experimental values appear in Table 2. The (mean) calculated and experimental distances and angles do not differ in more than 0.045 [Angstrom] (for the Se-Se distance) and 6.5[degrees] (for the CSeSeC dihedral angle), respectively. The theoretical tilt angles, existing between the C-Se bonds and the ideal symmetry axis of the C[F.sub.3] group, also appear in Table 2; this angle was calculated for the C[F.sub.3] groups as l/3[2[alpha]([F.sub.3,4]CSe)-2[alpha] ([F.sub.2]CSe)]. (16)

Vibrational results

Marsden (7) and Clase et al. (8) have reported and assigned the vibrational spectra of the two molecules studied. Clase et al checked Marsden's assignments and performed some changes, particularly in the C[F.sub.3] stretching region. A revision of the published assignments for both molecules was made by comparison between the existing experimental data and our theoretical results. The computed atomic displacement vectors for each vibrational mode served to understand qualitatively the nature of the molecular vibrations and were used also for such revision. This analysis showed that the assignments proposed by Clase et al. were correct.

The bands observed in the IR spectra of [(C[F.sub.3]).sub.2]Se at 1142 and 1065 [cm.sup.-1] correspond to the C[F.sub.3] symmetric stretching modes ([v.sub.3] and [v.sub.14], respectively), whereas the bands at 1152, 1193, and 1200 [cm.sup.-1] are assigned to the C[F.sub.3] antisymmetric stretching modes ([v.sub.13], [v.sub.12], and [v.sub.1], respectively). The calculated band at 1162 [cm.sup.-1], which seems to be too weak to appear in the experimental spectra, is attributed to the C[F.sub.3] antisymmetric stretching mode ([v.sub.2]), unless it corresponds to the very weak band at 1178 [cm.sup.-1] only reported by Clase et al.

Concerning the [(C[F.sub.3]Se).sub.2] molecule, the IR band at 1188 [cm.sup.-1] corresponds to the C[F.sub.3] antisymmetric stretching modes ([v.sub.1] and [v.sub.2], respectively), whereas the band located at 1144 [cm.sup.-1] seems to be spurious, since our theoretical calculations did not predict bands near that frequency.

The assignments adopted in this work for the [(C[F.sub.3]Se).sub.2]Se molecule are based on the [C.sub.2] symmetry, assuming local [C.sub.3v], symmetry for the C[F.sub.3]Se group. That agrees with Marsden's proposition and the present theoretical results, whereas Clase et al. assumed a [C.sub.2v] symmetry for this molecule.

The normal vibrational modes of the studied molecules are classified as 11A + 10B for [(C[F.sub.3]Se).sub.2]Se and 13A + 11B for [(C[F.sub.3]Se).sub.2], respectively, in accordance with their [C.sub.2] symmetry.

There is a fair agreement between the simulated spectra and the experimental data (8) for both molecules. The calculated frequencies and IR and Raman intensities as well as the corresponding experimental values are shown in Tables 3 and 4. The agreement between measured and calculated frequencies was evaluated by means of the root-mean-square deviation (RMSD), which was equal to 12 [cm.sup.-1] for [(C[F.sub.3]Se).sub.2]Se and 13 [cm.sup.-1] for [(C[F.sub.3]Se).sub.2]. After the force-field scaling procedure, these values fell to 5 and 7 [cm.sup.-1], respectively.

Force constants

The harmonic force fields in Cartesian coordinates, as generated by the Gaussian programs for the two molecules, were transformed to the set of coordinates defined in Tables 5 and 6. Such coordinates consider the local symmetry of the C[F.sub.3] groups and follow the proposals of Fogarasi et a1. (13) The resulting force constants were subsequently scaled according to the methodology proposed by Pulay et a1., (9) as mentioned before (in the Calculation procedure Section), to reproduce as well as possible the experimental frequencies.

The final scaling factors, corresponding to each force constant for the studied molecules, appear in Table 7. It can be seen that most of these factors are greater than one; this is the case when heavy atoms (after the second row of the Periodic Table) appear in the molecule. This fact has been reported for many molecules containing nonmetallic heavy atoms (17) as well as for several C[F.sub.3]S[O.sub.2]X molecules (18) and C[F.sub.3]SeX species. (1,2) The scaling factors previously obtained for common coordinates of other selenium compounds (1,2) were similar to those calculated for [(C[F.sub.3]).sub.2]Se and [(C[F.sub.3]Se).sub.2] molecules in this work. The resulting SQM force-constant matrices are available as Supplementary data for this work.

