Dispersion and polarization forces associated with the ion-pair states of diatomic molecules

Chemical Physics 127 (1988) North-Holland, Amsterdam

DISPERSION ASSOCIATED Kenneth

363-371

AND POLARIZATION WITH THE ION-PAIR

MOLECULES

LAWLEY

Department of Chemistry, University ofEdinburgh, Received

FORCES STATES OF DIATOMIC

West Mains Road, Edinburgh EH9 3JJ, UK

6 April 1988

Heteronuclear ion-pair states have large dipole moments that are absent in the corresponding homonuclear states. It is shown that the large intermolecular polarization forces that arise in the heteronuclear case are precisely matched by anomalously large dispersion forces in the homonuclear case that come from a giant g - u electronic transition. In the halogen and interhalogen IP states orbiting cross sections at thermal energies are typically > 150 A’, making most inelastic and reactive processes of IP states orbiting controlled. Collision induced g - u transitions may have a small ( 6 20 A’) direct contribution from b values greater than the critical value for orbiting.

1. Introduction

level because the sum over states in second-order perturbation theory may involve some downward virtual transitions resulting in partial cancellation in the sum. It is the purpose of this paper to point out that a reliable lower limit for C, values of ion-pair states of the second type (those of large I,), especially in high vibrational levels, can easily be obtained. At least an order of magnitude enhancement over ground electronic state C, values can be expected for experimentally accessible states. Some consequences for kinetic rate measurement involving the halogens and interhalogens are outlined.

All diatomic molecules have ion-pair (IP) states and these hve a particularly simple electronic structure at larger bond distances. Sometimes, as in the well known alkali halides and the less well characterised group IIA and IIIA halides [ 1,2] the ground electronic state is an IP configuration. In all other cases the IP states lie closer to the Rydberg states (and are sometimes embedded in them). In the most favourable cases spectroscopically, IP states are comfortably above the repulsive valence states correlating with ground state atoms and they then have characteristically large bond lengths r, and small 0,. The ionpair states of the halogens, interhalogens, rare gas halides and hydrogen halides fall into this category and are the subject of considerable spectroscopic and experimental interest [ 3-7 1. Direct measurement of C, dispersion coefficients associated with an electronically excited molecule and a ground state partner is rare, although inelastic cross sections (R * T and V ++ T) can be very large ( > 100 A’ in the A ‘Xc,state of Na, [ 8 ] ) in such cases, pointing to enhanced long-range intermolecular forces. Theoretical estimates of the change in C, accompanying electronic excitation in molecules are equally sparse and are apt to be unreliable at a quantitative 0301-0104/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division )

2. The electronic structure and dipole transition moments of IP states There are two limiting models of IP states, the dominant MO + spin pairing description [ 9 ] and the pure precession model [ 10,111. In the latter, the individual ion quantum numbers JA+ , MA+, JB- , MBare assumed good. In zeroth-order approximation to the bonding, mixing of projection quantum numbers that leads to the same resultant Q( = IMA+ +MB- I ) may be necessary to achieve the required reflection and inversion symmetry (see, e.g., ref. [ 121 for the pure precession description of ordinary valence states B.V.

K. Lawley /Ion-pair

364

at large atomic separation r) but all the states to be discussed in this paper have JB- = 0 and the problem does not arise. Thus, the lowest 0 + IP state of ICl can be represented in the pure precession or J,4+, JBcoupling scheme as

+~II+(‘D~o))IIC~-(‘SO)),

(1)

where the coefficient c arising from the usual spinorbit mixing between states of the same (JM,) is x 0.2 in the free I+ ion (the exact extent of mixing is difficult to calculate because the levels of I (II) cannot be fitted to the interval formula for intermediate coupling [ 131 within the 5s25p4 configuration there is apparently another configuration perturbing some of the levels). The IP states under discussion already have a large equilibrium separation (typically r,> 3 A) and for r> r, the pure precession model seems, on spectroscopic ground to be quite closely obeyed and, furthermore, it seems that the pure Russell-Saunders coupling scheme can be adopted. For r
states ofdiatomics

