Structure, polarized micro-Raman and FT-IR spectra, and ab initio

Vladimir A. BasiukLina M. Bolivar-PinedaVictor Meza-LagunaElena V. Rybak-AkimovaElena V. Basiuk. The Journal of Physical Chemistry Letters 2018 9 (15)...
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J . Phys. Chem. 1993, 97, 10561-10569

10561

Structure, Polarized Micro-Raman and FT-IR Spectra, and ab Initio Calculations of 1,2-Dicyanobenzene J. T. L6pez Navarrete,t J. J. Quirante,t M. A. C. Aranda,* V. HernPndez,? and F. J. Ramirez*'t Departamento de Quimica Fisica and Departamento de Quimica Inorgbnica, Facultad de Ciencias, Universidad de Mblaga. 29071 -Mhlaga. Spain Received: February 3, 1993; I n Final Form: May 25, 1993'

The infrared and polarized Raman spectra of solid 1,2-dicyanobenzene (phthalonitrile) have been recorded and measured. A general assignment of the vibrational fundamentals has been proposed on the basis of the intensity changes observed in the polarized spectra. A powder X-ray diffraction study has been performed showing that this compound crystallizes in the orthorhombic space group, Pmmn, with lattice parameters of a = 12.625(4) A, b = 6.974(3) A, c = 3.909(2) A, and Z = 2. A b initio quadratic force field calculations a t the 3-21G and 6-3 1G levels were carried out. The frequencies, normal modes, and infrared intensities obtained from scaled quantum mechanical force fields support the previous results from experimental data.

Introduction

In the last few years the interpretation of vibrational spectra of medium-size molecules has been performed on the basis of ab initio quantum chemical force field calculations using large basis sets.' The theoretical normal mode analysis, in addition to the experimental data, allows for a more reliable assignment of the observed bands in the infrared and Raman spectra. Among the numerous information which can be obtained by experimental methods, those found in polarized Raman spectra are very useful in this respect since they let us identify vibrations which belong to different symmetries.* As is known, the analysis of these spectra requires knowledge of the crystal structure concerned. Prior to this work, some attention has been paid in this laboratory to the infrared and Raman spectra and force field computations on benzene derivatives,>' such as terephthal~nitrile~ and i~ophthalonitrile~ molecules. In order to complete the analysis on dicyanobenzenes, we are presenting here an experimental and theoretical study on 1,Zdicyanobenzene (phthalonitrile) molecule involving both structural and vibrational features. The infrared and Raman spectra of this compound have been reported previo~sly,*~~ and a general vibrational assignment has been proposed on the basis of the measured frequencies andvibrational shifts upon deuterium substitution.9 Normal coordinate analysis and force field calculations have not been found in the literature. In the present paper we report the polarized Raman spectra of microcrystalline samples of phthalonitrile, in addition to the Raman and Fourier transform infrared (FT-IR) spectra from usual solid samples. Raman microspectroscopy10 permits the analysis of crystalline samples of a few square micrometers of surface by coupling a conventional Raman spectrometer to an optical microscope which focuses the laser beam upon the sample and collects the scattered radiation. Because the axial resolution that can be obtained with a crystalline sample is about 10 pm, the spectra will correspond to very small crystals where a highly ordered structure occurs, thus appearing to be a single crystal. In order to profit from these results for assignment purposes, some crystal parameters must be previously known; therefore, we have performed a powder X-ray diffraction study of this compound. Here, we report the space group, the unit cell dimensions, and the indexed powder X-ray diffraction pattern. On the other hand, normal coordinate analysis of phthalonitrile has been obtained by using different levels of calculations, both

* Author to whom correspondence should be addressed.

Departamento de Qufmica Ffsica. de Qulmica Inorghica. *Abstract published in Advance ACS Absrracrs, August IS, 1993.

f

t Departamento

0022-365419312097- 10561$04.00/0

semiempirical and ab initio, in order to compare the results and to support the proposed assignments. Force constant evaluation requires the molecular geometry to be optimized to reach a point of minimal energy; the equilibrium geometry for each method was thus calculated and compared with the structure obtained from proton satellite spectrum techniques." The present work is organized as follows: first we give the experimental details and the methods of calculation, and then we discuss the results of the X-ray diffraction study and the molecular structure. In the next section we report the infrared and Raman spectra and discuss the assignments, and finally we present the results from the normal coordinate analysis in terms of theoretical frequencies and potential energy distribution. In the last section we will present our conclusions.

Experimental Section Phthalonitrile (Aldrich, 98% purity) was always used after three recrystallization processes from ethanol solution. The powder X-ray diffraction pattern of this compound was recorded on a Siemens D501 automated diffractometer using graphitemonochromated Cu Ka radiation. The diffraction profile was collected in the 28 range of 10'-50°, counting 1 s/O.O2O for each step. An infrared spectrum between 4000 and 400 cm-1 was obtained from a potassium bromide pellet on a Perkin Elmer 1760X FTIR spectrophotometer purged with Ar gas. In order to increase the signal-to-noise ratio a minimum of 50 scans were accumulated in all cases, with a spectral resolution of 2 cm-I. Raman spectra of microcrystalline powder were recorded on a Jobin Yvon Ramanor U 1000 spectrometer using excitation radiation wavelengths at 488.0 and 514.5 nm generated by a Spectra Physics argon ion laser working at 300-500 mW. The measurements of the depolarization ratio of each Raman line were done in dimethyl sulfoxide solutions. The best resolution obtained was 1 cm-1. Polarized Raman spectra over the range 100-3500 cm-1 were recorded on a MOLE micro-Raman spectrometerlo fitted with a double monochromator and a single-channel detection system which allows us to work with microcrystals which are a few tens of micrometers in size. The molecules in such small crystals occur in a highly ordered structure similar to a single crystal. A DILOR XY Raman spectrometer (Societe Dilor, France) fitted with a double premonochromator, a spectrograph, and multichannel detection system made up of an intensified diode array was also used. Multichannel detection allows for a large number of scans to be recorded and averaged in a short time scale, providing a substantial increase in the signal-to-noise ratio. Both spec@ 1993 American Chemical Society

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L6pez Navarrete et al.

