Collision-theory calculations for reactions of atomic oxygen with OH, ClO, CH, NO2 and PH3

Volume 165, number 6

COLLISION-THEORY

CHEMICAL PHYSICS LETTERS

CALCULATIONS

2 February 1990

FOR REACTIONS OF ATOMIC OXYGEN

WITH OH, ClO, CH, NO, AND PHs

L.F. PHILLIPS Chemistry Department, Universityof Canterbury, Christchurch, New Zealand Received 1 September 1989; in final form 16 November 1989

Rate constants have been calculated for capture over the centrifugal barrier in a dipole-quadrupole + dipole-induced dipole + Morse + London potential over the temperature range lo-600 K. With allowance for electronic degeneracy factors, the calculated rate constants are in excellent agreement with experimental data for the reactions of0 with CH and ClO. The calculated results for 0 + OH are too large by a factor of 1.6,a result which is consistent with the recent conclusion that a second, shortrange barrier is involved in this reaction. For the 0 + NO* reaction the capture rate exceeds the experimental reaction rate by a factor of I .7, a difference which in this case is attributed to the existence of a potential barrier between the NO, complex and the products NO+Oz. For the 0+ PHs reaction, the capture rate is ten times larger than the experimental bimolecular rate constant for formation of an OPH, adduct, and this difference is tentatively attributed to the need for a triplet-singlet transition to stabilize the adduct

1. Introduction

Recently Graff [ I] has presented calculations of low-temperature rate constants for reactions of atomic carbon and oxygen with OH and CH radicals, and emphasized that these reactions, which involve an attractive, long-range dipole-quadrupole potential, have rate constants that tend to become larger rather than smaller as the temperature tends towards zero. Graff’s calculations used values of quadrupole moments calculated for the atoms by Gentry and Giese [2], in the framework of the ACIOSA approximate quantum-scattering method of Clary [ 31. A number of other calculations have been made for the reaction of 0 with OH, including quantum-scattering calculations by Clary and Werner [4], statistical adiabatic channel calculations by Troe [ 5 1, and quasiclassical trajectory calculations by Markovic, Nyman and Nordholm [ 61. The present paper gives the results of approximate classical trajectory calculations of capture rates over the centrifugal barrier in a potential that incorporates dipole-quadrupole, dipole-induced dipole, London, and Morse (or hard-sphere) interactions. The same computer program, which is described in detail elsewhere [ 7 1, has been used previously with

considerable success to calculate rate constants for the reaction of BH with NO [ 81 and for several ionmolecule reactions [ 91. The advantage of the present approach over the ACIOSA method is the ease with which a variety of different interactions, having different ranges, can be included in the potential. ACIOSA calculations that concentrate attention on the long-range part of the potential are liable to give results that are too low near room temperature [ 10,111. An obvious disadvantage of the present method is that it ignores quantum effects such as interference and tunnelling. However, such effects are quite difficult to demonstrate experimentally, and this seems unlikely to be a serious source of error. The present calculations do not yield the kind of detailed information that can be obtained from calculations using an ab initio surface, such as those of Markovic et al. [ 6 1, but they are also much less demanding of computer speed and capacity. The reactions discussed here, of 0 atoms with OH, ClO, CH, NO, and PH3, all involve initial capture over the centrifugal barrier in a potential whose long-range part is an angle-dependent dipole-quadrupole interaction, but the relationship between the capture rate and the experimental rate constant varies in an in-

