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On the mechanism of the reaction K + HBr → KBr + H
Volume 6, number4
ON THE
CHENICAL
MECHANISM
OF
PHYSICS
THE
LETTERS
REACTION
15
K -I- HBr
-
KBr
August 1970
+ H
A C.ROACH Department
of Chemis!ry,
Manchester.
University of Manchester, kp,3 9PL. UK
Received 21 June1970 A potential-energy surface with a low barrier in the exit valley can accountfor large isotope effects observed in the reaction of K with FrEW,DBr or TBr. Reaction is confined to a range of incidentangles determinedby the reactanttranslational and vibrational energies.
1. INTRODUCTION
2. THE POTENTIAL-ENERGY
The reaction K + HBr - KBr + H was the subject of pioneering work [l] in the application of crossed molecular beam techniques to chemical kinetics. Gillen et al. [Z], on the basis of a very careful experiment, at 2.8 kcal mole-l initial relative energy, have shown that the product angular distributions are broad, and peaked backwards in the HBr reaction, but forwards in the DBr case. Martin and Kinsep [3] have investigated the TBr reaction at 1.4 kcal mole-l and conclude that the scattering in that case is predominantly backwards. (Backward scattering corresponds to “recoil” of the products.) The total cross section is of the order of 35A2 [4], but is around 46% larger with HBr than with DBr [2]. The probable shape of the potential-energy surface for this family of reactions is discussed in the next section. In section 3 it is argued that the critical point in reaction is the surmounting of a small barrier in the exit valley, at which point the “crossing” from covalent (reactant) to ionic (product) surfaces occurs. Due to the relative lightness of the H isotope, the reactive dynamics may be simply approximated, enabling prediction of product distributions. The experimentally observed isotope effects are consistent with the model thus formulated. The dynamical arguments used are essentially classical, but it is critically important to take account of the mass-dependent zero-point vibrational energy of the reactant molecule,
The great limitation in the comparative theoretical dfscussion of related chemicaL reactions is the difficulty of establishing differences in potential-energy surfaces. Here we are concerned purely with isotopic variations and are thus involved with a single surface, uncertatn in form though it is. This qualitative discussion follows the tradition of Ggg and Polanyi [5]. The reactants are generally envisaged as essentiaily covalent, whilst the product molecule KBr has an ionic structure. Following success-
SURFACE
ful descriptions of reactions suctt as K t Br2 KBr + Br [63, we assume that there is an abrupt
crossing between a covalent and an ionic surface, and that the energetically lower governs the dynamics. We dfscu’ss first the covaient surface. Let 1y be the angle between the HBr and KBr bonds. As the reactants approach the potential curve of HBr is perturbed as K is polarised by the permanent dipole of HBr. For (L = B (colfinear approach) this inter$ction is x2 kcal mole-l attractive at YKBr = 3A [7,8]. Repul$ve fOrCeS will become apparent by ~~~ = 2.8A. (The bond length of KBr- is little greater than that of KBr [8].) ff the approach angle, cy, is decreased, the attractive polarisation forces wilL diminish, reaching a minimum close to cy = r/2. The K-Br overlap repulsion should not be dramatically altered but, for a d n/2, repulsions
essentially
between K and H should be taken into account. (The closeness to which K approaches Br is important for reaction: If r&r = l-4& the eqUili-
389
Volume 6. number
4
CHEMICAL
brium value, whilst ~1,= s/6, then to achieve rmr = 3A, P-m must diminish to 1.9& short compared to 3.5& the 4s mean-radius for K [Ml.) The magnitude and angular range of this repulsiqe contribution are difficult to estimate. The exit valley of the covalent surface will be energetically unfavourabie at all angles. Turning attentior to the ionic surface, we are concerned with the perturbation of the product KBr potential curve on bringing H towards the Br’ ion. Here polarisation forces will be relatively weak. For HBr’ alone, an electronic calculation [9] indicates that attractive and r,epulsive interactions cancel around rHBr = 2A; this potential is ~30 kcal mole-l repulsive at the neutral HBr equilibrium distance of 1-d. An essentially similar picture is expected even in the (relatively distant) presence of K+. This interaction should be rather weakly dependent $n (Y, except very close to 0 = 0. (If Y r =2.8Athe equilibrium value, whil$ CY=.r K$ 6, then if ‘HBr = 2A we have rHK = 1.5A, still larger than 1.2A, tbe IP ionic radius [ll].) F’lg. 1 suggests the general form of the lower potential-energy surface for (Y = 71. It is based on the experimental dissociation ene,rgies, bond lengths and force constants of HBr and KBr [12,13], the polarisability of K [7] and the dipole moment of HBr [8], supplemented by a calculated semi-em irical HBr’ -potential curve [9] and a Kir Vrz repulsive potential (the latter chosen to give the covalent minimum at ?K13r = 2.85A). The most important feature of this surface is the small barrier at :he cross ing point to the exit valley. We have special coxern with points X and Y, which both lie on the line rKBr = Y*, X at the covalent minimum path and Yon the crossY* is chosen so that (Ey -Ex) is mining curve.
