J. Phys. Chem. 1992, 96,7346-7351
7346
for all amplitudes of perturbation. So care must be taken when determining the autonomous frequency, as slight differences may result in varying dynamics. In our experiments on a stable focus, described in the preceding article,5a negligible NADH response to perturbation suggests that NADH is a nonessential species in a stable focus, while the DOP calculations on a stable focus suggest that NADH is an essential species in a stable focus. This is a major disagreement, probably resulting from the simplicity of the DOP model. The numerical perturbation studies on a stable focus also showed that the DOP model exhibits 0 - S bistability, and the average oxygen concentration of the oscillatory state is the same as the oxygen concentration of the steady state. This is in good agreement with experiments performed by Aguda, Hofmann Frisch, and Olsen.2 Sinusoidal perturbations on a chaotic state of the DOP model show chaotic responses for low amplitudes of perturbation and periodic responses for high amplitudes of perturbation. The dissipation increases as the amplitude of perturbation increases, whereas the opposite is found for sinusoidal perturbations on an experimental limit cycle and for sinusoidal and nonsinusoidal perturbations on a calculated and experimental stable focus. Both the form of the external perturbation and the dynamic state of the system are of importance in determining the dissipation.
References rad Notes (1) Degn, H. Nature 1968, 217, 1047.
(2) Aguda, B. D.;Hofmann Frisch, L.-L.; Olsen, L. F. J . Am. Chem. Soc.
1990, 112,6652.
(3) Nakamura, S.; Yokota, K.; Yamazalti, I. Nature 1969, 222, 794. (4) Olsen, L. F.; Degn, H. Nature 1977, 267, 177. (5) Samples, M.S.; Hung, Y.-F.; Ross, J. J. Phys. Chem. P r d n g paper in this issue. (6) Lazar, J. G.; Ross, J. Science 1990, 247, 189. (7) Lazar, J. G.; Ross, J. J. Chem. Phys. 1990, 92, 3579. (8) Degn, H.; Olsen, L. F.; Perram, J. W. Ann. N.Y. Acad. Sci. 1979,316, 623. (9) Aguda, B. D.; Larter, R.J . Am. Chem. Soc. 1990, 112, 2167. (IO) Steinmetz, C. G.; Larter, R. J . Chem. Phys. 1991, 94, 1388. (11) Olson, D. L.; Schecline, A. Anal. Chim. Acta 1990, 237, 381. (12) Olsen, L. F.; Hofmann Frisch, L.-L.; Schaffer, W. M.The Peroxidase0xida.w Reaction: A Case for Chaos in the Biochemistry of the Cell. In A Chaotic Hierarchy; Baier, G., Klein, M.,Eds.; World Scientific Publishers: Singapore, 1991. (13) Hindmarsh, A. C. ACMSignum News. 1980, 15, 10. (14) Hjelmfelt, A.; Harding, R. H.; Tsujimoto, K. K.; Ross,J. J. Chem. Phys. 1990, 92,3559. (15) The AGO for reaction 1 is found from the following two halfell reactions and their Eo values: '/zOz + 2H+ + 2e- HzO, Eo (pH = 0) = 0.6145 V (ref 16); NADH + H+ NADt + 2Ht 2e; Eo (pH = 7) = 0.32 V (ref 17). These values are then converted to AG by AG = -rrFE, adjusted to pH 6.0, and then added together to obtain the overall AGO for reaction 1. (16) CRC Handbook of Chemistry and Physics, 65th ed.; Weast, R. C., Astle, M.J., Beyer, W. H., Us.CRC ; Press: Boca Raton, FL. 1984-1985; Acknowledgment. This work was supported in part by the p D-157. National Institutes of Health. (17) Stryer, L. Biochemistry, 3rd ed.; W. H. Freeman and Co.:New York, Registry No. NADH, 56-68-8;O2,7782-44-7;peroXidase,9003-73-O; 1988; p 401. oxidase, 9035-73-8. (18) Aizawa, Y.; Ueza, T. Prog. Theor. Phys. 1982,68, 1864.