The internal force constants for the two molecules, appearing in Table 8, were also calculated from the corresponding SQM force fields. These force constants are compared with the values previously obtained for other selenium derivates using the same calculation procedure. (2)

The SQM force fields were used to calculate the potential energy distribution (PED) for each molecule. These values appear in Tables 3 and 4, and show that the coordinates corresponding to v C[F.sub.3] sYMM, [delta] C[F.sub.3] symm., and v C-Se are strongly mixed, as expected and observed also for other C[F.sub.3]SeX molecules. (1,2)

Supplementary data

Supplementary data for this article are available on the journal Web site (canjchem.nrc.ca) or may be purchased from the Depository of Unpublished Data, Document Delivery, CISTI, National Research Council Canada, Ottawa, ON K1A 0R6, Canada. DUD 3874. For more information on obtaining material, refer to cisti-icist.nrc-cnrc.gc.ca/cms/ unpub_e.shtml.

Acknowledgements

Research grants from the following institutions from R. Argentina are gratefully acknowledged: CONICET (Consejo Nacional de Investigaciones Cientificas y Tecnicas), ANPCYT (Agencia Nacional de Promocion Cientifica y Tecnologica, BID 1728/OC-AR, PICT 11127), UNLP (Universidad Nacional de La Plata), and CIUNT (Consejo de Investigaciones de la Universidad Nacional de Tucuman). We also thank Dr. G. Arteca, Laurentian University, Canada, for providing access to some published articles.

References

(1) Fernandez, L. E.; Varetti, E. L. J. Mol. Struct. (Theochem.) 2006, 761, 217. doi:10.1016/j.theochem.2005.12.016.

(2) Fernandez, L. E.; Varetti, E. L. Can. J. Chem. 2006, 84, 1626. doi:10.1139/V06-171.

(3) Dale, J. W.; Emeleus, H. J.; Haszeldine, R. N. J. Chem. Soc. 1958, 2939. doi:10.1039/jr9580002939.

(4) Emeleus, H. J.; Dunn, M. J. J. Inorg. Nucl. Chem. 1965, 27, 752. doi:10.1016/0022-1902(65)80289-5.

(5) Marsden, C. J.; Sheldrick, G. M. J. Mol. Struct. 1971, 10, 405. doi:10.1016/0022-2860(71)85063-9.

(6) Marsden, C. J.; Sheldrick, G. M. J. Mol. Struct. 1971, 10, 419. doi:10.1016/0022-2860(71)85065-2.

(7) Marsden, C. J. J. Fluor. Chem. 1975, 5, 401. doi:10.1016/ 50022-1139(00)82499-9.

(8) Clase, H. J.; Wahi, P. K.; Bomford, D. R. L. Can. J. Spectros. 1977, 22, 92.

(9) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Soc. 1983, 105, 7037. doi:10.1021/ ja00362a005.

(10) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. doi:10.1063/1. 464913.

(11) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785.

(12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, L; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. GAUSSIAN 03 [computer program]; Gaussian, Inc.: Pittsburgh, Penn., USA, 2003.

(13) Fogarasi, G.; Zhou, X.; Taylor, P. W.; Pulay, P. J. Am. Chem. Soc. 1992, 114, 8191. doi:10.1021/ja00047a032.

(14) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular vibrations; MacGraw-Hill: New York, USA, 1955.

(15) Collier, W. B. Program FCARTP (QCPE #631). Department of Chemistry. Oral Roberts University, Tulsa, OK. 1992.

(16) Francisco, J. S. Spectrochim. Acta [A], 1984, 40, 923.

(17) Kalincsak, F.; Pongor, G. Spectrochim. Acta [A], 2002, 58, 999. doi:10.1016/S1386-1425(01)00572-8.

(18) Fernandez, L. E.; Ben Altabef, A.; Varetti, E. L. J. Mol. Struct. 2002, 612, 1. doi:10.1016/S0022-2860(01)00940-1.

Received 24 July 2008. Accepted 29 October 2008. Published on the NRC Research Press Web site at canjchem.nrc.ca on 27 February 2009.

L.E. Fernandez. Instituto de Quimica Fisica, Facultad de Bioquimica, Quimica y Farmacia, Universidad Nacional de Tucuman, San Lorenzo 456, 4000 S.M. de Tucuman, Republica Argentina.

E.L. Varetti. [1] Centro de Quimica Inorganica (CEQUINOR, CONICET-UNLP), Departamento de Quimica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.Correo 962, 1900 La Plata, Republica Argentina.

[1] Corresponding author (e-mail: varettiC&quimica.unlp.edu.ar).

Table 1. Calculated energy of the conformations with [C.sub.2] and
[C.sub.2v] symmetries of the [(C[F.sub.3]).sub.2]Se molecule at
different level of theory.