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

TABLE I: Symmetrized Pulay Coordinates Used in This Work for the Vibrational Analysis of the Phthalonitrile Molecule no.' coordinateb description 1 2 3 4 5 6 7 8 9 10 11

C-H stretch C-H stretch C-C stretch C-C stretch C-C stretch C-C stretch C-CN stretch C=N stretch C-H in-plane bend C-H in-plane bend C-C in-plane bend

12 13

C-CN in-plane bend C=N in-plane bend

14 15 16 17

C-CN out-of-planebend C-H out-of-plane bend C-H out-of-plane bend C-C out-of-plane bend

18

C-C out-of-plane bend

19

C=N out-of-planebend

20 21 22 23 24

C-CN out-of-plane bend C-H out-of-plane bend C-H out-of-planebend C-C out-of-plane bend C=N out-of-planebend

25 26 27 28 29 30 31 32 33

C-H stretch C-H stretch C-C stretch C-C stretch C-CN stretch C=N stretch C-H in-plane bend C-H in-plane bend C-C in-plane bend

C-C in-plane bend C-CN in-plane bend C=N in-plane bend a Arbitrary numbering. The atomic numbering is defined in Figure 1. r i j are the stretching vibrations of the bond between atoms i and j . B i , k is the in-plane bending vibration of the angle between atoms i, j , and k. '$t is the out-of-planebending vibration of the atom i. ~i is the torsion vibration respect to the bond between atoms i and j . 34 35 36

troscopic systems belong to the Laboratoire de Specrrochimie Infrarouge et Raman (LASIR)of the University of Lille (France).

Computational Methods The equilibrium geometry for the phthalonitrile molecule was predicted at the SCF level using the 6-31G and 3-21G basis sets.l2 The corresponding vibrational force fields in Cartesian coordinates were also evaluated each using optimized geometry as a starting point, where the second derivatives of the energy are computed analytically. All ab initio calculations were carried out by means of the GAUSSIAN 90 program implemented on a micro-VAX 3800. Maximum forces (in atomic units) after geometry optimization were lower than 4.0 X lo4. Maximum deviations from the ideally zero translation and rotation frequencies were 4.4 and 5.2 cm-1 for the 6-31G and 3-21G basis sets, respectively, and they were obtained by mean of the diagonalization of the mass-weighted Cartesian force constant matrix. Infrared absorption intensities were evaluated at the 6-31G level from the atomic polar tensors.13 The semiempirical

TABLE 11: X-ray Powder Diffraction Data for Phthalonitrile do&

(A)

6.337 6.120 3.908 3.734 3.607 3.485 3.41 1 3.293 3.161 3.054 3.002 2.870 2.650 2.548 2.373 2.340 2.214 2.121 2.036 2.009

CI

(A)

6.313 6.105 3.909 3.734 3.603 3.487 3.410 3.292 3.156 3.052 3.000 2.876 2.864 2.649 2.549 2.374 2.340 2.213 2.121 2.035 2.008

hkl 200 110 00 1 101 310 020 01 1 111 400 220 21 1 410 301 31 1 121 510 420 321 501 330 42 1

I/Im (%) 100 66 3 16 33 10 19 41 36 7 9 3 9 3 5 6 4 3 4 3

TABLE III: Correlation between Molecular, Site, and Unit Cell Symmetries in Solid Phthalonitrile (In Parentheses, the Activity of Modes for Every Species) molecule site unit cell

c2.

CZl,

5B1(IR,Ra)10BI(IR,Ra)

D2h

'13B1,(IR)

MNDO methodI4 was also used to evaluate the quadratic force constants for the phthalonitrile molecule and to compare the results with those obtained from ab initio calculations. The Cartesian force constants were transformed into a set of CzUsymmetry coordinates, which were defined according to the Pulay definition method.ls The force fields were subsequently scaled taking into account our experimental vibrational frequencies, but not the previous assignments by other authors, in order to compensate for the systematic overestimation of the force constants. We have used the method proposed by Pulay and co-workers16 to scale the diagonal and off-diagonal elements in the force constant matrix. Frequencies and normal coordinates were calculated by the Wilson FG methods1'

Results and Discussion A. Crystal and Molecular Structure. The powder X-ray diffraction pattern of phthalonitrile (Table 11) was indexed from 19 accurately measured reflection positions by using the program Treor.18 An orthorhombic unit cell of dimensions a = 12.625(4) A, b = 6.974(3) A, c = 3.909(2) A (volume = 344.2 A3) was obtained, giving the following figures of merit: Mi9 = 26,19and F19 = 3 3 (0.018,33).20 All the observed diffraction peaks could be accounted for on the basis of this unit cell. For Z = 2 the volume per non-hydrogen atom is 17.2A3,indicating twochemical formula units in the crystallographic unit cell. The observed absence conditions were hkO = 2n + 1 ; hOO = 2n + 1; OkO = 2n + 1. The possible space groupswere therefore the acentrics Pm2ln or P2lmn (No. 3 1 ) , or centric Pmmn (No. 59). The following resultsare fullycompatible with the higher symmetryspacegroup Pmmn, which corresponds to the D2t,I3 punctual group, and the molecule in the crystal has a C2, site symmetry.2 Table 111 shows

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10563

Structure Analysis of 1,ZDicyanobenzene

TABLE I V Comparison between Theoretical and Experimental Geometrical Parameters (UnitsAre angstrom (Lengths) or degrees (Angles)) bonds