-
-+
Fast Reactions between Diatomic and Poiyatomic Molecules T. Stoecklin Laboratoire de Physico- Chimie Thgorique, 351 Cows de la Libgration, 33405 Talence Cedex, France
and D. C. Clary* Department of Chemistry, University of Cambridge, Lenrfield Road, Cambridge CB2 I E W,U.K, (Received: March 3, 1992;In Final Form: May 20, 1992)
Calculations of rate constants are presented for fast neutral reactions between polar diatomic and polyatomic molecules. The method applies the infiniteordersudden approximation to treat the rotations of the diatomic molecule and a rotationally adiabatic approximation with asymmetrictop wavefunctions to describe the rotations of the polyatomic. A captureapproximation is used to calculate reaction cross sections and rate constants. The interaction potential is expressed as a sum of dipoldpole and dispersion contributions. The calculated rate constants compare well with analytical formulas derived for the limits of high and very low temperatures. The NaO + H20, NaO + 03,CH + CH20, and SH + NO2 reactions are considered as examples and calculated rate constants are compared with experiment for these four fast reactions. Quite good agreement is obtained for the NaO O3and CH + CH20 reactions.
+
1. Introduction
A rotationally adiabatic capture theory (AC) combined with various sudden approximations has been applied previously to calculate cross sections and rate constants for a wide range of fast reactions involving neutral or charged particles.'-'O For such reactions, a large amount of experimental rate constant data is now available and is needed in areas such as atmospheric,"J2 comb~stion,'~ and interstellar chemistty.l4 Most previous theoretical studies on neutral fast reactions were concerned with r e actions involving only atoms or diatomic molecules, although some calculations have been reported on the reactions of ions with symmetric and asymmetric top m ~ l e c u l e s . ~ ~ ~ J ~ A particularly powerful version of the rotationally adiabatic theory for fast moleculemolecule reactions is the adiabatic capture partial centrifugal sudden approximation (ACPCSA).I This method uscs the infiniteorder-sudden approximation (IOSA) for one molecular partner with a small rotor constant and the rota-
tionally adiabatic theory for the other molecular partner. The technique has, so far, been applied to several reactions between diatomic molecules.' It is reviewed and compared with other methods in ref 7. We present here an extension of this method to the fast reaction between a polar diatomic molecule and a polar polyatomic molecule described as an asymmetric top. We use an analytical expansion of the long range part of the interaction potentialI5 including electrostatic and dispersion terms. Also, for each angular configuration of the diatomic molecule we apply a classical capture theoryI6 to calculate cross sections and rate constants which are state-selected in the rotational states of the asymmetric top molecule. All molecules are treated as having closed electronic shells. The theory gives rate constants that refer to a summation over all product states and is most appropriate for very exothermic reactions with strongly attractive long-range potentials in the reactant channel. We apply the ACPCSA to the fast reactions 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7347
Diatomic and Polyatomic Reactions NaO(%)
+ H 2 0 -,NaOH + OH
Na0(211)
----
+ O3
CH(211) + CH20
+
Na 202 Na02 + O2
4
CH2 + HCO
+
CH, CO CH2CO + H
AHo298 AH'298 m 2 9
K-+j
=
-6 f 12 kJ mol-' = -138 kJ mol-' 8 = -301 kJ mol-'
w 2 9 8 &YO298
= -48 kJ mol-' -443 kJ mol-'
w 2 9 8
-308 kJ mol-' = -95 kJ mol-' AH'298 = -73 kJ mol-' and compare with experimental rate constant measurements made at rmm temperature. The calculations of rate constants for these reactions are compared with an analytical formula derived using the IOSA, which is appropriate for higher temperatures. An analytical formula is also derived using perturbation theory for the rate constants when the temperature is very low. In section 2 the ACPCSA for the fast reactions of diatomic molecules with polyatomic molecules is described. The derivation of an analytical rate constant for low temperatures is given in section 3. Section 4 presents results and compares with experimental rate constants for the NaO + H20, NaO 03, CH + C H 2 0and SH NO2 reactions. Conclusions are in section 5.