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Volume 165, number 6

tcrcsting reactant. Gentry effective substate

way with

CHEMICAL PHYSICS LETTERS

the nature

of the molecular

and Giese’s calculations gave values of the quadrupole moment Q for each J and MJ of atomic oxygen [ 1,2]. Thus Q (in units 1Omz6 esu cm*) = + 1.04, -0.54 and - 1.07 for the IV.,= +2, IL 1 and 0 sub-levels of 0(3P,), respectively, Q= -0.54 and + 1.07 for M,= + 1 and 0 sublevels of 0 (‘PI ), and Q = 0 for 0 (‘Pa). Because no moment of inertia is associated with rotation of the J vector of the atom, the system of atomic quadrupole plus molecular dipole automatically adjusts itself so that the largest quadrupole moment of the proper sign for an attractive interaction is oriented towards the nearer pole of the dipole. For example, for O(3P,) the quadrupole moment of magnitude + 1.07 x 1O-26 esu cm* directs itself towards the negative end of the dipole when that is nearer, and a moment of the same size but opposite sign is directed towards the positive end of the dipole when that is nearer. For 0(3P,), the negative end of a dipole attracts a moment + 1.07 x 10Wz6esu cm*, whereas the positive end of the dipole calls the quadrupole moment - 0.54 x 1O-26 esu cm* into play. For 0 (‘P,) there is no dipole-quadrupole interaction. The angular part of the dipole-quadrupole interaction must always correspond to an attractive orientation so, as outlined by Graff [ 11, the usual cos e, (3 cos%* - 1)

2 February 1990

moment Q takes the value + 1.07~ 10mz6 esu cm2 forbothO(3Pz)andO(3P,),andiszerofor0(3P,,). Calculated capture rates are given in table I for these values of Q, for both Morse and hard-sphere interactions. (The Morse potential normally supersedes the other potentials at short range. In the hard-sphere case the Morse potential is omitted and the other potentials are truncated by a vertical wall at r=r_) The effect of the quadrupole interaction, as shown by the difference between columns 2 and 3 of the table, amounts to a factor of 4 in the capture rate at 10 K, decreasing to a factor of 1.9 at 300 K. The effect of the Morse potential, as shown by the difference between columns 2 and 4, is quite small when the quadrupole interaction is present, but is much more significant (column 3 versus column 5) when the quadrupole potential is absent. The large difference between columns 3 and 5 arises because the program requires the anisotropy of the potential to be great enough for the OH radical to stop rotating, if a collision is to be counted as effective and, in the absence of both Morse and quadrupole interactions, this means that only OH radicals with J= 0 can react. The Table 1 Capture rates for 0 +OH with Morse (M ) and hard-sphere (hs) potentials at short range, and thermally averaged rate constant. Units of k: IO-” cm3 moleculec’ ss’. k,,ar,M= 10” xk,.,(Q=1.07~10~~~esucm~,Morse);~.~,,..=IO”k,,(Q=O, hard-sphere potential); k,,,,= thermally averaged rate constant, calculated as described in text a1

- 2sin8Asin8,cos$cos(@A-@a) angular factor simplifies to cos f3, (3 c0s%, - 1) - 2 sin 6, sin $ cos

eB ,

where 0, is variable and f3n must be chosen to optimize the attractive potential at each value of 0,. The present calculations were run with fixed values, 1.07~ lo-*“, 0.54x 1O-26 or 0 esu cm*, of the quadrupolc moment, depending on which state of 0( ‘P) was involved and which end of the molecular dipole was required for a reactive collision. 2. Results and discussion

2.1. The reaction 0+ OH+ 02+ H For reaction to occur, the 0 atom must collide with the negative end of the dipole, so the quadrupole 546

10 20 30 50

75 100 150 200 250 300 350 400 500 600

53.1 51.1 49.5 48.3 47.7 47.4 47.5 47.5 47.7 48.2 48.3 48.5 49.0 49.3

13.4 15.1 16.1 17.5 18.8 19.8 21.6 23.1 24.4 25.7 26.9 28.2 29.9 31.6

52.7 51.7 49.2 48.3 47.6 47.3 47.4 47.7 47.8 47.9 48.0 48.3 48.6 48.9

13.6 12.8 10.8

8.00 6.07 4.92 3.59 2.84 2.35 2.02 1.78 1.60 1.40 1.16

5.31 5.11 4.95 4.85 4.85 4.90 5.06 5.19 5.32 5.46 5.55 5.65 5.82 5.94

‘) Morse parameters: r,=1.3 A, De=272 kJ mol-’ [13], w,= 1800 cm-‘; London-potential frequencies 77000 and 33000 cm-’ [ 131; dipole moment OH= 1.67 D; polarizabilities 1.14 and 0.802~ IO-*“cm).