               [C.sub.2]        [C.sub.2v]
Method        conformation     conformation
                                                    [DELTA]E
              E (Hartree)      E (Hartree)      (kJ [mol.sub.-1])

B3LYP
6-31G *       -3074.617261     -3074.617220           0.109
6-311G *      -3076.993702     -3076.993676           0.067
6-311+G *     -3077.016765     -3077.016745           0.054

B3PW91
6-31G *       -3074.356303     -3074.356261           0.109
6-311G *      -3076.723494     -3076.723470           0.063
6-311+G *     -3076.742751     -3076.742728           0.058

Table 2. Optimized and experimental geometric parameters for
the molecules [(C[F.sub.3]).sub.2]Se and [(C[F.sub.3]).sub.2].

                                    [(C[F.sub.3]).sub.2]Se

                                Calculated     Experimental (5)

Bonds lengths ([Angstrom])
C-F (a)                         1.338          1.332
C-Se                            1.986          1.980
Se-Se                           --             --

Bond angles ([degrees])
F-C-F (a)                       108.3          108.9
F-C-Se (a)                      110.6          --
C-Se-Se                         --             --
C-Se-C                          96.4           94.1

Dihedral angles ([degrees])
F-C-Se-C                        174.0          --
C-Se-Se-C                       --             --
F-C-Se-Se                       --             --
Twist angle                     6.0            4.2
Tilt angle                      4.1            2.0 (fixed)

                                     [(C[F.sub.3]).sub.2]

                                Calculated     Experimental (6)

Bonds lengths ([Angstrom])
C-F (a)                         1.338          1.326
C-Se                            2.000          2.018
Se-Se                           2.337          2.292

Bond angles ([degrees])
F-C-F (a)                       108.3          109.9
F-C-Se (a)                      110.6          109.1
C-Se-Se                         99.8           98.0
C-Se-C                          --             --

Dihedral angles ([degrees])
F-C-Se-C                        --             --
C-Se-Se-C                       91.0           84.5
F-C-Se-Se                       175.4          -
Twist angle                     9.2            11.8
Tilt angle                      4.3            --

(a) Mean of the calculated values.

Table 3. Experimental and calculated frequencies, IR and Raman
intensities, and potential energy distribution (PED) for
[(C[F.sub.3]).sub.2]Se.

                                                           Calculated
Mode              Experimental (a)    Calculated (b)       SQM (c)

A
[v.sub.1]         1200 vs             1202                 1210
[v.sub.2]         ?                   1162                 1166
[v.sub.3]         1142 vs (vw)        1126                 1138
[v.sub.4]         749 (vs) *           743                  751
[v.sub.5]         553 (vvw) *          551                  554
[v.sub.6]         538                  532                  534
[v.sub.7]         363 s (m)            358                  364
[v.sub.8]         278 vw (vs)          268                  275
[v.sub.9]         267 (vw) *           259                  252
[v.sub.10]        109 (w) *             96                  100
[v.sub.11]        ?                     25                   25

B
[v.sub.12]        1193 vs             1188                 1192
[v.sub.13]        1152 vs             1148                 1153
[v.sub.14]        1065 vs (vw)        1050                 1060
[v.sub.15]        746 s                738                  747
[v.sub.16]        535 w (w)            531                  533
[v.sub.17]        535 w (w)            527                  529
[v.sub.18]        340 m (w)            323                  339
[v.sub.19]        258 (w) *            294                  286
[v.sub.20]        253 vw               252                  245
[v.sub.21]        ?                     49                   48
RMSD                                    12                    5
  ([cm.sup.-1])

                                      Raman intensity
                  IR intensity        ([Angstrom].sup.4]
Mode              (km [mol.sup.-1])   [amu.sup.-1])

A
[v.sub.1]         432.53              0.79
[v.sub.2]           0.36              0.08
[v.sub.3]         143.00              1.63
[v.sub.4]          11.38              8.35
[v.sub.5]           0.17              1.69
[v.sub.6]           0.00              0.24
[v.sub.7]           4.57              4.50
[v.sub.8]           0.01              5.94
[v.sub.9]           0.00              1.51
[v.sub.10]          0.71              0.30
[v.sub.11]          0.00              0.05

B
[v.sub.12]        512.57              1.35
[v.sub.13]        246.39              0.65
[v.sub.14]        598.80              3.25
[v.sub.15]         43.77              0.14
[v.sub.16]          0.62              0.69
[v.sub.17]          2.30              1.64
[v.sub.18]          0.56              3.47
[v.sub.19]          0.03              0.87
[v.sub.20]          0.42              0.90
[v.sub.21]          0.10              0.07
RMSD
  ([cm.sup.-1])