HS(Q)
+ NOz
HSO + NO SO HNO
+
AH'298
+
+
+
2. The ACPCSA for Diatom Asymmetric Top Reactions The method is an extension of the ACPCSA presented before for the fast reactions between two diatomic molecules.'*' The formulation is similar to the case of the reaction of ions with polar polyatomic molecules.8 For fixed orientations of the diatomic molecule, the intermolecular potential is diagonalized,using a set of asymmetric top basis functions, on a grid of distances of the intermolecular coordinate R. This diagonalization yields a set of rotationally adiabatic potential curves which are state selected in the initial rotational states of the asymmetric top molecule. Application of classical capture theory to each of these potential curves and averaging over the orientation angles of the diatomic molecule give cross sections which are state selected in the rotational states of the asymmetric top molecule. Both molecules are treated as rigid rotors as molecular vibrations are normally not important for this type of reaction.' We use a body fixed frame of coordinates" which is the most convenient for the application of sudden approximations. It is obtained by a rotation R($R,BR,O)of the space fmed frame, where R, OR and & are the polar coordinates which describe the relative orientation vector of the two interacting molecules in the spacefixed frame. The polar coordinates of the dipole moment of the diatomic molecule are the angles 8, and CPl in the body fxed frame and the Euler angles which describe the orientation of the molecular frame of the asymmetric top are (a,8, r).Upon applying the IOSA to the diatomic molecule, the Hamiltonian (in atomic units) of the interacting system takes the form
where
and is a Wigner rotation matrix.18 This gives then, for each value of j , the asymmetric top energy levels Ej,r as eigenvalues and the coefficients Cj,,(K)as eigenfunctions of the operator H, in the symmetric top basis set. The global basis set used to diagonalize the intermolecular potential V is
For a fixed value of R and Bl the wave function is expanded in this basis set
E
j , n. r
(4)
Furthermore, for the molecules considered here, we assume that the dipole moment of the asymmetric top molecule lies along its z molecular fixed axis (az = a and Bz = 8) so a body-fixed expansion of the potential surface can be used in terms of the Wigner rotation matrices
v(R,B~,B~,@) = C .L\,L(R,Bl)Dm,oL.(0,B2,0) ( 5 ) L.m
The only nonvanishing coefficients of this expansion are given by (6)for the dipole-dipole and dispersion contributions to the potential f " 1
where pl and p2 refer to the dipole of the molecules 1 and 2, respectively, and C6is the dispersion coefficient. Moreover, in the present treatment it is assumed that the molecules have closed electronic shells and, within the CSA approximation,the coupling between different values of the projection of the total angular momentum along the z axis of the body fmed frame is neglected. The matrix to diagonalize is then WJVMj,n>,; y,nl,ARA) = b j & t , d r , * 1)
(1) where H, is the Hamiltonian of the free asymmetric top molecule, j is its rotational angular momentum operator in the body fixed frame with associated quantum number) and projection Q on the z axis of the body-fixed frame, J is the total angular momentum of the system, I.( is its reduced mass, B2 and a2are the polar coordinates of the dipole moment of the asymmetric top molecule in the body fixed frame, and CP = CP, - CP2. K is defined as the component of the rotational angular momentum of the asymmetric top molecule projected along the molecular fied z axis and T is the quantum number associated with the Merent energy levels of the free asymmetric top molecule for a given value of j . The usual symmetric top expansion (2.a) is used to calculate the different energy levels of the asymmetric top moleculela
Gj,n,$M(R,Bl)vQ7JM)
1
+ ju + 1) - 2Qz]
[
Ej,r
1 2pR2
+ -[J(J
+
(j62TJ~v(R,8',Bla)vn'7'JM)(7)
The potential matrix element is independent of J and M. Thus, omitting these indices and using the expansions 3-5, the matrix elements of the potential can be written as (jQ71V(R,B,,B,a)vWf) 1
+i
+i'
where +Mj,Kj#,K
= (-1) '"4'1[(2j
+ 1)(2j' + l)]'%n,nx
7348 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 TABLE I: Rotational Degtmemcy Factors of the Asymmetric Top Mokepks with at Lust Two Ideatid Nuclei"
molecule
H20
CHZO
S
1
1
a
3
3
NO2 1 0
0, 1
0
"The symmetric and antisymmetric weights are noted s and a. are the matrix elements of the symmetric top problem obtained using the usual definition of the 3j symbol.Is The diagonalizationof Wfi,,n,r;l,n,,(R,Bl) over a range of fmed R values yields the rotationally adiabatic potential energy curves eJ,?,r(R,BI) where the labels refer to the quantum numbers of the initial rotational state of the polyatomic (jn~).In the context of the rotationally adiabatic capture theory,' for a collision energy E,, a maximum value of the total angular momentum J,,(Blj,Q,7,E,) is obtained above which the classical reaction probability is equal to 0. The state-selected cross sections in the initial rotational states j and 7 , are then obtained by averaging over all the configurations of the diatomic molecule
QU,T,E,)= +I
$*sin (8,) n=-/ c [J,,,,,(~lj,n,7,E,)+ W +j 1)
U
4 ~
0
112 d 4
(10)
Stoecklin and Clary dependence of the rate constant. In the following calculations the open shell nature of the reactants and the rotational structure of the diatomic molecule are neglected. Thus, the calculated rate constants apply strictly to reactions between linear molecules in 'Z states and nonlinear molecules in 'A states. The first-order contribution (1 3 ) to the perturbation of the fundamental state (j = 0, 7 = 1, Q = 0), is due to the dispersion term
(13) The state (j = 0, 7 = 1, Q = 0) is coupled via the dipoldipole potential to the states (j = 1, 7 2, Q = 0) and (j = 1, T = 3, Q = 0) and, we fmd then for the second-order perturbation energy term
(14) where A, B, and C are the rotational constants for the asymmetric top molecule.'*J9 The dispersion contribution is neglected since the electrostatic term is much more important for very large R and we obtain the following rate constant
Then, by averaging the cross sections over translational energy, a rotationally selected rate constant &J, 7') is obtained. Finally the total rate constant is obtained by Boltzmann averaging over the initial rotational states of the asymmetric top molecule where
where k@ is the Boltzmann constant and the degeneracies &,7) of the rotational states j T for the H20, 03,NO2, and CH20 molecules are given by HerzbergI9 and are listed in Table I.
