- Email: [email protected]
Atmospheric reaction between the HS radical and chlorine
25 February 2000
Chemical Physics Letters 318 Ž2000. 340–344 www.elsevier.nlrlocatercplett
Atmospheric reaction between the HS radical and chlorine Stella M. Resende, Fernando R. Ornellas
)
Instituto de Quımica, Departamento de Quımica Fundamental, UniÕersidade de Sao ´ ´ ˜ Paulo, Caixa Postal 26077, Sao ˜ Paulo, SP, 05513-970, Brazil Received 16 November 1999; in final form 13 December 1999
Abstract The mechanism and the kinetics of the reaction between HS and Cl 2 leading to HSCl and Cl were studied theoretically. The effect of the complete basis set limit ŽCBS. was included by extrapolating the results obtained with cc-pVDZ, cc-pVTZ and cc-pVQZ correlation consistent basis sets functions. At the highest level of calculation, CCSDŽT., the calculated rate constant is 1.0 = 10y12 cm3 moleculey1 sy1. The activation Gibbs free energy was calculated to be 7.4 kcalrmol, which is only 0.2 kcalrmol above the value determined experimentally. The enthalpy and Gibbs free energies of the reaction are y6.9 and y6.5 kcalrmol, respectively. q 2000 Published by Elsevier Science B.V. All rights reserved.
1. Introduction Sulfur compounds are released into the atmosphere, in reduced and oxidized forms, by means of biogenic and anthropogenic sources w1x. The oxidation of sulfur reduced compounds plays a very important role in atmospheric processes, due to the fact that it leads to the production of SO 2 , which is oxidized to sulfuric acid in the troposphere. Sulfuric acid forms sulfur aerosol, and it is related to biological climate regulation w2x. Hydrogen sulfide, H 2 S, is a large source of sulfur in the atmosphere, and it is produced through both aerobic and anaerobic organic decomposition. The major tropospheric process that removes H 2 S is the reaction with OH, producing HS and H 2 O w3x. It was believed that all the HS generated is oxidized to SO 2 , in reactions with common tropospheric oxi) Corresponding author. Fax: q55-11-815-5579; e-mail: [email protected]
dants such as O 3 , NO 2 and O 2 , being thus completely consumed in the troposphere w4x. However, volcanic eruptions can inject sulfur compounds in the stratosphere in large amounts, and H 2 S seems to be the dominant sulfur species emitted in these situations w5x. In the stratosphere, reaction of HS with Cl 2 andror Cl may be important, leading to a coupling between chlorine and sulfur chemistries. It can also occur in extraterrestrial atmospheres where H 2 S is abundant, as that of Venus. Surprisingly, to the best of our knowledge, very little is known about this reaction, as well the mechanism, and the nature and structure of the products formed w6x. Studies of this type of reactions are certainly very important, since they can significantly contribute to a better understanding of the chlorine and sulfur atmospheric cycles. So far, the only study reported in the literature about the kinetics of the reaction between HS and Cl 2 is that of Nesbitt and Leone w7x, in which the authors have analyzed a laser-induced chemical chain reaction of the
0009-2614r00r$ - see front matter q 2000 Published By Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 0 1 9 - 1
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344
341
Cl 2rH 2 S system. They have obtained an average value of Ž1.36 " 0.2. = 10y1 2 cm3 moleculey1 sy1 for the rate constant of the reaction
Table 1 Harmonical frequencies calculated for all stationary points obtained at the UMP2rcc-pVTZ level of calculation Available experimental values are given in parentheses w10x
HS q Cl 2
HS
™ HSClq Cl .
Considering, on one hand, that all methods of study of the HS kinetics are susceptible to errors associated with secondary processes, which can lead to regeneration of the HS radical w3x, and, on the other hand, the high performance of present-day theoretical ab initio methods, it is our understanding that theoretical methods can be a valuable aid in the investigation of this kind of reactions, especially for systems of a few atoms. Therefore, our aim in this work is to present a detailed and very accurate investigation of thermodynamical properties and of kinetics data which can help us elucidate the mechanism of the above atmospheric reaction.
2. Calculation
Cl 2
577.6 Ž559.7. 2 765.1 Ž2 712.
