Faraday Discuss, Chem. SOC., 1983, 75, 211-222 Energy Distributions in the CN(X 2E+) Fragment from the Infrared Multiple-photon Dissociation of CF,CN A Comparison between Experimental Results and the Predictions of Statistical Theories BY J. Ross BERESFORD, GRAHAM HANCOCK AND ALEXANDER J. MACROBERT Physical Chemistry Laboratory, Oxford University, Oxford OX1 3 4 2 AND JOSEPH CATANZARITE, GOURI RADHAKRISHNAN, HANNA REISLER AND CURT WITTIG Departments of Chemistry and Electrical Engineering, University of Southern California, Los Angeles, California 90089, U.S.A. Received 20th January, 1983 Rotational and vibrational distributions in CN( X 'Z+) produced in the collisionless infra- red multiple-photon dissociation (MPD) of CF3CN have been measured by laser-induced fluorescence. Both distributions appear Boltzmann, and may be assigned " temperatures '' of Tvib = 2400 f 200 K and Trot = 1200 k 100 K.Phase-space theory (PST) and statis- tical adiabatic-channel theory (SACT) have been used to calculate the CN internal excitations. Both theories predict Boltzmann-like behaviour to within the availableexperimental resolution, with this being more pronounced in calculations using a distribution of CF3CN energies above dissociation threshold (as expected for the case of multiple-photon absorption) than in those using a single excited level of CF3CN. PST consistently predicted similar values of Tvib and Trot, in contrast to the observations. SACT calculations, however, reproduced the experi- mental temperatures using a parameter cc which describes the range of the angular potential between separating fragments and whose value lies in the range 0.5-1.0 A-l.The data are also qualitatively consistent with a simple model which assumes that fragment rotational and translational excitations derive from parent R,T motions in combination with the kinetic energies of those parent vibrations which are converted to product R,T excitations. Thus, statistical theories other than PST can be used to explain the experimental results, and such comparisons offer insight into details of the dissociation process. 1. INTRODUCTION For many years unimolecular decomposition theories have been successfully used to model the kinetic behaviour of gas-phase molecules excited to energies above the dissociation limit by thermal, chemical or photolytic means.'-3 One of the basic assumptions of such theories is that intramolecular energy transfer takes place rapidly amongst the internal degrees of freedom of the excited molecule, so that the rates of unimolecular decomposition can be calculated statistically using assumed properties of the activated complex.Detailed dynamics of the decomposition process (for example, the ways in which the available energy is partitioned amongst the degrees of freedom of the dissociation products) are not considered explicitly in transition-state theories such as R.R.K.M. However, such distributions can be computed using formalisms such as the phase-space 4-10 or adiabatic-channel 11*12 models, both of212 ENERGY DISTRIBUTIONS IN MPD which assume statistical behaviour of internal energy in the parent moIecule, but which contain different assumptions concerning the dynamical constraints associated with the decomposition. In PST, angular-momentum couphg together with the form of the radiaI potential describing the separating fragments are included, whereas in SACT a further constraint on the angular dependence of the potential is included.Experimental tests of these theories clearly need a method of producing excited parent moIecules with statistical distributions of internal energy. This would allow US to study simple bond-fission reactions, in which the reverse process has little or no activation-energy barrier which might affect the dissociation dynamics non-statistically , The technique of i.r. multiple-photon dissociation (MPD) is known to meet this requirement, with evidence for this corning both from experimental observations of a complete lack of any bond-specific dissociation effects and from theoretical models of the multiple-photon absorption process.13 Furthermore, the method has the advan- tage that molecules are prepared under collision-free conditions on the same (ground- state) electronic surface upon which they dissociate.The i.r. MPD method has the disadvantage that