PHYSICS LETTERS
15 August 1970
imised. In fig. 1 Y* = 2.8& E -0.6 kcal mole-i and Ey = ‘7 kcal mole- r=. Evidently tbis crude discussion leaves Ey somewhat uncertain; one point is that the exact surfaces‘will be pushed apart-at the crossing. We believe, however, that the barrier itself is a real feature. The basic physical reasons for its appearance are the small electron affini of HBr and the shortness of the HBOr bond (1.4 B ) relative to the Br’ ion radius (~1.7A) [ll]. As LYdecreases from s, the energy of the complex at covalent geometries will rise, due to diminishing polarisation interactions, and, for (Y 5 a/2, because of additional K-H repulsions. Fig. 2 indicates a qualitatively plausible dependence of EX and Ey on CY. EX increases and (Ey -Ex) diminishes. The horizontal line is at the minimum reactant energy. In detail, these curves take account of the variation of the polarisation interaction for CY2 s/2, but have otherwise been chosen to enable our description of the collision dynamics to match experiment.
3. THE REACTION DYNAMICS The interaction between the covalent reactants is relatively weak. For this reason, because of tbe largeness of vibrational energy spacings in HBr and because of the gross dis@rity in the masses of K and H, it seems improbable that the HBr vibrational motion will be much affected by the appearance of K. Under tbe conditions studied sperimentally, vibration of HBr is rapid
Fig. 2. Schematic variation of the potential barrier with angle of approach. Ex, Ey and the zerc reactant energy are ‘plotted. Threshold angles are indicated by vertical arrows. The lengths of VH,. VD and VT represent
Fig. 1. The collinear .. 390
potential-energy
K + Wr
(a, =.7r).
surface
for
the zero-point vibrational energies of RBr, DBr and experimen-
TBr; those of ZK, TD acd TT the respective tai translational energies.
Volume 6, number 4
CHEMICAL PHYSICSLETTERS
compared to the rate of approach of K: during a complete HBr vibrational period the KBr distance decreases by only =O.lA. Initially we shall neglect rotational motion of HBr. Classically, reaction occurs if the H-isotope reaches the crossing-line. As vibration is rapid, this will always first occur close to an outer turning-point, where the vibrational velocity is near zero. The light H-isotope will then be swiftly accelerated away by the H-Br- repulsion on the ionic surface, without time for further interaction with &. The product translational energy, essentially all vested in motion of H, will be close to the magnitude of this repulsive potential at the crossing. (The translational velocity of H before reaction is extremely small, corres onding to a kinetic-energy of x0.01 kcal mole’ P.) This reasoning is consistent with the near isotope-independence of the translational energy distributions [2 1. If before crossing the HBr vibrational motion is indeed undisturbed, then there are two conditions for reaction. First, the energy difference (Ey-EX) must be less than the HBr zero-point vibrational energy. Second, point X must be energetically accessible to the initial relative translational motion (essentially movement of K relative to Br). Surveying fig. 2, we conclude that reaction is confined to a limited range of LY. Near Q = B the reactant zero-point energy may be insufficient to overcome the barrier. Near (Y = 0 the initial translational energy does not permit ?-KBr to become small enough. r*, for fig. 2, should strictly be chosen notsimply to minimise (Ey -EX), but, where possible, as the largest KBr distance for which both reaction
conditions
are satisfied.