Complex Transition HSCl state 54.7 58.6 66.4 176.6 552.9 2 760.4
450.0 i 153.2 255.9 420.0 653.9 2 759.3
554.9 927.7 2 753.5
parameters are given. In Table 1 are presented the harmonical frequencies calculated. Experimental values are available only for the reactants w10x. Using MP2rcc-pVQZ and CCSDŽT.rcc-pVTZ single-point calculations and the additivity approximation w11,12x, we have achieved the CCSDŽT.rcc-pVQZ level of theory, through the equation ECCSDŽT .r cc - pVQZ s ECCSDŽT .r co - pVTZ
Our calculations were performed with the GAUSSIAN w8x and the MOLPRO w9x packages of programs. The optimizations and harmonical frequency analysis w e re d o n e a t th e U M P 2 r D 9 5 Ž d , p . , UCCSDŽT.rD95Žd, p. and UMP2rcc-pVTZ levels of theory. Besides the reactants, products and the transition state, we have found a weakly bound complex between the reactants. The structures of all stationary points considered in this work are presented in Fig. 1, where the relevant geometrical
q Ž E MP 2 r co - pVQZ y EMP2 r co - pVTZ . .
Ž 1.
In order to obtain the limit for the basis set completeness, we have performed an MP2rcc-pVDZ single-point calculation, and used the approximation developed and tested by Dunning and co-workers w13,14x, which states that the dependence on basis set of several molecular properties, as the stabilization energy, is well represented by a simple exponential function in this form F Ž n . s A` y B exp Ž ycn . ,
Ž 2.
where n is the index of the basis set, and A` is the asymptotic limit for the function. The limiting value of this function provides an estimate of the complete basis set ŽCBS. limit. In our calculation, n ranged from 2 to 4, and the function extrapolated was the energy for every stationary point at the MP2 level. The values for the CCSDŽT.rCBS level of calculation were obtained through the following expressions ECCSDŽT .r CBS s ECCSDŽT .r cc - pVTZ q Ž EMP 2 r CBS y EMP2 r cc - pVTZ . . Fig. 1. Geometries and relevant geometrical parameters for the stationary points involved in the reaction between HS and Cl 2 , at the UMP2rcc-pVTZ level of theory. Available experimental values are given in parentheses w10x.
Ž 3. We have also included the effect of the core in the calculation of the electronic energy through an
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344
342
MP2Žfull.rcc-pVTZ single-point calculation. Using the additivity approximation again, we have obtained the values for the CCSDŽT, full.rCBS levels of calculation as ECCSDŽT ,full.r CBSs ECCSDŽT .r CBS q Ž EMP 2 Žfull.r ccypVTZ y EMP2 r ccypVTZ . .
Ž 4.
Finally, the rate constant for this reaction was calculated using conventional transition state theory ŽTST. w15x, and the possibility of quantum-mechanical tunneling was addressed by means of Wigners’ approach, which implies multiplying the TST rate constant by the factor below
Gs1q
1
hv
24 k B T
2
,
Ž 5.
where v stands for the absolute value of the imaginary frequency of the transition state of the reaction. 3. Results and discussion The energy values obtained with all approaches are presented in Table 2. The calculations at the MP2rcc-pVDZ, MP2rcc-pVQZ, CCSDŽT.rccpVTZ and MP2Žfull.rcc-pVTZ levels were performed with the geometry optimized at the MP2rcc-pVTZ level. The adjusted values for the CBS limit at the MP2 level are also in Table 2. In
