Molecular structure and energetics of sym-ClO3

14 November 1997

CHEMICAL PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 279 (1997) 158-164

Molecular structure and energetics of sym-C10 3 Margaret A. Workman, Joseph S. Francisco Department of Chemistry. and Department of Earth and Atmospheric Sciences Purdue UniversiO', West Lafayette, IN 47907-1393, USA

Received 7 July 1997; in final form 9 September 1997

Abstract The equilibrium structure, vibrational spectra and heat of formation for sym-ClO 3 have been investigated using high levels of ab initio theory. Methods include second-order M¢ller-Plesset perturbation theory (MP2) and singles and doubles coupled-cluster theory which incorporates a perturbational estimate of effects of connected triples excitation [CCSD(T)]. Two density functional methods were also investigated. At the highest level of theory, CCSD(T)/6-311 + G(3df)//CCSD(T)/6-311G(2df), the heat of formation for sym-CIO 3 is predicted to be 46.0_+ 3 kcal mol-I at OK. © 1997 Elsevier Science B.V.

1. Introduction It has been known for years that molecular oxygen inhibits the C12 sensitized photodecomposition of 0 3 [1]. Studies of Byrns and Rollefson [2,3] showed that this is due to involvement of CIO 3 in the reaction process. The reaction, which transforms active chlorine into an inactive form, was proposed as follows: C10 + 0 2 ~ C10

•0 2 .

(l)

In 1980, Prasad [4] proposed that C 1 0 . 0 2 species could be involved in stratospheric chemical reactions. If reactions involving C10 3 were included in atmospheric models of the stratosphere, Prasad found that it could resolve discrepancies between observed and theoretical values of the CIO mixing ratio. Prasad proposed that a CIO - 0 2 intermediate was the probable form of C10 3. In experimental studies that have examined the reaction of CIO with 0 2, the formation of a long-lived C10 - 0 2 intermediate has been sug-

gested [5]. Handwerk and Zellner [6] studied the reaction of ClO with 0 2 (lAg) and suggested that the formation of CIO 3 would be slow from the reaction because of the large barrier to its formation. Studies of Colussi et al. [7] and Gleason et al. [8] have provided indirect evidence for the existence of C10 3 from the reaction of atomic oxygen with OC10, viz. OCIO + 0 + M

~

CIO 3

+ M.

(2)

Rathmann and Schindler [9] found there are three possible CIO 3 isomers: (1) C1OOO; (2) OC1OO; and (3) sym-C10 3 structure that are bound at the second-order M ¢ l l e r - P l e s s e t perturbation theory (MP2) with the medium 6-31G(d) basis set. Using G I theory, Rathmann and Schindler [9] calculated the heat of formation at 0 K to be 41 kcal m o l - J for CIOOO, 58 kcal mo1-1 for OCIOO; and 48 kcal mol - l for sym-C10 3. However, there is a large discrepancy between the value for sym-CIO 3 from G I theory and that determined from thermochemical additivity (55.6 __+4 kcal mol - I ) [10]. Colussi et al.

0009-2614/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0009-26 14(97)01 033-6

M.A. Workman, J.S. Francisco/Chemical Physics Letters 279 (1997) 158-164 [7] later revised this value to 51.9 kcal mo1-1 . Rauk et al. [ 1 1] did a more complete ab initio study of the C103 potential energy surface. They found the only possible structure of C103 to be the symmetric, C3v structure. They predicted a heat of formation value even less than the previous studies, e.g. 47.3 kcal m o l - J using G2 theory. However, it was not until 1994 when the first experimental evidence for C10 3 was reported. Grothe and Willner [12] reported IR and a UV spectra of the C3v structure of CIO 3. They produced C10 3 by the pyrolysis o f chlorine perchlorate. However, there is some controversy as to whether the UV spectrum is really due to C10 3 or whether it can be attributed to Cl206. In the present work, the equilibrium structure, vibrational frequencies, and heat of formation of sym-C10 3 is examined with high levels of ab initio molecular orbital methods and density functional theory to evaluate the structure and the thermochemical stability of the symmetric C103 structure.