For
15 August 1970
straightforwardly derived for the angu1a.r distribution, a function only of amax and @min. We select ranges of (Y from 400 to 1800 for HBr, 40° to 120° for DBr and 900 to IlOo for TBr. The values for amin are consistent with the translational energies used in the experiments, and those for (Ymax reflect the isotopic dependence of the zero-point vibrational energies. Within these restrictions the parameters were chosen to fit experiment. The resuiting angular distributions are the dashed tines of fig_ 3, which may be compared, for HBr and DBr. with (shaded) experimental bounds, and, for TBr, with the less precise experimental finding of predominantly backward scattering. Reactant
rotation
by assuming
in an angular
range
czm&
incor-
that
an ele-
mentary treatment of the reaction dynamics we take Y* to be a constant, independent of N. In fig. I, the barrier height increases rapidly as Y+ is varied from 2.8A. Our further assumption is that the weak covalent interactions experienced before crossing by a reactive encounter do not significantly deflect the straight-line approach of K towards randomly-oriented HBr. We consider as reactive all such collisions reaching a sphere of radius Y* about Br,
is straightforwardLy
the H atom retains its initial rotational velocity after crossing. This motion is perpendicular to that induced by the HBr’ repulsion, giving an additive contribution to the product translational energy. The determination of angular distributions invoLves a further (numerical) average over an azimuthal rotational angle. Taking a (thermal) rotational energy of 0.6 kcal mole-l and a constant repulsive energy of 1.2 kcal mole-l, the solid lines of fig. 3 result. This choice gives a product transiational energy close to the experimental maximum. As well as being in accord with experimental porated
/-
2 Q! 2 CYST
Upon crossing, the H atom is propelled directly away from Br-. The scattering angle is then the angle between the initial relative velocity vector and the HBr bond at the instant of crossing. By averaging over the reactive .initial conditions a messy analytical expression can be
, OQ
--
em
Fig. 3. Centre of mass angular dfstrihutfous, normaLised to unity
at O” for the HBr
and DBr cases
(as in
[2]). b?lt at 180’ in the TBr case. (a) ---- without rotarotatiotil energy = f (repuh3ionenergy), uon, -04 (c) . _. * experiment2.l Limfts [2]. 391
Wlume 6. number 4
CHEMICAL PHYSICS-LETTERS
angular distributions, for total cross we calculate the ratios
sections
and bperiment
[2] gves
o(K+KBr) o(K+TBr)
_ 9 - ’
1.4 f 0.2 for the former.-
The absolute value of u(K+ HBr), taking Y+‘= 2.8& is 2fi2, a little below the experimental range of 35 * 9A2 [4]. A larger value of r+, or allowance for the deflection of the incoming K by polarisation forces, would increase u. Our simple model predicts the Isotope independence of the product translational energy distributibn and its peak at low values [2]. The f%ii experimental breadth could, however, only be duplicated by taking full account of the reactant rotational energy distribution, the variation of the repulsion energy with 01, the retention of some vibrational veiocity at the crossing and, possibly, tuunelling effects; We believe that quanium mechanics will preserve the essential features of the classical model outlined here: in a future paper we shall investigate’the importance of quantum effects in this situ&ion.
4. CONCLUSIONS Given a potential-energy surface with a iow in-the exit valley, the unusually large isotope effects in the reaction of K with HBr may be rationalised. For K + HCL, there is experimental evidence for a more substantial barrier
barrier
PI.