Tables 3 and 4 are the relative energies and the thermodynamical properties, calculated at 298.15 K, for the formation of the weakly bound complex, and for the reaction, respectively. The rate constants calculated at the different levels of theory are also in Table 4, as well as the results for our highest-level calculations, obtained with the CBS limit. From Table 3, we can see that increasing the size of the basis sets leads to a higher stabilization of the weakly bound complex, whether at the MP2 or at the CCSDŽT. level. This behavior can also be observed in Table 4 for the activation energy results. In all cases, the MP2 values overstabilize the species relative to CCSDŽT.. It can also be noted that the values obtained for the formation of the weakly bound complex and those for the energy of the reaction are very small, showing that the convergence is reached with medium basis set functions as the cc-pVTZ one. For the weakly bound complex, our best value for the stabilization energy is y2.61 kcalrmol. All other results differ from this value by - 1 kcalrmol. The enthalpy variation is y2.0 kcalrmol, and the Gibbs free energy for this species is positive, but of a small value. For the products of the reaction, a similar behavior is observed. The reaction is spontaneous by y6.5 kcalrmol, and exothermic by y6.9 kcalrmol. Once again, the values obtained at several levels of calculation do not differ by more than 1 kcalrmol of the
Table 2 Calculated energies Žin hartree. and zero-point energies ŽZPE, in kcalrmol. for the species studied The optimizations were performed at the UMP2rD95Žd, p., UCCSDŽT.rd95Žd, p. and UMP2rcc-pVTZ levels
UMP2rD95Žd, p. PMP2rD95Žd, p. ZPE UCCSDŽT.rd95Žd, p. ZPE UMP2rcc-pVTZ PMP2rcc-pVTZ ZPE PMP2rcc-pVDZ a PMP2rcc-pVQZ a PMP2rCBSb CCSDŽT.rcc-pVTZ a PMP2Žfull.rcc-pVTZ a a b
HS
Cl 2
Complex
Transition state
HSCl
Cl
y398.17657 y398.17803 3.99 y398.19981 3.88 y398.25633 y398.25844 3.95 y398.20251 y398.27614 y398.28435 y398.28706 y398.29288
y919.17362
y1 317.35351 y1 317.35502 5.28 – – y1 317.63655 y1 317.63868 5.25 y1 317.43735 y1 317.70471 y1 317.73692 y1 317.71619 y1 317.74040
y1 317.33269 y1 317.34360 6.03 y1 317.39702 5.63 y1 317.62362 y1 317.63403 6.06 y1 317.42399 y1 317.70221 y1 317.73498 y1 317.70987 y1 317.73669
y857.81392
y459.55079 y459.55198 0.00 y459.56868 0.00 y459.64336 y459.64524 0.00 y459.58213 y459.66599 y459.67616 y459.67181 y459.67760
0.80 y919.20619 0.74 y919.37678 0.83 y919.23156 y919.42453 y919.44792 y919.42647 y919.44371
Single-point calculations at the UMP2rcc-pVTZ optimized geometry. Results obtained fitting Eq. Ž2..
6.13 y857.85114 5.96 y858.00248 6.06 y857.86694 y858.04688 y858.06851 y858.05402 y858.07184
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344 Table 3 Relative energies and thermodynamical values Žin kcalrmol. for the weakly bound complex between HS and Cl, at different levels of theory ŽT s 298.15 K.
PMP2rD95Žd, p. PMP2rcc-pVTZ PMP2Žfull.rcc-pVTZ CCSDŽT.rcc-pVTZ PMP2rcc-pVQZ CCSDŽT.rcc-pVQZ a PMP2rCBS CCSDŽT.rCBSb CCSDŽT, full.rCBS c
DE
D EZP E
DH
DG
y2.11 y2.17 y2.39 y1.64 y2.53 y2.00 y2.92 y2.39 y2.61
y1.63 y1.70 y1.92 y1.17 y2.06 y1.53 y2.46 y1.92 y2.14
y1.50 y1.56 y1.78 y1.03 y1.92 y1.39 y2.32 y1.78 y2.00
3.65 3.55 3.33 4.08 3.19 3.72 2.80 3.33 3.11
a
From Eq. Ž1.. From Eq. Ž3.. c From Eq. Ž4.. b
best values for stabilization energies, enthalpies and Gibbs free energies. In their work, Nesbitt and Leone have indicated an D H of y3.6 kcalrmol for this reaction. Since they do not have informed how that value was obtained, we cannot attest for its precision, but we are certain that the value reported in the present investigation is more accurate, due to the fact that we are using a high level of theory. In the case of the transition state, there is however a significant variation in the electronic and thermodynamical values until the quadruple-zeta basis set.
