13664
J. Phys. Chem. 1995,99, 13664-13669
Product CN Rotational Distributions from the H
+ HCN Reaction
David C. Clary Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 IEW, U.K. Received: February 17, 1995; In Final Form: April 5, I995@
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Quantum scattering calculations are reported of the CN rotational distributions obtained in the reaction H HCN H2 CN. The rotating bond approximation ( M A ) is used with a potential energy surface based on ab initio data. The product rotational distributions of CN are found to be relatively insensitive to the degree of excitation of the CH stretching vibration and the collision energy. They are very sensitive, however, to the degree of initial excitation in the HCN bending mode and show the structures predicted by a simple Franck-Condon projection of the HCN bending mode onto the product CN rotation. Good agreement with experiment is obtained for the CN rotational distributions calculated for the reaction with four quanta in the initial CH stretching vibration of HCN. The importance of the CN rotational distributions for providing HX CN reactions (X = H, 0, and Cl) information on the potential energy surfaces for the X HCN is also discussed.
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tions using various quantum scattering methods for the OH H2 reaction.24 Furthermore, the most recent form of the RBA5 Bond- and mode-selective effects in chemical reactions have gives cumulative reaction probabilities for the OH H2 H been the subject of many recent e~perimental'-~ and the~retical~-~ H20 reaction that agree well with exact2" results. studies. The A particular advantage of the RBA is its ability to calculate directly the rotational distributions of the spectator bond taking H HCN- H2 CN part in a chemical reaction. We wish to exploit this advantage in the present paper and report calculations of the CN rotational reaction is an important example and was the subject of the distributions in first quantum reactive scattering calculations on a four atom reaction.*-I0 In calculations for collinear geometry it was found that the CN bond acted as a spectator and was not excited during the This reaction has also been the subject of several measurements of the CN rotational product distributions.' ! - I 4 Here m and n are bending and CH stretching vibrations of the Furthermore, the CN product rovibrational distributions for this HCN reactant with vibrational angular momentum K , v is the reaction and the related 0 HCN and C1 HCN reactions H, vibrational quantum number, and j is the CN rotational have been measured from HCN in the initial (004)state, with quantum number. We compare our calculations of the CN the CH stretching vibration being excited to its fourth quantum rotational distributions with those obtained in e ~ p e r i m e n t ' ~ . ' ~ state.l4,l5 An interesting finding in these latter experiment^'^,'^ and also by a simple Franck-Condon theory.25 is that the CN bond behaves as a spectator in the reactions of In section I1 the RBA for the H HCN reaction is briefly HCN with H and 0 atoms but CN can be produced in an excited described. Section I11 discusses the simple Franck-Condon vibrational state in the C1 HCN reaction. Furthermore the theory for predicting the rotational distributions of the spectator CN product rotational states for the C1 HCN reaction are bond in a four-atom reaction. Details of the potential energy much more highly excited than for the H and 0 reactions with surface used in the computations and numerical details of the HCN. RBA calculations on the H HCN reaction are given in section Recently, a quantum dynamical method for studying reactions IV. Section V describes calculations of the CN rotational involving polyatomic molecules was developed that moved away product distributions for a range of selected initial vibrational from the collinear approximation and is capable of treating states of the HCN molecule and for several different collision explicitly the bending mode in HCN and the rotational motion energies. Comparison with experiment is also made. We also of product CN.I6 This rotating bond approximation (RBA) compare the CN rotational distributions obtained from the simple enabled the first quantum scattering calculations to be performed Franck-Condon theory with those calculated by the RBA. on the H H20 OH H2 reactioni6 and has allowed detailed Furthermore, we discuss, on the basis of the Franck-Condon comparison^^^'^ to be made with measurements of rate