Mode              PED (contributions [greater than or equal to] 10%)

A
[v.sub.1]         90 [S.sub.1] + 17 [S.sub.5]
[v.sub.2]         101 [S.sub.2] + 18 [S.sub.6]
[v.sub.3]         64 [S.sub.3] + 46 [S.sub.4] + 21 [S.sub.7]
[v.sub.4]         42 [S.sub.4] + 37 [S.sub.3] + 12 [S.sub.7]
[v.sub.5]         65 [S.sub.5]
[v.sub.6]         74 [S.sub.6]
[v.sub.7]         32 [S.sub.7] + 30 [S.sub.8] + 13 [S.sub.5] +
                  10 [S.sub.10]
[v.sub.8]         39 [S.sub.8] + 41 [S.sub.7]
[v.sub.9]         99 [S.sub.9] + 12 [S.sub.6]
[v.sub.10]        86 [S.sub.10] + 36 [S.sub.8]
[v.sub.11]        107 [S.sub.11]

B
[v.sub.12]        101 [S.sub.12] + 17 [S.sub.17]
[v.sub.13]        104 [S.sub.13] + 19 [S.sub.16]
[v.sub.14]        81 [S.sub.14] + 50 [S.sub.15] + 24 [S.sub.18]
[v.sub.15]        47 [S.sub.15] + 28 [S.sub.14] + 15 [S.sub.18]
[v.sub.16]        78 [S.sub.16]
[v.sub.17]        74 [S.sub.17]
[v.sub.18]        68 [S.sub.18] + 15 [S.sub.15]
[v.sub.19]        96 [S.sub.19] + 11 [S.sub.17]
[v.sub.20]        98 [S.sub.20]
[v.sub.21]        101 [S.sub.21]
RMSD
  ([cm.sup.-1])

Mode              Main coordinate

A
[v.sub.1]         v (C[F.sub.3]) antisymm.
[v.sub.2]         v (C[F.sub.3]) antisymm.
[v.sub.3]         v (C[F.sub.3]) symm.
[v.sub.4]         [delta] (C[F.sub.3]) symm.
[v.sub.5]         [delta] (C[F.sub.3]) antisymm.
[v.sub.6]         [delta] (C[F.sub.3]) antisymm.
[v.sub.7]         v (C-Se)
[v.sub.8]         [rho] (C[F.sub.3])
[v.sub.9]         [rho] (C[F.sub.3])
[v.sub.10]        [delta] (CSeC)
[v.sub.11]        Torsion (C[F.sub.3])

B
[v.sub.12]        v (C[F.sub.3]) antisymm.
[v.sub.13]        v (C[F.sub.3]) antisymm.
[v.sub.14]        v (C[F.sub.3]) symm.
[v.sub.15]        [delta] (C[F.sub.3]) symm.
[v.sub.16]        [delta] (C[F.sub.3]) antisymm.
[v.sub.17]        [delta] (C[F.sub.3]) antisymm.
[v.sub.18]        v (C-Se)
[v.sub.19]        [rho] (C[F.sub.3])
[v.sub.20]        [rho] (C[F.sub.3])
[v.sub.21]        Torsion (C[F.sub.3])
RMSD
  ([cm.sup.-1])

(a) From [Ref..sup.8]. Starred frequencies were measured in the
Raman spectrum of the liquid substance; other frequencies are from
the infrared gas spectrum. Qualitative intensities for observed
bands in IR and Raman (in parentheses): w, weak; m, medium;
s, strong; v, very.

(b) B3LYP/6-311G * calculations.

(c) From scaled quantum mechanics force field.

Table 4. Experimental and calculated frequencies, IR and Raman
intensities, and potential energy distribution (PED) for
[(C[F.sub.3]).sub.2].

                                                           Calculated
Mode              Experimental (a)    Calculated (b)       SQM (c)

A
[v.sub.1]         1188 vs             1194                 1175
[v.sub.2]         1188 vs             1170                 1198
[v.sub.3]         1115 vs (vvw)       1098                 1107
[v.sub.4]         742 (s) *            738                  744
[v.sub.5]         531 mw (w)           540                  541
[v.sub.6]         531 mw (w)           530                  530
[v.sub.7]         333 (m) *            328                  333
[v.sub.8]         318 (mw) *           304                  318
[v.sub.9]         245 (vs) *           285                  239
[v.sub.10]        245 (vs) *           239                  273
[v.sub.11]        101 (s) *             90                   94
[v.sub.12]        ?                     53                   53
[v.sub.13]        ?                     27                   27