(16) The values of J(A,B,C) are given in Table IV for the asymmetric top molecules considered here and are all close to 2.5.
3. Analytical Rate Constants 4. C d C l l b ~ O l l S 3.1. High Temperature: The ACIOSA. In the ACIOSA, the In this section, calculationson the reactions NaO + HzO, NaO IOSA is applied to both molecules. It is the simplest approxi+ 03,CH + CH20, and SH + NO2 are reported. For each of mation of the problem and yields an analytical expression of the these reactions the role played by the dispersion contribution to rate constant which for the dipoltdipole potential is' the potential is examined and, at 300 K, the values of the ACIOSA, and experimental rate constants are comk'OSA(T) = 1 . 7 6 6 ( ~ / ~ ) ' / ~ [ ~ ~ r ~ ] ~ / ~(12) ~ k ~ T ] - 'ACPCSA, /~ pared. An estimate of the zero temperature limit for the rate constant is also given. 3.2. Low Temperature: Perturbation Theory. At very low 4.1. Tbe ACPCSA clleuhtioaa For the ACPCSA calculation temperaturm, it is possible to calculate the rotationally adiabatic between 30 and 510 K, the rotationally adiabatic potential energy potential energy curves and rate constants analytically by using perturbation theory. This is because,for very low collision energies, curves were calculated on a grid along the intermolecular coorthe centrifugal barriers in the effective potentials occur at very dinate R with the values 100.0,80.0,60.0,40.0,20.0, 10.0,8.0, 7.0.6.0, 5.0,4.0,3.0, and 2.0 bohr. For each of these distances large R where the interaction is so small that perturbation theory eight different angular orientations of the diatomic molecule were is applicable. This approach is denoted RAPT (rotationally considered. The 12 collision energies used to calculate cross adiabatic perturbation theory). Neglecting the open shell nature sections were 1 X lo-', 1 X 1.75 X lo4, 3.3 X lo4, 4.9 X of the reactants, this type of calculation has been done for dilo4, 6.5 X lo4, 8.1 X lo4, 9.7 X lo4, 1.12 X lV3, 1.28 X poldipole and dipolquadrupole reactions between closed-shell 1.44 X and 1.60 X hartree. diatoms' and for ion-dipole reactions involving symmetric top and asymmetric top molecules.8 A similar approach was first used For temperatures up to 500 K, excellent convergence of the rate by TrkZ0in a statistical adiabatic channel analysis of the T constants was obtained with j having a maximum value of 7 in the basii set of cq 3. In the following calculations, the rotational 0 limit of the rate constant for ion-dipole reactions. It should be noted that in a recent studg' Wickham et al. found basis set used for both symmetric top and asymmetric top molecules involves integer j values from 0 to 7. that the zlInature of the OH reactants in the H3++ OH H20+ + H2 reaction leads to a temperature dependence of the rate Figure 1 shows the asymmetric top rotationally selected rate constant that is different from that for a closed-shell molecule constants for different pairs of initial (j, 7 ) states for the NaO + H 2 0reaction. Only the rate constants for the two initial states for temperatures below about 100 K. Also, in a study on diatom-diatom reactions in which calculations were done with a more of HzO, (j = 0, T = 1 ) and (j = 1, 7 = l), are seen to decrease accurate rotationally adiabatic capture theory that involves using in magnitude when the temperature is increased. All others a rotational basis set for both reacting diatomic~,~ it was found increase with temperature. However, a regular behavior of the that the ACPCSA rate constants were not accurate for very low rotationally selected rate constant can be seen; the magnitude for temperatures close to T = 0, but the accuracy did improve cona given value of j decreases when r increases. siderably for temperatures higher than this. However, the (a) DipmionTerm Meek In a previous paper7we proposed ACPCSA results for very low temperatures derived here should a criterion to estimate which contribution to the potential (the be useful in giving a qualitative description of the temperature dipoltdipole interaction or the dispersion term) is driving the
-
-
Diatomic and Polyatomic Reactions
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7349 TABLE 11: M0klll.r Pllrclmetera
(a) Asymmetric Top Molecules molecule
CHzO 2.33 2.50 10.9 9.405 1.295 1.134
IilD
a/A3
E*/eV A1cm-I B1cm-I C/Cm-'
molecule 1
100
0
200
300
400
+
8.1 3.40 6.5
a/A3
E*feV
NO2 0.21 2.80 9.8 8.001 0.434 0.410
0 3
0.53 3.21 12.3 3.553 0.445 0.395
(b) Diatomic Molecules NaO CH
PllD
500
TK Figure 1. ACPCSA rotationally selected rate constants kU(HZ0),7(H20),T) for the reaction NaO HzO ( T is denoted tau).
