J. Phys. Chem. 1992,96, 10697-10707
10697
4. Coacluaion Electronic spectra and geometry of pdicyanobenzene and its complex with H 2 0 and the dimer of pDCNB were investigated by jet spectroscopy. Several vibronic bands in the SI+ transition of free pDCNB were assigned. The pDCNB-H20 complex was found to have geometry which is stabilized mostly by dipoledipole interaction. (pDCNB)2 takes stacked geometry, forming excimer in the electronic excited state. Acknowledgment. We thank N. Okada for a helpful support in constructing the pulsed nozzle for high temperature. This work is partly supported by a Grant-in-Aid for Scientific Research on Priority Areas from the Ministry of Education, Science and Culture. References and Notes
-1 0 +1 +2 WAVENUMBER(cm-1) Figure 7. Optimized geometry of the p-DCNB dimer (a) and rotational band envelope of the 0 band; (b) observed spectrum and (c) calculated one assuming the optimized geometry of (a) and the rotational temperature of 5 K.
-2
rings is 0.36 nm in the ground state and 0.34 nm in SI.In Figure 7a, the assumed geometry of the dimer is shown. This is the mast stable structure stabilized by van der Waals force^.^ In Figure 7c, the calculated rotational contour for the dimer is shown in comparison with the experimental one. The observed and calculated data coincide well with each other, which confirms the validity of the dimer structure presented in this work.
(1) Jones, G., 11; Chiang, S.-H.; Becker, W. G.; Welch, J. A. J . Phys. Chem. 1982,82, 2805. (2) Fuke, K.; Kaya, K. Chem. Phys. Lett. 1982, 91, 311. (3) Nakagawa, T.; Oyanagi, Y. Program system SALS for non-linear least-squares fitting in experimental sciences. In Recent Deuelopments in Statistical Inference and Data Analysis; Matusita, K., Ed.; North-Holland: Amsterdam, 1980; p 221. (4) Bethe, H. A.; Salpeter, E. E. Quantum Mechanics of One-and TwoElectron Atoms; Plenum Press: New York, 1957. ( 5 ) Kimura, K.; Katsumata, S.; Achiba, Y.; Yamazaki, T.; Iwata, S. Handbook of He1 Photoelectron Spectra of Fundamental Organic Molecules; Japan Scientific Societies Press: Tokyo 1981. (6) Mirek, J.; Buda, A. Z . Naturforsch. 1984, 39A, 386. (7) Kobayashi, T.; Honma, K.; Kajimoto, 0.;Tsuchiya, S.J. Chem. Phys. 1987,86, 1111. (8) Castro-Pedrozo, M. C.; King, G. W. J. Mol. Specrrosc. 1978, 73,386. (9) Watanabe, H.; Koguchi, T.; Suzuka, I. Manuscript in preparation. (10) Briks, J. B. Phorophysics of Aromatic Molecules; Wiley: New York, 1970; pp 301-371. (11) Kato, S.;Amatatsu, Y. J . Chem. Phys. 1990, 92, 7241. (12) Kajimoto, 0.; Yokoyama, H.; Ooshima, Y.; Endo, Y. Chem. Phys. Lett. 1991, 179, 455. (13) Saigusa, H.; Sun, S.;Lim, E. C. J . Phys. Chem. 1992, 96, 2083. (14) Itoh, M.; Sasaki, M. J . Phys. Chem. 1990, 94,6544. (15) Salvi, P. R.; Foggi, P.; Castellucci, E. Chem. Phys. Lett. 1983, 98, 206.
Assignment of Vibrational Bands of Chlorofluoroethanes Based on ab Initio Molecular Orbital Calculations Tetsuo Sakka,* Yukio Ogata, and Matae Iwasaki Institute of Atomic Energy, Kyoto University, Vji, Kyoto 61 1. Japan (Received: July 17. 1992; In Final Form: October 1 , 1992)
The vibrational spectra of CClF2CH2Cland CC1F2CHCl2were measured, and the absorption bands were assigned on the basis of the scaled force field originally obtained by ab initio molecular orbital calculations. The scale factors were transferred without any modifcation from those obtained by comparing the ab initio frequencies of CC1F2CH3,CH2C1CH3,and CHC12CH3 with the experimental frequencies. Although CClF2CH2CIand CC1F2CHCl2show very complicated spectra due to the low structural symmetry and the existence of two rotational isomers, the assignments seem to be sufficientlyreliable. The assignment of the bands in the frequency range 900-1 100 cm-' was revealed to be consistent with the interpretation proposed in our preceding paper (Chem. Phys. f e r r . 1991,187,433)for the frequency effects upon the rate of infrared multiphoton d d a t i o n of CClF2CH2Cland CCIF2CHC12.