0

MNDO

3-2 1G

6-31G

expo

1.427 1.415 1.406 1.404 1.091 1.091 1.428 1.162

1.396 1.386 1.383 1.383 1.07 1 1.07 1 1.428 1.140

1.401 1.390 1.386 1.386 1.07 1 1.07 1 1.434 1.147

1.407 1.407 1.402 1.391 1.067 1.080 1.438 1.1 10

angle

MNDO

3-2 1G

6-31G

119.3 120.6 120.1 120.1 119.2 119.8 120.1 121.4 119.3 179.3

119.7 120.3 120.1 119.4 120.4 119.5 120.4 120.7 119.7 179.7

119.6 120.3 120.1 119.4 120.3 119.6 120.3 121.0 119.4 179.7

expo

120.3 120.8 119.0 118.8 178.8

Proton satellite spectrum results.ll

6 Figure 1. Molecular structure of the phthalonitrile molecule with the atomic numbering used in this work.

the correlation between the molecular group, site group, and crystal symmetry; as we can see, every molecular vibration gives rise to an infrared active unit cell mode, belonging to BIU,Bzu, or B3u species of the factor group, and a Raman active one, belonging to As, Big, B28, or B38 species. The only exception to this is found in the molecular vibrations of A2 symmetry, which produce only Raman active modes. This feature is particularly helpful in the assignmentof the observed bands because the nature of the Raman spectrum depends on the orientation of the crystal with respect to the polarized excitation beam.2 In elongated microcrystals the direction of the major axis is well defined in orthorhombic or monoclinic systems, and it coincides with the longest dimension of the crystal, the axis a in this case; the rest of the axes cannot be established before analyzing the spectra. The force field calculations required the previous optimization of the molecular structure until it had a minimal point of energy, as was discussed above. The parameters obtained are compared in Table IV with the experimental values obtained by the proton satellite method.' The three levels of calculation predict a planeCZ,structure for the isolated phthalonitrile molecule (Figure l), although the molecule in the solid state is expected to be slightly distorted from this symmetry, due to the interactions present in the crystal. The obtained out-of-plane deviations are always negligible. The calculated bond lengths were subject to mean absoluteerrorsof0.018 A(MNDO),O.O15A (3-21G),and0.013 A (6-31G); keeping in mind the features of each method, these results were expected in spite of the fact that the differences are minimal for most of parameters. Carbon-carbon bonds lengths are accurately evaluated, although MNDO overestimates the values for these parameters while both 3-21G and 6-31G basis sets provide shorter C-C distances than the experimental ones. The calculated C-N bond lengths show the highest deviations from the observedvalues, being always overestimated. The mean

Wavenumber (cm. ')

Figure 2. Polarized Raman spectra of phthalonitrilein the 100-3200-~m-~ region: 11 I, bottom; 11 1 , top.

3000

2500

2000 1500 Wavenumber ( e m 1 )

1000

500

Figure3. Raman spectrumof phthalonitrile in the 100-3200-~m-~ region.

absolute error for the angles was of 0.7' in the three cases, and the differences with respect to the benzene structure are lower than 2O. In summary, the theoretical structural parameters predict a planar CZ,symmetry for this molecule. The optimized bond lengths and angles compare satisfactorily with the experimental values,' and out-of-plane distortions were estimated to be negligible. B. Assignment of the Spectra. The polarized Raman spectra of phthalonitrile molecule are shown in Figure 2, and the microcrystalline powder Raman spectrum is shown in Figure 3. Figure 4 displays the infrared spectrum from KBr pellet. The polarized Raman spectra were obtained by using an elongated microcrystal oriented along the analyzer polarization direction, thex-axis; the notation 11 11 thereforedenotes that both the polarizer and analyzer were oriented in the same direction as the crystal,

10564

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

I

3085 m

3087 m

2238 vs 1594 w 1577 w 1488 w

2238 vs 1594 m 1577 w 1489 w

1230 wm 1208 m

1301 w 1230 wm 1208 m 1181 wm

1038 ms

1038 m

3106 w 3083 s 3052 vw 3030 w 2231 vs 1590 m 1574 w 1486 w 1457 vw 1299 vw 1227 wm 1207 m 1187 w 1155 w 1096 vw 1038 ms

771 wm 737 vw 708 wm

737 vw 707 wm

771 w 739 vw 708 m

561 m 526 ms 472 ms

562 m 526 m 474 m 412 w

381 w 364 vw 198 w 176 vs 149 sh 119sh

363 wm 199 m 175 wm 149 sh 121 s

560 wm 524 wm 474 m 414 w 381 w 364 w 201 m 175 m

3105 m 3080 m 3041 m 3029 w P 2232 s dP 1589 m P 1573 m P 1485 s 1447 ms 1296 m P 1228 m P 1206 ms ll82w P

1095 vw 1035 vw 944 vw 928 w 885 vw 807 m 769 vs 706 m 610 vw P 563 w dP 525 vs P 473 m dP 414 wm

P

120 w

0 p = depolarization ratios; s = strong; m = medium; w = weak; v = very; p = polarized; dp = depolarized. 6 = bending; v = stretching; a = antisymmetric; s = symmetric; y = out-of-plane bend.

while 1) I indicates that the polarizer has the perpendicular orientation with respect to the crystal, Le., the y-axis. The frequencies, intensities, and depolarization ratios measured on these spectra are listed in Table V, together with the proposed assignments for the fundamentals. Assignments are grounded on a Cb symmetry for the isolated molecule, and distortions arising from the ordered arrangement of molecules in the solid state are not significant here. Wilson’s nomenclature21 for the normal modes of benzene was adhered to as far as it was possible. The 36 fundamentals for the phthalonitrile molecule can be distributed into the irreducible representations of the C2,* punctual group as follows: 13AI 12B2 inrplane and 6A2 + 5Bl out-of-plane vibrations, according to the orientation for the coordinate axis laid down by the Joint Commission for Spectroscopy.22 The assignments were based on the previous data reported and correlations with related molecules, the activity of the normal modes in the infrared and Raman

+

L6pez Navarrete et al. spectra and the depolarization ratios measured, the analysis of the intensity changes observed in the polarized Raman spectra, and the normal coordinate calculations. 2000-4000-~m-~Region. Four C-H stretching modes can be observed up to 3000 cm-I, which are all active in both infrared and Raman spectra. One of these is measured as a polarized band at 3083 cm-1 and has been assigned to the mode 2,A1 in the Wilson nomenclature. The rest of u(CH) vibrations wereassigned following the range of usual appearance in 1,2-benzene derivative@ and are in accordance with previous assignments for the phthalonitrile m ~ l e c u l e . *In ~ ~this region, the CEN stretching vibration has been measuredat 2232 cm-I in theinfrared spectrum, which appears as a strong band; no splitting was observed for the A, and B2 molecular modes of this vibration; this suggests a weak dynamical coupling between them. I000-2000-cm-’ Region. Here we expect the skeletal stretching vibrations and the C-H in-plane bending modes. As is usual in benzene derivatives, between 1600 and 1400 cm-I the pairs 8a8b and 19a-l9b, which have v(CC) character, were measured. Their assignements were based on the depolarization ratios. The infrared frequencies measured for these four modes are close to the ones observed for b e n ~ o n i t r i l enamely, ,~~ 1598, 1580, 1492, and 1448 cm-I, supporting our assignments. The band at 1296 cm-* was assigned to the 3,B2, C-H bending vibration, on the basis of the frequencies reported for phthalonitrile-d4,9 which also let us assign the rest of b(CH) modes to the Raman lines at 1155,1096, and 1038 cm-I. The two polarized bands measured at 1227 and 1207 cm-1 in the Raman spectra have to be assigned to the modes 14,v(CC) and 7a,v(C-CN), both belonging to the totally symmetrical species; unfortunately there are not experimental data in order to discriminate between them. For other 1,Zdisubstituted benzenes, the 14vibration wasassigned at higher frequency than the 7a mode; in the case of o-phthalic acid, two lines a t 1303 and 1263 cm-I, respectively, are reported on the basis of the polarized Raman spectra,2s and, for o-difluorobenzene,26these two modes were assigned at 1292 and 1272 cm-I, respectively, in the infrared spectrum. The analysis of the polarized Raman spectra is consistent with these assignments. From Table V we can see that all the bands corresponding to B2 vibrations have higher intensity in the I( I polarized Raman spectrum than in the 11 11 polarized one. As is shown in Table 111, the B2 molecular modes correspond to the B3, Raman-active crystal vibrations, to which the y z component of the polarizability tensor, a, belongs. The AI vibrations are observed with similar or slightly lower intensity in the11 11 spectrum than in the perpendicular one, in accordance with the fact that the diagonal components of a belong to the AI, species of the factor group. As was pointed out before, the b and c crystallographic axes cannot be accurately established in the microcrystal, and this fact would allow us to observe the B28 crystal modes (Le., the BI molecular vibrations) in the 11 I polarized Raman spectrum, whereas the BI, modes (from the A2 symmetry in the molecule) would be somewhat more intense in the 1111 spectrum. 100-1000-cm-~ Region. Between 950 and 850 cm-1 we have assigned three y(CH) out-of-plane modes in accordance with previous data reported for the deuterated derivative.9 The 5 and 10b vibrations are recorded in the infrared spectrum as very weak bands because they belong to the A2 species; that is, they are infrared inactive. This is because in the crystal the molecule is affected by interactions with its neighbors which lightly modify the Cz, symmetry toward a C, planar conformation, where all the vibrations are infrared active. These two modes also show very weak intensity in the Raman spectrum. N o other bands were observed in this region. Below 800 cm-1 three peaks were measured as polarized in the Raman spectrum, being assigned to the modes 1,6a, and b(CN), all of AI symmetry. Two infrared bands at 769 and 525 cm-1

