Ab initio quantum chemical calculations of geometry and vibrational frequencies of chlorine heptoxide

SPECTROCHIMICA ACTA PART A

ELSEVIER

Spectrochimica Acta Part A 51 (1995) 2453-2458

Ab initio quantum chemical calculations of geometry and vibrational frequencies of chlorine heptoxide S. P a r t h i b a n a, B . N . R a g h u n a n d a n

a,,, R . S u m a t h i b

" Department of Aerospace Engineering, Indian Institute of Science, Bangalore-560 012, India b Department ok/ Inorganic and Physical Chemistry, Indian Institute o]" Science, Bangalore-560 012, India

Received 16 May 1995; accepted 30 June 1995

Abstract

Ab initio force fields for the vibrations of C1207 in its ground electronic state have been determined at the Hartree-Fock level using the 6-31G* basis set. The calculated geometries of C1207 at HF/6-31G* and MP2/6-31G* have been compared with the corresponding X-ray crystallographic structure. The calculated vibrational frequencies of C1207 are discussed in comparison to those determined from experiment and to the corresponding quantities for some similar molecules of the type CIO3-O-X (X is F, Cl, Br, H).

1. Introduction

The abundance of chlorine oxides in the Antarctic stratosphere, and their direct link to the destruction of ozone there, has led to significant research activity on the theoretical studies of these species [1-3]. Sander et al. [4] and Anderson et al. [5] have proposed that higher oxides of chlorine such as CIO3, C1203, C1204, C1206 and C1207 may be formed when the concentrations of CIO, C120 and OC10 are elevated. These higher oxides could be important if they are produced in sufficient amounts to act as temporary or long-term chlorine reservoirs or if they engage in 03 destruction cycles. Considering the importance of the higher oxides of chlorine, recently, an extensive and systematic ab initio calculation on CI206 [6] has been carried out. The present work constitutes the second phase of the program and deals with the structure and vibrational frequencies of C1207. Fonteyne [7] reported the Raman spectrum of C1207 and established that the molecule consists of two CIO 3 groups linked by a non-linear oxygen bridge. Several studies [8-10] have confirmed this, but have disagreed as to the orientation of the C103 groups. Savoie et al. [8] proposed a C2v symmetry for C1207 based on IR spectrum. Alternatively, Akishin et al. [9] suggested a Cs structure based on their electron diffraction study. Later, Beagley [10] showed that each of the CIO 3 groups is staggered by 15° about the three fold axis of the other and possesses a C2 symmetry. A recent X-ray diffraction study [11] has confirmed the C2 symmetry and showed that the molecule possesses two corner-sharing CIO 4 tetrahedra. As far as the assignment of vibrational frequencies is concerned, several IR studies [7,8,12] on ClzO 7 have been done. In these studies, however, the C I - O - C 1

* Corresponding author. 0584-8539/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved S S D I 0584-8539(95)01516-7

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S. Parthiban et al./Spectrochimica Acta Part A 51 (1995) 2453-2458

bending mode was not observed due to its low frequency. Later, Witt and Hammaker [13] have recorded the IR and Raman spectra of vapor, liquid and solid phases of C 1 2 0 7 to assign the skeletal bending mode. Although the crystal structure and vibrational spectra of C 1 2 0 7 a r e known, so far no quantum chemical calculations have been performed o n C I 2 0 7. In recent years, reliable prediction of the vibrational spectra using ab initio molecular orbital theory has proven to be useful. Therefore, in an attempt to resolve the uncertainties about the molecular structure and to assign the vibrational spectra of C 1 2 0 7 , ab initio calculations on C1207 at HF/6-31G* level have been performed. The vibrational frequencies have been calculated for the optimised structure. The structure has been further optimised at the correlation level. The structural parameters and vibrational frequencies are then compared with the available experimental data.