1. Introduction In the interpretation of frequency-dependent behavior of infrared multiphoton dissociation (IRMPD),'" reliable IR band assignment of the molecules under consideration will give great information. Our preceding work' revealed that the excitation of the two different vibrations of the same molecule results in different decompition rates, although the two bands have nearly the same absorption intensity. This may result from different To whom correspondence should be addressed.
characteristics between the two bands. The assignment of these bands would be the starting point of the interpretation of the IRMPD mechanism. On the other hand, when IRMPD is applied to a tritium s e p aration the working molecule, which would be irradiated with intense IR radiation, should have absorption in the frequency range in which high-intensity IR lasers, such as a TEA C 0 2 laser, are available. Therefore, vibrational spectral data are necessary in surveying candidates for the working molecule. However, very few data are available for tritium-containing
0022-36S4/92/2096-10697$03.00/00 1992 American Chemical Society
10698 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
molecules because of their radioactivity. The measurement of the IR spectra in a search for candidates is laborious. If a theoretical prediction of the IR absorption frequencies is reliable enough, the effort will be considerably reduced. In the present work, we aim at a theoretical prediction of absorption frequencies and a reliable band assignment of CClFzCH2Cland CCIFzCHClz, of which IRMPD has been studied in our preceding work.’ In addition to elucidating the IRMPD mechanism, the vibrational analysis of these molecules is an important subject in the field of IR spectroscopy because the molecules are relatively large compared with those studied previously in this field and have two rotational isomerslZ-l6and very low structuralsymmetries, such as C, and Cl. The second property especially provides great difficulty in band assignment, because the total number of fundamentals will be as many as 36; i.e., the experimental spectrum is the superposition of the individual spectra of the two rotational isomers. Although, in general, similar types of vibrations of the different rotational isomers appear very close in frequency, in some cases they are considerably apart from each other and can be clearly resolved in the spectra.I2 However, vibrational analyses based on empirical force fields, such as Urey-Bradley force field,” do not seem to have the required accuracy in distinguishing the difference in the rotational isomers without experimental support.’* Recently, it has become well accepted that force fields obtained by ab initio molecular orbital (MO) calculations give results which Especially are in good agreement with experimental when electroniccorrelation is taken into account, the agreement is considerably improved.28 However, the size of the molecule for which force fields may be calculated with taking electronic correlation into account is very limited; Le., such a calculation for relatively large molecules, e.g., CClF2CHzClor CC1F2CHCl2, is not practical. Nevertheless, ab initio MO calculations can be used for molecules of this size, because the errors in the HartreeFock (HF) level calculations are very systematic and scaling by the use of a few scale factors for an ab initio force field often leads to very good agreement with e~periments.”~’ Refinement of the scale factors seems to have potential in providing a satisfactory molecular force field in order to carry out a reliable IR band assignment for relatively large molecules. From the point of view of the use of the scaled ab initio force field for the frequency analysis of CCIFzCHzCland CC1F2CHCl2,the following points should be clarified: the size of the basis set required to get results accurately enough for the assignment for the relatively large and chlorine-containing molecules, and whether the difference in frequency between the rotational isomers can be correctly calculated. The clarification of these points is also the aim of the present study. Determining the scale factors for these molecules is problematic. Usually, the scale factors are classified into several groups on the basis of their physical meaning, and the same value is given for the scale factors in the same g r o ~ p ? ~However, J~ for the molecules in this work, the grouping of the scale factors seems not to be definite, because their structural symmetry is very low. Therefore, all the scale factors were regarded as independent. However, this causes difficulty in the evaluation of the scale factors; there appears to be too many scale factors. We, therefore, determined these scale factors by comparing the experimental and calculated frequencies of the reference molecules which are more simple, and hence, fairly reliable experimental frequencies are available. Because scale factors depend on the basis set l e ~ e 1 , a2 certain ~~~~ basis set should be used commonly for both the reference and target molecules in order for the transfer of the scale factor to be valid. The obtained scale factors were transferred to CClF2CH2C1and CClF2CHC12without any modification. The reference molecules, CC1F2CH3,CH2ClCH3,and CHClZCH3,were employed because they have the same halomethyl groups as the target molecules and also because fairly reliable experimental frequencies and IR band assignments are available.’z3s32 The scaling was conducted for the force-constant matrix with respect to local symmetry coordinates. The use of the local symmetry coordinates enables the clear transferability of the scale