Our simple account of the classical
dynamics
is expedited by the weakness of the interaction between the approaching reactants, by the rapidity of HBr vibrations and, most important, by the relative lightness of H. Product angular distributions are sensitive to initial vibrational and translational energies. At
392
15 August 1970
constant translational energy we predict A >D >T as regards backward-scattering. For htgher
translational en&g!es all distributions should stift for-ward, towards a limit of isotropic scattering in the HBr case (tf reaction becomes accessible at all Q). Vibrational excitation of reactants should decrease isotope effects. Total cross sections should depend only weskly on energy. ACKNdWLEDGEMENT The author thanks’ Dr. P. J:Knntz ing discussions.
for stimuiat-
REFERENCES [l] E. H. Taylor and 9. Da& J. Chem. Phys. 23 (l955) 1711. [2] K.T. Gilien,’ C-Riley and R. B. Bernstein, J. Chem. Phys. 50 (1969) 4019. [3] L. R. Martin and J. L.Kinsey. J. Chem. Phys. 46 @967) 4934. [4] J. R. Airey, E. F. Greene, K.Kodera, G.P. Reck and J. Ross, J. Chem. Phys. 41 (1964) 1917. I51 _ _ R. A. 0a-s and M. Poianvi. _ Trans. Faradav Sot. 31 (1935) 604. 161 _ . J. Chem. Phvs. 49 - . M. Godfrey and MKarolus. (1966) 3602; P. J.Kuntz, M.H.Mok and J. C. Polanyi, J. Chem. Phys. 50 (1969) 4623. [‘i].R. M. Sternheimer. Phys. Rev. 36 (l962)1220. [&] A. L. McClellan. Tables of experimental dipole moments (Freeman, San Francisco, 1963). [9] A. C. Roach, to be published. [16] E. Clementi, J. Chcm. Phys. 41 (3964) 295. [ll] E.S.RWner, J. Chem.Phys. 19 (1951) 1030. [12] G. Herzberg. Molecular spectra and molecular structure, I. Spectra of diatomic molecules (Van ’ Nbstrahd, Princeton, l950). [lS] L. Brewer and E.Brackeit, Chem. Rev. 61 (1961) 425. [14-l T. J. Odiorne and P.R. Brooks, J. Chem. Phys. 51 (1969) 4676.
ON THE
CHENICAL
MECHANISM
OF
PHYSICS
THE
LETTERS
REACTION
15
K -I- HBr
-
KBr
August 1970
+ H
A C.ROACH Department
of Chemis!ry,
Manchester.
University of Manchester, kp,3 9PL. UK
Received 21 June1970 A potential-energy surface with a low barrier in the exit valley can accountfor large isotope effects observed in the reaction of K with FrEW,DBr or TBr. Reaction is confined to a range of incidentangles determinedby the reactanttranslational and vibrational energies.
1. INTRODUCTION
2. THE POTENTIAL-ENERGY
The reaction K + HBr - KBr + H was the subject of pioneering work [l] in the application of crossed molecular beam techniques to chemical kinetics. Gillen et al. [Z], on the basis of a very careful experiment, at 2.8 kcal mole-l initial relative energy, have shown that the product angular distributions are broad, and peaked backwards in the HBr reaction, but forwards in the DBr case. Martin and Kinsep [3] have investigated the TBr reaction at 1.4 kcal mole-l and conclude that the scattering in that case is predominantly backwards. (Backward scattering corresponds to “recoil” of the products.) The total cross section is of the order of 35A2 [4], but is around 46% larger with HBr than with DBr [2]. The probable shape of the potential-energy surface for this family of reactions is discussed in the next section. In section 3 it is argued that the critical point in reaction is the surmounting of a small barrier in the exit valley, at which point the “crossing” from covalent (reactant) to ionic (product) surfaces occurs. Due to the relative lightness of the H isotope, the reactive dynamics may be simply approximated, enabling prediction of product distributions. The experimentally observed isotope effects are consistent with the model thus formulated. The dynamical arguments used are essentially classical, but it is critically important to take account of the mass-dependent zero-point vibrational energy of the reactant molecule,
The great limitation in the comparative theoretical dfscussion of related chemicaL reactions is the difficulty of establishing differences in potential-energy surfaces. Here we are concerned purely with isotopic variations and are thus involved with a single surface, uncertatn in form though it is. This qualitative discussion follows the tradition of Ggg and Polanyi [5]. The reactants are generally envisaged as essentiaily covalent, whilst the product molecule KBr has an ionic structure. Following success-