Structure Analysis of 1,2-Dicyanobenzene

TABLE VI: Experimental and MNDO Frequencies (cm-1) for Phthalonitrile Molecule vibration

frequency exp cald

assignmentb

P E D (greater than 10%)

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10565

TABLE VII: Experimental and 3-216 Frequencies (cm-1) for the Phthalonitrile Molecule vibration

A ISpecies 3080 3149 3041 3136 2232 2348 1573 1562 1485 1480 1228 1156 1206 1270 1155 1079 1038 1065 753 706 563 551 473 48 5 122 148 944 885 739 364 120

957 863 720 476 350 92

928 769 525 381 175

919 760 558 334 162

3105 3142 3029 3134 2232 2347 1590 1584 1447 1419 1296 1237 1182 1198 1095 1086 807 610 414 20 1

743 61 1 392 210

Frequenciesobtained by using the scaling factors of 0.85 for stretching and 0.80 for bending force constants. Wilson nomenclature.21e v = stretching; 6 = in-plane bending; y = out-of-plane bending.

were assigned, because of their high inten~ity,~3 to modes 1 1 , ~ (CH) and 16b,y(CC),respectively, which belong to the Bl species since theywereobserved with higher intensity in the([ Ipolarized Raman spectrum than that in the 11 11 polarized one. The rest of skeletal and substituent vibrations were assigned on the basis of the range of usual a ~ p e a r a n c e ,taking ~~ into account their intensities measured from the polarized Raman spectra. C. Force Field and Normal Coordinate Calculations. The results concerning theoretical frequencies and descriptions for phthalonitrile molecule from the three methods employed here are compiled in Tables VI-VI11 while Table IX lists the diagonal force constants which correspond to in the internal coordinates given in Table I. In order to minimize the systematic errors of the calculations used here in the evaluation of vibrational frequencies, the theoretical force constants were scaled empirically following the Pulay method.2' We have employed two scaling factors, each one corresponding to the normal stretching and bending coordinates, which have been chosen by taking into account the assignments proposed for the experimental frequencies. Correlations between calculated and observed values were guided by the potential energy distribution (PED) and the Cartesian atomic displacements obtained for each frequency. Several improvements can be observed when comparing the ab initio results with those obtained by MNDO method. For the skeletal ring vibrations the differences between experimental and MNDO calculated frequencies shown in Table VI are signifi-

assignment*

P E D (greater than 10%)

A ISpecies

2 100v(CH) 20b 101w(CH) CN vibration 89w(CN), 16w(C-CN) 8a 98u(CC) 19b 56w(CC), 24v(C-CN), 236(CH) 14 81v(CC), 386(CH) 7a 39v(CC), 286(CH), ZOu(C-CN) 15 45w(CC), 316(CH) 18b 52v(CC), 366(CH) 1 32w(CC), ~OV(C-CN),146(CC) CN vibration 456(CN), 276(C-CN), I46(CC) 6a 636(CC), 176(CN) 9a 706(C-CN), 346(CN) A2 Species 5 1OSy(CH), 14y(CC) 10b 82y(CH), IZy(C-CN) 4 59y(C-CN), 18y(CN) 16a 6 W C C h 22y(CN) CN vibration 44y(CN), 26y(CC), 20y(C-CN) 17a 93y(CC), 14y(CN), I3y(C-CN) BISpecies 1Oa 96y(CH), 16y(CC) 11 9 0 ~ ~ ) 16b 55y(CN), 32y(C-CN) CN vibration 52y(CC), I9y(CN), 16y(C-CN) 17b 47y(C-CN), 33y(CC), 23y(CN) B2 Species 20a 101w(CH) 7b IOlu(CH) CN vibration 89v(CN), 16w(C-CN) 8b 104v(CC), 126(CH), lO6(CC) 19a 61v(CC), 3 16(CH), lOV(C-CN) 3 896(CH) 13 35v(C-CN), 346(CH), 146(CC) 9b 376(CH), 23v(CC), 16w(C-CN), 156(CC) 12 876(CC), lOV(C-CN) CN vibration 436(CN), 356(C-CN) 6b 746(CC) 18a 546(C-CN), 516(CN