Sakka et al. factors. In order to determine the scale factors for these molecules, the least-squares fit was not used, though it is a popular method in the previous studies in this field.z’ Especially in the spectral range 500-1200 cm-l, two or more local symmetry coordinates are usually responsible for a single normal coordinate. This means that, if an ab initio frequency differs from the corresponding experimental frequency, the local symmetry coordinate responsible for this discrepancy cannot be specified. If the least-squares fit is used, a small discrepancy between the calculation and the experiment would result in a very large revision in some scale factors, which is not acceptable in view of the fact that the scale factors are restricted in a relatively small range. It seems that the use of the least-squares method for the scale factors should be limited to the case where the number of adjusting scale factors is considerably smaller than the number of available experimental frequencies. In the present case, the number of experimental frequencies and the number of scale factors to be adjusted are the same. Therefore, the least-squares method was not used. Instead, the scale factors were determined by a new method, which is based on the potential energy distribution (PED). Given the experimental frequencies of CClF2CH3,CHzClCH3, and CHC12CH3,most scale factors for CClF2CH2Cland CClF2CHClzwere obtained without any assumption. In view of the prediction of the vibrational frequencies, it is noteworthy that, in the present method, the experimental frequencies of the target molecules, CClF2CH2Cland CC1F2CHCl2,were not used in the scalefactor-detennining process. The method is especially suitable for comparatively large and low-symmetry molecules, because an empirical assignment often implies a large ambiguity for such molecules and, therefore, the adjustment of the scale factor using such experimental frequencies sometimes leads to an erroneous result. In sections 2 and 3, experimental and computational procedures are described, respectively. In section 4, the results are shown briefly. The results were compared with the experiment, and the accuracy of the calculation is discussed in section 5. Furthermore, band assignments were made, and the reliability of these assignments is discussed. The meaning of the assignment in IR photochemistry is also discussed briefly. 2. Experiment The IR absorption spectra of CC1F2CHzCland CClF2CHC12 in the gaseous state at room temperature and in the liquid and solid states at various temperatures in the range 77-175 K were measured. The IR measurements were carried out with a Fourier transform infrared (FT-IR) spectrometry, Model FT/IR 5M (Japan Spectroscopic Corp.). A 10-cm gas cell with KRS-5 windows at both ends was used in the gaseous-state measurement. The resolution was 1 cm-I, and the sample pressure was 10 Torr. The method for the liquid- and solid-state measurements is described elsewhere.13 The resolution of the measurements in the liquid and solid states was 4 cm-I. The Raman spectra of CClFzCH2C1and CC1FzCHC12in the liquid states were also obtained at room temperature in the spectral range 50-800 cm-I. The measurements were carried out with a spectrometer, Model NR-1000s (Japan Spectroscopic Corp.), equipped with a double monochromator. The excitation source was a 514.5-nm line of the argon ion laser. The samples were purchased from PCR Inc. and used without further purification. No appreciable impurity was detected in these reagents, except a trace amount of CClFzCH2Clin CClFzCHCl2 and vice versa. 3. Computational Details The calculations of the geometry optimization and for the numerical harmonic force field were carried out at an ab initio SCF level using the GAUSSIAN82 computer program.33 The 3-21G** basis set, which contains six d polarization functions on a chlorine atom and three p polarization functions on a hydrogen atom, was used for all the molecules in this work, namely, CClFzCH3,CHzClCH3,CHCl2CH3,CClF2CHzCl (trans and gauche isomers), and CCIFzCHC12(C, and CIisomers). Besides
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10699
Vibrational Bands of Chlorofluoroethanes the 3-21G** calculation, the 6-31G** calculations for CClF2CH3 and CH2C1CH3and the 3-21G calculation for CC1F2CH3were performed in order to examine the dependence of the quality of the force field upon the size of the basis set. The geometrical structures around which the force field was calculated were the stationary point obtained with the same basis set as used in the force-field calculation. The transformation of the coordinate from the rectangular coordinates, on which the force field of GAUSSIAN82 output is based, to the local symmetry coordinates and the calculations for the scaled force field and for the potential energy distribution (PED) were carried out with the computer program originally developed by S h i m a n ~ u c hand i ~ ~revised ~ by Hirakawa and Hamada.34b According to the method of Pulay et al.,2493sthe scaling of the force-constant matrix was carried out as follows:
Fy = ( C a C , ) m y (1) where GId and 6' are 'the elements of the scaled and unscaled force-constant matrices, respectively, and C,,is the scale factor for the ath diagonal element of the force-constant matrix. Here, the force-constant matrix is based on the local symmetry coordinate. The determination of the scale factors was carried out for CC1F2CH3,CH2C1CH3,and CHC12CH3. The experimental vibrational frequencies and their assignment are fairly reliable for these molecules, because each of them is restricted to a single conformation. In order to determine the scale factors for the force constant matrices, the least-squares fit was not used because of the reason described in the Introduction. Instead, we developed the method in which reasonable scale factors are always obtained by the use of the PED-weighted mean. The scale factor for the diagonal element corresponding to the local symmetry coordinate a is obtained by
whereflp andf"' are the experimental and ab initio frequencies of the ith normal vibration, respectively, and Dai is the element of the PED matrix, (3) where LQiis the transformation matrix form the normal coordinate to the local symmetry coordinate and X i is an eigenvalue of the force constant matrix F. The use of the PED for the weight is meaningful in view of the fact that it is a measure of the potential energy contribution of a local symmetry coordinate to a normal vibration, and hence, it seems to be more important than the mere transformation matrix elements, LUi,in determining the feature of the normal vibrati~n.'~The scale factors for diagonal elements of the force-constant matrix with respect to local symmetry coordinates were obtained for CClF2CH3,CH2ClCH3,and CHC12CH3.They have the halomethyl groups, CClF2, CH2Cl, and CHC12, two of which form CClF2CH2Cl or CC1F2CHCl2. Therefore, the same local symmetry coordinates as CC1F2CH2C1 or CClF2CHC12are found in CClF2CH3,CH2ClCH3,or CHC12CH3,and their scale factors were transferred to the corresponding diagonal elements of the force-constant matrix of CClF2CH2Cl(trans and gauche) and CClF2CHC12(C, and C1 isomers) without any modification. Although the same definition of the local symmetry coordinates has been employed for CC1F2CH2Cland CC1F2CHCl2and for CClF2CH3,CH2CICH3,and CHC12CH3,transferability of the scale factors corresponding to the CC stretching and torsion vibrations raises some question; they are highly affected by both of the two (ha1o)methyl groups composing a molecule and, hence, may change from molecule to molecule. Furthermore, the experimental frequencies of the band assigned to the torsion mode are very ambiguous. Therefore, the
(b) CHzCICH3
-
W
(c) CHCIzCH3
Figure 1. Definition of the structure parameters of (a) CCIF2CH,, (b) CH2CICH3,and (c) CHCI2CH3. Some structural parameters are omitted in the figure to avoid complication. The conformation having C, symmetry is the only stable form for these molecules.
scale factor for the torsion mode of CC1F2CH2C1and CClF2CHC12 was taken to be unity. It can be easily seen that this does not cause any ambiguity in the assignment of the torsion mode, since the frequency of the torsion mode is very low, and therefore, a 20% change in the scale factor results in only a 10-20-~m-~ shift in the scaled frequency. On the contrary, the scale factor for the CC stretching is very important, because the contribution of the CC stretching spreads over several normal vibrations. The scale factors obtained for the CC stretchings of CClF2CH3,CH2ClCH3, and CHC12CH3are somewhat different. Since, as will be discussed below, the CC stretching is strongly mixed with CF2s stretching in the presence of CF bonds, the scale factor for the CC stretching is expected to be strongly affected by the CF2s stretching. Since both of the target molecules, CClF2CH2Cland CC1F2CHCl2,have CF bonds, the value obtained by CClF2CH3was employed for the scaling of the CC stretchings of CClF2CH2Cland CClF2CHC12. By use of the scaled ab initio force field obtained by eq 2, frequencies were calculated for all five molecules. The observed vibrational bands for CClF2CH2Cland CC1F2CHCl2were assigned with reference to the PED obtained on the basis of the scaled 3-21G** force field. Two sets of local symmetry coordinates were examined by the CC1F2CH3molecule. In one of the two sets, the definition of the local symmetry coordinates treats the substituents of the carbon atom having halogen atoms as CZX3 (Z = C1, X = F and CH3) type, where F and CH3 are regarded as equivalent in constructing the local symmetry coordinates. The scale factors and the scaled ab initio frequencies were also obtained by this set of scale factors. 4. Results 4.1. Calculations for CczF2CHJ,CH2CICHJ,pad CHC12CH3.