343
Since the rate constant varies exponentially with the activation Gibbs free energy, the values of this constant fall over a large interval. The results computed at the limit for the complete basis set present a small variation, showing the importance of the basis set size for this system. Our best calculation, CCSDŽT, full.rCBSrr UMP2rcc-pVTZ, produced an activation free energy of 7.47 kcalrmol, which leads to a rate constant of 8.5 = 10y1 3 cm3 moleculey1 sy1 . The imaginary frequency of the transition state is 450 cmy1 , at the UMP2rcc-pVTZ level. Taking into account Wigners’ tunneling correction, the rate constant changes to 1.0 = 10y1 2 cm3 moleculey1 sy1 , and an effective activation free energy of 7.36 kcalrmol is then obtained. This value for the rate constant is slightly smaller than that obtained experimentally, which is Ž1.36 " 0.2. = 10y1 2 cm3 moleculey1 sy1 w7x. This small discrepancy corresponds to a difference of only 0.2 kcalrmol in the activation Gibbs free energy. Considering that we are using a high level of theory and that fact that this reaction is isogyric, this value is certainly a very good result. Also, the influence of secondary reactions could be invoked to explain this small difference, but we think that the agreement is already excellent. From a broad perspective, the fact that the reaction between HS and Cl 2 is predicted to be fast, if
Table 4 Relative energies, thermodynamical values Žin kcalrmol., and rate constant Ž k, in cm3 moleculey1 sy1 . for the reaction between HS and Cl 2 leading to HSCl and Cl, at different levels of theory ŽT s 298.15 K. Activation DE PMP2rD95Žd, p. CCSDŽT.rD95Žd, p. PMP2rcc-pVTZ PMP2Žfull.rcc-pVTZ CCSDŽT.rcc-pVTZ PMP2rcc-pVQZ CCSDŽT.rcc-pVQZ a PMP2rCBS CCSDŽT.rCBSb CCSDŽT, full.rCBS c Best value d a
5.05 5.64 0.75 y0.07 2.29 y0.96 0.58 y1.71 y0.16 y0.98
k D EZP E 6.29 6.65 2.04 1.22 3.58 0.33 1.87 y0.42 1.13 0.31
DH 5.41 5.89 1.12 0.30 2.66 y0.59 0.95 y1.34 0.21 0.61
Reaction
DG 13.37 13.56 9.19 8.38 10.74 7.48 9.03 6.74 8.28 7.47 7.36
y17
4.0 = 10 2.9 = 10y1 7 4.6 = 10y1 4 1.8 = 10y1 3 3.4 = 10y1 5 8.3 = 10y1 3 6.1 = 10y14 2.9 = 10y1 2 2.1 = 10y13 8.5 = 10y13 1.0 = 10y12
From Eq. Ž1.. From Eq. Ž3.. c From Eq. Ž4.. d CCSDŽT, full.rCBSrrUMP2rcc-pVTZ with Wigners’ correction for tunneling. b
DE
D EZPE
DH
DG
y8.95 y8.67 y7.84 y8.06 y7.72 y7.66 y7.53 y7.79 y7.66 y7.88
y7.61 y7.33 y6.57 y6.79 y6.44 y6.38 y6.25 y6.51 y6.38 y6.60
y7.88 y7.59 y6.82 y7.04 y6.70 y6.64 y6.51 y6.77 y6.64 y6.86
y7.50 y7.20 y6.46 y6.68 y6.33 y6.27 y6.14 y6.40 y6.27 y6.49
344
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344
the atmospheric conditions are such that the concentrations of the species HS and Cl 2 are significant, this reaction will certainly occur, thus contributing to the coupling of the sulfur and chlorine cycles.
Acknowledgements The authors thank the Fundac¸ao ˜ de Amparo a` Pesquisa do Estado de Sao ˜ Paulo ŽFAPESP. for the academic support, and the Laboratorio de ´ Computac¸ao Avanc¸ada ŽLCCArUSP. for ˜ Cientıfica ´ the computational resources. F.R.O. also thanks the Conselho Nacional de Desenvolvimento Cientıfico e ´ ŽCNPq.. Tecnologico ´
References w1x E.S. Saltzmann, W.J. Cooper ŽEds.., Biogenic Sulfur in the Environment, Am. Chem. Soc., Washington, DC, 1989. w2x R.J. Charlson, J.E. Lovelock, M.O. Andreae, S.G. Warren, Nature ŽLondon. 326 Ž1987. 655. w3x G.S. Tyndall, A.R. Ravishankara, Atmos. Environ. 23 Ž1991. 483. w4x C. Wilson, D.M. Hirst, Prog. React. Kinet. 21 Ž1996. 69.