2. Ab initio calculations

Hartree-Fock self-consistent field (HF-SCF) molecular orbital calculations were performed using the quantum chemistry program GAUSSIAN92 [14] with split valence basis set, 6-31G*. The requested HF convergence on the density matrix w a s 10 - 9 units and the threshold value of maximum displacement was 0.018 deg/~ and that of maximum force was 0.00045 hartree bohr -1. The optimised geometries have also been computed with corrected second order M~ller-Plesset (MP2) perturbation theory. Vibrational analysis at the HF/SCF level often yields too high vibrational frequencies due to neglect of the influence of dynamic correlation. This can only be helped by using methods which go beyond the HF limit, such as MP2, MCSCF or CI methods, but such calculations are extremely resource demanding for larger molecules. Therefore in the present study, the vibrational analysis have been done with the unscaled force constants obtained at HF/6-31G* level.

3. Normal coordinate analysis

For the normal coordinate analysis, the force field in Cartesian coordinates was calculated by GAUSSIAN92 program with the 6-31G* basis set. The following procedure was used to transform the ab initio results which are in terms of cartesian coordinates. The cartesian coordinates obtained for the optimised structures were input into the B-MATRIX program [15] together with the complete set of internal coordinates. This complete set of internal coordinates was then used to form the symmetry coordinates with no zero frequency redundancies in accordance with the general standards and are shown in Table 1. The output of the B-MATRIX program consists of the B-MATRIX elements and was used to convert the ab initio force fields in cartesian coordinates to force fields in the desired internal and symmetry coordinates. The force field in symmetry coordinates, Fs, was obtained by the transformation matrix A, which corresponds to M-1RttT,-~ - - --sym • These symmetrised force fields were then used as input along with the G-symmetric matrix (Gsym) in the normal coordinate analysis program. The secular equation IGF-121= 0 was then solved using unscaled force constants to obtain vibrational frequencies along with potential energy distributions for C 1 2 0 7.

4. Results and discussion

Because the IR [13], X-ray [11] and electron diffraction [10] studies have confirmed that the C1207 molecule possesses two C103 groups bonded through a nonlinear oxygen bridge, we have not considered the other possible connectivities of the atoms in C 1 2 0 7. To start with, we have considered 6"2 and C2v symmetry for C1207 structure. The energy

s. Parthiban et al./Spectrochimica Acta Part A 51 (1995) 2453-2458

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d i f f e r e n c e b e t w e e n t h e s e t w o c o n f o r m e r s a t b o t h t h e S C F a n d t h e c o r r e l a t e d levels is n o t s i g n i f i c a n t ( < 1 k c a l m o l ~). H o w e v e r , t h e v i b r a t i o n a l f r e q u e n c y c a l c u l a t i o n s a t H F / 6 3 1 G * level s h o w e d o n e i m a g i n a r y f r e q u e n c y f o r t h e C2~ s y m m e t r y , s u g g e s t i n g t h e s t r u c t u r e t o b e a s a d d l e p o i n t r a t h e r t h a n a t r u e m i n i m u m . T h e r e f o r e in t h e p r e s e n t s t u d y we h a v e c o n s i d e r e d t h e C~ s y m m e t r y f o r C 1 2 0 7 s t r u c t u r e .