4

frequency exp c a b

3080 3136 2 99v(CH) 3041 3118 20b 100w(CH) 2232 2392 CN vibration 90w(CN), IOv(C-CN) 1573 1570 8a 83w(CC), 166(CH), 1 l6(CC) 1485 1476 19b 49v(CC), 416(CH) 1228 1190 14 65dCC). 356(CH) 1206 1204 7a 35v(C&N), 33w(CC), 236(CH) 1155 1140 15 47u(CCI, 386(CH) 1038 1034 18b 61v(CC), 406(CH) 706 702 1 396(CC), 27v(CC), 24u(C-CN) 563 568 CN vibration 296(CN), 226(C-CN), I56(CC) 473 486 6a 346(CC), 286(CN) 148 120 9a 676(C-CN), 406(CN) A2 Species 944 1004 5 98y(CH), 3ly(CC) 885 893 10b 76y(CH), I6y(C-CN) 739 775 4 45yW-CN). 15r(CC), 13y(CN), 12-W-I) 582 16a 51y(CC), 2ly(CN), 13y(CH) 378 CN vibration 42y(CN), 27y(C-CN), 25y(CC) 364 112 17a 120 78y(CC), 25y(CN), 14y(C-CN) BI Species 928 964 769 759 525 575 16b 55y(CN), 24y(C-CN), I5y(CH) 381 382 CN vibration 53y(CC), I3y(CN), I3y(C-CN), 12y(CH) 175 164 17b 60y(C-CN), 29y(CN), 19y(CC) B2 Species 3105 3126 20a 100u(CH) 3029 3110 7b 1OOw(CH) 2232 2390 CN vibration 90w(CN), lOu(C-CN) 1590 1598 8b 87w(CC), 226(CH), I26(CC) 1447 1432 19a 52dCC). 446(CH1 1296 1270 3 696(CH); 17u(CC) 1182 1172 13 27v(C-CN), 256(CH), 256(CC), I7v(CC) 1095 1082 9b 316(CH), 316(CC), 26w(CC), I lu(C-CN) 797 12 807 646(CC), 25w(C-CN) 610 628 CN vibration 3461CN). 3261C-CNl I ~ u ( C C ) 414 411 6b 606iCCj,' 2 16iC-CN j ' 201 206 18a 606(C-CN), 546(CN)

. ,

~ 3 5

y36

Frequencies obtained by using the scaling factors of 0.90 for stretching and 0.70 for bending force constants. Wilson nomenclature.2l c Y = stretching; b = in-plane bending; y = out-of-plane bending.

catively higher than in the cases of the ab initio calculations at the 3-21G and 6-31G levels. The stretching modes 14 and 1 are predicted with differences of 72 and 49 cm-1, respectively, while 3-2 1G gives errors of 38 and 4 cm-I. A similar behavior is observed for the in-plane bending vibrations 12 and 6b and for the outof-plane skeletal modes. Concerning carbon-hydrogen vibrations, the three methods predicted correctly both stretching and outof-plane modes because they are not extensively coupled with other vibrations. However, the differences between experimental and theoretical frequencies for the in-plane 6(CH) vibrations decreased in the order MNDO > 3-2 1G > 6-3 1G, as was expected; these modes are usually mixed with the C-C stretchings, and this fact was well described by both ab initio and semiempirical methods. The frequencies and normal modes calculated by the 3-21G and 6-31G basis sets do not present great differences between them, although some improvements can be emphasized. As happened with MNDO, the order for the 14 and 7a vibrations is changed with respect to the experimental assignment when a 3-21G basis set is used, but that was correctly predicted at the 6-3 1G level. On the other hand, the description of the normal modes, guided by the PED matrix, permits a better assignment with the more extended basis set, especially for the 1000-1300 cm-I region, where vibrations are greatly coupled.

L6pez Navarrete et al.

10566 The Journal of Physical Chemistry, Vol. 97,No. 41, 1993

TABLE VIII: Experimental and 6-316 Frequencies (cm-I) and Infrared Intensities (km/mol) for the Phthalonitrile Molecule vibration

exp freq

intensitya

calc freqb

AI

3080 3041 2232 1573 1485 1228 1206 1155 1038 706. 563 473 148

m m S

m S

m ms vw

m W

m

assignmentc

intensity

PEDd (greater than 10%)

Species

3143 3125 2360 1605 1490 1235 1217 1149 1045 702 554 466 115

8.6 3.8 28.7 1.3 25.5 9.0 0.2 6.6

1002 883 737 546 342 106

0.0 5 0.0 10b 0.0 4 0.0 16a 0.0 C N vibration 0.0 17a B1 Species 5.4 1Oa 92.4 11 16.3 16b 0.5 CN vibration 3.7 17b

2 20b CN vibration 8a 19b 14 7a

15

18b

1.1 5.3 0.2 1.5 1.6

1 C N vibration 6a 9a

99v(CH) 1OOv(CH) 89v(CN), 12v(C-CN) 84v(CC), 136(CH), 116(CC) 51v(CCI, 366(CHI m i c c j , i2aicsj 31dC-CN). 31dCC). 246(CH) 726(CH), 25v(CC) 646(CH), 6Ov(CC) 376(CC), 28v(CC), 25v(C-CN) 246(CC), 226(C-CN), 166(CN) 346(CC), 286(CN) 6OB(C-CN), 496(CN) , I

.

I

A2 Species

944 885 739

vw vw

364 120 928 769 525 381 175

W

vs vs

960 752 509 368 156

97y(CH), 3ly(CC) 84y(CH), lOy(C-CN) 557(C-CN), 22y(CC) 48y(CC), 15y(CN), 13y(CH), 12y(C-CN) 5ly(CN), 25y(CC), lZy(C-CN) 76y(CC), 30y(CN), 14y(C-CN)

B2 Species

3105 3029 2232 1590 1447 1296 1182 1095 807 610 414 20 1

m W

S

m ms

m W

vw

m vw vw

3134 3115 2358 1632 1442 1269 1177 1085 796 599 407 189

5.6 0.1 17.0 2.8 11.2 0.2 1 .o 2.8 4.2 0.2 0.4 5.9

20a 7b C N vibration

8b 19a 3 13

9b 12 CN vibration

6b 18a

100u(CH) 100v(CH) 89v(CN), 1 lV(C-CN) 89v(CC), 156(CH), 126(CC) 57v(CC), 406(CH) 716(CH), 15v(CC) 27v(C-CN), 276(CH), 236(CC), 15v(CC) 256(CH), 256(CC), 24v(CC), 12v(C-CN) 656(CC), 24v(C-CN) 41 G(C-CN), 266(CN) 626(CC), 176(C-CN) 696(CN), 456(C-CN)

s = strong; m = medium; w = weak; v = very.