w5x J.P. Kotra, D.L. Finnegan, W.H. Zoller, M.A. Hart, J.L. Moyers, Science 222 Ž1983. 1018. w6x F.R. Ornellas, Theor. Chem. Acc. Ž2000., in press. w7x D.J. Nesbitt, S.R. Leone, J. Chem. Phys. 72 Ž1980. 1722. w8x M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, GAUSSIAN 94, Revision D.2, Gaussian, Inc., Pittsburgh, PA, 1995. w9x MOLPRO is a package of ab initio programs written by H.-J. Werner, P.J. Knowles, with contributions from J. Almlof. ¨ R.D. Atmos, A. Berning, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert, S.T. Elbert, C. Hampel, R. Lyndh, A.W. Lloyd, W. Meyer, A. Nicklass, K. Petersson, R. Pitzer, A.J. Stone, P.R. Taylor, M.E. Mura, P. Pulay, M. Schutz, ¨ H. Stoll, T. Thorsteinsson. w10x A.A. Radzig, B.M. Smirnov, Reference Data on Atoms, Molecules and Ions, Springer, Berlin, 1985. w11x L.A. Curtiss, K. Raghavachari, J.A. Pople, J. Chem. Phys. 98 Ž1993. 1293. w12x R.H. Nobes, W.J. Bouma, L. Radom, Chem. Phys. Lett. 89 Ž1982. 497. w13x S.S. Xantheas, T.H. Dunning, J. Phys. Chem. 97 Ž1993. 18. w14x D.E. Woon, T.H. Dunning, J. Chem. Phys. 99 Ž1993. 1914. w15x J.I. Steinfeld, J.S. Francisco, W.L. Hase, Chemical Kinetics and Dynamics, Prentice-Hall, Englewood Cliffs, NJ, 1989.
Chemical Physics Letters 318 Ž2000. 340–344 www.elsevier.nlrlocatercplett
Atmospheric reaction between the HS radical and chlorine Stella M. Resende, Fernando R. Ornellas
)
Instituto de Quımica, Departamento de Quımica Fundamental, UniÕersidade de Sao ´ ´ ˜ Paulo, Caixa Postal 26077, Sao ˜ Paulo, SP, 05513-970, Brazil Received 16 November 1999; in final form 13 December 1999
Abstract The mechanism and the kinetics of the reaction between HS and Cl 2 leading to HSCl and Cl were studied theoretically. The effect of the complete basis set limit ŽCBS. was included by extrapolating the results obtained with cc-pVDZ, cc-pVTZ and cc-pVQZ correlation consistent basis sets functions. At the highest level of calculation, CCSDŽT., the calculated rate constant is 1.0 = 10y12 cm3 moleculey1 sy1. The activation Gibbs free energy was calculated to be 7.4 kcalrmol, which is only 0.2 kcalrmol above the value determined experimentally. The enthalpy and Gibbs free energies of the reaction are y6.9 and y6.5 kcalrmol, respectively. q 2000 Published by Elsevier Science B.V. All rights reserved.
1. Introduction Sulfur compounds are released into the atmosphere, in reduced and oxidized forms, by means of biogenic and anthropogenic sources w1x. The oxidation of sulfur reduced compounds plays a very important role in atmospheric processes, due to the fact that it leads to the production of SO 2 , which is oxidized to sulfuric acid in the troposphere. Sulfuric acid forms sulfur aerosol, and it is related to biological climate regulation w2x. Hydrogen sulfide, H 2 S, is a large source of sulfur in the atmosphere, and it is produced through both aerobic and anaerobic organic decomposition. The major tropospheric process that removes H 2 S is the reaction with OH, producing HS and H 2 O w3x. It was believed that all the HS generated is oxidized to SO 2 , in reactions with common tropospheric oxi) Corresponding author. Fax: q55-11-815-5579; e-mail: [email protected]
dants such as O 3 , NO 2 and O 2 , being thus completely consumed in the troposphere w4x. However, volcanic eruptions can inject sulfur compounds in the stratosphere in large amounts, and H 2 S seems to be the dominant sulfur species emitted in these situations w5x. In the stratosphere, reaction of HS with Cl 2 andror Cl may be important, leading to a coupling between chlorine and sulfur chemistries. It can also occur in extraterrestrial atmospheres where H 2 S is abundant, as that of Venus. Surprisingly, to the best of our knowledge, very little is known about this reaction, as well the mechanism, and the nature and structure of the products formed w6x. Studies of this type of reactions are certainly very important, since they can significantly contribute to a better understanding of the chlorine and sulfur atmospheric cycles. So far, the only study reported in the literature about the kinetics of the reaction between HS and Cl 2 is that of Nesbitt and Leone w7x, in which the authors have analyzed a laser-induced chemical chain reaction of the
0009-2614r00r$ - see front matter q 2000 Published By Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 0 1 9 - 1
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344
341
Cl 2rH 2 S system. They have obtained an average value of Ž1.36 " 0.2. = 10y1 2 cm3 moleculey1 sy1 for the rate constant of the reaction
Table 1 Harmonical frequencies calculated for all stationary points obtained at the UMP2rcc-pVTZ level of calculation Available experimental values are given in parentheses w10x
HS q Cl 2
HS
™ HSClq Cl .