(2)

where A and B now serve to distinguish identical ends of the molecule and any ,+jcoupling tendency has been neglected. Note that, in contrast to the asymptotic description of states dissociating to atoms containing an odd number of electrons [ 121, the + combination is associated with g-molecular states dissociating to ions containing even numbers of electrons. In the halogens, these g/u pairs have very similar T, values, typically differing by a few hundred cm- ’ . T, values of g/u pairs in the light diatomics, e.g., Hz or Liz are separated by several thousand cm --I (see, e.g., ref. [ 151) but this splitting is due to strong mixing of the gerade states with the rather close-lying ground state. Such strong mixing around r, of the IP state is largely absent in the halogens and purely interionic Coulomb, polarisation and dispersion forces are identical in each g/u or + / - pair of states when t-2 r,. The outer limb of an IP potential energy curve is essentially purely Coulombic and the shallow gradient of the potential leads to a wide vibrational amplitude for even a modest amount of vibrational excitation. Especially beyond the point of inflection of V(r), the vibrational wavefunctions have an increasingly large amplitude near the outer turning and expectation values point as v’ increases ( U’ ]f( r) 1v’ ) approach f( ro) the value at the outer turning point, r, ( v’ ). No unperturbed homonuclear IP state can have a permanent dipole, but the corresponding heteronuclear states have dipoles that increase essentially linearly with bond length until the outer crossing with a Rydberg asymptote is reached. The g/u pairs of the homonuclear IP states are, however, connected by a giant dipole transition which increases linearly with r when t-2 r,. Thus, using the example of the lowest 0,/O, pair in the halogens (eq. (2) ),

<(),‘I

Cw,lOZ>=

+(‘SoI

!

<3P201

Ce,,z,HI’So)H--

6

Ce,.,z,,13P20).+ A

>

=er+O(r-‘),

where the origin of all coordinates

is the mid-point

(3) of

K. Lawley ~Ion-pair states of diatomics the bond and the sums run over all electrons on each centre. This result is independent of the extent o f j j coupling in the positive ion. The leading correction, O ( r - 2 ) is a mutual polarisation one that reduces the resultant dipole moment and is not, strictly speaking, included in the unpolarised wavefunctions ofeq. (2). We note in passing that the permanent qu~drupole moment of any homonuclear IP state doe~ not increase as ( v ' Ir: Iv' ), but is asymptotically just the sum of the rather small permanent ionic quadrupoles (that of the positive ion only in the case of the halogens). I f there are several IP states of the same symmetry each dissociating to different states of the ions, the transition moment between g and u states correlating with different ion states vanishes in thejAja coupling scheme. Thus, for the two IP states dissociating to, say 3Pjl and 3Pj2 of the halogen positive ion (e.g., the E and F states of I2), (nlt2~- [ ~ eiziln2g2 + ) ~(Jlg21 Z e,z, IJzI2)A+ = 0 ,

(4)

because dipole transitions between different J states (or M j states) of the same atomic configuration vanish. For the same reason it is clear that the perpendicular component of a g/u transition among IP states vanish in the pure precession limit: (n~t21 ~ e~x~ln2t2+ l ) --) ( J~ g21 ~ e~x~ lJzg2+_ 1)a+ = 0 .

(5)

Thus, the dipole-allowed transitions from an IP state can be divided into three classes; (i) those to, valence states not of IP character, amongst which will be some lower-lying states perhaps including the ground state and to Rydberg states, (ii) a parallel transition to the g/u IP partner in the homonuclear case only, and (iii) transitions to other IP states. What is important here is that these three classes have distinctive r-dependent behaviour. The valence transitions (i) fall off exponentially at large r, reflecting the decreasing overlap of the two atomic orbitals on centres A and B between which an electron must be transferred - these are the so called charge transfer bands [ 15 ], (ii) the g/u IP ~ IP transition increases linearly with r, (iii) other IP,--IP transitions, if allowed in the separated ion limit, become independent of r.

365

In the homonuclear case, the giant IP ~ IP transition contributes a vanishingly small amount to the sum rule for oscillator strengths ( E g - E u ~ 0 at large r) but, as we will see, come to dominate the intermolecular force associated with these states.

3. Polarisation and dispersion forces We consider the interaction of an ion-pair state with an isotropically polarisable partner, M, which in practical terms will usually be an inert gas atom. If the diatomic has a permanent dipole moment function #AB(r), the standard induction energy expression is Ev,, = -- ½O~M
(6)

where 0 is the angle between the interparticle (AB...M) vector R and r. The averaging is over the vth vibrational state of the molecule. In the case of heteronuclear IP states the large permanent dipole will give rise to very large induction forces, especially for high vibrational states, but this contribution might seem to be absent in the non-polar homonuclear case. However, we must first examine the other contribution to the R -6 term in the intermolecular potential, that arising from dispersion forces. The standard second-order expression for the C6 coefficient is C6 (n"...; riM) =e 4 • n'...;n~