Frequencies obtained by using the scaling factors of 0.85 for stretching and 0.75 for bending force constants. Wilson nomenclature.2’ v = stretching; 6 = in-plane bending; y = out-of-plane bending. The force constants listed in Table IX show a similar behavior to that previously discussed for frequencies and normal modes. Significant differences can be found for the skeletal ring vibrations. Thus, while the v(CC)-MNDO force constants are higher than the a b initio values, both 6(CC) and r ( C C ) ones are lower. The greatest difference is observed for the v(C-CN) force constant, which is evaluated as 7.235 (MNDO), 5.334 (3-21G), and 5.561 (6-31G) mdyn/A for the corresponding A1 coordinate. No significant deviations have been observed between symmetrical (AI)and antisymmetrical (B2) stretching forceconstants provided by each calculation and in the same way for the in-plane bending ones. An exception is the symmetrical 6(C-CN) vibration, which decreases the N-N distance in this molecule; as a consequence, the repulsion between the lone pairs on the nitrogen atoms is enhanced. This fact makes the 6(C-CN),AI force constant to be evaluated, after scaling, at 0.815 mdyn/A, whereas the corresponding Bzvalue is 0.701 mdyn/A, showing the data from the 3-21G basis set and the MNDO method have identical trends. In accordance with the close C-H geometrical parameters obtained by both a b initio and semiempirical calculations (see Table I), the corresponding force constants do not present great differences. Concerning the out-of-plane species, we would like to emphasize the small value given by the 6-31G basis set with respect to the other methods for the r ( C N ) coordinate, 0.296 mdyn/A versus 0.469 and 0.422 mdyn/A from 3-21G and MNDO, respectively (seeTable IX). The former value compares favorably with the reported y(CN) force constant for benzoni-

trilez7 by using a 4-21G basis set, 0.327 mdyn/A after scaling with a specific factor for this coordinate. With the low level of scaling that was performed being taken into account, these results can be considered satisfactory. However, we have chosen the 6-3 1G force field as a starting point of a more refined scaling process, using a greater number of factors, in order to reproduce the observed frequencies with minimal errors. In this way, we have optimized a scaled factor for every force constant which has a different character, and the final values are listed in Table X. The results concerning frequencies, assignments, and potential energy distribution are listed in Table XI, whereas Table XI1 lists the complete quadratic force field obtained in this scaling refinement. As we can see in Table XI, the descriptions of the calculated frequencies are not very different from the obtained one by using two scaling factors; however, the deviations with respect to the experimental frequencies are smaller, in most of the cases lower than A10 cm-1, supporting the previous assignments. In addition, the resulting force constants are more realistic, and they compare favorably with the values reported for other related molecules, such as benzene28 or ben~onitrile,~’,both from a b initio calculations. Concerning the off-diagonal force constants in Table XII, the highest values were obtained for the v(CC)/v(CC) interactions, some of these being greater than 1.000 mdyn/A; as expected,29 their signs are positive for ortho andpara interactions and negative for meta interactions, and the absolute values follow the expected trend.29 The small value found for the v(C-CN)/V(CN)

Structure Analysis of 1,2-Dicyanobenzene

TABLE I X Diagonal Scaled' Force Constants (mdyn/A) Obtained for Phthalonitrile no.6 MNDO 3-21G 6-31G description AI Species 1 5.453 5.366 5.366 C-H stretch 2 5.479 C-H stretch 5.354 5.371 6.340 6.595 3 7.049 C-C stretch 4 C - C stretch 6.054 6.300 6.725 5 6.784 C-C stretch 6.046 6.325 6 C-C stretch 7.371 6.586 6.897 7 7.235 C-CN stretch 5.334 5.561 19.19 8 20.02 19.29 C=N stretch 9 0.457 0.499 0.494 C-H in-plane bend 10 C-H in-plane bend 0.443 0.484 0.476 11 C-C in-plane bend 1.212 1.194 1.020 12 0.783 0.815 C-CN in-plane bend 0.722 CEN in-plane bend 13 0.404 0.312 0.448 A2 Species 14 C-CN out-of-plane bend 0.359 0.354 0.342 C-H out-of-plane bend 0.341 0.344 0.341 15 C-H out-of-plane bend 0.307 0.305 0.304 16 0.333 0.326 17 C-C out-of-plane bend 0.192 0.276 0.270 18 C-C out-of-plane bend 0.174 0.422 0.469 0.296 19 C=N out-of-plane bend B1 Species 20 0.428 0.379 0.383 C-CN out-of-plane bend 21 C-H out-of-plane bend 0.308 0.290 0.288 22 0.345 0.332 0.332 C-H out-of-plane bend C - C out-of-plane bend 23 0.181 0.280 0.279 24 0.420 C-N out-of-plane bend 0.460 0.293 B2 Species 25 5.451 5.344 5.364 C-H stretch 26 5.467 5.335 5.348 C-H stretch 27 7.692 C-C stretch 7.016 7.308 C-C stretch 28 7.840 7.114 7.431 C-CN stretch 29 7.153 5.314 5.564 19.19 30 20.00 19.26 C=N stretch 0.487 0.498 0.493 C-H in-plane bend 31 0.459 32 0.497 0.493 C-H in-plane bend 1.220 1.212 C-C in-plane bend 0.962 33 1.240 1.217 1.032 34 C-C in-plane bend 0.674 0.701 C-CN in-plane bend 0.590 35 0.402 0.294 0.438 36 C=N in-plane bend See footnotes of Tables VI-VIII. The numbering corresponds to the coordinates defined in Table I. TABLE X Scaling Factors Applied to the 6-316 Force Field of Phtbalonitrile coordinates' description factor 1,2,25,26 C-H stretching 0.82 3,4,5,6,27,28 C-C stretching 0.79 7,29 C-CN stretching 0.85 8,30 C-N stretching 0.75 9,10,3 1,32 C-H in-plane bending 0.80 11,33,34 C-C in-plane bending 0.78 12,35 C-CN in-plane bending 0.78 13,36 C-N in-plane bending 0.90 15,16,21,22 C-H out-plane bending 0.67 17,18,23 C-C out-plane bending 0.63 14,20 C-CN out-plane bending 0.75 19,24 C-N out-plane bending 0.85 The numbering corresponds to the coordinates defined in Table I. interaction force constant in both A1 and B2 species is surprising, indicating that the nitrile group is scarcely conjugated with the aromatic ring. The specific correction for the v(CN) force constant reduces the calculated-bserved difference to 2 cm-1 for the symmetrical vibration, and we obtain a corresponding diagonal force constant of 17.02 mdyn/A. This value is close to those reported for aliphatic nitriles, about 17-1 8 mdyn/A.30J1 In addition, the coupling between this coordinate and the ring modes is very small (0.105 mdyn/A, thegreatest absolutevalue); previous data reported on benzonitrile2' agree well with the small