SURFACE
ful descriptions of reactions suctt as K t Br2 KBr + Br [63, we assume that there is an abrupt
crossing between a covalent and an ionic surface, and that the energetically lower governs the dynamics. We dfscu’ss first the covaient surface. Let 1y be the angle between the HBr and KBr bonds. As the reactants approach the potential curve of HBr is perturbed as K is polarised by the permanent dipole of HBr. For (L = B (colfinear approach) this inter$ction is x2 kcal mole-l attractive at YKBr = 3A [7,8]. Repul$ve fOrCeS will become apparent by ~~~ = 2.8A. (The bond length of KBr- is little greater than that of KBr [8].) ff the approach angle, cy, is decreased, the attractive polarisation forces wilL diminish, reaching a minimum close to cy = r/2. The K-Br overlap repulsion should not be dramatically altered but, for a d n/2, repulsions
essentially
between K and H should be taken into account. (The closeness to which K approaches Br is important for reaction: If r&r = l-4& the eqUili-
389
Volume 6. number
4
CHEMICAL
brium value, whilst ~1,= s/6, then to achieve rmr = 3A, P-m must diminish to 1.9& short compared to 3.5& the 4s mean-radius for K [Ml.) The magnitude and angular range of this repulsiqe contribution are difficult to estimate. The exit valley of the covalent surface will be energetically unfavourabie at all angles. Turning attentior to the ionic surface, we are concerned with the perturbation of the product KBr potential curve on bringing H towards the Br’ ion. Here polarisation forces will be relatively weak. For HBr’ alone, an electronic calculation [9] indicates that attractive and r,epulsive interactions cancel around rHBr = 2A; this potential is ~30 kcal mole-l repulsive at the neutral HBr equilibrium distance of 1-d. An essentially similar picture is expected even in the (relatively distant) presence of K+. This interaction should be rather weakly dependent $n (Y, except very close to 0 = 0. (If Y r =2.8Athe equilibrium value, whil$ CY=.r K$ 6, then if ‘HBr = 2A we have rHK = 1.5A, still larger than 1.2A, tbe IP ionic radius [ll].) F’lg. 1 suggests the general form of the lower potential-energy surface for (Y = 71. It is based on the experimental dissociation ene,rgies, bond lengths and force constants of HBr and KBr [12,13], the polarisability of K [7] and the dipole moment of HBr [8], supplemented by a calculated semi-em irical HBr’ -potential curve [9] and a Kir Vrz repulsive potential (the latter chosen to give the covalent minimum at ?K13r = 2.85A). The most important feature of this surface is the small barrier at :he cross ing point to the exit valley. We have special coxern with points X and Y, which both lie on the line rKBr = Y*, X at the covalent minimum path and Yon the crossY* is chosen so that (Ey -Ex) is mining curve.
PHYSICS LETTERS
15 August 1970
imised. In fig. 1 Y* = 2.8& E -0.6 kcal mole-i and Ey = ‘7 kcal mole- r=. Evidently tbis crude discussion leaves Ey somewhat uncertain; one point is that the exact surfaces‘will be pushed apart-at the crossing. We believe, however, that the barrier itself is a real feature. The basic physical reasons for its appearance are the small electron affini of HBr and the shortness of the HBOr bond (1.4 B ) relative to the Br’ ion radius (~1.7A) [ll]. As LYdecreases from s, the energy of the complex at covalent geometries will rise, due to diminishing polarisation interactions, and, for (Y 5 a/2, because of additional K-H repulsions. Fig. 2 indicates a qualitatively plausible dependence of EX and Ey on CY. EX increases and (Ey -Ex) diminishes. The horizontal line is at the minimum reactant energy. In detail, these curves take account of the variation of the polarisation interaction for CY2 s/2, but have otherwise been chosen to enable our description of the collision dynamics to match experiment.