B
[v.sub.14]        1169 vs (vvw)       1172                 1163
[v.sub.15]        1169 vs (vvw)       1158                 1176
[v.sub.16]        1090 vs (vvw)       1069                 1078
[v.sub.17]        741 vs               736                  743
[v.sub.18]        531 mw (w)           540                  542
[v.sub.19]        531 mw (w)           526                  527
[v.sub.20]        321 ms (mw)          319                  328
[v.sub.21]        280 m (w)            279                  275
[v.sub.22]        280 m (w)            272                  260
[v.sub.23]        101 (s) *             96                   99
[v.sub.24]        ?                     28                   29
RMSD                                    13                    7
  ([cm.sup.-1])

                                      Raman intensity
                  IR intensity        ([Angstrom].sup.4]
Mode              (km [mol.sup.-1])   [amu.sup.-1])

A
[v.sub.1]         329.68                0.70
[v.sub.2]           0.11                1.76
[v.sub.3]         282.79                2.39
[v.sub.4]          17.38               11.00
[v.sub.5]           0.03                2.74
[v.sub.6]           0.83                1.27
[v.sub.7]           1.13                5.44
[v.sub.8]           0.63                3.24
[v.sub.9]           0.07                2.31
[v.sub.10]          0.02                7.42
[v.sub.11]          0.01                2.02
[v.sub.12]          0.17                0.43
[v.sub.13]          0.01                0.06

B
[v.sub.14]        397.70                0.17
[v.sub.15]        246.21                0.64
[v.sub.16]        653.29                3.78
[v.sub.17]         33.39                0.29
[v.sub.18]          0.10                0.22
[v.sub.19]          1.19                0.38
[v.sub.20]          1.75                3.69
[v.sub.21]          1.64                1.35
[v.sub.22]          0.14                0.39
[v.sub.23]          1.34                1.28
[v.sub.24]          0.02                0.04
RMSD
  ([cm.sup.-1])

Mode              PED (contributions [greater than or equal to] 10%)

A
[v.sub.1]         79 [S.sub.1] + 21 [S.sub.2] + 15 [S.sub.5]
[v.sub.2]         78 [S.sub.2] + 18 [S.sub.1] + 14 [S.sub.6]
[v.sub.3]         71 [S.sub.3] + 48 [S.sub.4] + 20 [S.sub.7]
[v.sub.4]         45 [S.sub.4] + 33 [S.sub.3] + 12 [S.sub.7]
[v.sub.5]         74 [S.sub.5]
[v.sub.6]         75 [S.sub.6]
[v.sub.7]         27 [S.sub.7] + 22 [S.sub.9] + 20 [S.sub.8] +
                  10 [S.sub.11]
[v.sub.8]         57 [S.sub.8] + 39 [S.sub.7]
[v.sub.9]         57 [S.sub.9] + 27 [S.sub.8]
[v.sub.10]        92 [S.sub.10] + 12 [S.sub.6]
[v.sub.11]        98 [S.sub.11] + 19 [S.sub.9]
[v.sub.12]        92 [S.sub.12]
[v.sub.13]        98 [S.sub.13] + 13 [S.sub.12]

B
[v.sub.14]        57 [S.sub.14] + 47 [S.sub.15] + 11 [S.sub.18]
[v.sub.15]        55 [S.sub.15] + 45 [S.sub.14]
[v.sub.16]        77 [S.sub.16] + 49 [S.sub.17] + 22 [S.sub.20]
[v.sub.17]        46 [S.sub.17] + 30 [S.sub.16] + 13 [S.sub.20]
[v.sub.18]        74 [S.sub.18]
[v.sub.19]        78 [S.sub.19]
[v.sub.20]        56 [S.sub.20] + 12 [S.sub.17]
[v.sub.21]        65 [S.sub.21] + 16 [S.sub.20]
[v.sub.22]        95 [S.sub.22]
[v.sub.23]        89 [S.sub.23] + 30 [S.sub.21]
[v.sub.24]        101 [S.sub.24]
RMSD
  ([cm.sup.-1])

Mode              Main coordinate

A
[v.sub.1]         v (C[F.sub.3]) antisymm.
[v.sub.2]         v (C[F.sub.3]) antisymm.
[v.sub.3]         v (C[F.sub.3]) symm.
[v.sub.4]         [delta] (C[F.sub.3]) symm.
[v.sub.5]         [delta] (C[F.sub.3]) antisymm.
[v.sub.6]         [delta] (C[F.sub.3]) antisymm.
[v.sub.7]         v (C-Se)
[v.sub.8]         v (Se-Se)
[v.sub.9]         [rho] (CF3)
[v.sub.10]        [rho] (CF3)
[v.sub.11]        [delta] (CSeSe)
[v.sub.12]        Torsion skeletal
[v.sub.13]        Torsion (C[F.sub.3])

