Statistical adiabatic channel model rate constants for the reaction O+ ...

React.Kinet.CataI.Lett. Vol. 57, No. 1, 43-47 (1996)

Jointly published by Elsevier ScienceB.V., Amsterdam and Akad6miai Kiado, Budapest

RKCL2675

STATISTICAL ADIABATIC CHANNEL MODEL RATE CONSTANTS FOR THE REACTION O + CN -~ CO + N(2D) AT 300-5000 K C.J. Cobos Instituto de Investigaciones Fisicoquimicas Te6ricas y Apficadas (INIFTA), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 16, Sue, 4, (1900) la Plata, Argentina

Received February 15, 1995 Accepted September 22, 1995

Abstract The fifll version o f the statistical adiabatic channel model has been employed to calculate rate constants for the title reaction. In very good agreement with available experimental data, the computed values increase by almost one order of magnitude between 300 and 5000 K.

Keywords: Rate constants, chemical kinetics, combustion chemistry

INTRODUCTION The reaction between O atoms and CN radicals plays a relevant role in the oxidation of several CN-containing molecules in combustion chemistry. This reaction can either proceed via the 2y~ground-state surface of the NCO radical

O(3P) + CN(X2Z +) ~ [NCO(X2FI)] ~ CO(Xl~] +) + N(2D)

(1)

0133-1736/96/US$12.00. 9 Akaddmiai Kiad6, Budapest. All rights reserved.

44

COBOS:RATECONSTANTS

(AH~ =-92 kJ tool ~ [1] or directly, via a quartet state, to the ground state products CO(XlY', +) and N(4S) [2] (AH~ =-322 kJ mol -l [1]). At room temperature, 80+10% of the reaction proceeds through channel (1) [3]. The second channel appears also to contribute at 2000 K [4]. Recent shock tube experiments lead, for the overall process, to the rate constant k=(1.3+0.3)x10 ~~ cm 3 molecule -1 s ~ over the 3000-4500 K temperature range [5]. This value is notably higher than (1.7+0.7)x10 H c m 3 molecule ~ s ~, determined by a flash photolysis/discharge-flow technique at 300 K [1,3]. In order to investigate if both sets of experiments [3,5] can be theoretically reconciled, we present in this Letter a statistical adiabatic channel model (SACM) study for reaction (1) over the 300-5000 K temperature range.

T H E O R E T I C A L F O R M A L I S M , RESULTS AND DISCUSSION It is assumed that reaction (1) proceeds via the formation of a strongly bound NCO collision complex, which afterwards dissociates preferentially to CO and N(2D), with increasing importance of the redissociation to O and CN as the temperature increases. Besides, this complex is considered too short-lived to be collisionally stabilized. Thus, k can be computed with the full version of the SACM [6] as follows, kBT Ft Fo Fred k-

h

Qw

a+N Y~ L=IJ-N[

. . Y~ ~

.

. Y.

. Z

Eo(L,J,N,vba,Vb,2,%) Z exp[-

J-0 N=I Vb,l~0 Vb,2=0 Vs=0

-]

(2)

kBT

Here Ft-Qt,NCo/(Qt,oQt,cN) denotes the ratio of the translational partition functions, while F~ is a similar ratio for the electronic partition functions. QvR is the rovibrational partition function of CN. The summations are performed over all state-resolved threshold energies E0(L,J,N,Vu, l,vb,a,Vs) of the corresponding adiabatic open channels (referred to that of the lowest reaction channel). L and J are the quantum numbers for the orbital and total angular momentum, respectively. N is the rotational quantum number for the CN radical, and Vb,i and v~ are the vibrational quantum numbers for the degenerate bending mode of the linear NCO complex and for the N-CO stretching mode, respectively. The redissociation factor F,~=Tis calculated from the number of open channels at the entrance W~(E,J) and at the exit W2(E,J) sides for the average energies E and total angular moment J at the temperature T [7].

COBOS:RATECONSTANTS

45

The threshold energies are obtained from the maxima of rovibrationally adiabatic potential curves. These are given by the sum of the electronic potential, the channel eigenvalues, and the centrifugal energy as a function of the reaction coordinate r (the O-CN bond distance) [6]. In the absence of an ab initio potential energy surface, a Zavitsas function was employed to describe the electronic potential [8]. The channel eigenvalues were interpolated between the eigenvalues of the reactant states and those of the product states by means of a Gaussian switching function, S(r)=exp[-6(r-r~)2], with an ~adjustable parameter [9]. The Zavitsas potential has been successfully tested against several RKR potentials and the NH3 and CH4 ab initio potentials [8], while S(r) is probably the simplest one-parameter function that reproduces satisfactorily the attenuation of ab initio derived bending force constants as bonds are stretched [9]. Further details of the SACM can be found elsewhere [6,10,11].

I

10-10

- - -

T - - - - T

,--

u o

I

Z 3 / ~

?o ///~

"T

I

O

E E

t3 ..%

10-~1 I

~ooo

I.

I

I

I

2000

3000 T(K)

4000

5ooo

Fig. 1. Rate constants as a function of temperature. Experimental values (I-1, [3], A, [5]), trajectory calculations (O, [2]), and SACM calculations fxom this work (e). The dashed line is a spline fit through the data of Refs 3 and 5 [5]

46

COBOS:RATECONSTANTS

Unfortunately, the lack of a quantum-chemical potential energy surface precludes an absolute prediction of k [10]. Thus, the scaling criterion here adopted consisted in matching the theoretical and experimental rate constants at 300 K [3]. In this way, the value 8=0.592 A-z was obtained and the temperature dependence of k up to 5000 K predicted. The rate constants: 1.40xlO n , 2.41x10 -n, 3.46x10 -11, 5.09x10 qa, 8.10x10 -ll, 1.01xl0 -l~ 1.19x10 -~~ 1.29x10 -1~ and 1.34x10 1~ cm3 molecule1 sl were computed at 300, 500, 700, 1000, 1500, 2000, 3000, 4000 and 5000 K, respectively. The experimental values together with spline fits through the calculated values are depicted in Figure 1. The present model calculations reproduce very well the high temperature experiments [5] without invocation of an electronic energy barrier. However, as Figure 1 shows, by contrast with the Arrhenius expression derived in Ref. 5 (including data of Ref. 3), our calculations give an appreciable non-Arrhenius behavior of k. Figure 1 also shows that the three-dimensional classical trajectory calculations of Ref. 2 lead to rate constants (evaluated as ~ = e~, where ~ is the reaction cross section and the mean velocity) a factor of two smaller than those calculated here between 300 and 3000 K. A complex potential energy surface that resembles the London-Eyring-Polanyi-Sato (LEPS) potential with rdependent Morse parameters and a threshold energy for the entrance channel of 0.29 kJ toolq was employed in these calculations. Even though the present potential and the one of Ref. 2 have different functional forms, the similitude between the temperature dependencies of k indicates that both potential surfaces lead to similar minimum energy paths along the reaction coordinate. This fact suggests that nonstatistical recrossing effects seem to be of small importance for reaction (1). On the other hand, statistical recrossing, accounted for by Fr~ in eq. (2), reduces the capture rate constants from 13.5% to 37.5% between 300 and 5000 K. State-resolved k values exhibit a general behavior similar to those of the H+NO--~HNO [10] and N+OH--,,NO+H [11] reactions, which are not presented here. Additional calculations carried out by using the function, S(r)=exp[-cc(r-ro)] [6,12] with a=0.950 A"1 fit the room temperature rate constant but give k values at 3000-5000 K approximately 22% higher than those above given. The present reaction is also of importance in relation to processes occurring in interstellar clouds (T