the CO, laser typically prepares an ensemble of excited parent molecules, with a range of energies and in a distribution of which only the gross features are known.13 Despite this restriction, studies of the fragments of i.r. MPD can, as we shall show, offer some insight into the behaviour of the excited parent molecule. Energy disposal in the fragments of i.r.MPD has been measured in a number of cmes using molecular-beam methods I4-l7 and laser-induced fluorescence (LIF) 18-31 for product detection. Although the latter technique is restricted to a limited number of diatomic or small polyatomic fragments, the internaLenergy dis- tributions (rotational, vibrational and in some cases electronic) can be characterized in detai1, and translational-energy distributions may also be measured by time-of- flight 1872s*27 or spectral-linewidth 31 measurements. The results obtained for the internal energies show two distinct features. First, rotational and vibrational distri- butions appear Boltzmann-li ke and thus for convenience can be characterized by “ temperatures ”.Secondly, even in instances where there is no significant barrier for the reverse reaction (e.g. the formation of two free radicals), and therefore exit channel effects do not control product distributions, the “ temperatures ” for these two degrees of freedom are markedly different. This study describes comparisons between experiment and theory for the internal- energy distributions in the CN(X 2E+) fragment produced via the i.r. MPD of CF,CN and observed using LIF. The experimental results obtained in two laboratories again show distributions which can be characterized by ‘‘ temperatures ”, with Tvlb % 2000 and Trot = 1200 K. The calculations indicate that Boltzmann like distributions amongst the degrees of freedom of the i.r. MPD fragments is predicted by statistical theories, and that SACT, but not the more extensively used PST, is able to reproduce the differences in vibrational and rotational “ temperatures ”.2. EXPERIMENTAL METHODS AND RESULTS CN(X 2E+) product distributions have been measured at U.S.C. and Oxford using similar experimental techniques, details of which have been described p r e v i ~ u s I y . ~ ~ * ~ ~ Low-pressure CF,CN vapour was dissociated under collision-free conditions using the pulsed output from a C 0 2 laser, and the nascent rotational and vibrational distri- butions of the CN fragment were determined by LIF of the B %+-X 2C+ system. The major experimental difference in the two laboratoties was in the type of CO, laser used, At U.S.C. this was a conventional multimode TEA laser (Lurnonics 103)operating on the (001)-(020)P14 transition at 1052 cm-'.The 0.8 .I output was focused to a spot of approximately constant fluence (ca. 102 J cm-2) over an area of ca. 0.5 mm2, At Oxford, a single-mode " tailored " pulse was used 33 with 10 ns rise and fall times and constant power during the 200 ns pulse length. The output from this arrangement [35 mJ, (001)-(100)P20, 944 cm-'1 was brought to a Gaussian shaped spot of area 0.3 mm2 at the e-l points, resulting in an " average fluence" Over this area of 7 J cm-2. With the tailored-pulse system, measurements were restricted to the (0,O) and (1,l) band regions of the B-X system, resulting in rotational distributions for u = 0 and an estimate of the ratio of the vibrational populations in u = 0 and 1 .More extensive measurements at U.S.C. enabled rotational distributions within v = 0, 1 and 2, together with relative vibrational level populations for u = 0, 1,2 and 3, to be determined. Where the two sets of results overlap, agreement is good. Fig. 1 0 200 400 600 800 1000 J ( J + 1) Fig, 1. Plots of the relative populations in the rotational €eveIs, J , of CN(X %*, u = 0) produced in the collision-free i.r. MPD of CF&N as a function ofJ(J + 1). A straight-line plot would be obtained for a Boltzmann distribution. Data were taken from experiments with the 200 ns " tailored " pulse (0) and the 200 ns multimode pulse (a), and show essen- tially the same temperature for the two sets of measurements. The pressure was 3 mTorr, TR = 1240 K. and the delay between the onsets of the two lasers was 1 p s .shows data for the rotational distributions in II = 0, pIotted in such a way that a straight line would be expected for a Boltzmann distribution. It is clear