3. THE REACTION DYNAMICS The interaction between the covalent reactants is relatively weak. For this reason, because of tbe largeness of vibrational energy spacings in HBr and because of the gross dis@rity in the masses of K and H, it seems improbable that the HBr vibrational motion will be much affected by the appearance of K. Under tbe conditions studied sperimentally, vibration of HBr is rapid
Fig. 2. Schematic variation of the potential barrier with angle of approach. Ex, Ey and the zerc reactant energy are ‘plotted. Threshold angles are indicated by vertical arrows. The lengths of VH,. VD and VT represent
Fig. 1. The collinear .. 390
potential-energy
K + Wr
(a, =.7r).
surface
for
the zero-point vibrational energies of RBr, DBr and experimen-
TBr; those of ZK, TD acd TT the respective tai translational energies.
Volume 6, number 4
CHEMICAL PHYSICSLETTERS
compared to the rate of approach of K: during a complete HBr vibrational period the KBr distance decreases by only =O.lA. Initially we shall neglect rotational motion of HBr. Classically, reaction occurs if the H-isotope reaches the crossing-line. As vibration is rapid, this will always first occur close to an outer turning-point, where the vibrational velocity is near zero. The light H-isotope will then be swiftly accelerated away by the H-Br- repulsion on the ionic surface, without time for further interaction with &. The product translational energy, essentially all vested in motion of H, will be close to the magnitude of this repulsive potential at the crossing. (The translational velocity of H before reaction is extremely small, corres onding to a kinetic-energy of x0.01 kcal mole’ P.) This reasoning is consistent with the near isotope-independence of the translational energy distributions [2 1. If before crossing the HBr vibrational motion is indeed undisturbed, then there are two conditions for reaction. First, the energy difference (Ey-EX) must be less than the HBr zero-point vibrational energy. Second, point X must be energetically accessible to the initial relative translational motion (essentially movement of K relative to Br). Surveying fig. 2, we conclude that reaction is confined to a limited range of LY. Near Q = B the reactant zero-point energy may be insufficient to overcome the barrier. Near (Y = 0 the initial translational energy does not permit ?-KBr to become small enough. r*, for fig. 2, should strictly be chosen notsimply to minimise (Ey -EX), but, where possible, as the largest KBr distance for which both reaction
conditions
are satisfied.
For
15 August 1970
straightforwardly derived for the angu1a.r distribution, a function only of amax and @min. We select ranges of (Y from 400 to 1800 for HBr, 40° to 120° for DBr and 900 to IlOo for TBr. The values for amin are consistent with the translational energies used in the experiments, and those for (Ymax reflect the isotopic dependence of the zero-point vibrational energies. Within these restrictions the parameters were chosen to fit experiment. The resuiting angular distributions are the dashed tines of fig_ 3, which may be compared, for HBr and DBr. with (shaded) experimental bounds, and, for TBr, with the less precise experimental finding of predominantly backward scattering. Reactant
rotation
by assuming
in an angular
range
czm&
incor-
that
an ele-
mentary treatment of the reaction dynamics we take Y* to be a constant, independent of N. In fig. I, the barrier height increases rapidly as Y+ is varied from 2.8A. Our further assumption is that the weak covalent interactions experienced before crossing by a reactive encounter do not significantly deflect the straight-line approach of K towards randomly-oriented HBr. We consider as reactive all such collisions reaching a sphere of radius Y* about Br,
is straightforwardLy
