comparative study of reaction rate constants for the ... - World Scientific

January 22, 2010 12:3 WSPC/178-JTCC

00532

Journal of Theoretical and Computational Chemistry Vol. 8, No. 6 (2009) 1227–1233 c World Scientific Publishing Company

COMPARATIVE STUDY OF REACTION RATE CONSTANTS FOR THE NH3 + H → NH2 + H2 REACTION WITH GLOBE DYNAMICS AND TRANSITION STATE THEORIES

JU LIPING Department of Physics, Shenyang Institute of Aeronautical Engineering Shenyang 110136, P. R. China LU RUIFENG Division of Chemistry and Biological Chemistry School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637616, Singapore Received 25 March 2009 Accepted 13 April 2009 The nine-dimension quasi-classical trajectory (QCT) calculations have been carried out for the title reaction with a global potential energy surface (PES) constructed by Corchado and Espinosa-Garc´ıa (J Chem Phys 106:4013, 1997). The detailed dynamics calculations cover the specific collision energies falling in the range of 0.62–3.04 eV, which are sufficient to fit the calculated reactive cross-sections into a barrier-type excitation function and to obtain the thermal rate constants. The present QCT rate constants are in good agreement with the recent quantum dynamics (QD) results, both of which are much lower than that of the previous variational transition state theory (VTST). Keywords: Transition state theory; QCT; reaction rate constants.

1. Introduction The hydrogen abstraction reaction NH3 + H → NH2 + H2 plays an important role in ammonia pyrolysis and combustion process, which attracts much interest of experimental and theoretical researchers.1–18 Experimentally, followed with the pioneer work of Dove and Nip,1 extensive experimental investigations have been put into understanding the title reaction.2–9 At the same time, much effort has been put into the theoretical studies.10–18 Among them, Garrett et al.12 and Espinosa-Garc´ıa et al.13,14 have calculated the rate constants with the ab initio electronic structure calculations (including the energies and their derivatives along the minimum energy path) at different levels. Then, using the above electronic structure information, they have obtained the variational transition state theory (VTST) rate constants. There after, an analytical and global potential energy surface (PES) 1227


1228

00532

J. Liping & L. Ruifeng

for the title reaction and its reverse has been constructed first by Corchado and Espinosa-Garc´ıa (CE PES).15 The classical barrier height is 15.75 kcal/mol. The CE PES was calibrated with the experimental and the theoretical stationary points (reactants, products, and transition state) properties as well as the experimental thermal rate constants. At the same time, they calculated the VTST rate constants based on the CE PES, which are in agreement with the available experimental data.6,9 Recently, Yang and Corchado16 have carried out the seven-dimensionality quantum dynamics (QD) calculations on the CE PES, which are based on timedependent wavepacket (TDWP) method.19 The TDWP method has been extensively employed to study the quantum scattering dynamics including adiabatic and nonadiabatic processes.20−27 In the present paper, we carry out the global dynamics calculations with the quasi-classical trajectory method based on the CE PES to investigate the properties of the title reaction. Section 2 introduces the QCT approach briefly and Sec. 3 presents the results and discusses them. The conclusions are given in Sec. 4.

2. Trajectory Calculations The QCT method has been used to study the present pentatomic reaction NH3 + H → NH2 +H2 . The NH3 molecule is set in its ground vibrational state. In turn, the rotational energy of ammonia molecule is approximated by Erot = 32 kB T with T = 300 K, where kB is the Boltzmann constant. The step size of numerical integration has been determined by trial-and-error to be 6 as, which is found to be sufficient for the conservation of the energy and the angular momentum within four digits. The initial separation between hydrogen atom and ammonia molecule has been fixed at 20 ˚ A, which is sufficiently large to make the interaction negligible. The relative translational energy (Etr ) between hydrogen atom and the ammonia molecule varies from 0.62 to 3.04 eV. For each selected energy Etr , the reactive cross-section σr is approximately equal to σr = πb2max pr ,

(1)

where bmax is the maximum of the impact parameter which has been determined by the usual procedure with the uncertainty of about ±0.1 ˚ A; pr = NNr is the reactive probability, Nr is the number of the reactive trajectories and N is the number of the total trajectories. In turn, the associated uncertainties are ∆σr =

N − Nr N Nr

1/2 σr .