In Table I, the optimized structure parameters for CClF2CH3, CH2ClCH3, and CHC12CH3 are listed. The experimental structure parameter^^'-^^ are also shown. In Tables 11,111, and IV, the local symmetry coordinates used in this work are listed for CCIF2CH3,CH2ClCH3, and CHC12CH3,respectively. In
10700 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Sakka et al.
TABLE I: Optimized Structural ParametersQfor CClF,CH, CHzCICHh .ad CHClzCH3 CClF2CH3 CH2ClCH3 6-31GC* 3-21G expC 6-31GC* coordb 3-21G** 3-21G** expdd 1.516 R 1SO3 1SO3 1.493 1.490* 1.534 1.520 0.003 1.080 1.083 1.086 1.083 1.090 1.09 0.01 r3 1.083 1.078 1.090 1.083 1.080 1.081 1.077 1.091 0.01 r4 (=rd 1.776 1.877 1.736, 1.800 1.822 1.788 f 0.002 r6 1.775 1.362 1.352 1.328* 1.079 1.075 1.089 0.01 r7 (=rd 1.328 109.59 109.41 108.10 108.50 108.89 108.5 f 0.5 a 3 4 (=a35) 109.59 110.04 109.98 108.10 108.51 108.85 108.5 0.5 a45 109.75 108.22 108.49 109.21 109.23 110.43* 823 107.84 109.68 109.76 111.03 110.47 110.43* 8 2 4 (‘825) 110.02 107.99 106.94 106.19 105.90 a67 (=a68) 107.85 107.40 108.37 108.99 110.12 109.2 0.5 a78 106.99 110.37 111.49 110.51 111.03 0.13 112.63 112.48 816 817(=fils) 110.65 110.41 111.99 111.83 112.03 111.6 f 0.5 T36 180.00 180.00 180.00 180.00 180.00
*
*
CHCl,CH, 3-21G*’ exfJ 1.529 1.540 0.01 1.079 1.09* 1.080 1.09* 1.070 1.09* 1.797 1.766 0.01 109.31 110.2’ 109.52 110.2* 110.01 108.73. 109.34 108.73* 106.56 110.02 112.0 f 0.5 112.44 111.28. 110.55 111.0 0.5 180.00
* *
*
QUnits: length in angstrom and angles in degree. bSymbols for bond lengths and angles follow Figure 1. (Reference 37. Asterisks denote estimated values. Reference 38. Asterisks denote derived values. Reference 32. /Reference 39. Asterisks denote estimated values.
TABLE II: Definition of the Local Symmetry Coordinates of CClFzCH3 local symmetry coordQ*b
SI = AR
scale nature (species) factof CC stretch (A’) 0.8564 CH, s stretch (2)0.8153 CH, d stretch (A’) 0.8095 CH3 d stretch (A”) 0.7997 0.9332 CCl stretch (A’) CF2 s stretch (A’) 0.8387 CF2 a stretch (A’’) 0.7802 0.7963 CH, s bend (A’) CHI rock (A’) CHI d bend (A’) CH3 rock (A”) CH, d bend (A”) CF2 bend (A’)
0.8376 0.8109 0.8160 0.8000 0.9222
CCCl bend (A’)
0.8637
CF2 rock (A”) CF2 wag (A’) CF2 twist (A”) torsion (A”)
0.9516 0.9201 0.9169 0.9957
(a)trans
v
W
(b) gauche
Figure 2. Definition of the structure parameters of the two rotational isomers of CClF2CH2CI: (a) trans isomer, (b) gauche isomer. Some structural parameters are omitted in the figure to avoid complication.
aSymbols for bond lengths and angles follow Figure la. *Not normalized. cDetermined by comparing the calculated frequncies with the observed values using the method based on potential energy distribution (see text). = (f36 f 3 7 t 738 746 T47 + f 4 8 T56 + f 5 7 T58)/9, where T’S are dihedral angles.