159

3. Results and discussion 3.1. Geometry and vibrational frequencies f o r symCIO 3 As a starting point, the four structures that Rauk et al. [11] found as minima on the R O H F / 6 - 3 1 G ( d ) potential energy surface were used to start optimizations of CIO 3 using increasing levels of theory. However, the only structural isomer we found to be stable and that would optimize at the higher levels of theory was the C3v symmetrical CIO 3, denoted symC10 3. The fact that the only structure that optimized at the higher levels of theory was the sym-C10 3 is very significant. This implies that the possibility of C10 3 existing as a C 1 0 . O 2 complex is very low. The optimized geometries for sym-C10 3 at various levels of theory are given in Table 1. The structure is illustrated in Fig. 1. At all levels of theory, the OC10 bond angle is estimated to range between I 14.0 and 114.8. At the best level of theory C C S D ( T ) / 6 311G(2df) the angle is 114.1 °. The CIO bond length has a large variation in the values with level of

2. Computational methods Calculations were performed using the G A U S S I A N 94 series of programs [13]. Geometry optimizations were carried out for all structures to better than 0.001 A for bond lengths and 0.1 A for angles. With a SCF convergence of at least l0 9 on the density matrix, the root-mean-square (rms) force was 10 4 atomic units. The geometries were fully optimized using Schlegel's analytical gradient method [14] with the second-order M ~ l l e r - P l e s s e t (MP2) method and B e c k e ' s exchange functional and LYP correlation functional (BLYP and B3LYP) methods. The Hessian from the MP2 calculations were used with either the F l e t h e r - P o w e l l or eigenvalue following algorithms at the couple cluster including singles, doubles excitations with perturbative corrections for the triples [CCSD(T)]. MP2 calculations were carried out with all orbitals active, but the frozen core approximation was used for all other levels. The following basis sets were used in the calculations, 6-31G(d), 6-31 1G(d), 6-311G(2d), 6-311G(2df), 6-311G(3df), and 6-311 + G(3df).

Table 1 Optimized geometric values and total energies for C3v sym-CIO3 Level of theory Parameter ~ Energy b C10

OC10

BLYP/6-31G(d) BLYP/6-311G(2d) BLYP/6-31 lG(2df) BLYP/6-311 + G(3df)

1.541 1.515 1.501 1.488

114.1 114.3 114.1 114.2

-685.50776 - 685.64149 -685.66186 - 685.69005

B3LYP/6-31G(d) B3LYP/6-311G(2d) B3LYP/6-311G(2df) B3LYP/6-311 + G(3df)

1.502 1.476 1.465 1.454

114.0 114.2 114.0 114.1

-685.51325 - 685.64513 - 685.66978 - 685.69737

MP2/6-31G(d) MP2/6-31 IG(2d) MP2/6-311G(2df) MP2/6-311 + G(3df)

1.483 1.461 1.445 1.436

114.6 114.8 114.6 114.7

-684.36907 - 684.61205 - 684.85796 - 684.94087

CCSD(T)/6-31G(d) CCSD(T)/6-311G(2d) CCSD(T)/6-31 lG(2df)

1.505 1.477 1.458

114.1 114.4 114.2

- 684.39899 - 684.64289 -684.76816

" Geometric parameters are in ~ngstriSm for bond lengths and degree for bond angles. b In units of hartree.

160

M.A. Workman. J.S. Francisco/Chemical Physics Letters 279 (1997) 158-164

Fig. I. Structural representation of sym-C103. Geometric parameters are from B3LYP/6-311 + G(3df) optimization while numbers in parentheses are from the CCSD(T)/6-311G(2dp) optimization,

theory and basis set. All levels of theory show basis set effects in the C10 bond distance. With the medium size 6-31G(d) basis set the C10 bond lengths are the longest. For example, at the CCSD(T)/6-31G(d) level the C10 bond is 1.505,~ but increase in basis set size and flexibility reduces the CIO bond length to 1.458A at the CCSD(T)/6-311G(2df). Results from previous density functional studies have shown that geometries from B3LYP/6-311 + + G(3df,3pd) optimizations are comparable to CCSD(T) results with large basis sets [15,16]. In fact a comparison between CCSD(T)/6-311G(2df) and B3LYP/6-311 + G(3df) optimized geometries for sym;ClO 3 shown the CIO bond lengths differ by 0.004A. BLYP results predict C10 bond lengths that are too long; while the MP2 levels predict bond lengths that are too short compared to the B3LYP and CCSD(T) results. Calculated harmonic vibrational frequencies for sym-C10 3 are listed for each correlated method in Table 2, along with the experimental frequencies from the work of Grothe and Willner [12]. Frequencies obtained at the MP2/6-311G(2d) level of theory over-estimate the frequencies for ul, u 2, and u 3