constants, theory, the information on the transition state of a reaction that product OH rotational distribution^,'^ vibrationally selected cross can be inferred from measurement of the CN rotational product sections,I8and differential cross sections" for this reaction. The distributions from the X HCN HX CN (X = H, 0, C1) RBA also gives quite good agreement with vibrationally selected reactions. Conclusions are in section VI. reaction probabilities obtained from an exact quantum mechanical treatment of the H H20 reaction for planar geometry.I9 11. Rotating Bond Approximation The RBA has also been applied to the reactions OH f CO We present a brief description of the rotating bond apC02 H,20OH HCl H20 CA2' OH HBr H20 proximation applied to the H HCN(OmKn) H2(v) CNBr,21,22and OH CHq H20 CH3.23 Building upon the (j,K) reaction. The details of the method are presented RBA calculations, there have been several other recent calculae l ~ e w h e r e . ~ As . ' ~ shown in Figure 1, the vector joining the centers of mass of the H2 and CN molecules is denoted R1 and Abstract published in Advance ACS Abstracrs, July 15, 1995. I. Introduction
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0022-3654/95/2099-13664$09.00/0
0 1995 American Chemical Society
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CN Rotational Distributions from the H
+ HCN Reaction
J. Phys. Chem., Vol. 99, No. 37, 1995 13665 channel form:
where the initial quantum state label is k‘. Diagonalization of the Hamiltonian of eq 1 with = ei gives the basis functions {(?#t(6,8;ei)). These are expanded as
I Y
\
H - - L
H
R3
Figure 1. Coordinates for H2
+ CN.
the vector between the C and N atoms of CN is R2. The vector R3 that joins the two H atoms of H2 has an angle y with respect to R I . The angle between R I and R2 is 8 and the torsional angle is 4. In the RBA, the angles y and 4 are not accounted for explicitly by the use of basis sets and are treated using an adiabatic bend approximation which is described below. We have found in previous calculations on the H HCN reaction that it is an excellent approximation8 to keep the length of the CN spectator bond fixed in the scattering calculations. Given the above approximations, we wish to solve the timeindependent Schrodinger for the reactive problem. We transform to the Delves’ form of hyperspherical coordinates:26
+
i = 1 and 3
sf = (Mi/p)R:,
where the functions the Hamiltonian
{?#k,(d;@i)}
are obtained by diagonalizing
(4) with a basis set of na equally spaced distributed Gaussian functions.29 An appropriate potential Vo(G;ei)is obtained by using the bond angle OeS = 180° of HCN in V(@i,6,8,,). The functions {yj$e;ei)}are expanded as linear combination of ne spherical harmonics (YjK(8, 0)) and are obtained from diagonalization of the Hamiltonian
where
Vl(8;eJ = (Vl(a;ei) I V(Qi*6,@IVl(’;ei)) with
sI= e cos(d),
s3 =
e sin 6
Here
(6)
For large e, the potential V(e,6,8) has minima around a small value of 6 and a large value of 6. The first of these minima gives the quantum states corresponding to the channel H2( v) CNG), while the second minimum gives vibrational states of the form HCN(OmKn) H. For the reaction of a linear triatomic such as HCN, K (20) is identified with the vibrational angular momentum quantum number, and we use the triatomic notation (OmKn),with the bending mode quantum number m = K , K 2, ..., and CH stretching quantum number n. Most of the calculations reported here are for the H HCN reaction with K = 0, and thus (OOOO) and (02OO) are the first and second excited vibrational states of HCN in such calculations. With K = 1, the states of HCN are (Olio), (03IO), etc. The close-coupled equations are solved by propagating the R matrix from a small value of 4 in the classically forbidden region to a large value where the interaction between the two arrangement channels becomes negligible. The S-matrix elements $:,(E) for collision energy E are then obtained by applying scattering boundary conditionsI6 with the states being labeled, as described above, by the quantum numbers of the reactant and product channels, vj and mnK, which arise naturally from diagonalization of the hamiltonian of eq 1. Repetition of the calculations for different values of J gives the RBA stateselected integral reaction cross sections:
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where the masses of the C, H, and N atoms are mc, mH, and mN, respectively. The Hamiltonian is16