+
+ +
+
+
Table V, another definition of the local symmetry coordinates for CClF2CH3is given. The scale factors obtained by comparing the 3-21G** frequencies with the experimental frequencies by the use of eq 2 are also listed. In Tables VI, VII, and VIII, the ab initio frequencies and the experimental frequencies are listed together with the ab initio frequencies scaled by the use of the scale factors given in Tables 11, 111, IV, and V. The ab initio frequencies at the basii set levels of 3-21G, 3-21G**, and 6-31G** for CClF2CH3,3-21G** and 6-31G** for CH2ClCH3,and 321G+* for CHC12CH3are indicated. 4.2. CakuIation~for CcLFm&l md ccLF,cHcI,. In Table IX, the optimized structure parameters for CClF2CH2Cland CClF2CHClzare listed. In Tables X and XI, definitions of the local symmetry coordinates are given for CClF2CH2Cl and CC1F2CHC12,respectively. The same definition was employed for both rotational isomers for each molecule. The scale factors transferred from CClF2CH3,CH2ClCH3,and CHCl2CH3are also listed. Frequencies for CClF2CH2Cland CC1F2CHC12obtained from the scaled 3-21G** force field are listed in Tables XI1 and XIII, respectively. Also listed in these tables are the difference between the calculated and experimental frequencies, the PED obtained from the scale 3-21G** force field, and the approximate assignments based on the PED.
-
(b) C1 symmetry Figure 3. Definition of the structure parameters of the two rotational isomers of CCIF2CHC12: (a) C, symmetry isomer, (b) C, symmetry isomer. Some structural parameters are omitted in the figure to avoid complication.
4.3. Vibratiad spoctrp of CCIFzCH.pmd CClF2CHQ. The vibrational spectral data of CC1F2CHCl2have not been reported previously. Therefore, we give the FT-IR and Raman spectra in
Vibrational Bands of Chlorofluoroethanes
The Journal of Physical Chemistry, Vol. 96, No. 26, 1992 10701 TABLE V Another Definition of k CCIFZCH,
TABLE 111: Definition of the Local Symmetry Coordinrtes of aZWH3 local symmetry mrd’** SI= AR S2 = Ar, + Ar4 + Ar5 S, = 2Ar3 - Ar4 - Ar5 S4 = Ar4 - Ar5 s5 Ar.5 S6 Ar8 + Ar7 S7= Ar8 - Ar7 Sa = - Aa45 -
+
+
A817 SI4
= - A q 8 - Aa68 - A818 + sa816-
- A817 si5 = Aa68 + Apia - Aa67 - A817 s i 6 = Aa68 - AB18 + - A817 s i 7 Aa68 - A818 - Pa67 + Ab17 4
nature (species) CC stretch (A’) CHI s stretch (A’) CH, d stretch (A’) CH, d stretch (A”) CCI stretch (A’) CH2 s stretch (A’) CH2 a stretch (A”) CH, s bend (A’)
scale facto? 0.9324 0.7846 0.7848 0.7935 1.0263 0.7869 0.7810 0.8038
CH, rock (A’) CH, d bend (A’) CH, rock (A”) CHI, d bend (A”) CHI bend (A’)
0.8685 0.8063 0.8309 0.7980 0.8051
CCCI bend (A’)
0.9004
CH2 rock (A”) CH2 wag (A’) CH2 twist (A”) torsion (A”)
0.8424 0.8251 0.8195 0.8452
’Symbols for bond lengths and angles follow Figure lb. *Not normalized. Determined by comparing the calculated frequencies with the observed values using the method based on potential energy distribution (see text). d e = (T36 + f j 7 + rj8 + rM+ T~~ + 748+ 756 + 757 + rS8)/9,where T ’ S are dihedral angles.
TABLE I V Definition of the Local Symmetry Coordinates of CHC12CH3 local symmetry coord‘>* SI = hR S2 = Ar, + Ar4 + Ar5 S, = 2Ar3 - Ar4 - Ar5 S4 = Ar4 - Ar,
s5 s6
Ar6
= Are + Ar7
S7= Ar8 - Ar7 Sa = Ad2, A&4
+
+ A@25- Aa45 -
+
- Aa35 S9 24323 - A824 - A825 Slo = 2Aa45- A q 4 - Aa15
nature (species) CC stretch (A‘) CH, s stretch (A’) CH, d stretch (A’) CH, d stretch (A”) CH stretch (A‘) CC12 s stretch (A’) CC12 a stretch (A”) CHI bend (A’)
scale facto? 0.8918 0.7741 0.7892 0.7699 0.7736 0.9341 0.9395 0.7947
CH3 rock (A’) CH, d bend (A’) CH, rock (A”) CH, d bend (A”) CCCI2 deform (A‘)
0.8334 0.7991 0.8362 0.7979 0.9081
CCCI2 deform’ (A’) CH bend (A’) CCC12 deform” (A”) CH bend’ (A”) torsion (A”)
0.8702 0.8144 0.8561 0.8189 0.6661
“Symbols for bond lengths and angles follow Figure IC. *Not normalized. Determined by comparing the calculated frequencies with the observed values using the method based on potential energy distriT ~+ , rj8+ T~ + T~~ + r48 + + 757 bution (see text). de = (‘36 + iS8)/9,where 7’s are dihedral angles.