HzO 1.85 1.45 12.6 21.871 14.512 9.285
1.46 2.20 10.64
SH 1.01 1.12 10.43
TABLE IIk Exponents I and b of the Fitted ACPCSA Rate Comtants between 30 nod 510 KO reaction a b N a O HzO -0.21 -0.26 NaO + O3 -0.26 -0.09 C H CHzO -0.28 -0.08 S H NO2 -0.04 +0.19
+
+
+
+
ACPCSAdiy,
300 400 500 TK Figure 2. Comparison of the ACPCSA rate constants of the reaction NaO HzO when calculated with (denoted disp) and without the dispersion term in the potential. 100
0
200
'Here, k(T) = P and k(T) = Tb refer to the temperature dependence of the rate constants obtained in calculations without and with the dispersion term in the potential, respectively. TABLE N: Values of J ( A ,E$) for the Asymmetric Top Molecllks (See Equation 16) molecule HzO 0, NO, ' CH,O J(A,B,C) 2.530 2.412 2.467 2.413
+
reaction at a given temperature. If we take the angular dependence of the dipole-dipole (C3/R3)term as a constant, it can be shown that the temperature above which the dispersion contribution to the potential c6/R6 is dominant (yielding a rate constant that increases with temperature) is determined approximately by
We estimate
c 6
from the London formula" 3alE1*a2E2* c 6 = 2[E'* E2*]
oL 0
+
where E,*, E2*, a', and a2 are the ionization energies and polarizabilities of the reactants. As a result of this criterion, it can be expected that some dipole-dipole reactions involving molecules with large dipoles (such as NaO) might be driven by the electrostatic potential even at high temperatures. Several molecules exhibiting very different values of their dipole moment and polarizability were chosen in order to check the validity of this criterion. For example the values of the dipole moments in debye (D) are ranking from 8.7 D (NaO) to 1.01 D (SH)for the diatoms and from 2.33 (CH20) to 0.21 D (NO2) for the asymmetric top molecule. The relevant molecular constants necessary for the evaluation of the potential are presented in Table II.19 It can be seen in Figure 2 that the effect of the dispersion term in the potential is temperature dependent. For a reaction such as NaO + H 2 0 the effect is only small, whereas, for a reaction such as SH NO2, Figure 3 shows that the dispersion contributions are dominant at 300 K. Between these two extreme behaviors, intermediate casea exist such as NaO + O3(see Figure 4) and are summarized in Table 111. All of them are in good agreement with the criterion (17). As has been shown in a previous paper,' higher order multipole interactions, such as quadrupole-
+
'
100
200
300
400
I
500
TK
Figure 3. Comparison of the ACPCSA rate constants of the reaction SH
+
NO2 when calculated with (denoted disp) and without the dispersion term in the potential.
I
~~~
0
100
200
300
400
500
TK Figwe 4. Comparison of the ACPCSA rate constants of the reaction NaO + O3 when calculated with (denoted disp) and without the dispersion term in the potential.