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

10567

TABLE XI: Experimental and 6-31C Frequencies (cm-1) for Phthalonitrile (Refined Scaling) vibra- frequency exp c a b assignmentb PEDC(greater than 10%) A I Species

v35

Y36

3080 3041 2232 1573 1485 1228 1206 1155 1038 706 563 473 148

3087 3069 2234 1573 1492 1221 1205 1151 1023 698 568 480 121

944 885 739 364 120

967 868 749 539 356 104

928 769 525 381 175

934 748 537 365 162

3105 3029 2232 1590 1447 1296 1182

3078 3158 2232 1603 1452 1291 1181

1095 1090 807 803 610 620 414 413 201 201

2 20b C N vibration 8a 19b 14

99v(CH) 100v(CH) 87v(CN), 14v(C-CN) 76v(CC), 206(CH), 126(CC) 56v(CC), 366(CH) 76v(CC), 296(CH) 7a 40v(CC), 31v(C-CN), 226(CH) 15 626(CH), 34v(CC) 18b 65v(CC), 626(CH) 1 416(CC), 29v(CC), ~OY(C-CN) CN vibration 256(CN), 236(C-CN), 156(CC) 6a 326(CC), 286(CN) 9a 636(C-CN), 456(CN) A2 Species 5 99r(CH), 27y(CC) 10b 78y(CH), lSy(C-CN) 4 5 3y( C-CN), 16y( CC) 16a 54r(CC), 18y(CN), 12y(CH) C N vibration 5Oy(CN), 24y(CC), 15y(C-CN) 17a 80y(CC), 25y(CN), 13y(C-CN) B1 Species 10a 86r(CH), 26y(CC) 11 877(CH) 16b 45y(C-CN), 35y(CN) C N vibration 52y(CC), 25y(CN) 17b 5 37( C-CN) ,33y(CN), 2 1y (CC) B2 Species 20a 100v(CH) 7b 1OOv(CH) C N vibration 87v(CN), 14v(C-CN) 8b 8Ov(CC), 266(CH), 126(CC) 19a 64v(CC), 416(CH) 3 716(CH), 21v(CC) 13 21v(C-CN), 276(CC), 216(CH), 2Ov(CC) 9b 346(CC), 316(CH), 20v(CC) 12 626(CC), 25v(C-CN) CN vibration 356(C-CN). 296(CNI 6b 606(CC), 1 8 6 ( C k N j 18a 666(CN), SOS(C-CN)

a Frequencies obtained by using the scaling factors listed in Table X. Wilson nomenclature.21 Y = stretching; 6 = in-plane bending; y = out-of-plane bending.

interaction found here between the benzene ring and the nitrile groups, supporting the above discussion. The C-H stretching force constants in phthalonitrile do not differ appreciably from the values of the benzene molecule,2* for which 5.218 and 5.156 mdyn/A are reported corresponding to the symmetrical, Al, and the antisymmetrical, BI,nondegenerate v(CH) force constants, respectively. The values obtained in this work, 5.178 (AI) and 5.167 (Bz), are close to those of benzene. Besides, the symmetrical v(CH) force constant is slightly greater than the antisymmetrical one, following the aforementioned trend. Interactions involving the v(CH) modes are also very small, and only the v(CH)/G(CC) force constants are greater than 0.100 mdyn/A in both Al and B2 species. D. Infrared Absorption Intensities. In addition to force constants, normal coordinates, and vibrational frequencies, infrared absorption intensities for the normal modes of phthalonitrile have been obtained from the dipole moment derivatives. The whole set of calculated values is listed in Table VIII, whereas Figure 5 displays a comparison between the observed infrared spectrum and the theoretical nonscaled 6-3 1G spectrum. In spite of the fact that calculated frequencies show typical deviations, it is not difficult to correlate them with experimental bands. As we can see in Table VIII, the theoretical spectrum satisfactorily predicts most of the observed absorptions, and the intensity data

10568 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

L6pez Navarrete et al.

TABLE XII: Scaled 6-316 Force Field’ for the Pbthalonitrile Molecule (Force Constants in mdyn/&. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

no. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 a

1

2

3

4

5

6

8

7

9

10

11

5.176 0.013 5.181 -0,016 -0.025 6.129 0.026 -0.026 0.988 5.856 0.036 0.054 -0.732 1.147 5.878 -0.003 0.086 0.419 -0.747 1.029 6.410 0.012 0.006 0.468 0.330 -0.076 -0.078 5.561 0.006 0.004 -0.105 -0.040 0.000 -0.012 0.043 17.02 0.004 0.000 0.012 0.167 -0.140 -0.017 -0.003 0.005 0.527 -0,012 0.009 -0.029 0.031 0.150 -0.220 0.009 0.003 0.017 0.508 -0.113 0.055 -0.181 0.219 0.130 -0.256 0.172 0.014 -0.005 0.093 1.242 -0.020 0.006 -0.425 0.206 0.051 -0.002 -0.001 0.019 -0.010 0.008 0.055 -0.001 0.002 0.005 0.015 0.005 -0.016 -0.004 0.011 0.000 0.003 0.035

12

13

14

15

16

17

18

19

A1

0.847 0.054 0.375 0.366 -0.032 0.327 -0.007 0.030 0.291 A2 0.033 0.029 -0,033 0.293 0.034 -0.009 0.027 0.000 0.243 -0.024 0.010 0.001 0.034 0.028 0.359

20

21

22

0.410 -0,006 0.276 -0.053 -0.007 0.318 -0.019 0.034 -0.016 -0.039 -0.005 0.008

23

24

25

26

27

28

29

5.174 0.009 0.055 0.072 -0.003 -0,001 0.004 -0.001 -0.119 -0.002 0.011 -0.002

5.159 0.014 0.064 -0.004 -0.002 0.012 -0,003 0.122 -0.102 -0.006 -0.001

6.793 0.266 -0,369 0.094 0.207 -0.007 0.025 -0.222 -0.249 -0.018

6.907 -0.032 -0.042 -0,167 0.176 0.024 0.312 -0.003 0.004

30

31

32

33

34

35

36

B1 0.251 -0.014 0.355

5.564 0.036 16.99 0.022 0,001 -0,009 -0.003 -0.313 -0.024 -0.298 -0.036 -0.014 0.001 -0.004 0.024

B2 0.526 -0.001 0.526 -0.001 0.001 1.261 -0.101 0.052 0.034 1.266 -0.009 -0.010 0.000 0.047 0.729 -0.005 -0.004 -0.001 0.015 0.082 0.353

Scaled factors from Table X. See Table I for numbering.