4. 1. S t r u c t u r e T h e o p t i m i s e d C2~ a n d C2 s t r u c t u r e s o f C 1 2 0 7 a l o n g w i t h t h e i r o p t i m i z e d b o n d l e n g t h s , bonds angles, dihedral angles and absolute energy values calculated at HF/6-31G* and M P 2 / 6 - 3 1 G * a r e s h o w n in Fig. 1. A s c a n b e seen, t h e r e is n o a p p r e c i a b l e c h a n g e in b o t h the structural and energy parameters of these two conformers. X-ray diffraction studies [11] h a v e s h o w n t h a t t h e C 1 0 b o n d d i s t a n c e s a r e 1.723 A f o r b r i d g i n g O a t o m a n d [ . 4 1 6 A ( a v e r a g e d ) f o r t h e t e r m i n a l a t o m s . T h e p r e s e n t l y c a l c u l a t e d v a l u e s o f t h e fully o p t i m i s e d s t r u c t u r e ((72 s y m m e t r y ) a r e in g o o d a g r e e m e n t w i t h t h i s o b s e r v a t i o n . C a r e f u l e x a m i n a t i o n o f t h e Fig. l b r e v e a l s t h a t b o n d s b e t w e e n t h e CI a t o m s a n d t h e t e r m i n a l a t o m s , w h i c h lie in t h e a p p r o x i m a t e C 1 - O - C I plane, are slightly shorter than those b e t w e e n t h e C1 a t o m a n d t h e r e m a i n i n g t e r m i n a l O a t o m s . F u r t h e r , it is i n t e r e s t i n g t o n o t e t h a t t h e s t r u c t u r a l b e h a v i o u r o f C1~O7 r e s e m b l e s t h a t o f M n 2 0 7 [16]. H o w e v e r , t h e O M n -O a n g l e s in M n 2 0 7 v a r y f r o m 107.8 ° t o 111.3 ° a n d h e n c e , t h e l a r g e s t d e v i a t i o n o f t h e a n g l e s a t M n f r o m i d e a l t e t r a h e d r a l is 1.8 °. I n c o n t r a s t in t h e C 1 2 0 7 m o l e c u l e a n g l e s v a r y b e t w e e n 99.2 ° a n d 115.2 ° a t H F level a n d 97.4 ° a n d 115.8 ° a t M P 2 level. T h i s a g a i n is in g o o d a g r e e m e n t w i t h c r y s t a l l o g r a p h i c d a t a [11] o f C1207 ( t h e a n g l e s v a r y b e t w e e n 98 ° a n d 116°). T h e s t r u c t u r a l d e t a i l as well as t h e l a r g e C 1 - O d i s t a n c e s f o r t h e b r i d g i n g a t o m p r o v i d e s e v i d e n c e o f h i g h l y p o l a r b o n d i n g in t h e s e n s e o f t h e f o r m u l a t i o n ( C 1 0 ~ ~ ) 2 0 2'~ . T h e d e l t a v a l u e w a s f o u n d t o b e 0.35 a n d 0.38 a t M P 2 / 6 - 3 1 G * a n d

Table I Symmetry coordinates and calculated frequencies of C 1 2 0 7 distributions

at

H F/6-31 G* level along with their potential energy

No.

Coordinate

Calcd. freqs in cm-~

Expt. freqs ~' in cm

Potential energy distribution

S; S,

1383.9 1341.7 1129.4 819.6 553.4 604.9

1300 1300 1060 704 567 600

90% 91% 91% 41% 34% 87%

715.6 324.6 316 167.4 53.7 1371.4 1352.3 1078.9 752.8 582.5 636.6

512 283 283 154

S~7

2r~ -- r4 -- r 5 + 2r6 - r v - r 8 r4 r 5 + r 7 - r ~ r~ + r 4 + r s + r6 + r 7 4- r8 r~ + r 2 2 4 ~ - - 4 3 - - ~4 4- 2~8 -- :% -- ~"; ~ + 44 + ~9 - ~m :~5 + 4~,+~7--3¢2--z¢3--~4+ ~ + ~12 + ~13 + ~ t ~ - ~ s - ~ 9 - ~lo 4~, - 47 + ~12 - ~13 2 ~ - % - z~7 + 2~1 - ~t2 - ~13 ~1 rt + r2 2r~ - - r 5 - 2 r 6 4- r 7 4- r 8 r~ - r 5 - r 7 4- r 8 r~ + ra + r5 - r6 - r7 - - r8 r~ r2 2 ~ . - - ~ 3 - ~ 4 - - 2~8 + ~9+ ~10 4~ - ~4 - ~9 + 410

Sis

4 5 + ~ 6 + ~ 7 - - °~2 - - g¢3 - - ~ 4 - -

SI,~ S~,

~ - ~ 2 - ~13 + ~8 + ~9 + ~lO :% - ~7 - ~1~ + zq3 2:% - :% - ~7 -- 2 ~ + ~ z + ~l~

$21

r I -

S3

$4 S~

S~, $7 $8 S,~ S I~ $1~ S~2 S~ $14 S;s SI~,

r2

466.1 466 304.20 86.9

~' Experimental frequencies are quoted from Ref. [13].