(2)

The calculated reactive cross-sections for all specified energies are fitted with leastsquares method to a barrier-type excitation function28 0 n 0 σr (Etr ) = C(Etr − Etr ) exp[−m(Etr − Etr )],

(3)


00532

Comparative Study of Reaction Rate Constants

1229

0 where C, n, and m are the least-square parameters and Etr is the threshold energy. In sequence, assuming the Boltzmann distribution of translational energy Etr , the thermal rate constant was obtained by29 3/2 1/2 ∞ 2 1 k(T ) = Etr σr (Etr ) exp(−Etr /kB T )dEtr . (4) kB T πµ 0

3. Results and Discussion Table 1 present the results of the present QCT calculations for the NH3 +H → NH2 + H2 reaction. Figure 1 shows the integral cross-sections (ICSs) vs. collision energy for the present reaction. Generally, the calculated ICSs are an increasing function of the considered collision energies. To describe quantitatively the relationship of the ICS with the collision energies, we use Eq. (3) to fit the calculated ICSs with the least-squares method. After fitting, the values of the parameters of Eq. (3) are 0 = 0.62 eV. As shown in obtained as C = 0.309, n = 0.359, m = −0.025, and Etr Fig. 1, the solid line represents the fitting ICSs, which are in agreement with the calculated QCT ones. Subsequently, substituting Eq. (3) into Eq. (4), the rate constant for the NH3 + H → NH2 + H2 reaction can be obtained by integrating Eq. (4) numerically. The present QCT rate constants, the previous VTST rate constants calculated by Corchado and Espinosa-Garc´ıa,15 the recent QD results obtained by Yang and Corchado,16 and the experimental data6,9 are compared in Fig. 2. As shown in Fig. 2, we can see that the rate constants have an approximately linear dependence of temperature over the present temperature range of 300–2000 K. Generally, our QCT rate constants have good agreement with the seven-dimensionality QD calculations, while both our QCT results and that of the previous QD are much less than the available experimental data6,9 as well as the VTST results15 over the considered temperature range. This is because the CE PES overestimates the barrier height of the title reaction. The VTST approach overestimates the rate constants for CN + H2 reaction30 and a series of X + CH4 (X = H, O, Cl) reactions31 which has been reported recently. The present study indicates that NH3 + H → NH2 + H2 reaction obeys the rule deduced in Ref. 32, i.e. the rate constants from VTST calculations are systematically higher than those obtained from global dynamics calculations, indicating large recrossing effect for these systems. Also, the MCTDH results33,34 are not supported in the present study. Furthermore, QCT method is not only used to calculate the scalar and vector properties of chemical reactions,35,36 but also to testify the convergence of QD calculations. 4. Conclusions We have presented the detailed QCT calculations for the NH3 + H → NH2 + H2 reaction based on a global PES reported previously by Corchado and EspinosaGarc´ıa. The calculated ICSs at the specific translational energies over the range


1230

00532

J. Liping & L. Ruifeng Table 1. Maximum impact parameter (bmax ), reaction probability (pr ), and ICS (σr ) as a function of translational energy (Etr ) for the title reaction. Etr (ev)

bmax (˚ A)

pr

σr (˚ A2 )

∆σr (˚ A2 )