Considering, on one hand, that all methods of study of the HS kinetics are susceptible to errors associated with secondary processes, which can lead to regeneration of the HS radical w3x, and, on the other hand, the high performance of present-day theoretical ab initio methods, it is our understanding that theoretical methods can be a valuable aid in the investigation of this kind of reactions, especially for systems of a few atoms. Therefore, our aim in this work is to present a detailed and very accurate investigation of thermodynamical properties and of kinetics data which can help us elucidate the mechanism of the above atmospheric reaction.
2. Calculation
Cl 2
577.6 Ž559.7. 2 765.1 Ž2 712.
Complex Transition HSCl state 54.7 58.6 66.4 176.6 552.9 2 760.4
450.0 i 153.2 255.9 420.0 653.9 2 759.3
554.9 927.7 2 753.5
parameters are given. In Table 1 are presented the harmonical frequencies calculated. Experimental values are available only for the reactants w10x. Using MP2rcc-pVQZ and CCSDŽT.rcc-pVTZ single-point calculations and the additivity approximation w11,12x, we have achieved the CCSDŽT.rcc-pVQZ level of theory, through the equation ECCSDŽT .r cc - pVQZ s ECCSDŽT .r co - pVTZ
Our calculations were performed with the GAUSSIAN w8x and the MOLPRO w9x packages of programs. The optimizations and harmonical frequency analysis w e re d o n e a t th e U M P 2 r D 9 5 Ž d , p . , UCCSDŽT.rD95Žd, p. and UMP2rcc-pVTZ levels of theory. Besides the reactants, products and the transition state, we have found a weakly bound complex between the reactants. The structures of all stationary points considered in this work are presented in Fig. 1, where the relevant geometrical
q Ž E MP 2 r co - pVQZ y EMP2 r co - pVTZ . .
Ž 1.
In order to obtain the limit for the basis set completeness, we have performed an MP2rcc-pVDZ single-point calculation, and used the approximation developed and tested by Dunning and co-workers w13,14x, which states that the dependence on basis set of several molecular properties, as the stabilization energy, is well represented by a simple exponential function in this form F Ž n . s A` y B exp Ž ycn . ,
Ž 2.
where n is the index of the basis set, and A` is the asymptotic limit for the function. The limiting value of this function provides an estimate of the complete basis set ŽCBS. limit. In our calculation, n ranged from 2 to 4, and the function extrapolated was the energy for every stationary point at the MP2 level. The values for the CCSDŽT.rCBS level of calculation were obtained through the following expressions ECCSDŽT .r CBS s ECCSDŽT .r cc - pVTZ q Ž EMP 2 r CBS y EMP2 r cc - pVTZ . . Fig. 1. Geometries and relevant geometrical parameters for the stationary points involved in the reaction between HS and Cl 2 , at the UMP2rcc-pVTZ level of theory. Available experimental values are given in parentheses w10x.
Ž 3. We have also included the effect of the core in the calculation of the electronic energy through an
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344
342
MP2Žfull.rcc-pVTZ single-point calculation. Using the additivity approximation again, we have obtained the values for the CCSDŽT, full.rCBS levels of calculation as ECCSDŽT ,full.r CBSs ECCSDŽT .r CBS q Ž EMP 2 Žfull.r ccypVTZ y EMP2 r ccypVTZ . .
Ž 4.
Finally, the rate constant for this reaction was calculated using conventional transition state theory ŽTST. w15x, and the possibility of quantum-mechanical tunneling was addressed by means of Wigners’ approach, which implies multiplying the TST rate constant by the factor below
Gs1q
1
hv
24 k B T
2
,
Ž 5.