(n"...;01Z2 i

(x~Bx~q-Y~aY~ j

_2ziABz~)ln,...; riM) , 2/(En,..;n,M-En,,...;o) ,

(7)

where n... refers to the collective quantum numbers (ne, v,j, m ) of the diatomic ( n e being the appropriate electronic quantum numbers) and nM to those of the ground state partner. The sum runs over valence electrons only and electronic coordinates are with respect to space-fixed axes. In the homonuclear case we estimate the contribution of the unique g,--, u IP transition (ii) by using closure only over the IP vibration and rotation states. The energy difference in the denominator of eq. (7) is dominated by the excitation energy of M (typi-

K. Lawley /Ion-pair states of diatomics

366

tally > 10 eV) and this is effectively constant during the restricted sum over molecular states (this remains true even if the T, values of the g and u states are separated by some thousands of wavenumbers). We then proceed with closure over the rzMto obtain

xe2(OI

c ri IO)bllEM 2 I

(8)

where the molecular electronic transition moment must be a parallel one. Introducing the atomic polarisability (x~ we obtain the contribution of term (ii) to the London dispersion formula: C&“) = foM (v”j” (piB(r)

1v”j”)

X(j”m,“~1+3cos28~j”m;‘),

(9)

which is identical to that derived from the induction energy in the heteronuclear case, eq. (6). If we use closure over all AB and M virtual states,

xc

J.,

+‘%,I

>

(10)

where EAB is some effective electronic excitation energy of the molecule that takes downward transitions into account as well as valence+Rydberg ones. There is considerable correlation between the motion of any pair of electrons in these IP states. Thus, if the two electrons are on opposite ends of the molecule, e.g. ( ZJ,) -+ - (r2/4) cos26 as r-+co (the origin being at r/2). Taking all these correlations into account, C, in eq. ( 10) has the following limiting form for large r when terms of the type e-’ can be neglected:

x3~(j+1)+m~-1] (2j+3)(2j-1)

’

Photochemical studies on ion-pair states can easily be carried out on very high vibrational levels, typically v’ > 100 for the heavier halogens [ 16 1, containing in excess of 10000 cm-’ of vibrational energy. We adopt the simple Rittner potential [ 171 (eq. ( 12) ), as the universal IP potential in order to estimate the mean square dipole moment and hence C, as a function of vibrational energy,

(11)

where the first term is nearly the contribution C&l’) in eq. (9) and ( rf ) is the mean-square radius of the active electron distribution in an ion and nA+, nB_ the number of such electrons. In order to obtain exactly the heteronuclear formula, the unique g +-+ u transition must be isolated from the sum over states. The other two terms, predominantly from type (iii)

(13)

Typical values in the halogens and interhalogens for the two parameters might be Az7.759~ lo6 cm-‘, b=2.1 A-‘, leadingto r,=3.565 A, De=28217 cm-‘. We expect (v” I rz I v” ) evaluated using the exact vibrational eigenfunctions to approach the value for a purely Coulombic potential at the same energy E (=E,-E,,) below dissociation ( (r”>E=ie4E-‘). This is indeed the case to a few percent as can be seen from fig. 1. Inserting the appropriate values of constants into the m,-averaged form of eq. ( 12 ) gives

10’ LYE

x(vl (r-a_/r2)21v)

X[r2(1+3cos28)~--2nA+(rf)A+

(12)

4. The orbiting radius and quenching cross sections of IP states

=1.162x

C 6={~hl(n”...Ie2

+2nB-(r,‘)B-]In”...)~M/(~M+~*B),

C~“)(j,m,)=aMe~(v”~r2~v”),~,

V(r) =A exp( -br) -e2/4zeOr.

(x~Bx,ABfy~ByJAB+42;4Bz/AB)I,~...)

x&,/(&I

transitions as r increases give rise to “normal” dispersion forces. Performing the angular integration in (9 ) or ( 10) for a given molecular rotational state urn,) gives

cm-‘,

(14)

where r is in A and (Y in A’ in the final form. With (r2)&25 A’ and a,=1 A’, we find C6>3x106 cm-’ A”. Such large dispersion forces (C6 between 10’ cm- ’ A” and 5 x 1O5cm- ’ A” would give van der Waals well depths 2 40-200 cm-’ ) will result in spiralling or orbiting in a large fraction of thermal energy collisions with almost any partner. The C, coefficient has become dominated either by the polarisation term in the heteronuclear IP case, or by