CHEMICALPHYSICSLETTERS

Volume 165,number 6

final rate constant, k,,,, is obtained by forming a thermal average of k,.,,7,M from table I for O(3P1) and 0( 3P,), and kO.O,Mfor 0t3P,), with an electronic degeneracy factor that depends on the states of 0 and OH involved in a way that depends on certain assumptions, as follows. We assume ( 1) that the spin-orbit splitting in this system is large enough to permit collisions of individual fine-structure states of 0 and OH to be considered separately, (2) that the quantum numbers J for the resultant electronic angular momentum of the oxygen atom and G for the component of electronic angular momentum along the OH radical’s internuclear axis are still good quantum numbers at a reactant separation which corresponds to the onset of chemical forces, but the quantum number M, is no longer fixed at the value required for optimum orientation of the quadrupole moment, (3) that rcaction occurs only on the lowest potential energy surface available to each pair of reactants, and (4) that for the reactions of 0 with OH, Cl0 and CH this surface correlates with a *Z state of a linear triatomic complex. The final rate constant for the O+OH reaction then becomes

2 February 1990

with the positive end of the dipole do not contribute to the reaction. The values of km,, in the last column of table 1 are not in particularly good agreement with experiment, a recent evaluation [ 14 ] giving k,,, = 3.3 X 1O- ’ ’ cm3 molecule-’ s-’ at 300 K, with a small negative temperature coefficient and an uncertainty of only 2 20% (expressed as an uncertainty factor of 1.2). The discrepancy cannot be due to a poor choice of Morse parameters: for example, changing o, from 1800 to 1200 cm-’ causes k,,, to increase by only 1% at 300 K, and reducing the Morse well depth to 50 kJ mol-’ also makes very little difference. The detailed trajectory calculations of Nordholm and coworkers [ 61 have led them to conclude that the formation of a reactive O-OH complex requires the crossing of two potential barriers, such that collisions in which the outer, centrifugal barrier is crossed do not necessarily lead to reaction. It would appear that this unusual, even pathological, situation is responsible for the fact that the present calculations, which recognise only the outer barrier, give values of k,,,, that are too large. 2.2. The reaction 0 + ClO-+ O2+ Cl

+ 13Pol[‘~,,,l&,~km,~

+ [3p,l [2n3,21h,3,2 +

[9’21

+ [3p21

[‘n,,,lf2,3,2)k,.0,,Mj

[2h,2ti,1,2 3

(1)

where, for example, [3P,] stands for the fractional population of 0(3P,), [2H,,2] stands for the fractional population of OH (*II, ,2), and the degeneracy factor& is 1 or 0, depending on whether or not there is a ‘C resultant state, divided by the total number of resultant states. For example, for 0 ( 3Pa) reacting with OH(*H,,,), the vector J has a component IV,= 2, 1, 0, - 1 or -2, in units /2/2x, along the collision axis. A *C state is identified as one of the + l/2 states that is among the total of five + Q states which result from combining the five M, values with 9= * l/2 from alI,,z, so fi,,,z= l/S. The other f,,* values are:.L,312=1/5, fi,Llz=fi,31z= l/3, fo,l,2=l, and f0,3,2=O_ The initial factor of 0.5 on the righthand side of eq. (I) arises because collisions of 0