Table 2 Vibrational frequencies of sym-CIO3 Mode symmetry Modenumber Modedescription

modes. While the BLYP/6-311G(2d) level of theory underestimate all the frequencies. Both CCSD(T) and B3LYP frequencies calculated with the 6311G(2d) basis set are comparable. The rms errors are 7.0% and 6.9%, respectively. Vibrational frequencies calculated at the B3LYP/6-311 + G(3df) level of theory show the best agreement with the experimental observations of Grothe and Willner [ 12]. The rms error between theory and experiment is 4.1%. Detail descriptions of each of the normal vibrational modes of sym-C10 3 are shown in Fig. 2. 3.2. Heat o f formation f o r sym-ClO 3

In order to estimate the heat of formation for sym-C10 3. The following isodesmic reaction is used CI + CIO 3 ---) OCIO + CIO. An isodesmic reaction is one in which the number of each type of bond as well as the spin multiplicities are conserved in the reaction scheme. Listed in Table 3 are the total, zero-point, and thermal energies for species involved in the isodesmic reaction. From these energies, the heat of reaction for the above isodesmic reaction can be calculated. These are listed in Table 4. From these heats of reactions and known heats of formation of CI, C10, and OC10 (28.6 ___0.0, 24.2 + 0.5 taken from J A N A F [17], and 23.2 + 1.0 kcal m o l - l [18], respectively), the heat of formation for sym-ClO 3 can be calculated. The results can be seen in Table 5. The heat of formation calculated at the C C S D ( T ) / 6 - 3 1 1 + G ( 3 d f ) / / C C S D ( T ) / 6 311G(2df) level of theory is 46.0 kcal mo1-1. Note that at the CCSD(T)/6-311 + G ( 3 d f ) / / B 3 L Y P / 6 31 1 + G(3df) level of theory the heat of formation is only 0.1 kcal tool- 1 larger. The estimate of the heat

Frequencies (cm- i ) 6-311G(2d)

a~ a2 e

1 2 3 4

CIO symmetricstretch CIO3 symmetricdeformation C10 antisymmetric stretch C10 asymmetricdeformation

6-311 + G(3df)

MP2

BLYP

CCSD(T) B 3 L Y P B 3 L Y P expt.

978 577 1216 467

771 488 891 400

850 535 1016 445

865 534 1005 445

923 564 1080 471

905 567 1081 476

M.A. Workman, J.S. Francisco / Chemical Physics Letters 279 (1997) 158-164

Mode 1 : CIO symmetric stretch

161

Mode 2 : C I O 3 symmetric deformation

Mode 3: CIO antisymmetric stretch

Mode 4 : C 1 0 asymmetric deformation

Fig. 2. N o r m a l v i b r a t i o n s for s y m - C I O 3.

of formation for sym-C103 is 46.0 kcal mol- 1 at 0 K and 44.6 kcal mol-1 at 298 K. Using thermochemical additivity Colussi [10] estimated the sym-C103 heat of formation at 298 K to be

55.6 kcal mol -l . This value was later revised to 51.9 kcal mol-l [7]. This revised value was derived from the analysis of kinetics data from the study of the temperature dependence of the reaction between

Table 3 T o t a l e n e r g i e s a o f s p e c i e s u s e d in the i s o d e s m i c r e a c t i o n L e v e l o f theory

CI

C10

OC10

B 3LYP/6-31G(d)

- 460.13624

- 535.29227

- 610.41726

- 685.51325

B3LYP/6-311G(2d)

- 460.16633

- 535.34856

- 610.51183

- 685.64513

B3LYP/6-311

- 460.16841

- 535.36509

- 610.54931

- 685.69737

CCSD(T)/6-31G(d)