361

K. Lawley /Ion-pair states of diatomics 26 I

24

22

20

18

16

(E,-E")/;OLl-l 30-

G/IA2

26-

2

4

6

8

E,/103cm-' L 1 10 12

Fig. I. The expectation value of r* in a Rittner potential as a function of vibrational excitation energy. Potential parameters (eq. (13))A=7.759x106cm-‘,b=2.1 k’.I, withoutapolarization correction; II, ( (r-a/r’)*)~u=5 A’. Values of (r*) using Coulomb wavefunctions ( x ) are plotted as a function of the energy below dissociation, &-I!?,,.

the equivalent g-u dispersion term in the homonuclear case. Using the standard formula for the orbiting impact parameter under the influence of an R -’ potential, bor,,

=

(27G/4E,,)“6

(15)

(the relative kinetic energy Et, in cm - ’ ) , we find that for the collision of any ion-pair state containing, say, 10000 cm-’ of vibrational energy (such that ( r2) = 27 A” from fig. 1) with an atom of polarisability 1.6 A3 (for Ar ) the orbiting impact parameter is 7.44 8, for a relative kinetic energy of 200 cm-‘. This, in turn, implies a cross section for orbiting and hence the total cross section for all orbiting controlled processes of 1; /Ar of at least 170 A’, rising to 320 A’ for WI, ( cx( 12) z 10 A3). Some preliminary quenching rate data [ 18 ] for the halogen IP states has been interpreted, using the approximate formula k= a, F, as being due to processes with cross sections in excess of 200 AZ. It is clear that attention must be paid to unsuspected quenching by residual background gases and especially to self-quenching when

these more highly vibrationally excited states are investigated. A more detailed quantum analysis of these collisions is complicated by the fact that the C, coefficient depends quite strongly on the projection quantum number mj of the AB* molecular rotation onto the interparticle axis R (eq. ( 12) ). There is considerable splitting of the adjacent mj states, except for 1WZjlx 0, amounting to x 1 cm-’ for m,x j/2. Since a typical AB : M rotational period for borb=7 A is T,=~x lo-” s-l, the Massey criterion adapted for rotational adiabaticity, T,CM (where & is the splitting between adjacent m, states in cm-‘) is z 3. This implies that the cone of precession of the diatomic follows the moving R axis only in the higher m, states, but the jmj averaged Ce in eq. ( 14) is not affected. Another complication limiting the accuracy of the approximation ( 15 ) is that barbincreases as (r)hg if the limiting form of the transition dipole is applicable. This means that, as the amplitude of vibration is increased, higher terms in the interaction multipole expansion must be taken into account and convergence problems will quickly arise. In the homonuclear case these higher terms can only come from odd moments and it can readily be seen that all the odd moments have the same sign. The orbiting impact parameter can thus only be increased by the inclusion of higher terms in the dispersion interaction. However, before it is concluded that the quenching collisions of ion-pair states are all orbiting controlled - at least at room temperature - the alternative mechanism of harpooning must be examined. If electronic transfer from M to AB is to the nearer end of the diatomic (say A) the critical M...A distance Rh at which E(AB...M) =E(AB-...M+) is given by

ELAB)(r) ,Ef”’

-e2/r+:((YA-(Yg-)e2/r4,

(16)

where EAAB)(r) is the vertical electron affinity of the ion-pair state and Ef”’ the ionisation potential of M and where Rh is assumed to be sufficiently large for polarisation of the newly formed B by M+ to be neglected. The electron affinity is strongly dependent on r, reaching its maximum at the outer turning point r, of the vibrational level. In keeping with our previous model we will assume that electron transfer oc-

368

K. Law&v /Ion-pair states of diatomics

curs exclusively at this point in order to calculate an upper limit to the harpoon cross section. For our reference IP state, the D state of I2 containing 10000 cm-’ of vibrational energy, the electron affinity at the outer turning point (I+._-+e+I...I-), EA(rc) = 7.78 eV. With Ar as the collision partner (E,=15.76eV),wefindR,=1.8Aincreasingto2.6 A if polarisation of I- in the field of the newly formed Art included ((Y(I- ) = 5 A3). The largest impact parameter at which charge transfer could occur is thus R,, + r,( v ) /2 = 4.6 A, leading to a maximum capture cross section of z 66 A’ (92 8, with polarisation). This estimate is probably grossly inflated because it assumes unit probability of electron transfer M+A+, with the simultaneous intramolecular transfer of a second electron to create the dipole B-A-...M+. We can safely conclude that orbiting is the precursor to charge transfer in the Rg+ halogen IP systems [ 19 1. Furthermore, if harpooning were to be the quenching cross section determining process, a wide variation in a, would be expected both between different IP states of the same molecule and between different diatomic species because of the wide range in electron affinities which shift with the absolute vibrational term value of the state under consideration. 5. Collision-induced g e+ u transitions in homonuclear IP states The exceptionally large transition dipole moment connecting g and u states correlating with the same separated ion states makes it likely that such transitions are readily induced by collision. The general selfquenching process is