that the distributions from the two experimental arrangements can be represented by the same rotationa1 temperature of ca. 1200 K. Vibrational distributions were also found to be Boltzmann-like and the data are summarised in table 1 . Two comments on the experimental data are in order. First, although the rotational temperatures in the studies are identical, the vibrational temperatures differ. The more substantial body of data obtained with the mdtimode laser is probably more realiable, since in the tailored-pulse studies only the ratio of u = 0 to v = 1 populations could be estimated, using a wavelength region in which the overlap of the (0,O) and (1,l) bands seriously limits the accuracy.Secondly, it may initially appear surprising that the multimode measurements at high fluence (ca. lo2 J cm-2) and the single-mode measurements at lower fluence (7 J ~ m - ~ ) , both using similar (200 ns) pulse widths, give very simiIar214 ENERGY DISTRIBUTIONS IN MPD TQble 1. CN(X %+) energy distributions from the collision-free i.r. MPD of CFKN - multimode pulse, single-mode pulse, degree of freedom 1052 cm-l 944 cm-l rotational 1200& 100" 1240 & 100 vibrational 2400 f 200 ' 1900 f 300 a Rotational temperature was the same for v = 0,l and 2. Estimated from the relative popula- ions of t, = 0,1, 2 and 3.20 Estimated from the relative populations of II = 0 and 1.temperatures, as it is known that the laser intensities, which are very different in the two cases, control the energy available for partitioning into the fragments' degrees of freedom.23p29*34 For 200 ns multimode pulses the rotational temperature in CN is observed to increase with fluence (and hence intensity) up to ca. 20 J cm-2 but remains constant at higher fluences, owing to significant parent-molecule depletion.21 The dissociation yield (which is predominantly fluence dependent) is a steep function of fluence near 7 J cm-2,21 and since the single-mode experiments were carried out with a Gaussian fluence profile the predominant signal will be from those molecules dissoci- ated near the centre of the beam, at fluences of ca.15 J cm-2. Thus a single-mode pulse with a constant fluence of 15 J cm-2 and a multimode pulse of 20 J cm-2 would appear to produce the same CN distributions, indicating that at these fluences either the average intensities are similar for the two pulses of differing temporal behaviour within their 200 ns widths or the effect of intensity is minimal. One should also bear in mind that fluences which are estimated from the laser energy and the spot size are not very accurate for tightly focused geometries. 3. CALCULATIONS Both PST 4-10 and SACT 11*12 assume that a reaction complex A, produced with sufficient internal energy to decompose into fragments B and C , will dissociate with equal probability into each of the accessible product channels, thereby enabling the product-state distributions to be calculated statistically.Intramolecular energy transfer within the reaction complex is assumed sufficiently complete so that all of the available phase space is sampled, yet no transitions between channels occur as the complex dissociates, i.e. the motions are considered adiabatic.35 By accessible (" strongly coupled ") 35 channels is meant those that satisfy the normal conservation laws of energy and angular momentum between reactants and products, together with a constraint which is related to the dynamics of the separating fragments, namely that the reactant total internal energy E exceeds the maximum value of the effective channel potential V , i.e. The form of the channel potential distinguishes PST from SACT, as discussed below.E 2 V,,,. (1) PHASE-SPACE THEORY CALCULATIONS PST assumes that V takes the form W) = K1(r) + B(r)L(L + 1) + E m (2) where V,,(r) is the one-dimensional electronic potential as a function of r, the centre- of-mass separation of the fragments, B(r) is the effective rotational constant for theJ. R. BERESFORD et aI. 215 orbital motion (= h2/2pr2) whose quantum number is L, and Em is the internal energy of the separated products. Ve,(r) was deduced from the attractive part of the Lennard-Jones potential. (3) where Et is the relative translational energy of the separating fragrnents.