1300 1300 1025 698 571 600 488 488 272

St S2 S~ $4~.-30% S7 S 5 + 44% S 4 S 6 -[- 11% S 5

45% $7+ 21% Ss 100% S 8 68% $9 + 9°/,, $4 79% Sio + 17% S 5 91% SII 53% $12 + 44% 53% $13 + 44% Si, 98% S14 81% SI5 71% SI6 + 18% St5 70% SI7 + 15% $2o 95% St8 100% SI9 71% S.,o + 14% Sly 96% S_~I

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S. Parthiban et al./Spectrochimica Acta Part A 51 (1995) 2453 2458 (a)

(b)

01

05

01

05

~

09

06

TOlCttCt4 05 =0.0 (0.0) AbsOlute : -1442.0@757 ~O1 CI,2CI,4 06 = 122.6(t22.6) Energy (-1443.7306793) "~"01Ct2CL408 =-122.6(-122.6)

08

07

06

"JffOlCt2 Ct405 : - 4 6 . 2 ( - : ~ . 1 ) AbSolute :-1442.0664633 TOlCt2Ct406 = 83.0 ( 9 5 . 0 ) Energy (-1443.7308618) TOICL2Ct408 =-162.7(-150.5)

Fig. 1. Atom numbering schemeand optimizedparameters with absolute energyvalues of (a) C2~ and (b) C2 structures at HF/6-31G* level. The bond lengths and bond angles are given respectively in A and degrees. The numbers in parentheses refer to the results obtained at MP2/6-31G* level. HF/6-31G* levels respectively. The O 1 - C 1 2 - C 1 4 - O 5 dihedral angle at HF/6-31G* and MP2/6-31G* is 44.2 and 33.3 respectively, in contrast to the electron diffraction study [10] which showed that the C103 groups are staggered by 15°. 4.2.

Vibrational assignments

For the C2 structure of C1207, the 3 N - 6 = 21 normal modes of vibration can be classified as 11 of A and 10 of B symmetry, and all of them are active in IR and Raman spectra. Witt et al. [13] have earlier proposed the vibrational assignments for C1207based on experimental frequencies with relative intensities, depolarisation values and band contours. The ab initio calculated vibrational frequencies of C1207 along with the experimental assignments and potential energy distributions are given in Table 1. It can be seen that the calculated vibrational frequencies are in reasonable agreement with experimental values, though the calculated frequencies are slightly larger than experimental frequencies. Fig. 2 defines the internal coordinates for C1207, and the symmetry coordinates generated from these internal coordinates are listed in column 2 of Table 1. A careful examination of Table 1 reveals that the symmetry coordinates are described in terms of in-phase and out-of-phase motions of two C103 fragments and the skeletal bending mode. Basically, the C103 fragments in C 1 0 3 - O - X (X is H, F, Br, CI, C103) has antisymmetric and symmetric C103 stretches, antisymmetric and symmetric deformations and in-plane and out-of-plane C103 rocking vibrations. In this paper, an attempt has been made to compare the calculated frequencies of C1207 with the experimental frequencies of C I O 3 - O - X (X is H, F, Br, Cl, C103). The anti symmetric C103 stretching modes, Vl,~2 and Vz,~3are assigned to 1383v,,, 1371s, 1341 w and 1352s c m - i . Experimentally these modes appear to be degenerate and showed a strong band centered at 1300 c m - ~. The corresponding frequencies of similar molecules like FOCIO3 [17], C1OC103 [18], BrOC103 [18] and HOCIO3 [19] were found to be 1298,

~s at2~ a t ~

Fig. 2. Definition of internal coordinates for the C2 structure.