where v stands for the absolute value of the imaginary frequency of the transition state of the reaction. 3. Results and discussion The energy values obtained with all approaches are presented in Table 2. The calculations at the MP2rcc-pVDZ, MP2rcc-pVQZ, CCSDŽT.rccpVTZ and MP2Žfull.rcc-pVTZ levels were performed with the geometry optimized at the MP2rcc-pVTZ level. The adjusted values for the CBS limit at the MP2 level are also in Table 2. In
Tables 3 and 4 are the relative energies and the thermodynamical properties, calculated at 298.15 K, for the formation of the weakly bound complex, and for the reaction, respectively. The rate constants calculated at the different levels of theory are also in Table 4, as well as the results for our highest-level calculations, obtained with the CBS limit. From Table 3, we can see that increasing the size of the basis sets leads to a higher stabilization of the weakly bound complex, whether at the MP2 or at the CCSDŽT. level. This behavior can also be observed in Table 4 for the activation energy results. In all cases, the MP2 values overstabilize the species relative to CCSDŽT.. It can also be noted that the values obtained for the formation of the weakly bound complex and those for the energy of the reaction are very small, showing that the convergence is reached with medium basis set functions as the cc-pVTZ one. For the weakly bound complex, our best value for the stabilization energy is y2.61 kcalrmol. All other results differ from this value by - 1 kcalrmol. The enthalpy variation is y2.0 kcalrmol, and the Gibbs free energy for this species is positive, but of a small value. For the products of the reaction, a similar behavior is observed. The reaction is spontaneous by y6.5 kcalrmol, and exothermic by y6.9 kcalrmol. Once again, the values obtained at several levels of calculation do not differ by more than 1 kcalrmol of the
Table 2 Calculated energies Žin hartree. and zero-point energies ŽZPE, in kcalrmol. for the species studied The optimizations were performed at the UMP2rD95Žd, p., UCCSDŽT.rd95Žd, p. and UMP2rcc-pVTZ levels
UMP2rD95Žd, p. PMP2rD95Žd, p. ZPE UCCSDŽT.rd95Žd, p. ZPE UMP2rcc-pVTZ PMP2rcc-pVTZ ZPE PMP2rcc-pVDZ a PMP2rcc-pVQZ a PMP2rCBSb CCSDŽT.rcc-pVTZ a PMP2Žfull.rcc-pVTZ a a b
HS
Cl 2
Complex
Transition state
HSCl
Cl
y398.17657 y398.17803 3.99 y398.19981 3.88 y398.25633 y398.25844 3.95 y398.20251 y398.27614 y398.28435 y398.28706 y398.29288
y919.17362
y1 317.35351 y1 317.35502 5.28 – – y1 317.63655 y1 317.63868 5.25 y1 317.43735 y1 317.70471 y1 317.73692 y1 317.71619 y1 317.74040
y1 317.33269 y1 317.34360 6.03 y1 317.39702 5.63 y1 317.62362 y1 317.63403 6.06 y1 317.42399 y1 317.70221 y1 317.73498 y1 317.70987 y1 317.73669
y857.81392
y459.55079 y459.55198 0.00 y459.56868 0.00 y459.64336 y459.64524 0.00 y459.58213 y459.66599 y459.67616 y459.67181 y459.67760
0.80 y919.20619 0.74 y919.37678 0.83 y919.23156 y919.42453 y919.44792 y919.42647 y919.44371
Single-point calculations at the UMP2rcc-pVTZ optimized geometry. Results obtained fitting Eq. Ž2..
6.13 y857.85114 5.96 y858.00248 6.06 y857.86694 y858.04688 y858.06851 y858.05402 y858.07184
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344 Table 3 Relative energies and thermodynamical values Žin kcalrmol. for the weakly bound complex between HS and Cl, at different levels of theory ŽT s 298.15 K.
PMP2rD95Žd, p. PMP2rcc-pVTZ PMP2Žfull.rcc-pVTZ CCSDŽT.rcc-pVTZ PMP2rcc-pVQZ CCSDŽT.rcc-pVQZ a PMP2rCBS CCSDŽT.rCBSb CCSDŽT, full.rCBS c
DE
D EZP E
DH
DG
y2.11 y2.17 y2.39 y1.64 y2.53 y2.00 y2.92 y2.39 y2.61
y1.63 y1.70 y1.92 y1.17 y2.06 y1.53 y2.46 y1.92 y2.14
y1.50 y1.56 y1.78 y1.03 y1.92 y1.39 y2.32 y1.78 y2.00
3.65 3.55 3.33 4.08 3.19 3.72 2.80 3.33 3.11
a
From Eq. Ž1.. From Eq. Ž3.. c From Eq. Ž4.. b
best values for stabilization energies, enthalpies and Gibbs free energies. In their work, Nesbitt and Leone have indicated an D H of y3.6 kcalrmol for this reaction. Since they do not have informed how that value was obtained, we cannot attest for its precision, but we are certain that the value reported in the present investigation is more accurate, due to the fact that we are using a high level of theory. In the case of the transition state, there is however a significant variation in the electronic and thermodynamical values until the quadruple-zeta basis set.