-XT(n;(~n,)v;j;)+X,(v;jg)+hE,

(17)

e.g., the F’-+f ’ or F-+f transition in I, (where the collision partner is in the ground electronic state) and two mechanisms can be postulated: a long-range multipole coupling for impact parameters b> barb (i.e. moving on essentially rectilinear trajectories) and a close coupling regime for b < barb involving multipolar interactions, overlap and generally some distortion of the potential energy surface. The relative importance of these two routes depends crucially upon the detailed energy mismatch AE.

The long range mechanism is essentially a near resonant one, while close coupling during orbiting presumably results in a much wider range of final states (n; 1v; , ...). We now calculate the critical impact parameter b, at which the first-order jm,-averaged transition probability reaches unity and compare this with the orbiting impact parameter. For self-induced transitions, the leading term in the multipole expansion [20] leading to the required transition is V (3), the interaction of the instantaneous electronic dipole of the excited molecule with the total quadrupole moment of the ground state partner, and the transition matrix element is

+c,-,(Q,

@)G,(@

P)l} >

(18)

where (cy, /3) are the polar angles of the orientation of the second diatomic CD. We will neglect the IJc3’ interaction in first order between the instantaneous dipole of the ground state partner which can also result in the required transition by excitation exchange. Even though this is an exactly resonant process, the additional FranckCondon factors would make the overall transition moment very small, and equally important, neither electronic transition is of the giant variety (both are of charge transfer type (ii) in section 2). The axial symmetry of the molecules and the fact that only the parallel g +-+u transition need be considered have been taken into account in expression ( 18 ). For all collision partners, irrespective of whether they possess a permanent multipole moment, g t-) u transitions can also be induced by dispersion forces via the cross term in second order between the virtual dipole-dipole and dipole-quadrupole terms, resulting in an R -’ coupling potential. Including this effect can only increase b, and so our estimate of b, to be obtained from Vc3) only will be a lower limit. From the angular dependence of V”), the g t-t u transition in first order must be accompanied by a I Aj, I = 1 transition in X: and by I Ajz ] = 0, k 2 in the ground state partner. The transition amplitude for a detailed transition is

K. Lawley /Ion-pair states of diatomics

369

(20 ) by 11/40. In order to assess the impact parameter b, at which the sum of g c* u collision process reaches unit probability, we put PDy,,,(b) = 1 to obtain the implicit equation for b,, b:=6*[(l+b:)exp(-b:)]‘/3,

(21)

where @=&la,

a=v,l2ncAE, 11rc2(n~1~1n;)*@& 240fi2v2R

“6 >

.

and

where b is the impact parameter, & the relative velocity of the collision and fi the energy mismatch in cm - ’ of the detailed process under consideration. The dipole transition moment is between the nearest resonant vibrational levels in the g and u IP state and we have assumed that the best energy matching is obtained without a vibrational transition in the ground state partner, though the quadrupole operator could induce I Avz I = 1 transitions if needed. Now, the B, values of the ground state are considerably greater than the values of the IP state (typically 0.05 cm-’ and 6 0.02 cm-’ respectively for iodine) and with a most probable value of jz x 45 at room temperature only one of the three possible Ajz changes need be considered - the one closest to resonance. For a selected Ajz, IAm 1 we average the detailed transition probability P~~!~~m~~~ym~yover m’,’ and m;’ assuming that the mj state degeneracy is not split by more than a few wave numbers during these distant collisions. Lastly, the final j’, and m’, states are summed over (still with Ajj, = 0 ) and the high-j approximation (2j+l)

jj2*1 o o

(

o

>

--+4,

is made for the remaining is:

--+%ir2(b)

, jl,i2

2+.1 .

3j coefficients.

The result

(20)

Had either of the I Ajl= 1 transitions been more nearly resonant, the factor 1 l/60 is replaced in eq.