S. Parthiban et al./Spectrochimica Acta Part A 51 (1995) 2453 2458

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1287, 1279 and 1263 cm -l respectively. The calculated symmetric CIO 3 stretching vibrations, v3,~4are 1129 and 1079 cm-~ respectively while this mode has been assigned to the absorptions at 1060 and 1025 cm-~ in the vapour phase Raman and IR spectra of C1207. Correspondingly, the symmetric CIO 3 stretching frequencies of FOCIO 3, CIOCIO3, BrOCIO3 and HOC103 have been assigned to the peaks at 1049, 1040, 1039 and 1050 cm ~ respectively. Thus, the assignment of calculated stretching modes of CI20 7 are consistent with that of experimental values of similar molecules of the type C 1 0 3 - O - X (X is H, F, Br, C1, C103). It is worthy of mention that the calculated intensities of v3 (IR intensity: 24, Raman intensity: 31) and v~4 (IR intensity: 131, Raman intensity: 0.2) show an inverse relationship of calculated intensities in IR and Raman spectra and a similar observation was observed by Witt et al. [13]. There are four frequencies left for assignment to antisymmetric deformations of CIO~ group and their symmetry coordinates correspond to Ss, $6, SI6 and 517 (Table 1). At the split valence basis set level, there frequencies were calculated to occur at 553, 604, 582 and 636 cm l respectively. Experimentally, the corresponding vibrations have been assigned to absorptions at 567, 600, 571 and 600 cm -~ in which v6 and Vl7 were found to be degenerate. The calculated values are having a wider range in comparison to the observed values, it should be pointed out here that, in the literature, there had been a controversy in the assignment of the band at 600 cm 1. Beagley et al. [12] assigned this band to symmetric skeletal stretch, while Witt et al. [13] attributed this absorption to antisymmetric deformation on the basis of depolarisation ratio. The present results are in accord with the Witt et al. [13] assignments, and thus we attribute this absorption band to antisymmetric deformations. In the gas phase infrared spectrum [13], the in-phase and out-of-phase symmetric deformations, v7,j~ are experimentally assigned to a polarised band at 512 cm ~ and a strong band at 521 cm ~. From the table it can be noticed that there is a significant difference between the calculated and experimentally assigned normal frequency for this symmetric deformation. It may probably be due to the mixing of this vibration with other vibrations as revealed by the potential energy distributions. Ab initio calculations are in progress on FOC103, C1OC103, BrOC103 and HOCIO3 to investigate the corresponding vibration in these systems. The four rocking modes of C103 ($8, $9, S~9 and S:0) occur at 324, 316, 466 and 304 cm ~ while experimentally they have been assigned to bands at 283, 283, 488 and 272 cm ~ respectively in the vapour phase IR and Raman spectra. The calculated values are in close agreement with the experimentally observed frequencies. The slight deviation may be attributed to neglect of electron correlation effects and unscaled force constant matrix. Finally, the three fundamentals of C1-O-CI skeleton were found to absorb at 820cm ~ ($4), 167cm -~ (S~0) and 753cm ~ (S~5). The symmetric and antisymmetric skeletal stretches ($4 and S~5) show significant deviations from the experimental value. The experimental frequencies (704 and 698 cm -~) are much lower thereby suggesting a relatively long O C1 bond (lower force constant). Inclusion of the effects of electron correlation has brought about an elongation of all bonds in C1207. The extent of elongation is more for the skeletal C1-O bond (0.12 A) when compared to the terminal C1- O bonds (0.04 A). This suggests that the reason for the discrepancy could be due to the neglect of electron correlation. Furthermore, the symmetric skeletal bending mode and hence these shifts in frequencies are well expected. Inspection of Table 1 reveals that the antisymmetric skeletal stretching mode in C1207 is essentially a pure mode.

5. Conclusions

In this study, ab initio calculations of C120 7 have been performed at HF/6-31G* and MP2/6-31G* level. The theoretical calculations suggest a C2 symmetry for C120 7 molecule. Each C103 group in C120 7 is found to be staggered by 44.2 and 33.3 with

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respect to the three fold axis of the other group at HF/6-31G* and MP2/6-31G* level respectively. The vibrational frequencies are well predicted by the theoretical calculations performed at HF/6-31G* level. In general, the agreement between the experimental and calculated values from the unscaled force constant matrix is reasonably close.

Acknowledgements The authors thank the Supercomputer Education and Research Centre of Indian Institute of Science, Bangalore, India for providing the computer facilities. One of us (S.P.) acknowledges CSIR (Govt. Of India) for a senior research fellowship.

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[7] [8] [9] [10] [11] [12] [13] [14]

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