343
Since the rate constant varies exponentially with the activation Gibbs free energy, the values of this constant fall over a large interval. The results computed at the limit for the complete basis set present a small variation, showing the importance of the basis set size for this system. Our best calculation, CCSDŽT, full.rCBSrr UMP2rcc-pVTZ, produced an activation free energy of 7.47 kcalrmol, which leads to a rate constant of 8.5 = 10y1 3 cm3 moleculey1 sy1 . The imaginary frequency of the transition state is 450 cmy1 , at the UMP2rcc-pVTZ level. Taking into account Wigners’ tunneling correction, the rate constant changes to 1.0 = 10y1 2 cm3 moleculey1 sy1 , and an effective activation free energy of 7.36 kcalrmol is then obtained. This value for the rate constant is slightly smaller than that obtained experimentally, which is Ž1.36 " 0.2. = 10y1 2 cm3 moleculey1 sy1 w7x. This small discrepancy corresponds to a difference of only 0.2 kcalrmol in the activation Gibbs free energy. Considering that we are using a high level of theory and that fact that this reaction is isogyric, this value is certainly a very good result. Also, the influence of secondary reactions could be invoked to explain this small difference, but we think that the agreement is already excellent. From a broad perspective, the fact that the reaction between HS and Cl 2 is predicted to be fast, if
Table 4 Relative energies, thermodynamical values Žin kcalrmol., and rate constant Ž k, in cm3 moleculey1 sy1 . for the reaction between HS and Cl 2 leading to HSCl and Cl, at different levels of theory ŽT s 298.15 K. Activation DE PMP2rD95Žd, p. CCSDŽT.rD95Žd, p. PMP2rcc-pVTZ PMP2Žfull.rcc-pVTZ CCSDŽT.rcc-pVTZ PMP2rcc-pVQZ CCSDŽT.rcc-pVQZ a PMP2rCBS CCSDŽT.rCBSb CCSDŽT, full.rCBS c Best value d a
5.05 5.64 0.75 y0.07 2.29 y0.96 0.58 y1.71 y0.16 y0.98
k D EZP E 6.29 6.65 2.04 1.22 3.58 0.33 1.87 y0.42 1.13 0.31
DH 5.41 5.89 1.12 0.30 2.66 y0.59 0.95 y1.34 0.21 0.61
Reaction
DG 13.37 13.56 9.19 8.38 10.74 7.48 9.03 6.74 8.28 7.47 7.36
y17
4.0 = 10 2.9 = 10y1 7 4.6 = 10y1 4 1.8 = 10y1 3 3.4 = 10y1 5 8.3 = 10y1 3 6.1 = 10y14 2.9 = 10y1 2 2.1 = 10y13 8.5 = 10y13 1.0 = 10y12
From Eq. Ž1.. From Eq. Ž3.. c From Eq. Ž4.. d CCSDŽT, full.rCBSrrUMP2rcc-pVTZ with Wigners’ correction for tunneling. b
DE
D EZPE
DH
DG
y8.95 y8.67 y7.84 y8.06 y7.72 y7.66 y7.53 y7.79 y7.66 y7.88
y7.61 y7.33 y6.57 y6.79 y6.44 y6.38 y6.25 y6.51 y6.38 y6.60
y7.88 y7.59 y6.82 y7.04 y6.70 y6.64 y6.51 y6.77 y6.64 y6.86
y7.50 y7.20 y6.46 y6.68 y6.33 y6.27 y6.14 y6.40 y6.27 y6.49
344
S.M. Resende, F.R. Ornellasr Chemical Physics Letters 318 (2000) 340–344
the atmospheric conditions are such that the concentrations of the species HS and Cl 2 are significant, this reaction will certainly occur, thus contributing to the coupling of the sulfur and chlorine cycles.
Acknowledgements The authors thank the Fundac¸ao ˜ de Amparo a` Pesquisa do Estado de Sao ˜ Paulo ŽFAPESP. for the academic support, and the Laboratorio de ´ Computac¸ao Avanc¸ada ŽLCCArUSP. for ˜ Cientıfica ´ the computational resources. F.R.O. also thanks the Conselho Nacional de Desenvolvimento Cientıfico e ´ ŽCNPq.. Tecnologico ´
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