+
Figure 4. Gaseous-state IR spectra a t room temperature, a liquid-state IR spectrum a t 193 K, a solid (maybe glassy) state IR spectrum a t 87 K, and a Raman spectrum of a liquid state are indicated in Figure 4a,b, c, d, and e, respectively. Because the spectra of CClF2CH2Clobtained in this work were substantially the same as those previously reported by Bucker and Nielsen,’* they are not provided in this issue. The band positions were identified using the spectra obtained in the present study and are listed in Table XII.
5. Discussion 5.1. Accuracy of the Frequency Calculations for CClFzCH3, CHzCICH, and CHCljCH3. It can be shown that the method of the scale factor determination employed in the present work is
-
nature (species) CC stretch (A’) CF2 s stretch (A’) CF2 a stretch (A”) CCI stretch (A’) CH, s stretch (A’) CH, d stretch (A’) CH3 d stretch (A”) CH, s bend (A’)
scale factof 0.8698 0.8342 0.7802 0.9332 0.8153 0.8095 0.7997 0.7963
CH3 rock (A’) CH, d bend (A’) CH, rock (A”) CH, d bend (A”) CCF2 deform (A’)
0.8376 0.8109 0.8160 0.8OOO 0.9144
CCF, deform’ (A’) CCI bend (A’) CCF2 deform” (A”) CCI bend‘ (A”) torsion (A”)
0.9226 0.8650 0.9348 0.9312 0.9957
Aa34
sll
= w24
- A825 +
SI2 = AaJ4 - Aa15 SI,= Aa78 A817 + A& - A816 Aa68 - Aa67 S i 4 = 2A% - AS17 - M i 8 s i 5
7
S18= Aed
local symmetry mrd‘.* SI= AR + Ar7 Are S2 = 2AR - Ar7 - Ar8 S, = Ar7 - Ar8 s 4 = Ar6 S5 = Ar, + Ar4 + Ar5 S6 = 2Ar3 - Ar4 - Ar5 S7= Ar4 - Ar5 Ss = A823 + A&4 + 11825 -
l Symmetry Coordinates of
2Afli6 - A(Y68 - Aa67
= A@17 - a 1 8 = Aff68 - Aa67 SI8= Aed SI6 s i 7
”Symbols for bond lengths and angles follow Figure la. *Not normalized. Determined by comparing the calculated frequencies with the observed values using the method based on potential energy distri= (736 + T , ~+ T~~ + 746 + r47+ 748 + 756 + q7 bution (see text). + 758)/9, where 7’s are dihedral angles. physically meaningful, because PED is a measure of the contribution from a local symmetry coordinate to a normal coordinate and directly related to the diagonal element of the force-constant matrix, as shown in eq 3. W e can examine the self-consistency in the calculation of the scaled ab initio frequencies of CClF2CH3, CH2ClCH3, and CHC12CHJby two extreme cases. One is the case where the PED matrix is diagonal. In this case, all the normal vibrations are completely localized to each local symmetry coordinate or, in other words, a local symmetry coordinate and the corresponding normal coordinate are identical. The use of eq 2, in this case, results in the exact agreement between the scaled a b initio and experimental frequencies. We may be able to approach this situation by the sophistication in the definition of local symmetry coordinates. The other is the case where all the ratios of an experimental frequency to the corresponding a b initio frequency are the same. This leads to the same value for all the scale factors and, as a result, to an exact agreement between the scaled a b initio and experimental frequencies. A situation close to this extreme case is attained by the use of a good basis set in the ab initio frequency calculations, in which the errors are perfectly systematic. Consequently, according to these characteristics of the method, the agreement between the experimental and scaled ab initio frequencies will be improved by the use of a larger basis set in a b initio calculations or by a sophisticated definition of the local symmetry coordinates. In fact, Tables VI-VI11 show that the scaled frequencies are in very good agreement with the experiment when a vibration is localized; i.e., the contribution to the vibration is mainly from a single local symmetry coordinate. On the other hand, several scaled a b initio frequencies show relatively large discrepancies from the experiment30 for CClF2CH3. This can be explained by the strong mixing among the local symmetry coordinates. Because the scale factor depends on the type of local symmetry coordinates, the difficulty in estimating the relative contribution of each local symmetry coordinate to a certain normal vibration may arise when two or more local symmetry coordinates are responsible. This results in the errors in the scaled a b initio frequencies. As shown above in this section, however, if a set of vibrations comprises a certain set of local symmetry coordinates and the ratios of the experimental frequency to the corresponding a b initio frequency for the vibrations in this set are very similar, the scale factors for these coordinates would result in very similar values, and then, the agreement between the scaled and experimental frequencies would be greatly improved. In view of the ratio of the experimental
10702 The Journal of Physical Chemistry, Vol. 96, No. 26, 1992
Sakka et al.