B
[v.sub.14]        v (C[F.sub.3]) antisymm.
[v.sub.15]        v (C[F.sub.3]) antisymm.
[v.sub.16]        v (C[F.sub.3]) symm.
[v.sub.17]        [delta] (C[F.sub.3]) symm.
[v.sub.18]        [delta] (C[F.sub.3]) antisymm.
[v.sub.19]        [delta] (C[F.sub.3]) antisymm.
[v.sub.20]        v (C-Se)
[v.sub.21]        [rho] (C[F.sub.3])
[v.sub.22]        [rho] (C[F.sub.3])
[v.sub.23]        [delta] (CSeSe)
[v.sub.24]        Torsion (C[F.sub.3])
RMSD
  ([cm.sup.-1])

(a) From [Ref..sup.8]. Starred frequencies were measured in the
Raman spectrum of the liquid substance; other frequencies are from
the infrared gas spectrum. Qualitative intensities for observed
bands in IR and Raman (in parentheses): w, weak; m, medium;
s, strong; v, very.

(b) B3LYP/6-311G * calculations.

(c) From scaled quantum mechanics force field.

Table 5. Natural internal (local symmetry) coordinates for
[(C[F.sub.3]).sub.2]Se.

Definition (according to Fig. 1)                      Description (a)

A
[S.sub.1] = 2d (1-2) - d (1-3) - d (1-4) + 2d (6-7)   v (C[F.sub.3])
  - d (6-9) - d (6-8)                                   antisymm.
[S.sub.2] = d (1-3) - d (1-4) + d (6-9) - d (6-8)     v (C[F.sub.3])
                                                        antisymm.
[S.sub.3] = d (1-2) + d (1-3) + d (1-4) + d (6-7)     v (C[F.sub.3])
  + d (6-9) + d (6-8)                                   symm.
[S.sub.4] = [alpha] (2-1-3) + [alpha] (2-1-4) +       [delta]
  [alpha] (3-1-4) - [beta] (2-1-5) - [beta] (3-1-5)     (C[F.sub.3])
  - [beta] (4-1-5) + [alpha] (9-6- 7) + [alpha]         symm.
  (9-6-8) + [alpha] (7-6-8) - [beta] (9-6-5) -
  [beta] (7-6-5) - [beta] (8-6-5)
[S.sub.5] = 2 [alpha] (3-1-4) - [alpha] (2-1-3) -     [delta]
  [alpha] (2-1-4) + 2 [alpha] (9-6-8) - [alpha]         (C[F.sub.3])
  (9-6-7) - [alpha] (7-6-8)                             antisymm.
[S.sub.6] = [alpha] (2-1-3) - [alpha] (2-1-4) +       [delta]
  [alpha] (9-6-7) - [alpha] (7-6-8)                     (C[F.sub.3])
                                                        antisymm.
[S.sub.7] = t (1-5) + t (6-5)                         v (C-Se)
[S.sub.8] = 2[beta] (2-1-5) - [beta] (3-1-5) -        [rho]
  [beta] (4-1-5) + 2[beta] (7-6-5) - [beta] (9-6-5)     (C[F.sub.3])
  - [beta] (8-6-5)
[S.sub.9] = [beta] (3-1-5) - [beta] (4-1-5) +         [rho]
  [beta] (9-6-5) - [beta] (8-6-5)                       (C[F.sub.3])
[S.sub.10] = [delta] (1-5-6)                          [delta] (CSeC)
[S.sub.11] = [Summation] [tau]                        Torsion
  [[F.sub.i]-[C.sub.1]-[Se.sub.5]-[C.sub.6]] +          (C[F.sub.3])
  [Summation] [tau]
  [[F.sub.i]-[C.sub.6]-[Se.sub.5]-[C.sub.1]]