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Here M = mH(mc mN)/(mH mc mN), B is the rotor constant of CN, V is the potential energy surface, and R is the distance from the H atom of HCN to the center of mass of CN. Also j22 is the rotational operator of CN, J is the total angular momentum quantum number, and K , which is assumed to be a good quantum number in the coupled-states appr~ximation,~~ is the projection of both j 2 and J along the intermolecular axis RI. The R-matrix propagator methodz8is employed to solve the The rotational motion of the H2 molecule is treated apcoupled-channel equations for the Hamiltonian of eq 1. In this proximately in the RBA.5 This is done by using an “adiabatic bend” procedure that follows the approach of Bowman and coapproach, the hyperradius splits up into sectors with midpoints w o r k e r ~ . ~First, , ~ ~ for fixed values of e, d, and 8, the full {el}.The wave function in sector i is expanded in the coupled-
13666 J. Phys. Chem., Vol. 99,No. 37, I995 potential energy surface is minimized with respect to the angles y and 4, to give Vm(@,S,e).Then the harmonic zero-point energies for the in-plane ( y ) and out-of-plane (4) bending vibrations of the HHCN complex that correlate with H2 motion This gives the potential V(@,S,@ in the are added to Vm(@,S,e), Hamiltonian of eq 1. By summing the cross sections of eq 7 over the collision energies that are identified with each bending energy level of the H2 molecule at the transition state that is open for a fixed total energy, a cumulative reaction cross section is obtained. This corresponds to a sum over all open final H2 rotational states for a given total energy. Since we are concentrating on product CN rotational distributions in this paper and these are very insensitive to translational energy, we report here the. collision cross sections calculated directly from eq 7.
TABLE 1: Morse and Sat0 Parameters in the LEPS Potential Energy Surfaces for the H HCN Reaction (in Atomic Units) parameter CN HC HH 0.9832 1.0277 1.34 B" 0.2914 0.2273 0.1746 De" rea 2.2144 2.0144 1.4022 Ab 0.125 0.125
111. Franck-Condon Theory
where 6, is the equilibrium bond angle of ABC, Hmis a Hermite polynomial, and a2= WZw, where Z is the moment of inertia associated with the bending motion of BC:
Many Franck-Condon (FC) theories have been applied before3' to three-atom chemical reactions and have also been successfully used to describe three-atom photodissociation p r o c e ~ s e s . ~ Such ~ - ~ ~ a simple theory would seem to be particularly appropriate for CN rotational distributions in the H HCN H2 CN reaction as the CN bond acts as a spectator and is not broken during the reaction. This is a distinctive new feature of four-atom reactions that is not met in three-atom reactions. The simplest Franck-Condon the01-y~~ applied to the H HCN reaction involves projecting the bending wave function of the HCN molecule onto the CN rotations. Thus if the bending wave function of the initial state HCN (Om%) is expanded in the form
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where ?(e) is a normalized associated Legendre polynomial then the FC prediction of the probability of CN being produced in particular rotational statej is just
Po.)= ( c y ) '
(9)
This distribution is, essentially, independent of collision energy. An important assumption in this simple FC theory, which assumes nothing about the potential energy surface apart from the potential for the triatomic HCN, is that the frequency of the bending mode of HCN is similar at the transition state for the reaction to its value in isolated HCN. That is the case in the potential energy surface used here. A more accurate procedure is to perform the expansion of eq 8 at a chosen geometry of the reaction (such as the transition state). This, of course, requires detailed knowledge of the potential energy surface. The simple FC approach has been applied to the H H20 OH H2 reaction25 and gives a clear explanation of the very low rotational excitation of the product OH that is observed in all experiments that have been done on that reaction.'-3 A slightly more complicated FC theory has also been proposed by Wang and Bowman,37and this would take into account the rotation of Hz together with that of CN. The simple FC theory for the spectator bond of a four-atom chemical reaction is entirely analogous to that used many times in the past for threeatom photodissociation p r o c e ~ s e s ~such ~ - ~as~HCN hv H CNG). In this case, the FC approximation has produced useful approximate formula^^^.^^ for the product rotational distributions and these can also be directly applied to our fouratom chemical reaction problem. For example, in the photodissociation of a non-linear triatomic molecule ABC from J = 0 with bending quantum number m,