This system resembles 0+ OH in that the 0 atom must react with the negative end of the dipole. Reaction of 0 with the positive end of the dipole results in the formation of a complex OClO* which is bound almost as strongly as ClOO*, but this complex would have to rearrange via a highly strained, three-membered-ring transition state to give the products O*+Cl, and it seems reasonable to neglect this rcaction channel. The results in table 2 were calculated in the same manner as those in table 1, with the difference that here WC obtain values in excellent accord with experiment. The recommended value of k,,,, at 300 K is 3.8x lo-” cm3 molecule-’ s-r, with an uncertainty factor of 1.2 and a temperature coefficient which is zero within experimental error [ 141. 2.3. The reaction 0-b CH- CO+ H This reaction was studied experimentally by Messing et al. [ 15 1, who measured the total rate of disappearance of CH in the presence of excess 0 atoms, and who point out the existence of more than 547

Volume 165, number 6

2 February 1990

CHEMICAL PHYSICS LETTERS

Table 2 Capture rates for O+ClO (Morse and hard-sphere potentials) and thermally averaged rate constant, as in table 1. Units of k: s-’ a)

Table 3 Capture rates for O+CH (Morse and hard-sphere potentials) and thermally averaged rate constant, as in table I. Units of k: IO-” cm3 molecule- ’ s-’ a)

IO-”

cm3 molecule-’

T(K)

h07,M

k O.O,M

kI.07.h.a

k0.o.h.s

km.

T(K)

kl.ow

kO.0,~

kl.w-s

ko.w-s

k,,,

10 20 30 50 75 100 150 200 250 300 350 400 500 600

33.0 33.6 34.2 35.4 36.9 38.0 39.2 39.7 39.9 39.8 39.8 39.7 39.7 39.7

15.7 19.9 22.4 25.8 27.2 27.8 27.6 27.3 26.9 26.6 26.6 26.6 26.8 27.5

33.1 33.6 33.8 34.0 34.0 34.0 33.9 33.5 33.2 32.8 32.3 32.1 31.5 31.1

1.159 0.664 0.483 0.32 I 0.230 0.181 0.129 0.102 0.085 0.073 0.065 0.059 0.05 1 0.045

3.30 3.37 3.42 3.56 3.75 3.92 4.16 4.30 4.39 4.45 4.51 4.55 4.63 4.72

10 20 30 50 75 100 I50 200 250 300 350 400 500 600

52.9 50.5 49.7 49.6 51.5 53.9 58.7 63.5 67.4 70.4 72.9 74.9 77.4 78.9

23.0 29.8 33.4 41.2 46.8 51.8 57.8 61.5 64.4 64.1 65.1 64.8 63.7 62.8

52.9 50.5 49.4 48.2 48.2 48.1 48.0 48.3 48.6 48.8 49.2 49.3 49.8 50.0

13.7 11.5 0.930 0.668 0.499 0.400 0.288 0.227 0.188 0.163 0.144 0.129 0.108 0.094

5.29 5.05 4.91 4.98 5.27 5.67 6.52 7.35 8.02 8.53 8.94 9.18 9.68 9.94

‘) Morse parameters: ye= 1.3 A, 0,=258

kJ mol-‘, w,= 1000 cm-‘; dipole moment ClO= 1.24 D; polarizabilities 3.1 and 0.802 x 10mZ4 cm3; London frequencies 30000 and 77000 cm-‘; all calculations for “Cl.

seven different sets of energetically accessible products. The products given in the heading are the most stable ones that can be formed by a bimolecular reaction. The value of k,,, was measured as (9.5+ I .4) x lo-” cm3 molecule-’ s-’ at 298 K. Table 3 shows results of calculations for 0+ CH, analogous to those in tables 1 and 2. Here, too, the agreement with experiment is excellent. 2.4. The reaction 0-t NOpNO+