‘-lo This condition simply requires that for the reverse direction the reactants have sufficient translational energy to surmount the centrifugal barrier to association.Fig. 2A illustrates the restrictions on the available phase space for the case of a parent moIecuIe (total angular momentum J,) dissociating into an atom and a linear molecule (angular- momentum J), showing the limiting value of the orbital angular-momentum quantum number L,, (which depends upon Et and hence upon J ) and the constraints imposed by conservation of angular momentum (L + J = Jo). For more complex cases the geometric interpretation is more laborious, but the principles and trends remain. the same. Energy distributions in CN were calculated by methods similar to those of ref. (8) and (9) using vibrational and rotational constants for CF3CN,36*37 CF, j8 and CN 39 from the literature, and C6 = 80 x 10-60erg c d . * Parent angular momentum (Jo) and disposable energy appearing in the degrees of freedom of the fragments (ES) were varied.produced by i.r. MPD, CN energies were calculated for the Gaussian function Eqn (I) and (2) reduce to the condition L(L + 1)h2 < 6pCtt3(E,/2>2i3 In an attempt to mimic the distribution of exp [ - ( I 3 - {E~})Z/2S2]dE~ (4) 1/2n 6 1 P(E1)dEt - where ( E l } is the average value of EZ, and S is the width of the distribution. Three such Gaussian distributions were used, with the foIlowing parameters: {Ex> = 10 000, 13 000 and 18 000 crnmf, and S = 4720 crn-l. The results are illustrated in fig. 2 and 3, and can be summarised as follows: (i) Rotational and vibrational populations at fixed Et show distributions which are well represented (within the resolution of the experimental observations) by Boltzmann ‘‘ temperatures.” (ii) Both vibrational and rotational temperatures show only a weak dependence upon the parent angular momentum Jo.(iii) For a given value of Et, vibrational and rotational temperatures are very similar, and such similarity is retained when using the P(E#) distribution. This is in striking contrast to the experimental observations. STATISTICAL ADIABATIC-CHANNEL-THEORY CALCULATIONS The form of the effective potential V(r) that is used in PST takes no account of any potential-energy barriers to dissociation that arise due to angular interactions of the separating fragments, and the statistical adiabatic-channel theory of Quack and Troe 11~12 attempts to rectify this by considering a different form of V(r).Since little is known of the details of potential-energy surfaces for poIyatomic moIecuIes, a simple interpolation procedure is used : w> = M-) + Eu(d &(p> = [E,(r,) - E,&xp[--a(r - re)] + E,, + B ( ~ ) P ( P + 1) (5) (6) (71 For a given dissociation channel a, &(re) is the parent internal energy at its bound equilibrium geometry [excluding the contribution B(r,)Jo(Jo + 1) which is added P = L + (Jo - L)exp[-a(r - re]. * C, was estimated using a Lennard-Jones potential. See also ref. (l), p. 134.60 50 40 30 20 10 0 L (A) L +J=J, L ma*a(E-E; - BJ (J* 1)) '1 3 for r - 6 attraction - 0 10 20 30 40 50 J E ,,(CN) := BJlJ -1- 1)/103 cm-l Fig. 2. Calculations indicating the effect of parent total angular momentum, Jo, on product V,R excitations.(A) shows the constraint imposed on the available product phase space by the conservation of angular momentum, for the case when the products are an atom and a linear molecule (see text for details), The shaded area indicates the allowed states for the case So = 10 and the dashed lines indicate the analogous region for the case Jo = 30. Clearly, low JO restricts the number of available product states. For more complex cases (e.g. CF3CN+CF3 + CN, JL -t J2 -I- L == Jo), the geometric interpretation is more laborious, but the principles and trends re- main intact. (B) shows the results of phase-space calculations of the CN rotational excitation (v = 0) which derives from the unirno- lecular reaction of CF,CN, for a fixed amount of disposable energy (18 000 crn-l) and different values of Jo.The curves are offset from one another for convenience and the " temperatures " associated with the curves are taken from the straight portions. (a) Jo = 70,3400 K; (b) Jo = 50,3430 K; (c) Jo = 30, 3450 K; ( d ) Jo = 10,3470 K. The trend suggested by (A) can be seen in the slowly changing slopes of the straight-line portions, and the results depend weakly on Jo. (C) shows the results of similar calculations for CN vibrational excitation. Energy is mcasured relative to the zero-point vibrational energy and, as with (B), the trend suggested by (A) is manifest in the calculations. 