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Morse parameters. SAT0 parameter. the BCO) rotational product distribution is32
PO.)= sin2ceeq+ (- 1)m;rc/4~(~m(aj)e-"2a2j'2)2; j = j + 1/2 (10)
(
I = 2 B + -MReq 2 ) '
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and w is the ABC bending frequency. Examination of the sine term in this formula clearly shows that an oscillatory distribution is predicted for variation in j. Furthermore, the Hermite polynomial produces a nodal structure in the rotational distribution of degree m and the proportion of rotational excitation will increase with m. The analogous FC formula for a linear triatomic molecule ABC with K = 0 and J = 0 is33
Here e = c/w where c depends only on the atomic masses and bond lengths of ABC.33 Also, L:,2 is a Laguerre polynomial that produces m/2 nodes in the rotational distribution. The main difference between eqs 10 and 11 is that the formula for the linear molecule does not contain the oscillatory sine function and the formula of eq 11 is remarkably similar to a Boltzmann distribution form = 0. This point is discussed further in section V. These FC formulas of equations 10 and 11 can also be used for parameters appropriate for the transition state of the reaction when the bending frequency or geometry of ABC is significantly changed at the transition state.
IV. Potential Energy Surface The potential energy surface for the H'HCN system used in the present RBA computations is very similar to that proposed by Sun and B ~ w m a n . ~
V = VLEPS(~HC, ~H'HJH'C)
+ VM(rcN) + V A M ( ~ N H )+ VAM(rNw)
-
(12)
Here rAB is the distance between atoms A and B, VLEPSis a LEPS potential appropriate for the H HC H2 C reaction, and VM and VAMare Morse and anti-Morse potentials. The antiMorse potential of Sun and Bowman was used? The relevant parameters are given in Table 1 and were chosen to fit ab initio data on the H HCN reaction3* as closely as possible. The main features of the potential, and comparison with ab initio and experimental parameters are shown in Table 2. The minimum energy reaction path of the potential energy surface has a linear geometry. The rotational constant for the CN radical was 1.9 cm-' and the CN bond length was held fixed at 1.172 %, throughout the
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CN Rotational Distributions from the H
+ HCN Reaction
J. Phys. Chem., Vol. 99, No. 37, 1995 13667 H+HCN(0110) + H,+CN(j)
H+HCN(OW2) + H2+CN(j)
1.00 d
0
e
5
--
u R B A 0.33eV --. -RBA 0.63eV - 9 - Franck-Condon
m
10
15
20
-.
+
+
0
25
j Figure 2. CN rotational distributions for the H HCN(0O02) HZ CN(j) reaction obtained in RBA calculations with translational energies of 0.33 and 0.63 eV, and with the Franck-Condon approxima-
tion.
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V. CN Rotational Distributions As was the case with the quantum mechanical calculations for linear it was found that vibrational excitation of the CH stretching mode n in HCN(OmKn) considerably enhanced the reaction probabilities. For example, at an initial translational energy of 0.18 eV the RBA cross sections of eq 7 summed over all product states were 2.78, 29.5, and 52.0 uo2 for n = 2, 3, and 4, respectively. Considerable excitation of the bending quantum number of HCN was needed to obtain cross sections approaching these values. For example, a collision energy of 0.22 eV gave a cross section of 1 6 . 4 ~ for 0~ the state with m = 10 quanta in the HCN bend (and K = 0) while a collision energy of 0.25 eV gives a cross section of 0 . 0 3 ~ for 0 ~ the m = 8 bending state. In the remaining part of the paper we concentrate on the CN rotational distributions in the H HCN(OmKn) H2 CNC) reaction. Figure 2 gives the RBA calculations of the CN rotational distributions for the initial state HCN(00°2) at the initial translational energies of 0.33 and 0.63 eV. Also shown in the figure are the rotational distributions obtained from the simple Franck-Condon formula of eq 9. It can be seen that the rotational distributions hardly change when the collisional
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5
10
- 0110 RBA U 0110 FC
15
20
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Figure 3. CN rotational distributions for the H HCN H2 CN0') reaction obtained in RBA calculations with a translational energy of 1.4eV for HCN(WOO)and HCN(O1IO). Also shown are the FranckCondon distributions for HCN(O1IO).