7350 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992
reaction NaO + H 2 0 NaO + O3 CH SH
+ CH20
+ NO2
kt0
kt
ke~,
ke-
8.94 1.89 2.95 0.36
9.06 3.00 4.99 3.46
1.80 1.9 3.1 0.45
2.60 2.2 4.5 0.89
Stoecklin and Clary
a We give the two values kt and kto of the theoretical rate constant calculated respectively with and without the dispersion term in the potential. Units for the rate constants are 1O-Io cm3 s-I molecule-'.
TABLE VI: Cocffidcnb I of the DipokDipok ACIOSA Rate Collrt.ds k ( T ) = IT'/' for Vuiop, Reactionsa
I 0
NaO + H 2 0
+ CHZO NaO + O3 CH SH
+ NO2
+
+
+
+
400
500
Figure 5. Comparison of the ACIOSA and ACPCSA rate constants for the reaction NaO + H 2 0 .
dipole, will not be so important as the dipoledipole or dispersion term due to their strong angular dependence and dependence on higher powers of Rn. (a) Compuisoawith E x p b n L We compare in Table V the experimentalzz-2sand ACPCSA values of the rate constants for the NaO HzO, NaO + O,, CH + CH20, and SH + NOz reactions at a temperature of 300 K. In order to see what is the importance of the dispersion terms for each reaction at this temperature, we give the ACPCSA values calculated with and without these terms. One problem when comparing with experiment is the inclusion, in the calculated rate constant, of factors to account for the electronic degeneracy of the reactants and the number of electronic stam involved in the reaction.% A proper treatment of this latter factor requirts electronic structure calculations of all the possible potential energy surfaces that correlate reactants with products.6 Such factors are not included here and the ACPCSA rate coefficients reported should correspond closely to upper bounds to the exact rate constants.6 The agreement between the ACPCSA and experimental values of the rate constant is quite good for the NaO O3and CH CH20 reactions with the calculated values being only slightly above the experimental results. Significantly, both of these reactions are very exothermic and have strong dipoledipole interactions and thus would seem to be excellent candidates for application of capture theory. The calculated rate coefficients for the NaO HzO reaction is about a factor of 4 above experiment. This reaction is thought to be only just and thus the application of capture theory to it is somewhat questionable. The capture theory is normally only appropriate for strongly exothermic reactions in which the importance for the rate constant of secondary barriers in the potential energy surface inside the centrifugal barrier are expected to be minimi~ed.',~ It should be emphasized that a full treatment of the reactions would require ab initio calculation of the potential energy surfaces for the systems chosen here. However, the aim in this work has been to examine how successful the simple dipoltdipole plus dispersion model is for predicting the rate constants for the four reactions. It can be seen that the dispersion term in the potential does not change the ACPCSA rate constant at 300 K by more than 1% for the NaO HzO reaction, whereas for the reaction SH NOz the value of the rate constant is augmented by a factor of 10 if the dispersion term is included in the potential. The calculated rate constant for the SH + NO2 reaction is also a factor of about 4 above experiment, and this could be due to electronic factors being needed.26 Also, this reaction is not so strongly exothermic as NaO + O3and CH + CHzO. The application of the IOSA formula (12) to the four reactions gives the rate constants shown in Table VI. These IOSA rate constants are also reported in Figure 5 for the NaO + HzO
+
300
200
TK
19.31 8.01 6.31 0.88
cm3 s-' molecule-' K1/6.
is in units of
100
+
reaction in order to enable comparison with their ACPCSA counterparts for a range of temperatures. It can be seen that the IOSA rate constants are in quite good agreement with the ACPCSA at higher temperature (>300 K), but the agreement is not so good at lower temperatures. Both the CH CHzO and SH + NOz rate constants calculated with the ACPCSA show almost no temperature dependence between 200 and 600 K. However, the experimental rate constants show a larger temperature dependence. In particular, the experimental rate constantx for the CH + CH20reaction dby a factor of nearly 2 between 298 and 670 K, although the ACPCSA rate constant is only slightly above the experimental value at room temperature. However, the capture theory with a potential purely calculated from long-range intermolecular forces is expected to break down at higher temperatures9as the centrifugal barriers in the effective potential will then be in the short range region where the multipole expansion breaks down and chemical forces are important. The best application of the capture theory is for lower temperatures and, in this regard, it would be very useful to have more experimental data for temperatures below 300 K. 4.2. Low Temperatures: The RAPT Formula. For reasons given in section 3.2 it is not appropriate to undertake a very detailed study of the behavior of the ACPCSA rate constant in the l i t of T = 0. However a comparison of the ACPCSA rate constants with the analytical RAPT formula in the limit of very low temperature is a useful check on the numerical procedures and provides interesting qualitative predictions. For example, the application of the RAPT formula (15 ) to the NaO + H 2 0reaction at 1 K gives 1.18 X lo4 cm3molecule-' s-l for the rate constant, which is in very good agreement with the computed ACPCSA value of 1.1 1 X cm3 molecule-' s-l. Note that the RAPT formula gives a temperature dependence of the rate constant of whereas the IOSA temperature dependence is Therefore, there will be a maximum at low temperatures in the ACPCSA rate constants when plotted as a function of temperature (see ref 7 for a more detailed discussion of this effect).