are good compared with those reported for related molecules, as is discussed below. Three u(CH) modes are expected to appear with a medium relative intensity, and only the 7b mode is calculated as a very weak infrared band, all of which agree with the experimental results (Figure 4). The calculated u(CN),A, intensity, 28.7 km/ mol, is very close to the value reported for the same vibration type in ben~onitrile,~’ namely, 28.2 km/mol from a scaled 4-21G basis set. The u(CC) stretching vibrations also compare satisfactorily with those of benzonitrile, their intensities being 0.6 (1.3), 0.9 (2.8), 18.8 (25.5), 11.6 (11.2), and 6.3 (9.0) km/mol for the modes8a,8b, 19b, 19a,and 14,respectively,in the Wilsonnotation (the values in parentheses corresponding to phthalonitrile molecule, Table VIII). The intensities for the in-plane bending modes correspond to the observed infrared bands with some exceptions. As an example, the vibration 15,6(CH) was not observed in the infrared spectrum; in spite of this, the theoretical intensity was 6.6 km/mol. The calculation predicts the most intense infrared absorption as being assigned to the 1 1,y(CH) vibration, although the obtained value, 92.4 km/mol, is rather overestimated compared with the reported one for ben~onitrile,~~ 54.4 km/mol, and with the observed relative intensity in the spectrum (Figure 4).

great helpin thediscussionof the assignments. Inorder to properly interpret the polarized spectra, a powder X-ray diffraction study was previously performed, reporting also here the lattice parameters. The results confirm the possibility of observing and interpreting intensity changes in the polarized micro-Raman spectra, using microcrystals without previously known orientation. Quadratic force field calculations using semiempirical MNDO and ab initio methods, at the 3-21G and 6-31G levels, have been obtained and compared. Previous optimized geometries were required, and the resulting structures do not differ appreciably from the experimental values. Theoretical frequencies and normal coordinates have supported our previous assignments, the best results being the ones from the more extended 6-3 1G basis set of the ab initio calculations. The force field obtained from the highest level of calculation was scaled using a set of optimized scaling factors, and the new set of theoretical frequencies reproduced the experimental values with differences lower by f 10 cm-l in most of cases; in addition, the corresponding diagonal and off-diagonal force constants were compared favorably with previous data reported for related molecules. Finally, the infrared intensities were also evaluated at the 6-3 1G level, and a satisfactory comparison with the experimental spectrum was done.

Conclusions The infrared and Raman spectra of phthalonitrile in the solid state have been recorded, and a general assignment of its fundamentals has been proposed. We have also recorded the polarized Raman spectra for microcrystals, and the predominant orientations have been inferred from the observed intensity changes and the factor group analysis, both of them being of

Acknowledgment. We wish to thank Prof. P. Dhamelincourt for extending research facilities at Laboratoire de Spectrochimie Infrarouge et Raman of the University of Lille (France), where the micro-Raman experimental work was carried out. F.J.R. is grateful to the Consejeria de Educacibn of the Junta de AndalucIa (EspaAa) for financial support.

Structure Analysis of 1,2-Dicyanobenzene

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10569 (3) Arenas, J. F.; Marcos, J. I.; Ramlrez, F. J. Spectrochim. Acta 1988, 44A, 1045. (4) Arenas, J. F.; Marcos, J. I.; Ramlrez, F. J. Can. J . Spectrosc. 1989,

1 . go r

400

I

1

2

.

o

,

o

. l

,

u

mvrrwr

o

.

#

o

d

m

~

(cn.9

Figure 5. Comparison between the experimental infrared spectrum (bottom) and the theoretical nonscaled 6-3 1G infrared intensities (top) of phthalonitrile.

References and Notes (1) Fogarasi, G.; Pulay, P. In VibrationalSpectra andStrucrure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1985; Vol. 14, pp 125-219. (2) Turrell. G. Infrared and Raman Spectra of Crystals; Academic Press: London, 1972.

34, I. (5) Arenas, J. F.; Marcos, J. I.; Ramlrez, F. J. Appl. Spectrosc. 1989, 43, 118. (6) Arenas, J. F.; Marcos, J. I.; Montafiez, M. A,; Ramlrez, F. J. Appl. Spectrosc. 1990, 44, 660. (7) Ramlrez. F. J.: L6mz Navarrete. J. T. Vib. Soectrosc. 1993.4. 321. (8) Barraclough, C. G:; Bissett, H.; Pitman, P.;Thistlewaite, P. J. i u s ? . J . Chem. 1977, 30, 753. (9) Castro-Pedrozo, M. C.; King, G. W. J . Mol. Spectrosc. 1978, 73, 386. (10) Delhayt, M.; Dhamelincourt, P. J. Raman Spectrosc. 1975, 3, 33. (1 1) Diehl, P.; Amrein, J.; Bosiger, H.; Moia, F. Org. Magn. Reson. 1982, 18, 20. (12) Hehre, W. J.; Radom, L.; Schleyer, P. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (1 3) Biarge, J. A.; Herranz, J.; Morcillo, J. An. R. Soc. Esp. Fis. Quim., Ser. A 1961, 57, 81. (14) Dewar, M. J. S.;Thiel. W. J. Am. Chem. Soc. 1977, 99.4899. (15) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. Soc. 1979, 101, 2550. (16) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J . Am. Chem. Soc. 1983, 105, 7037. (17) Wilson. E. B. J. Chem. Phvs. 1939. 7. 1047. (18) Werner, P. E. Z . Krystallogr. 1969, Z20, 375. (19) Wolff, P. M. J . Appl. Crystallogr. 1968, I , 108. (20) Smith, G. S.; Snyder, R. L. J . Appl. Crystallogr. 1979, 12, 60. (21) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955. (22) Mulliken, R. S.J . Chem. Phys. 1955, 23, 1997. (23) Varsanyi, G. Vibrational Spectra of Benzene Derivatives; Academic Press: New York, 1969. (24) Green, J. H. S.;Harrison, D. J. Spectrochim. Acta 1976,32A, 1279. (25) Colombo, L.; Volovsek, V.; LePostollec, M. J. Raman Spectrosc. 1984, 15, 252. (26) Green, J. H. S. Spectrochim. Acta 1970, 26A, 1913. (27) CsBszBr, A. G.; Fogarasi, G. Spectrochim. Acta 1989, 45A, 845. (28) Pulay, P.; Fogarasi, G.; Boggs, J. E. J. Chem. Phys. 1981,74,3999. (29) Kakitani, T. Prog. Theor. Phys. 1974, 51, 6561. (30) Needham, C. D.; Overend, J. Spectrochim. Acta 1966, 22, 1383. (31) Duncan, J. L.; McKean, D. C.; Tullini, F.; Nivellini, G. D.; Pefia, J. P. J. Mol. Spectrosc. 1978, 69, 123.