0.62011 0.62878 0.65046 0.69383 0.73719 0.78056 0.86728 0.95401 0.99738 1.01906 1.04074 1.0841 1.17083 1.2142 1.25756 1.30093 1.34429 1.38765 1.43102 1.44403 1.47438 1.51775 1.60448 1.64784 1.6912 1.73457 1.77793 1.8213 1.84298 1.88634 1.95139 1.99475 2.01644 2.03812 2.08148 2.16821 2.21157 2.25494 2.2983 2.38503 2.47176 2.51512 2.55849 2.60185 2.68858 2.81867 2.86204 2.9054 3.03549

1.37 1.38 1.37 1.48 1.58 1.68 1.77 1.77 1.77 1.85 1.94 1.94 1.94 1.94 1.85 1.77 1.77 1.94 1.94 1.94 1.94 2.09 2.09 1.94 1.94 1.94 1.94 1.94 1.94 2.09 2.09 1.94 1.94 1.94 2.17 1.94 1.94 1.94 1.94 2.09 2.09 2.02 2.02 2.02 2.02 1.94 1.94 1.94 1.94

0.0117 0.01122 0.01755 0.01276 0.01438 0.01661 0.01666 0.01883 0.01948 0.02251 0.01917 0.02078 0.01988 0.02364 0.02662 0.03144 0.02986 0.02311 0.02311 0.02346 0.02758 0.02633 0.02496 0.02454 0.024 0.0249 0.02633 0.02866 0.02991 0.02831 0.02937 0.03332 0.03081 0.02973 0.02321 0.0283 0.02991 0.03045 0.03529 0.03196 0.03515 0.03441 0.03114 0.02966 0.02819 0.03242 0.03511 0.03797 0.04155

0.06899 0.0671 0.10348 0.08784 0.1128 0.14728 0.164 0.1853 0.19169 0.24202 0.2266 0.24567 0.23508 0.27955 0.28622 0.30942 0.29393 0.2732 0.2732 0.27743 0.32614 0.36129 0.3425 0.29014 0.28379 0.29437 0.31132 0.33885 0.35367 0.38844 0.40306 0.39391 0.36426 0.35156 0.34335 0.33461 0.35367 0.36003 0.41721 0.43856 0.48242 0.44116 0.39915 0.38024 0.36133 0.38332 0.41509 0.44897 0.49133

0.01212 0.01198 0.01481 0.01363 0.01538 0.01758 0.01853 0.01968 0.02001 0.02231 0.0217 0.02257 0.02209 0.02404 0.02421 0.0284 0.02464 0.02377 0.02377 0.02395 0.02592 0.0271 0.02641 0.02448 0.02422 0.02466 0.02534 0.0264 0.02696 0.02808 0.02858 0.0284 0.02734 0.02688 0.0265 0.02624 0.02696 0.02719 0.0292 0.02978 0.03118 0.02991 0.0285 0.02784 0.02716 0.02803 0.02912 0.03024 0.03158


00532


1231

0.6

the QCT ICS the fitted ICS

ICS (Angstrom2)

0.5

0.4

0.3

0.2

0.1

0.0 0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

Etr (eV) Fig. 1. The ICS as a function of the translational energy for the reaction: the scattered points are the calculated ICSs with the associated 68% error bars at the specific translational energies; the solid line is the fitted curve given by Eq. (3).

k(T) (cm3molecule-1s-1)

1E-11

QCT(the present) QD(ref.16) VTST(ref.15) Expt.(ref.6,9)

1E-13

1E-15

1E-17

1E-19

1E-21 0

1

2

3

1000/T (K-1) Fig. 2. Comparison of the rate constants of the present QCT, the previous VTST,15 the recent QD,16 and the experimental data6,9 : the solid squares represent the present QCT results, the solid line is the QD results,16 the dotted line represents the VTST results,15 and the triangle represent the experimental data.6,9