+
5. Conclusions A variety of numerical and analytical calculations of rate constants for fast reactions between polar diatomic and polyatomic molecules have been presented. The method involves using the infinite order sudden approximation for the diatomic molecule and a rotationally adiabatic capture theory for the polyatomic molecule. The numerically calculated rate constants compare well with those obtained using analytical formulas derived for the limit of very low temperature (by perturbation theory) and for the limit of high temperature (by the infiinteorder-sudden approximation). The calculated rate constants for the NaO + O3and CH + CH20 reactions agree quite well with experiment. More experimental rate constant data for lower temperatures would be useful for comparison with our predictions. This study demonstrates once again that the rotationally adiabatic capture theory, combined with sudden approximations, is a useful and powerful way of calculating rate constants for fast
J. Phys. Chem. 1992,96,7351-7355 reactions involving polyatomic molecules. Work is now going ahead to extend the methods to the reactions between open-shell free radicals where interesting temperature effects on the rate constants are expected at low temperatures.2'
Acknowledgment. This work was supported by Science and Engineering Research Council and the CNRS.
References and Notes (1) Clary, D. C. Mol. Phys. 1984.53. 3. (2) Clary, D. C.; Werner, H.-J. Chem. Phys. Lett. 1984, 112, 346. (3) Clary, D. C. Mol. Phys. 1985,54, 605. (4) Clary, D. C. J. Chem. Soc., Faraday Trans. 2 1987.83, 139. (5) Dateo, C. E.; Clary, D. C. J. Chem. Soc., Faraday Trans. 2 1989,85, 1685. (6) Dateo, C. E.; Clary, D. C. J. Chem. Phys. 1989,90,7216. Clary, D. C.; Dateo, C. E.; Smith, D. Chem. Phys. Lett. 1990, 167, 1 . (7) Stoeckli, T.; Dateo, C. E.; Clary, D. C. J. Chem. Soc., Faraday Trans. 1991, 87, 1667. ( 8 ) Stoecklin, T.; Clary, D. C.; Palma, A. J. Chem. Soc., Faraday Trans. 1992, 88, 901. (9) Clary, D. C. Annu. Rev. Phys. Chem. 1990, 41, 61. 110) Rebrion. C.: Marauette.. I. B.:. Rowe. B. R.:- Claw. .. D. C. Chem. Phvs. mi.1'988, 143,. 136. (11) DeMore, W. B.; Sander, S. P.; Golden, D. M.; Molina, M. J.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. In Chemical Kinetics and Photochemical Data for Use in Stratospheric Mo-
7351
delling, Jet Propulsion Laboratory: Pasadena, CA, Jan. l , 1990. (12) Anderson, J. G. Annu. Rev. Phys. Chem. 1987,38,489. (13) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Reactions; Butterworths: Guildford, 1980. (14) Millar, T. J.; Williams, D. A. Rate Coefficients in Astrochemistry; Kluwer: Lancaster, 1988. (15) Hirschfelder, J. 0.;Curtiss, C. F.; Bird, R. B. Molecular Theory 01 Gases and Liquids; Wiley: New York, 1954. (16) Clary, D. C. In Rate Coefficients in Astrochemistry, Part I ; Millar, T. J., Williams, D. A., Eds.; Kluwer: Lancaster, 1988. (17) Brooks, G.; Van der Avoird, A.; Sutcliffe, B. T.; Tennyson, J. Mol. Phys. 1983, 50, 1025. (18) Zare, R. N . Angular Momentum; Wiley: New York, 1988. (19) Gray, C. G.; Gubbins, K. E. The Theory of Molecular Fluids; Clarendon Press: Oxford, 1984. Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules; van Nostrand: New York, 1979; II. Electronic Spectra of Polyatomic Molecules; van Nostrand: Princeton, NJ, 1966. (20) Trb, J. J. Chem. Phys. 1987,87,2713. (21) Wickham, A. G.; Stoecklin, T.; Clary, D. C. J . Chem. Phys. 1992, 96, 1053. (22) Ager, J. W., 111; Howard, C. J. J. Chem. Phys. 1987.87, 921. (23) Ager, J. W., III; Talcott, C. L.; Howard, C. J. J . Chem. Phys. 1986, 85, 5584. (24) Zabarnick, S.; Fleming, J. W.; Lin, M. C. Symp. Int. Combust. Proc. 1986,21, 713. (25) Wang, N. S.; Lovejoy, E. R.; Howard, C. J. J. Phys. Chem. 1987,91, 5743. (26) Phillip, L. F. J . Phys. Chem. 1990,94, 7482.