B
[S.sub.12] = d (1-3) - d (1-4) - d (6-9) + d (6-8)    v (C[F.sub.3])
                                                        antisymm.
[S.sub.13] = 2d (1-2) - d (1-3) - d (1-4) - 2d        v (C[F.sub.3])
  (6-7) + d (6-9) + d (6-8)                             antisymm.
[S.sub.14] = d (1-2) + d (1-3) + d (1-4) - d (6-7)    v (C[F.sub.3])
  - d (6-9) - d (6-8)                                   symm.
[S.sub.15] = [alpha] (2-1-3) + [alpha] (2-1-4) +      [delta]
  [alpha] (3-1-4) - [beta] (2-1-5) - [beta] (3-1-5)     (C[F.sub.3])
  - [beta] (4-1-5) - [alpha] (9-6-7) - [alpha]          symm.
  (9-6-8) - [alpha] (7-6-8) + [beta] (9-6-5) +
  [beta] (7-6-5) + [beta] (8-6-5)
[S.sub.16] = 2[alpha] (3-1-4) - [alpha] (2-1-3) -     [delta]
  [alpha] (2-1-4) - 2[alpha] (9-6-8) + [alpha]          (C[F.sub.3])
  (9-6-7) + [alpha] (7-6-8)                             antisymm.
[S.sub.17] = [alpha] (2-1-3) - [alpha] (2-1-4) -      [delta]
  [alpha] (9-6-7) + [alpha] (7-6-8)                     (C[F.sub.3])
                                                        antisymm.
[S.sub.18] = t (1-5) - t (6-5)                        v (C-Se)
[S.sub.19] = [beta] (3-1-5) - [beta] (4-1-5) -        [rho]
  [beta] (9-6-5) + [beta] (8-6-5)                       (C[F.sub.3])
[S.sub.20] = 2[beta] (2-1-5) - [beta] (3-1-5) -       [rho]
  [beta] (4-1-5) - 2[beta] (7-6-5) + [beta] (9-6-5)     (C[F.sub.3])
  + [beta] (8-6-5)
[S.sub.21] = [Summation] [tau]                        Torsion
  [[F.sub.i]-[C.sub.1]-[Se.sub.5]-[C.sub.6]] -          (C[F.sub.3])
  [Summation] [tau]
  [[F.sub.i]-[C.sub.6]-[Se.sub.5]-[C.sub.1]]

(a) v, stretching; [delta], deformation; [rho], rocking.

Table 6. Natural internal (local symmetry) coordinates for
[(C[F.sub.3]).sub.2].

Definition (according to Fig. 1)                      Description (a)

A
[S.sub.1] = 2d (1-7) - d (1-5) - d                    v (C[F.sub.3])
  (1-6) + 2d (4-9) - d (4-10) - d                       antisymm.
  (4-8)
[S.sub.2] = d (1-5) - d (1-6) + d                     v (C[F.sub.3])
  (4-10) - d (4-8)                                      antisymm.
[S.sub.3] = d (1-7) + d (1-5) + d                     v (C[F.sub.3])
  (1-6) + d (4-9) + d (4-10) + d (4-8)                  symm.
[S.sub.4] = [alpha] (5-1-7) + [alpha]                 [delta]
  (5-1-6) + [alpha] (6-1-7) - [beta] (5-1-2) -          (C[F.sub.3])
  [beta] (6-1-2) - [beta] (7-1-2) + [alpha]             symm.
  (10-4-8) + [alpha] (10-4-9) + [alpha] (8-4-9) -
  [beta] (10-4-3) - [beta] (8-4-3) - [beta] (9-4-3)
[S.sub.5] = 2[alpha] (5-1-6) - [alpha] (5-1-7) -      [delta]
  [alpha] (6-1-7) + 2 [alpha] (10-4-8) - [alpha]        (C[F.sub.3])
  (10-4-9) - [alpha] (8-4-9)                            antisymm.
[S.sub.6] = [alpha] (5-1-7) - [alpha] (6-1-7) +       [delta]
  [alpha] (10-4-9) - [alpha] (8-4-9)                    (C[F.sub.3])
                                                        antisymm.
[S.sub.7] = t (1-2) + t (4-3)                         v (C-Se)
[S.sub.8] = r (2-3)                                   v (Se-Se)
[S.sub.9] = 2[beta] (7-1-2) - [beta] (6-1-2) -        [rho]
  [beta] (5-1-2) + 2[beta] (9-4-3) - [beta] (8-4-3)     (C[F.sub.3])
  - [beta] (10-4-3)
[S.sub.10] = [beta] (6-1-2) - [beta] (5-1-2) +        [rho]
  [beta] (8-4-3) - [beta] (10-4-3)                      (C[F.sub.3])
[S.sub.11] = delta] (1-2-3) + [delta] (2-3-4)         [delta] (CSeSe)
[S.sub.12] = [tau] (1-2-3-4)                          Torsion skeletal
[S.sub.13] = [Summation] [tau]                        Torsion
  [[F.sub.i]-[C.sub.1]-[Se.sub.2]-[C.sub.3] +           (C[F.sub.3])
  [Summation] [tau]
  [[F.sub.i]-[C.sub.4]-[Se.sub.3]-[C.sub.2]]