the H atom retains its initial rotational velocity after crossing. This motion is perpendicular to that induced by the HBr’ repulsion, giving an additive contribution to the product translational energy. The determination of angular distributions invoLves a further (numerical) average over an azimuthal rotational angle. Taking a (thermal) rotational energy of 0.6 kcal mole-l and a constant repulsive energy of 1.2 kcal mole-l, the solid lines of fig. 3 result. This choice gives a product transiational energy close to the experimental maximum. As well as being in accord with experimental porated
/-
2 Q! 2 CYST
Upon crossing, the H atom is propelled directly away from Br-. The scattering angle is then the angle between the initial relative velocity vector and the HBr bond at the instant of crossing. By averaging over the reactive .initial conditions a messy analytical expression can be
, OQ
--
em
Fig. 3. Centre of mass angular dfstrihutfous, normaLised to unity
at O” for the HBr
and DBr cases
(as in
[2]). b?lt at 180’ in the TBr case. (a) ---- without rotarotatiotil energy = f (repuh3ionenergy), uon, -04 (c) . _. * experiment2.l Limfts [2]. 391
Wlume 6. number 4
CHEMICAL PHYSICS-LETTERS
angular distributions, for total cross we calculate the ratios
sections
and bperiment
[2] gves
o(K+KBr) o(K+TBr)
_ 9 - ’
1.4 f 0.2 for the former.-
The absolute value of u(K+ HBr), taking Y+‘= 2.8& is 2fi2, a little below the experimental range of 35 * 9A2 [4]. A larger value of r+, or allowance for the deflection of the incoming K by polarisation forces, would increase u. Our simple model predicts the Isotope independence of the product translational energy distributibn and its peak at low values [2]. The f%ii experimental breadth could, however, only be duplicated by taking full account of the reactant rotational energy distribution, the variation of the repulsion energy with 01, the retention of some vibrational veiocity at the crossing and, possibly, tuunelling effects; We believe that quanium mechanics will preserve the essential features of the classical model outlined here: in a future paper we shall investigate’the importance of quantum effects in this situ&ion.
4. CONCLUSIONS Given a potential-energy surface with a iow in-the exit valley, the unusually large isotope effects in the reaction of K with HBr may be rationalised. For K + HCL, there is experimental evidence for a more substantial barrier
barrier
PI.
Our simple account of the classical
dynamics
is expedited by the weakness of the interaction between the approaching reactants, by the rapidity of HBr vibrations and, most important, by the relative lightness of H. Product angular distributions are sensitive to initial vibrational and translational energies. At
392
15 August 1970
constant translational energy we predict A >D >T as regards backward-scattering. For htgher
translational en&g!es all distributions should stift for-ward, towards a limit of isotropic scattering in the HBr case (tf reaction becomes accessible at all Q). Vibrational excitation of reactants should decrease isotope effects. Total cross sections should depend only weskly on energy. ACKNdWLEDGEMENT The author thanks’ Dr. P. J:Knntz ing discussions.
for stimuiat-
REFERENCES [l] E. H. Taylor and 9. Da& J. Chem. Phys. 23 (l955) 1711. [2] K.T. Gilien,’ C-Riley and R. B. Bernstein, J. Chem. Phys. 50 (1969) 4019. [3] L. R. Martin and J. L.Kinsey. J. Chem. Phys. 46 @967) 4934. [4] J. R. Airey, E. F. Greene, K.Kodera, G.P. Reck and J. Ross, J. Chem. Phys. 41 (1964) 1917. I51 _ _ R. A. 0a-s and M. Poianvi. _ Trans. Faradav Sot. 31 (1935) 604. 161 _ . J. Chem. Phvs. 49 - . M. Godfrey and MKarolus. (1966) 3602; P. J.Kuntz, M.H.Mok and J. C. Polanyi, J. Chem. Phys. 50 (1969) 4623. [‘i].R. M. Sternheimer. Phys. Rev. 36 (l962)1220. [&] A. L. McClellan. Tables of experimental dipole moments (Freeman, San Francisco, 1963). [9] A. C. Roach, to be published. [16] E. Clementi, J. Chcm. Phys. 41 (3964) 295. [ll] E.S.RWner, J. Chem.Phys. 19 (1951) 1030. [12] G. Herzberg. Molecular spectra and molecular structure, I. Spectra of diatomic molecules (Van ’ Nbstrahd, Princeton, l950). [lS] L. Brewer and E.Brackeit, Chem. Rev. 61 (1961) 425. [14-l T. J. Odiorne and P.R. Brooks, J. Chem. Phys. 51 (1969) 4676.