0,

This reaction differs from the others in that the quadrupole has to interact with the positive end of the dipole, so for 0( 3P,) the magnitude of the effective quadrupole moment is only 0.54 x 1O-26 esu cm2. The second, third and fourth columns of table 4 show calculated capture rates for 0 ( 3P2), O( 3P,) and 0(3P,), respectively. All of these calculations include a Morse potential at short range. To calculate the degeneracy factor for this system we note that the interaction, of 0(3P) with N02(2A, ) under D3h symmetry gives rise to doublet and quartet A2 and Ey states of NOS. Assuming that the lowest potential surface corresponds to N03( ‘A’ ), we find a degeneracy factor of l/9, with an additional factor of 0.5 548

r,= 1.3 A, DC=794 kJ mol-‘, w,= 1800 cm-‘; dipole moment CH= 1.46 D; polarizabilities 2.0 and 0.802 x 10ez4 cm3; London frequencies 77000 and 20000 cm-‘.

‘) Morse parameters:

Table 4 Capture rate for O+NO, (Morse potential only) and thermally averaged rate constant, as in table I. Units of k: IO - ” cm3 mol-

ecule-’ s-’ 8) T(K)

k 1.07,t.l

k 0.54,t.i

km

k rate

10 20 30 50 75 100 150 200 250 300 350 400 500 600

18.7 19.8 20.5 21.6 22.8 23.9 25.9 21.3 28.3 29.0 29.5 29.9 30.1 29.9

15.9 17.2 18.3 19.9 21.5 22.8 24.8 26.4 27.2 27.9 28.3 28.4 28.7 28.2

13.5 15.1 16.3 18.2 20.2 21.4 23.6 25.2 26.0 26.7 26.8 26.9 21.2 26.3

1.04 1.10 1.14 1.20 1.26 1.33 I .43 1.51 1.54 1.59 1.62 1.63 1.64 1.62

n) Morse parameters: r,= 1.3 A, De= 206 k.l mol-I, w, = 1000 cm-‘; dipole moment N02=0.29 D; polarizabilities 2.8 and 0.802~ 1O-*4 cm-‘; London frequencies 20000 and 77000 cm-‘.

to allow for collisions with the wrong end of the dipole. This gives the k,,, values of table 4, which exceed the accepted experimental value [ 141 by a factor of 1.7 at 300 K. This result is not surprising, because there is a significant energy barrier between

Volume

the potential well corresponding to NO, and the products NO + O2 [ 16 1, and the overall reaction rate is therefore controlled by the relative rates of the NO: complex crossing this barrier and dissociating back to reactants. In the absence of values for the vibrational frequencies of the transition state for rearrangement, calculation of the overall rate constant has to be deferred. 2.5. The reaction of’0

2 February 1990

CHEMICALPHYSICSLETTERS

165.number 6

with PH3

This reaction was studied by Nava and Stief [ 17 1, who measured the rate of disappearance of 0 atoms in the presence of excess PH3 and obtained a value of (4.75f 1.09) x IO-” cm3 molecule-’ s-’ for the rate constant, independent of pressure in the range 7.5-100 Torr argon, and independent of temperature over the range 208-423 K. The process occurring was identified as addition to form a bound species 0PH3. The final OPHj product might be in a triplet state, but it seems more likely that it should be in a singlet state; thus the rate of the addition reaction should be equal to the capture rate multiplied by the probability of intersystem crossing from triplet to singlet states of 0PH3. Once the adduct had arrived in the singlet state the dissociation back to products would be spin-forbidden, which could help to explain why the association is bimolecular. Capture rates for formation of OPH: are shown in table 5, where the second column of the table gives rates for O(3P,) and 0(3P,), and the third column for 0( 3P0)_ To be counted as successful in these calculations, a collision had to lead to an O-P distance of closest approach less than 1.6 A. Because of the relatively small dipole moment of PHJ, the results are dominated by the Morse potential, which perhaps is unfortunate in view of the known inadequacies of the Morse potential at long range. Nevertheless, the calculated values of k,,,, are essentially independent of temperature between 250 and 400 K, in accord with experiment. Comparison with the experimental data suggests a value of about 0.1 for the probability of triplet-singlet transition during a close 0-PH, collision.