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c a l ~ u l a t i o n .Ninety-eight ~~ distributed Gaussians were used for the diagonalisation of eq 4, with an optimized exponent,I6 and the final basis set used for the CI expansion of eq 3 was Nd = 15 and Ne = 40 so that a matrix of size 600 x 600 had to be diagonalized in each sector. The R matrix was propagated between e = 4 and 14.5 au with 120 equally spaced sectors and with N = 99 contracted channels. The reaction probabilities calculated for all e values between 12 and 14.5 au were averaged in the way described in ref 17. The calculations were done on a Dec Alpha 3000/600 computer and required in total about 24 h of cpu time.
p m
j
H+HCN(0200) -+
TABLE 2: Properties of the Potential Energy Surface Used in the RBA Calculations on the HZ CN HCN H Reaction property present ab initio3* experiment39 R(CH), saddle point 1.55 8, 1.55 8, R(HH), saddle point 0.816 8, 0.826 8, barrier height 5.2 kcaumol 6.0 kcaYmol - 18.7 kcal/mol -19.2 kcaYmo1 exoergicity 727 cm-I HCN bend frequency 721 cm-' CH frequency in HCN 3334 cm-' 3441 cm-'
+
-o
-.OOOO RBA
4
4 .-b
H2+CNCj) Franck-Condon
PBA
0.80 I
0
5
15
10 j
20
+
25
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Figure 4. CN rotational distributions for the H HCN(02OO) H2 CNG) reaction obtained in RBA calculations with a translational energy of 1.26 eV and with the Franck-Condon approximation.
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energy is increased. Furthermore, as can been seen in Figure 2, the RBA distributions show only slightly more rotational excitation than those obtained with the Franck-Condon approximation, which are independent of collision energy. Figures 3 and 4 show similar plots of the CN rotational distributions from excited bending states of HCN. It can be seen from the results in Figure 3 that considerably more rotational excitation is seen in the CN product for reaction from HCN(O1'0) than from HCN(OOOO). Furthermore, the FranckCondon theory gives very good agreement with the RBA rotational distributions out of HCN(O1 IO). In accordance with the approximate Franck-Condon photodissociation theory for linear molecules,33 there is no node in the CN rotational distribution from HCN(O1'0). In Figure 4, the RBA and Franck-Condon rotational distributions are compared for reaction out of HCN(02OO). Here it can be seen that the comparison is not quite so quantitative as for HCN(Ol'O), but both distributions have a similar bimodal structure with a minimum almost in the same place. This bimodal distribution is directly predicted from the simple formula of eq 11. For reaction out of HCN(02OO), the RBA CN distribution has peaks at j = 2 and 11 with a minimum at j = 6, while the Franck-Condon distribution peaks at j = 2 and 13 with a minimum at j = 7. However, the overall maximum of the RBA distribution is at j = 2 while the maximum for the Franck-Condon distribution is at j = 13.