Infrared Multiphoton Decomposition of Diethylnitramine Yannis G.Lazarou, Keitb D. King,+ and Panos Papagiannakopoulos* Department of Chemistry, University of Crete, and Institute of Electronic Structure & Laser, F.O.R.T.H, Heraklion 714 09, Crete, Greece (Received: March IO, 1992; In Final Form: April 28, 1992)
Irradiation of gaseous diethylnitramine with infrared radiation from a pulsed C02laser under collision-free and collisional conditions resulted in the formation of diethylnitrosamine as the main product along with nitrogen dioxide, nitric oxide, formaldoxime, and diethyl nitroxide. Scavenging experiments with C12,NO, and (CD3)2NN02molecules have shown that the primary channel of unimolecular dissociation of diethylnitraminemolecules is the scission of the N-N02 bond, with a steady-state rate constant of 105.2M.1(Z/MW cm-2) s-l for laser intensities in the range 3-15 M W cm-2 at an irradiation frequency of 1075.9 cm-*. A qualitative analysis of the chemical mechanism leading to the formation of final products as well as the importance of the diethylamino radical oxidation reactions is presented.
Introductioa Nitramines are among the most important compounds in the area of high explosives and propellants with well-known members such as 1,3,5-trinitro-l,3,5-triazine (RDX) and 1,3,5,7-tetranitro-l,3,5,7-tetrazocine(HMX). These characteristics can be attributed to the energetics of the primary dissociation pathways as well as to the fast chemical reactions of the resultant primary product species.' The study of the industry-interestingnitramines of complex structure is often complicated by numerous side reactions, and their nonvolatile nature leads to mixed-phase chemi ~ t r y Simpler .~ Ntraminesoffer the advantage of gas-phase studies and extending the results to the bulky members. The gas-phase decomposition mechanism of the simpler dimethylnitramine (DMNA) has been the subject of earlier and recent works using various excitation sources, namely, pyroly~is,~.~ shock tubes? laser-powered homogeneous pyrolysis,6 and infrared multiphoton decomposition (IRMPD).' There is a general agreement on the scission of the N-NO2 bond as the main unimolecular dissociation channel, with a minor contribution from the isomerization to N-nitrite and subsequent NO elimination channel observed in the laser pyrolysis experiments. However, the larger and still simple diethylnitramine(DENA) has not received equal attention; 'On sabbatical leave from the Department of Chemical Engineering, University of Adelaide, Adelaide, South Australia 5001.
early pyrolysis experiments in the temperature range 180-240 "C revealed the N-NO2 bond fission as the primary dissociation pathway with a thermal rate constant expressed by the equation k = 1014.Be42.1/RT s-l ( R in kcal mol-' K-').B The proposed mechanism of the final products' formation incorporated the oxidation reaction of parent diethylnitramine molecules by nascent NO2 and the reaction of the diethylamino radical generated in the initial step with the secondary product NO to form diethylnitrosamine. In the present work, the IRMPD of diethylnitramine under collisionless conditions is studied in order to determine the primary channel of unimolecular decomposition and elucidate the chemical mechanism of the final products' formation. Scavenging experiments with C12,NO2, NO, and (CD3)2NN02are carried out in order to reveal the complete chemical mechanism that follows the initial energy absorption. Finally, the IRMPD of the first two symmetrical dialkylnitramines are compared, and the relative importance of the HONO elimination channel in diethylnitramine is examined. Experimental Section Diethylnitramine ((CH3CH2)*NN02)was prepared by the method of Wright: dehydrating the nitrate salt of diethylamine ((CH3CH2)2NH2+N03-) in acetic anhydride with the use of ZnC12 as catalyst. The mixture of the desired compound along with side
0022-3654/92/2096-735 1S03.00/0 , 0 1992 American Chemical Society ,
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