B
[S.sub.14] = 2d (1-7) - d (1-5) - d (1-6) - 2d        v (C[F.sub.3])
  (4-9) + d (4-10) + d (4-8)                            antisymm.
[S.sub.15] = d (1-5) - d (1-6) - d (4-10) + d (4-8)   v (C[F.sub.3])
                                                        antisymm.
[S.sub.16] = d (1-7) + d (1-5) + d (1-6) - d (4-9)    v (C[F.sub.3])
  - d (4-10) - d (4-8)                                  symm.
[S.sub.17] = [alpha] (5-1-7) + [alpha] (5-1-6) +      [delta]
  [alpha] (6-1-7) - [beta] (5-1-2) - [beta] (6-1-2)     (C[F.sub.3])
  - [beta] (7-1-2) - [alpha] (10-4-8) - [alpha]         symm.
  (10-4-9) - [alpha] (8-4-9) + [beta] (10-4-3) +
  [beta] (8-4-3) + [beta] (9-4-3)
[S.sub.18] = 2[alpha] (5-1-6) - [alpha] (5-1-7) -     [delta]
  [alpha] (6-1-7) - 2 [alpha] (10-4-8) + [alpha]        (C[F.sub.3])
  (10-4-9) + [alpha] (8-4-9)                            antisymm.
[S.sub.19] = [alpha] (5-1-7) - [alpha] (6-1-7) -      [delta]
  [alpha] (10-4-9) + [alpha] (8-4-9)                    (C[F.sub.3])
                                                        antisymm.
[S.sub.20] = t (1-2) - t (4-3)                        v (C-Se)
[S.sub.21] = 2[beta] (7-1-2) - [beta] (6-1-2) -       [rho]
  [beta] (5-1-2) - 2[beta] (9-4-3) + [beta] (8-4-3)     (C[F.sub.3])
  + [beta] (10-4-3)
[S.sub.22] = [beta] (6-1-2) - [beta] (5-1-2) -        [rho]
  [beta] (8-4-3) + [beta] (10-4-3)                      (C[F.sub.3])
[S.sub.23] = [delta] (1-2-3) - [delta] (2-3-4)        [delta] (CSeSe)
[S.sub.24] = [Summation] [tau]                        Torsion
  [[F.sub.i]-[C.sub.1]-[Se.sub.2]-[C.sub.3]] -          (C[F.sub.3])
  [Summation [tau]
  [[F.sub.i]-[C.sub.4]-[Se.sub.3]-[C.sub.2]]

(a) v, stretching; [delta], deformation; [rho], rocking.

Table 7. Scaling factors for the force field of the molecules
[(C[F.sub.3]).sub.2]Se and [(C[F.sub.3]).sub.2].

Coordinates (a)         [(C[F.sub.3]).sub.2]Se   [(C[F.sub.3]Se).sub.2]

v (C[F.sub.3]),         1.009                    1.008
[delta] (C[F.sub.3]),
Torsion (C[F.sub.3])

[delta] (CSeC),         1.136                    1.115
v (C-Se)

[delta] (CSeSe),        --                       1.115
v (Se-Se)

[rho] (C[F.sub.3])      0.935                    0.907

(a) v, stretching; [delta], deformation; [rho], rocking.

Table 8. Internal force constants for [(C[F.sub.3]).sub.2]Se,
[(C[F.sub.3]).sub.2], and the related molecules C[F.sub.3]SeX.

                                        This work

Force constant (a)   [(C[F.sub.3]).sub.2]Se   [(C[F.sub.3]Se).sub.2]

Bond stretchings
f (C-F) (b)          6.047                    5.982
f (C-Se)             2.73                     2.502
f (Se-Se)            --                       2.273
f (C-F/C-F) (b)      0.824                    0.809
f (C-F/C-Se)         0.39                     0.338
Deformations
f (F-C-F) (b)        1.287                    1.278
f (F-C-Se) (b)       0.818                    0.788
f (C-Se-Se)          --                       1.064
f (C-Se-C)           1.254                    --

                                          (2)

Force constant (a)   C[F.sub.3]SeCN           C[F.sub.3]SeC[H.sub.3]

Bond stretchings
f (C-F) (b)          6.167                    5.841
f (C-Se)             2.583                    2.742
f (Se-Se)
f (C-F/C-F) (b)      0.802                    0.789
f (C-F/C-Se)         0.39                     0.362
Deformations
f (F-C-F) (b)        1.269                    1.304
f (F-C-Se) (b)       0.854                    0.874
f (C-Se-Se)
f (C-Se-C)           0.973                    0.916

(a) Units are mdyn [[Angstrom].sup.-1] for stretchings and
stretch-stretch interactions and mdyn [Angstrom] [rad.sup.-2]
for angular deformations.

(b) Mean values.