0, lo = 70, 3060 K; @, Jo = 50, 3110 K; 0, Jo = 30, 3140 K; I, Jo = 10, 3160 K.J. R. BERESFORD et al. 217 separately], E,, is the channel energy of the products in their specific quantum states, B(r) and L are, as in PST, the effective rotational constant for orbital motion and the orbital quantum number.Eqn (6) and (7) show that &(Y) interpolates smoothly t n c c) ._ ErO1(CN) = BJ(J + 1)/103 m-' E,(CN)/103 cm-' Fig. 3. Calculations of CN product vibrational and rotational distributions for different values of disposable energy, EZ, using single values as well as distributions over E*. (C) and (D) show rotational and vibrational distributions, respectively, for single values of ES [(a) and 0 , 1 8 000; (6) and 0 , 1 3 000; ( c ) and 0 , l O 000 cm-'1 and .lo = 30. The curves are offset from one another for convenience and the associated " temperatures " are taken from the straight-line portions. (A) and (B) show CN product rotational and vibrational distri- butions for cases where a distribution of E3 values is considered.The distribution function is a symmetric Gaussian whose width is 4720 cm-l for ( E s ) = 18 000 [(a) and 01, 13 000 [(b) and 01 and 10 000 cm-' [(c) and 01 and Es intervals of 944 cm-l are used (see text for details). Since the Gaussian is symmetric, ( E s ) = ELax. between limiting values at r = Y, and co. This exponential form of the potential reproduces that calculated for dissociation of a triatomic when effects of hindered rotation upon the barrier height are included,35 and this is used to justify its extension to polyatomic molecules, the value of cc thus being loosely related to the range of the angular potential of the separating fragments.It can be seen that PST is a special case of the morc general SACT by putting o! = co in eqn (6) and (7). In the present calculations, o! has been used as an adjustable parameter, and its magnitude in com- parison with that used in previous applications of the theory 1132p35*40 will be discussed later. The molecular constants used were the same as those for PST, with the excep- tion of the form of the electronic potential which was taken as a Morse function, Vel(r> = De(1 - exp[-p(r - re>II2* (8)218 ENERGY DISTRIBUTIONS IN MPD /3 can be calculated from the force constant F, of the bond corresponding to the reac- tion coordinate [p = (Fr/2D,)'/2 = 1.84 A-l], but since the Morse curve may not be a suitable representation of the potential for polyatomic molecules, being too flat at large r,iiJ2 p has also been used as an adjustable parameter. Calculations were per- formed as a function of Et, Jo and p for three values of 01, namely 0.5, 1 .O and 1.5 A-1.Details of the channel-counting procedures, similar to those described in the original formulation of the theory,L1,12 are given el~ewhere.~' Fig. 4. Rotational and vibrational distributions calculated using SACT. In (A) vibrational distributions are plotted for two values of the disposable energy Et corresponding to 10 and 18 photons above the dissociation limit [9440 (0) and 16 992 cm-' (J), respectively], for the highest value of c1 used (1.5 A-'). In (€3) rotational distributions are plotted as a function of J(J + 1) for Ez = 16 992 crn-', with straight lines indicating rotational temperatures.Note the decrease in Trot with decreasing a: a = [7, 1.5; 0, 1.0; ,0.5 A- l. (A) and (B) were both calculated for Jo :-= 44. Comparison of these calculations with those from PST [fig. 3(a) and 3(6)] show that cc = 1.5 A- appears to be close to the high cc limit of SACT. Representative results are shown in fig. 4 and can be summarised as follows: (i) As in PST, for each I 3 the distributions appear Boltzmann-like, but there is noticeable curvature in the rotational distributions at high energies [see fig. 4(b)]. Calculations with a distribution of I 3 values similar to that given for PST tended to remove this and produce a more linear Boltzrnann plot. (ii) Both variations in Jo (in the range 0-70) and p (values of0.84, 1.84 and 2.84 A-') produced <5"/: change in the observed temperatures.The calculations reported below were carried out at J , = 44 and B = 1.84 A-l. (iii) Vibrational distributions showed little change with