- 459.57048

- 534.54274

- 609.48480

- 684.39899

CCSD(T)/6-311G(2d)

- 459.62456

- 534.65076

- 609.65971

- 684.64289

CCSD(T)/6-311G(2df)

- 459.65734

- 534.71024

- 609.75190

- 684.76816

+ G(3df)

CCSD(T)/6-311

C10 3

+ G(3df) b

- 459.66247

- 534.72878

- 609.78799

- 684.81350

CCSD(T)/6-31 l + G(3df) c

- 459.66247

- 534.72860

- 609.78784

- 684.81337

ZPE b

0

0.00196

0.00578

0.01046

t h e r m a l c o r r e c t i o n to e n e r g y b

0.00142

0.00439

0.00894

0.01407

a T o t a l e n e r g i e s in hartree. h C a l c u l a t e d w i t h the B 3 L Y P / 6 - 3 1 1

+ G(3df) geometry.

c C a l c u l a t e d w i t h the C C S D ( T ) / 6 - 3 1 1 G ( 2 d f )

geometry.

162

M.A. Workman, J.S. Francisco / Chemical Physics Letters 279 (1997) 158-164

Table 4 Heat of formation a for the C3~ sym-ClO~ radical from the isodesmic reaction C1 + C103 -* (OCIO + CIO Level of theory

CI + C103 ~ OCIO + C10

Sym-C103

AHr70

a HL~,,,

A/-/fo0

aHfo29~

B3LYP/6-31G(d) B3LYP/6-311G(2d) B 3 L Y P / 6 - 3 1 1 + G(3df)

- 39.4 - 32.4 - 32.2

- 39.0 - 32. l - 31.9

58.2 51.2 51.0

56.8 49.9 49.7

C C S D ( T ) / 6 - 3 I G(d) CCSD(T)/6-311G(2d) CCSD(T)/6-311G(2df) CCSD(T)/6-311 + G(3df) b CCSD(T)/6-311 + G(3df) ~

- 38.1 - 28.7 - 24.7 -- 27.3 - 27.2

- 37.8 - 28.4 - 24.4 -- 27.0 - 26.8

56.9 47.5 43.5 46.1 46.0

55.6 46.1 42.1 44.8 44.6

a In units of kcal m o l - J. h Calculated with the B 3 L Y P / 6 - 3 1 1 + G(3df) geometry. Calculated with the CCSD(T)/6-311G(2df) geometry.

atomic oxygen atoms and OCIO. 1UPAC reported a value for the heat of formation of 55.6 kcal m o l and is based on the unrevised Colussi [10] value [17]. The NASA94 compilation list a value of 52 _+ 4 kcal mol-J [19]. All these estimates for the 298 K value over-estimate the heat of formation of sym-C103. The theoretical estimate of Rauk et al. [11 ] based on a modified G2 calculation yield a value of 45.9 kcal mol-~. Our isodesmic heat of formation determination at the CCSD(T)/6-3I 1 + G(3df)//CCSD(T)/6-311G(2df) level of theory is consistent with the modified G2 estimate of Rauk et al. [11]. We did a G2 estimate of the heat of formation for sym-ClO 3 using standard G2 formation [20,21]. Our G2 estimate yields 51.7 kcal tool-~ for the OK value and 50.3 kcal tool -~ for the 298K value. This is 4.4 kcal mol-~ larger than the modified G2 estimate of Rauk et al. [11]. This large discrepancy between G2 values results from two sources that contribute to additive errors: (1) the poor description of geometry from the M P 2 / 6 3 l G(d) optimization which are used to calculate the G2 energies and (2) the poor representation of vibrational frequencies calculated at the Hartree-Fock level with the 6-31G(d) basis set. The thermochemistry data of Rauk et al. [11] is based upon G2 energy data and MP2/6-311G(2df) vibrational frequencies. The standard G2 formalism uses HF/6-31G(d) vibrational frequencies. One can see from calculations in the present study (Tables 1 and 2) that high-order electron correlation as well as large basis sets are