TABLE VI: Calculated and Observed Frequencies of the iR Absorption Band of CCIF2CH3 calculation scaled* (scld - exp) 3-21G (exp/calc) 3-21G** (exp/calc) 6-31G** (exp/calc) exp” 3035 3345.5A“ (0.9072) 3393.9A“ (0.8943) 3322.6A” (0.9134) 3035.1 (0.1) 3373.6A’ (0.8996) 3035.6 (0.6) 3306.2A’ (0.9 180) 3035 3315.9A’ (0.91 53) 3221.1A’ (0.9205) 3238.0A’ (0.9157) 3283.6A’ (0.9030) 2964.7 (-0.3) 2965 1447 1650.7A” (0.8766) 1616.2A” (0.8953) 1608.6A” (0.8995) 1447.9 (0.9) 1607.OA’ (0.9004) 1447 1640.OA’ (0.8823) 1607.6A’ (0.9001) 1451.1 (4.1) 1563.5A’ (0.8922) 1395.8 (0.8) 1568.9A’ (0.8892) 1395 1601.7A’ (0.8709) 1421.2A” (0.8655) 1381.4A” (0.8904) 1378.5A“ (0.8923) 1244.7 (14.7) 1230 1339.8A’ (0.8971) 1235.7 (33.7) 1375.1A’ (0.8741) 1202 1367.3A’ (0.8791) 1243.2A’ (0.9009) 1152.2 (32.2) 1251.7A’ (0.8948) 1 l20f 1245.0A’ (0.8996) 994.2 (27.2) 1133.2A” (0.8533) 11 12.6A” (0.8691) 1094.5A” (0.8835) 967 978.6A’ (0.9238) 905.7 (1.7) 1008.1A’ (0.8967) 904 963.3A’ (0.9384) 690.6A’ (0.9890) 654.4 (-28.6) 739.2A’ (0.9240) 653 666.1A’ (1.0254) 584.1A’ (0.9296) 548.0A’ (0.9909) 543.4A‘ (0.9993) 520.2 (-22.8) 543 427.9 (-7.1) 472.3A’ (0.9210) 435 445.2A‘ (0.9771) 41 1.2A’ (1.0579) 432.6A” (0.9917) 418.4 (-10.6) 462.6A” (0.9274) 4298 419.3A” (1.0231) 365.4A” (0.9141) 334.4 (0.4) 349.1A“ (0.9567) 332.0A“ (1.0060) 334 308.1 (3.1) 329.6A’ (0.9254) 328.6A’ (0.9282) 305 3 15.2A‘ (0.9676) 270.1 (-0.9) 271h 271.3A” (0.9989) 266.2A” (1.0180) 270.6A” (1.0015)
scaledC (scld - exp) 3035.1 (0.1) 3035.6 (0.6) 2964.7 (-0.3) 1447.8 (0.8) 1451.2 (4.2) 1395.6 (0.6) 1243.3 (13.3) 1232.4 (30.4) 1150.7 (30.7) 994.6 (27.6) 912.8 (8.8) 656.6 (-26.4) 518.9 (-24.1) 427.2 (-7.8) 414.8 (-14.2) 337.1 (3.1) 308.3 (3.3) 270.2 (-0.8)
PEDd
PEDC
“Reference 30. *Using the scale factors indicated in Table 11. The basis set is 3-21G**.