a, vibrational temperatures and average energies decreasing by ca. 10% as a: decreased from 1.5 to 0.5 Ad'. (iv) At a I= 1.5 A-' and €$ = 16992 cm-l, Tvib and Trot are close in value and to the PST results, as can be seen in fig. 5,where calculations using both theories are presented. (v) Rotational distributions show a marked change with X , as can be seen in fig. 4(b) for Et I- 16 992 cm-I. Fig. 5 shows that when c1 is changed from 1.5 to 1.0 Awl, Trot decreases by 10% at = 16 992 cm-' and 26% at 9440 crn-l.J. R. BERESFORD et al. 219 Between a = 1.0 and 0.5 A-' the changes for these values of ES are more dramatic, with Trot decreasing by factors of 1.8 and 2.2, respectively.For a given a this ratio depends only weakly on Et (for a = 0.5 A-l, Tvib/Trot = 1.8 and 2.1 for a is the only parameter which significantly affects the ratio Tvib/Trot. 3600 320 0 k4 .P 2800 2 8 2400 --- n c.' +I I (d 0 ';= 2 0 0 0 ' z' 2 1600' c.' 5 z' 1200, I3 800 - .O P 0 Fig. 5. Calculated variations of CN product vibrational and rotational " temperatures " with the disposable energy ES for the reaction CF3CN-+CF3 + CN. Temperatures deduced from plots such as those shown in fig. 2 4 are plotted against ES. Circles show vibrational (0) and rotational ( 0 ) temperatures from PST. Squares show vibrational (0) and rotational (W) temperatures from SACT for a = 1.5 A- and triangles show rotational temperatures for SACT with a = 1.0 A-' (A) and 0.5 A-' ( v). As explained in the text, vibrational temperatures from SACT show little variation with a.Et = 16 992 and 9440 cm-l, respectively), and this suggests that distributions of Ez within this range should not affect the ratio unduly. Taking into account the un- certainties in the experimental values of the CN temperatures (table l), we conclude that our data can be reproduced by SACT using a value of a between 0.5 and 1 .O A-l. 4. DISCUSSION It is clear that the PST calculations lead to product V,R excitations which are different from the V,R excitations found experimentally in the CN fragments. Small differences aside, the PST distributions can often be ascribed " temperatures ", in which case T, Tv, no matter how the calculations are done (different Jo, average over Jo, single Et, distribution of ES values etc.).This is in sensible accord with the basic premises of the theory, in which all accessible states are equally probable, and similar results can also be obtained using the computationally simpler formalism of220 ENERGY DISTRIBUTIONS IN MPD Levine et al.,42 albeit with the loss of some rigour. As discussed above, the SACT calculations are capable of a closer match between experiment and theory. The SACT addresses the issue of correlating motions between reagent and products in a conceptually pleasing way, using a single parameter CC, but requires an equilibration between accessible states as the reaction occurs.This is a strong assumption, but makes the calculations tractable. The striking accord between the experimental results and the SACT calculations suggests that the physical picture is quite sensible, regard- less of any possible ambiguity in the assumptions necessary for its development. The value of a that we use to model the experimental results, 0.5-1.0 A-l, should be compared with those used in other SACT calculations. Thermal high-pressure- limit recombination-dissociation rate constants have been calculated for a series of molecules (including NOCl, NO2, 03, H20, CH4 and C2H6), with a = 1 A-l fitting all the experimental data to within a factor of In these cases there is no reason to expect a significant barrier for the reverse reaction.In contrast, translational- energy distributions for bimolecular reactions of halogen atoms with unsaturated hydrocarbons, in which statistical complexes are thought to be formed and significant exit-channel barriers may be present, are reproduced with cc > 1 A-' (e.g. 0: = 2 for F + C,H5Cl, 2-4 A-' for C1 + C2H3Br), although the molecular parameters of the intermediates involved in these cases are only estimated, and their values may affect the calculated distrib~tions.