13668 J. Phys. Chem., Vol. 99, No. 37, 1995
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l
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Clary
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l
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t
(Crim et al) -
-Exp
minima including structures in which a ClHCN complex has a "Y-shaped" geometry in which HCN is bent.40 If the transition-state geometry is bent then the FranckCondon formula of eq 10 for a nonlinear parent molecule is a more appropriate description for the C1 HCN reaction. This formula gives an oscillatory sine function multiplied by an overall Gaussian overlap function and the degree of rotational excitation in the products does not depend significantly on the bond angle of HCN but is very sensitive to the bending frequency w. The sine function of eq 10 would suggest that the CN product distributions should show an oscillatory distribution in j if the geometry of HCN in the transition state of the reaction is bent. However, such an oscillatory distribution does not seem to be observed in the experiments.I4-l5 For a linear parent molecule (or transition state with a linear geometry) the rotational distribution from eq 11 is
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0
5
10
15
j
20
25
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Figure 5. CN rotational distributions for the H HCN(W04) H2 CNU) reaction obtained in RBA calculations with a translational energy of 0.04 eV and with the Franck-Condon approximation. Also shown is the experimental rotational distributi~n'~J~ for the same collision energy.
+
Despite this difference the ability of the simple Franck-Condon theory to predict the overall shape of the product distribution is significant. The main reason for this is that the minimum energy path has linear geometry for the whole reaction and the HCN bending mode frequency at the transition state is very similar to that for isolated HCN9. Figure 5 gives the RBA rotational distributions of CN for the HCN(004) initial state with a collision energy of 0.04 eV. It can be seen that these distributions are almost identical to that for HCN(00°2) of Figure 2. Also shown in this diagram is the experimental rotational distribution of Crim and co-workers, which corresponds to a Boltzmann distribution appropriate for a temperature of 200 K.I43l5 The agreement between the RBA and experimental distributions is excellent. Furthermore the comparison between the Franck-Condon, RBA, and experimental distributions is very good and this highlights just how "Franck-Condon" the CN rotational distributions are for the H HCN reaction. It is interesting also to consider the above findings, and the application of the Franck-Condon formulas of eq 10 and 11, to the related reactions
+
0
+ HCN(004)
and C1+ HCN(004)
-
OH
+ CNV)
HC1+ CNG)
+
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that have also been studied recently in experiments by Crim and co-workers.l4,I5 They find that the CN product rotational distributions are Boltzmann-like with temperatures of 300 and 450 K for the 0 HCN reaction with collision energies of 0.04 and 0.08 eV, respectively, and 800 K for the C1 HCN reaction with a collision energy of 0.25 eV. This would suggest that the mechanism for the 0 reaction and, in particular, the C1 reaction has some differences to that for the H HCN reaction where the temperature of the CN product distribution was 200 K for a collision energy of 0.04 eV. To discuss these experimental results for the C1 HCN HCl CN reaction it is instructive to consider the simple Franck-Condon formulas of eq 10 and 11 with parameters appropriate for HCN at the transition-state geometry of the reaction. Ab initio calculations provide evidence to suggest that the reaction path for this reaction is more complicated than that for H -t HCN Hz CN; there are several maxima and
+
for the ground-state bending mode of HCN. This shows a remarkable similarity to a Boltzmann distribution with e = BAT. Since e = clw, we have T = Bwl(kc), where w is the bending frequency of HCN at the transition state. All of the reactions of X HCN, with X = H, 0,and C1 give experimental product CN rotational distributions that are well-characterized by Boltzmann distribution^,'^-'^ and this suggests that the main transition states for these reactions have HCN with linear geometry. This analysis also suggests that the measurement of the temperature of the rotational product distribution for reactions of this type directly gives information on the bending frequency of HCN at the transition state of the reaction. Since the temperature of the experimental CN rotational distribution for the C1 HCN reaction is about four times that for the H HCN r e a ~ t i o n , ' ~ *this ' ~ , would suggest that the bending frequency w for the C1 reaction is four times that for the H reaction. However, this gives a value of w for the C1 HCN reaction of about 2800 cm-' which would seem to be an abnormally high bending frequency. It seems likely, therefore, that the very hot CN product rotational distribution for the C1 HCN reaction is not only determined by Franck-Condon overlap effects but is also partly determined by exit-channel dynamical interactions (such as the strong dipole-dipole interaction between HCl and CN). Such effects are known to be important in some molecular photodissociations and predissociations of van der Waals molecules.35 It is also important to point out that CN rotational distributions have been measured"-I3 for the H HCN(W0) H2 CNU) reaction with the "hot" H atom having a very large kinetic energy ('2 eV). We have not performed converged calculations at these very high collision energies in the present study, and the calculated cross sections for reaction from HCN(OOO0) for lower energies were very small (less than 0.5a02). The CN rotational distributions reported in these experiments were of a Boltzmann form with temperatures ranging from 750-2200 K. These temperatures are much hotter than the 200 K obtained in the present RBA calculation, Franck-Condon theory and experiment14g15for H HCN(0004)'4.'5at a translational energy of 0.04 eV. This would suggest that the potential energy surface for the H HCN reaction might need modification to model the hot atom experiments. In particular, new channels become open at higher energy. For example, although the reaction path to form HZ CN is linear in ab initio calculations, a Y-shaped H2CN bound state can also be formed,38 and it is likely that this can be accessed at high collision energies. Furthermore,
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CN Rotational Distributions from the H
+ HCN Reaction
-
at collision energies above 2 eV, the collision-induced isomerization HCN HNC becomes possible!'