needed in order to get an adequate description of geometry and vibrational frequencies for sym-ClO 3. In the light of this discussion, the G1 estimates of the heat of formation for sym-ClO 3 by Rathman and Schindler [9] of 48 kcal mol-~, although in good agreement with our isodesmic value of 46.0 kcal mol- 1 value for 0 K, may be fortuitous. To check the plausibility of our result for the heat of formation for sym-ClO 3 we have used our value for the heat of formation for sym-ClO 3 to estimate the C1-O bond dissociation energy for C I 2 0 3 dissociating into CI + C I O 3. Using the AHf°o ( C 1 2 0 3) o f 38.2 kcal mol i [22] and AHI°o ( C l O 3 ) of 46.0 kcal mol - I , we obtain a D°(CI-O) of 36.4 kcal mol This is consistent with the estimate of D°(C1-O) of 37.7 kcal mol -~ obtained for the C I 2 0 3 stability study [22]. Another check is to use the C1-O bond dissociation energy estimated for sym-C103 of 35.1 Table 5 Comparison of the heat of formation for sym-C103 with literature values Sym-CIO 3

Re~

51.9 55.59 52.01 55.59 48 47.25 46.0

45.91 44.6

[7] [17] [19] [10] [9] [11] this work

M.A. Workman, J.S. Francisco/Chemical Physics Letters 279 (1997) 158-164

163

kcal mol-1 reported by Zabel [23], which compares well with the D°(C1-O) we calculate. From the Zabel result we can estimate the heat of formation of sym-C103 to be 48 kcal mo1-1 at OK. This is consistent with our estimate. To assess the uncertainty limits of the calculated heat of formation for CIO 3 at the CCSD(T)/6-311 + G(3df)//CCSD(T)/6-311G(2df) level of theory, we have examined the heat of formation of CIO and OC10 with the same level of theory. Results for the calibration calculations are given in Table 6. At the CCSD(T)/6-311 + G(3df)//CCSD(T)/6311G(2df) level of theory, the estimated heats of formation for CIO and OC10 are within 0.7 and 2.1 kcal mol -T, respectively of the experimental determinations. Therefore, a conservative estimate of the uncertainty limits of our determination for the heat of formation of CIO 3 is _+3 kcal tool 1

q-I

~. -. ~. ~. ca..

IIII I

©

E

+l ~-,i t"xl ~-.I t,-.i I

,¢

IIII

4. Conclusions High level ab initio electronic structure theory has been applied to sym-C103. The sym-ClO 3 molecule is found to be of C3v symmetry. The best estimate of the equilibrium geometry for sym-ClO 3 is: rclo = 1.458 A and 0oclo = 114.2 °. The heat of formation is predicted to be 4 6 . 0 _ 3 kcal mol -~ at OK and 44.6 ___3 kcal mol- 1 at 298 K.

~[.N~N

NNN I I I ¢0 q

¢'q

-- II

ddd z

o ~ 0

~ ,~. ~

+

~"

"-~+,6 [-

IIII

~d~.q

,

o,< o ~ L)

~++ + = = =

~e I-L)

.2

References

I I I I

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164

M.A. Workman, J.S. Francisco/Chemical Physics Letters 279 (1997) 158-164

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[16] B.S. Jursic, J. Chem. Phys. 106 (1997) 2555. [17] R. Atkinson, D.L. Baulch, R.A. Cox, J. Phys. Chem. Ref. Data 21 (1992) 1125. [18] S.L. Nickolaisen, R.R. Friedl, S.P. Sander, J. Phys. Chem. 98 (1994) 155. [19] W.D. DeMore, S.P. Sander, D.M. Golden, R.F. Hampson, M.J. Kurylo, C.J. Howard, A.R. Ravishankara, C.E. Kolb, M.J. Molina, Chemical kinetics and photochemical data for use in stratospheric modeling, Jet Propulsion Lab., Pasadena, CA, JPL Publ. 94-26. [20] L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople, J. Chem. Phys. 94 (1991) 7221. [21] J.A. Pople, M. Head-Gordon, D.J. Fox, K. Raghavachari, L.A. Curtiss, J. Chem. Phys. 90 (1989) 5622. [22] J. Clark, J.S. Francisco, J. Phys. Chem. (in press). [23] F. Zabel, Ber. Bunsenges. Phys. Chem. 95 (1991) 893.