1232

00532

J. Liping & L. Ruifeng

of 0.62–3.04 eV have been fitted to an exponential function with the least-squares method. The calculated QCT rate constants agree well with the QD results, while both of which are less than the VTST ones and the experimental data. This is attributed to the overestimation of the barrier height of CE PES calibrated by VTST rate constants. Acknowledgment The authors thank Professor Keli Han for providing the QCT code. References 1. Dove JE, Nip WS, J Chem Phys 52:1171, 1974. 2. Yamura M, Asaba T, Proc 18th Int Symposium on Combustion, Combustion Institute, Pittsburgh, pp. 863–872, 1981. 3. Michael JV, Sutherland JW, Klemm RB, Int J Chem Kinet 17:315, 1985. 4. Michael JV, Sutherland JW, Klemm RB, J Phys Chem 90:497, 1986. 5. Marshall P, Fontijn A, J Chem Phys 85:2637, 1986. 6. Hack W, Rouver-irolles P, Wagner HG, J Phys Chem 90:2505, 1986. 7. Sutherland JW, Michael JV, J Chem Phys 88:830, 1988. 8. Demissy M, Lesclaux R, J Am Chem Soc 102:2897, 1980. 9. Ko T, Marshall P, Fontijn A, J Phys Chem 94:1401, 1990. 10. Gordon MS, Gano DR, Boatz JA, J Am Chem Soc 105:5771, 1983. 11. Leroy G, Sana M, Tinant A, Can J Chem 63:1447, 1985. 12. Garrett BC, Koszykowsky ML, Melius CF, Page M, J Phys Chem 94:7096, 1990. 13. Espinosa-Garc´ıa J, Tolosa S, Corchado JC, J Phys Chem 98:2337, 1994. 14. Espinosa-Garc´ıa J, Corchado JC, J Chem Phys 101:1333, 1994. 15. Corchado JC, Espinosa-Garc´ıa J, J Chem Phys 106:4013, 1997. 16. Yang MH, Corchado JC, J Chem Phys 126:214312, 2007. 17. Zhang XQ, Cui Q, Zhang JZH, Han KL, J Chem Phys 126:234304, 2007. 18. Collins MA, Moyano GE, Theor Chem Acc 113:225, 2005. 19. Han KL, He GZ, J Photochem Photobiol C Photochem Rev 8:56, 2007. 20. Xie TX, Zhang Y, Zhao MY, Han KL, Phys Chem Chem Phys 5:2034, 2003. 21. Yang BH, Gao HT, Han KL, Zhang JZH, J Chem Phys 113:1434, 2000. 22. Chu TS, Zhang Y, Han KL, Int Rev Phys Chem 25:201, 2006. 23. Chu TS, Han KL, Phys Chem Chem Phys 10:2431, 2008. 24. Hu J, Han KL, He GZ, Phys Rev Lett 95:123001, 2005. 25. Zhang H, Zhu RS, Wang GJ, Han KL, He GZ, Lou NQ, J Chem Phys 110:2922, 1999. 26. Chu TS, Han KL, Schatz GC, J Phys Chem 111:8286, 2007. 27. Chu TS, Han KL, J Phys Chem A 109: 2050, 2005. 28. LeRoy RL, J Phys Chem 73:4338, 1969. 29. Zhang Y, Xie TX, Han KL, J Phys Chem A 107:10893, 2003. 30. Ju LP, Han KL, Zhang JZH, J Theor Comput Chem 5:769, 2006. 31. Varandas AJC, Caridade PJSB, Zhang JZH, Cui Q, Han KL, J Chem Phys 125:064312, 2006.


00532


32. 33. 34. 35. 36.

1233

Ju LP, Han KL, Zhang JZH, J Comput Chem 30:305, 2009. Huarte-Larra˜ naga F, Manthe U, J Chem Phys 116:2863, 2002. Huarte-Larra˜ naga F, Manthe U, J Chem Phys 113:5115, 2000. Han KL, He GZ, Lou NQ, J Chem Phys 105:8699, 1996. Li RJ, Han KL, Li FE, Lu RC, He GZ, Lou NQ, Chem Phys Lett 220:281, 1994.