VI. Conclusions The rotating bond approximation has been used to calculate the CN rotational product distributions arising in the H HCN H2 CN reaction. A simple potential energy surface based on ab initio data is used in the calculations. The CN bond length is held fixed in the calculation. The rotational distributions of the CN radical calculated by the RBA are found to be in remarkably good agreement with those predicted by a simple Franck-Condon theory in which the appropriate bending mode of HCN is projected onto the rotational states of CN. In accordance with this Franck-Condon theory, the RBA rotational distributions of CN are relatively insensitive to the degree of excitation of the CH stretching vibration and the collision energy, but they are very sensitive to the degree of excitation in the HCN bending mode. Very good agreement with experiment is obtained for the CN rotational distributions calculated for the reaction with four quanta in the initial CH stretching mode of HCN. It is also shown that the rotational distributions expected from application of the simple Franck-Condon theory assuming a transition state with linear geometry for HCN are of a Boltzmann form with a temperature directly proportional to the frequency w of the HCN bending mode at the transition state of the reaction. Since the experimental CN rotational distributions for the three reactions X HCN HX CN (X = H, 0, Cl) all show Boltzmann distributions, it seems likely that the HCN is close to linear in the main transition states for these reactions. However, as the measured temperature of the Boltzmann distribution for the X = C1 reaction is about 4 times that for the H reaction this would suggest that w is much larger for X = C1 than H. More detailed dynamical calculations on realistic potential surfaces are required to examine these features and to determine explicitly what information on the potential energy surface can be extracted from the experimental CN rotational distributions for the X HCN reactions.
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Acknowledgment. This work was supported by the Engineering and Physical Sciences Research Council (Grants GR/ 567154 and GR/J23099), the Particle Physics and Astronomy Research Council (Grant GWJ23 105) and the European Union. Useful discussions with Fleming Crim, Joann Pfeiffer, and Ricardo Metz (University of Wisconsin) are gratefully acknowledged, and the Wisconsin group is also thanked for providing their experimental results before publication. References and Notes (1) Crim, F. F.; Hsiao, M. C.; Scott, J. L.; Sinha, A.; Vander Wal, R. L. Philos. Trans. R. SOC.London, Ser. A 1990, 332, 259. Sinha, A,; Hsiao, M. C.; Crim, F. F. J. Chem. Phys. 1990,92,6333. Sinha, A.; Hsiao, M. C.; Crim, F. F. J. Chem. Phys. 1991, 94, 4928. Hsiao, M. C.; Sinha, A,; Crim, F. F. J. Phys. Chem. 1991, 95, 8263. Sinha, A.; Thoemke, J. D.; Crim, F. F. J. Chem. Phys. 1992, 96, 372. (2) Bronikowski, M. J.; Simpson, W. R.; Girard, B.; Zare, R. N. J. Chem. Phys. 1991,95, 8647. Adelman, D. E.; Filseth, S. V.; Zare R. N. J.
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