We will generally only be interested in this long-range mechanism if b, 2 6 A, otherwise the whole process is orbiting controlled. This rather large value of b makes the value of the energy mismatch i7 in the Massey parameter 2x&b/v crucial. In effect, only nearly resonant g c* u transitions can be induced by this dipolequadrupole mechanism. The Franck-Condon factor for the IP electronic transition, S,.... , will not be far from unity if V’ and V” are both large and if there is fairly good vibronic energy matching. The outer limbs of the g and u state potentials are essentially identical (they are progressing towards a common asymptote) and so g and u states with similar energies with respect to their common asymptote will have the same outer turning point, where the two vibrational wave functions will be in phase and have large amplitude. Calculations for the model potential ( 13 ) with two different A values to simulate two electronic states with AT, = 1000 cm-‘showthat (n’v’~z~n”v”)~O.5(n”u”~z~n”v”) when the two vibronic energies are matched to within 20 cm-‘. The remaining parameters are the quadrupole moment of the ground state partner, which for I2 we take 8= 10x 1O-26 D A, and the mean relative velocity, 21~~ 1 x lo4 cm s- ’ appropriate to T= 300 K. With ( n” I p I n’ ) = 25 D, and an energy mismatch of 5 cm-’ we find the critical impact parameter to be l.l&andfor~B=6cm-‘,b,=6.8A.At~=2&we find that at A,??= 5 cm-’ b,= 11 A, reflecting the smaller Massey parameter. Thus, for A&5 cm-’ (whether achieved with IAjl= 0 or 2 ) we conclude that orbiting controls the g - u collision induced process. There is a slight enhancement of the cross section when this level of energy matching is achieved. Integrating CP( b) given by eq. (20) from the critical value b, to infinity to

K. Lawley /Ion-pair states of diatomics

370

obtain the section,

long-range

contribution

exp( -2b:)

to the

.

cross

(22)

Again with v= VRand the parameter values as above, we find a,, = 18 A’. The sort of accidental near resonance required in the g and u vibrational manifolds will be encountered from time to time as the vibrational energy increases. The average vibrational spacing in the various halogen ion pair states when E, k 10000 cm-’ is only 50-100 cm-‘, but because the local level spacing in the two electronic states is nearly identical, the two manifolds only shift very slowly relative to each other.

6. Conclusions Both homonuclear and heteronuclear ion-pair states have very large C, coefficients for their interactions with any collision partner. In the heteronuclear case the origin of these enhanced intermolecular forces is the usual dipole induction energy but in the homonuclear case an almost identical contribution arises from a giant transition dipole between pairs of g/u states. In the halogens, where g/u splitting is relatively small, we have demonstrated that at the most probable relative collision velocity at room temperature, a lower limit to orbiting cross sections aO,b ranging from 125 A’ (v”=O) to >150 A’ when &lb> 10000 cm- ’ can be expected with Ar and increasing as the one-third power of the polarisability of the collision partner. There is essentially no difference in o,,orbvalues for different IP states having the same amount of vibrational excitation. Since the orbiting cross section increases as the two-third power of the vibrational amplitude, vibrational excitation measurably enhanes a,,,b in all ion-pair states. Orbiting impact parameters for the halogen ion-pair states with inert gas partners are appreciably greater than the impact parameter for harpooning. Orbiting can thus be regarded as the precursor of harpooning in these collisions. That this was the case was originally suggested by Grice and Herschbach [ 2 1 ] for the alkali+ halogen systems, where the position of the centrifugal barrier is determined by the curvature of

the ground state potential arising from ionic-covalent configuration mixing just prior to the diabatic curve crossing. In the examples discussed here, the position of the centrifugal barrier is determined by dispersion or polarisation forces. Finally, all homonuclear IP states should exhibit large cross sections for the collision induced g ++ u transition between electronic states in the same cluster having the same Q value. In the absence of other exit channels (e.g. chemical reaction or other IP 52 states), the cross section for this transition would be ~7,-,~~/2if all memory of the original g/u symmetry is lost in the collision complex. There is, in addition, a long-range coupling that operates if the collision partner has a permanent multipole moment. In the case of self-quenching this is the transition dipolepermanent quadrupole interaction. The effect is essentially a near resonant one and in the specific case of I2 an energy mismatch of 5 cm- ’ between g and u vibronic levels would lead to an enhancement in the transition cross section of z 20 A, above the orbiting controlled value but the long-range effect rapidly decreases for larger energy mismatches.

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