~~ The present experiments involve complexes whose character is far more similar to the former cases than the latter, and the range of values of cc used in the present work agrees well with values used previously. The results also suggest that for the present case, a = 1.5 A-' may be close to the limit where SACT and PST are equivalent.An alternative statement of the present agreement between theory and experiment is that a lack of complete intramolecular energy transfer, resulting in non-statistical behaviour, is not necessary to explain our results. However, an interesting perspective on this problem comes from consideration of the degrees of freedom of the CF3CN parent molecule prepared by i.r. multiple-photon absorption. The 12 vibrations are highly excited, while the rotations and translations are essentially those of the 300 K starting mate~ial.~''~~ Thus, the sample is prepared in such a way that parent excitation is strongly biased in favour of vibration, with much lower rotational excitation. The statistical calculations, on the other hand, equilibrate 15 degrees of freedom (e.g.the PST calculations deal with 6 vibrational and 3 rotational degrees of freedom of CF3, 1 vibrational and 2 rotational degrees of freedom of CN, and 3 degrees of relative trans- lational motion-2 orbital, 1 radial). It is not possible to occupy all of the available product states without energy flowing from the vibrational reservoir into the R,T degrees of freedom of the separated fragments, and in applying PST to the present system we assume implicitly that such energy-transfer processes are rapid on the time scale of the dissociation event. This, in fact, may prove quite presumptuous for an important number of physical and chemical systems. Note that if the parent had sufficient rotational excitation, this motion would correlate to produce R,T excitation, and the need for intramolecular exchange would be reduced accordingly.Thus, the manner in which we prepare the sample allows us to measure the flow of energy from vibrations into product R,T excitations, and this is a rather central issue to the matter of intramolecular reaction dynamics. In comparing our experimental results to the PST calculations, it is clear that there is an important difference, with a marked deficiency in measured product R,T excitations,20p21 relative to those which are computed. It follows that the picture of a " very loose transition state ", with equal occupancy of all states which are allowed by energy and angular-momentum conservation, is not realistic. In this context,J. R. 3ERESFORD et d.221 intramolecular energy transfer is incomplete on the pertinent time scale, which corresponds approximately to the time required for the CN and CF3 species to move from near the equilibrium geometry to some critical configuration (ca. s), despite the statistical nature of the excited parent, and we expect that such behaviour will prove quite common as more detailed experimental results become available. If motion from near the equilibrium geometry to the transition state is so rapid that intramolecular V+R,T transfer is completely inhibited, we can estimate the likely product R,T excitatiom2' First, we take the 5 vibrations which are being converted into product R,T excitations and estimate the nuclear kinetic energies with the simple formula This quantity is then combined with parent R,T excitation (300 K, 620 crn-l) in order to obtain the average amount of product R,T excitation, which can be ascribed a temperature if one so desires. Tn doing this, we find that with Tv = 2400 K (using CN as a vibrational thermometer), we predict TR,T E 1200 K.This is in surprising accord with the experimentally determined values* and suggests that the above considerations have merit. We also note that this procedure is in accord with other similar experimental observations and that it is so conceptually enticing as to inspire further thinking along the same lines. We are particularly indebted to Dr M. Quack for help and guidance on the calculations of product-state distributions via the statistical adiabatic-channel theory. Assistance with computation from K.G. McKendrick and C . G. Atkins is acknowledged. Support for the joint project from the Collaborative Research Grants Programme of NATO (grant no. RG. ISO.Sl> is gratefully acknowledged. W. Forst, Theory of UnimoZecuIar Reactions (Academic Press, New York, 1973). P. J. Robinson and K. A. Holbrook, UnimuIecuZar Reactions (Wiley-Interscience, New York, 1972). 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