5 Capture rates for 0+ PH3 (Morse potential only) and thermally averaged rate constant, as in table 1. Units of k: lo-” cm’ mol-

Table

ecule-’

s-’ ‘)

T(K)

k L07,M

k 0.0

k ntc

IO 20 30 50 75 100 150 200 250 300 350 400 500 600

Il.6 21.8 25.1 29.8 34.1 31.4 42.6 46.0 49.0 50.6 52.5 53.6 54.7 55.2

17.4 22.1 25.4 29.9 34.3 31.4 42.6 45.8 48.6 50.1 51.8 52.6 53.2 53.4

17.6 21.8 25.1 29.8 34.1 37.4 42.6 46.0 49.0 50.6 52.4 53.5 54.6 55.0

‘~Morseparameters:r,=1.5.&0.=515kJmol-’,w,=800cm-‘; dipole moment PH,=0.55 D; polarizabilities 4.27 and 0.802~ 10-24cmJ;London frequencies50000and 77000cm- ‘.

3. Conclusions Approximate classical trajectory calculations have proven satisfactory for the prediction of radical-radical reaction rates for simple systems, such as O+CH and O+ClO, in which the rate is largely governed by the rate of capture over the centrifugal barrier in a dipole-quadrupole potential. However, because the dipole-quadrupole interaction is weak it is not always dominant, and the example of O+OH shows that the effective capture rate may be limited by short-range processes that are not easy to predict without making full-scale trajectory calculations. For more complex reaction systems, such as 0 + NOz and 0 + PH3, the difference between the calculated capture rate and the experimental rate constant can provide an indication of the importance of processes occurring subsequent to capture over the centrifugal barrier.

Acknowledgement This work was supported by the New Zealand Universities Research Committee.

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CHEMICAL PHYSICS LETTERS

References [ I ] M.M. Graf, Astrophys. J. 339 ( 1989) 239. [ 21 W.R. Gentry and C.F. Giese, J. Chem. Phys. 67 (I 977) 2355.

[ 31 DC. Clary, Mol. Phys. 53 (1984) 3. 141DC. Clary and H.-J. Werner, Chem. Phys. Letters I I2 (1984) 346. [S] J. Tree, J. Phys. Chem. 90 (1986) 3485. [ 6) N. Markovic, G. Nyman and S. Nordholm, Chem. Phys. Letters 159 (1989) 435. [ 7) L.F. Phillips, J. Comput. Chem., in press. 181L.F. Phillips, Chem. Phys. Letters, in press. [ 91 L.F. Phillips, .I. Phys. Chem., in press. [IO] L.F. Phillips, J. Chem. Sot. Faraday Trans. II 83 (1987) 857.

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[ I 1 ] I.R. Sims and I.W.M. Smith, Chem. Phys. Letters I51 (1988)481. [ I21 S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, R.D. Levin and W.G. Mallard, J. Phys. Chem. Ref. Data I7 (1988) supplement 1. [ I31 J.O. Hirschfelder, C.F. Curtiss and R.B. Bird, Molecular theory of gases and liquids (Wiley, New York, 1963). [ I41 W.B. DeMore, M.J. Molina,S.P. Sander, D.M. GoIden,R.F. Hampson, M.J. Kurylo, C.J. Howard and A.R. Ravishankara, Jet Propulsion laboratory Publication 874 I, Pasadena, California Institute of Technology ( 1987 ). [ I51 I. Messing, S.V. Filseth, C.M. Sadowski and T. Carrington, J. Chem. Phys. 74 ( 1981) 3874. [ 161P.E.M. Siegbahn, J. Comput. Chem. 6 (1985) 182. [ I71 D.F. Nava and L.J. Stief, J. Phys. Chem. 93 (1989) 4044.