State-selected ion-molecule reactions: N2+(X, v″), N2+(A, v′) + Ar → N2 + Ar+

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STAm&ELECJED 10%nirOLEtiLEdREAC-l-IOkS: , N,+(X, u”), N,+(A, ,o’) + Ar i N, + Ar +-

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Received

209~. Uniuersit& Paiis-Sud_

14 November

91405

Orsay,

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Thomas k. GOVERS ‘, Paul Marie GUYON 2, Thomas BAER ‘, Keith COLE Horst FRGHLICH ’ &rd Michel LAVOLLEE-’ _L U RE.~B&ment

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France

1983

The total. absolute cross sections for charge transfer.between N: (X. A, u) and Ar have been measured at 8, 14 _and- 20.eV center of mass translational energy_ The internal energy of the N+ ions was selected by threshold photoelectron-photomn coincidence using pulsed synchrotron~radiation from the AC0 storage ring The vibrational levels inve&igated‘were u”= O-4 for the X state, and u’ = O-6 for the A state. The data for the A state were corrected for the fraction of rons which fluoresced to the X state prior to reaction with Ar. The I$’ (X. u” = 0) state was found to be much less reactrvc (by a factor ,- IO) than the other X-state levels, at all three translational energies. The levels N-j+(A. u’& 3) were found to react with cross-sections which depend strongly on the relative translational energy. The data are interpreted in terms‘of the interaction between vtbronic curves as diiussed by Bauer, Fisher and Gilmore. Thus model accounts well for the low reactivity of the N: (X. 0) level. It is proposed that the variatton in the cross secti& of the Ng(A.u’> 3)i-Ar reactions is a result of competitron with a radiationless transitron which converts Nf (A. u’) ions into NT (X. u”) ions

1.Introduction Gas-phase charge-transfer reactions are prototypes of non-adiabatic processes which are the subject of increasingly sophisticated experimental and theoretical studies. Experiments on the effect of the internal energy of the reactant ion upon its reactivity are of interest, from a fundamental point of view, as a probe of theoretical descriptions of such reactions. From a more practical standpoint, the results of such studies and the insight into the relevant reaction mechanisms which they provide, may be of use in modelling the ion chemistry of planetary atmospheres or of low-pressure plasmas, for instance.

With these considerations in mind, we ‘haveconstructed an experiment‘which allows us to obtain total cross sections for reactions of vibronicstate-selected ions having internal energies between threshold and = 25 eV, and kinetic energies between a few eV and 100 eV. The reactant ions are prepared by photoionization by means of monochromatized synchrotron radiation. Delayed coincidences between threshold photoelectrons and photoions serve to state-select the reactants and to determine the masses and intensities of reactant _and product ions. The present paper reports experimental data obtained in this way for the charge transfer reaction: N,++Ar-+N,+Ar+.

Laboratoire de Physico-Chimre des Rayonnements. associe au CNRS, Batiment 350, Universtte ParisSud. 91405 Orsay, France. Present address: L’Air Liquide, Centre de Recherche Claude Delorme, B.P. 126;78350 Jouy en Josas, France.

Laboratoire des Collisions Atomiques et Mol&xlaires. assotit au CNRS. B&iment 351, UniversG Paris-Sud:91405 Orsay, France. Department of. Chemistry, &Jniversity of North Carolina, Chapel Hill, -North +roIina 27514. USA. -

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internal-energy effects for this reaction haverecently been studied _by means of drift tube‘[l], selected-ion flow tube (SIFT) [2] and laser-induced fluorescence [3] techniques, as we@ as by &&hold electron/secondary^iop coincidence measurements [4]. The present da& -comple’ment tbisinformation by pro&iing absoiute cross s&ons -f&lNT rio& . . -.

0301-0104/84/$03.00 0 E!sevier Science Publishers B.V. (North-Holland Physics Publishing Division) ._

T. R. Goners et al. /

374

Srare-seterred

selected in each of the vibrational levels u” = O-4 of the X ‘Z+ ground state and d = O-6 of the long-lived A’JJ u state. at collision energies E, m_= 8. 14 and 20 eV. Possible interpretations of the observed internal- and kinetic-energy effects are proposed which are amenable to verification by further theoretical and experimental work.

2. Experimental procedure The experimental technique employed is an extension of the threshold photoelectron-photoion comcidence technique (TPEPICO) as used in Orsay For the study of the unimolecular dissociation of vtbronic-state-selected molecular ions [5,6]. Synchrotron radiation from the electron storage rmg AC0 is dispersed by a 1 m normal incidence McPherson monochromator, equipped with a 2400 lines/mm platinum-coated holographic grating. It is then refocused into the photoionization region of a dual time-of-flight spectrometer (fig. l)_ This chamber contains the parent gas of the reactant ton. In the present experiment, the wavelength resolution was 1.4 A, fwhm, corresponding to an energy halfwidth of 28 meV at hv = 15.77 eV. Photoelectrons are accelerated over 0.7 cm by a 2

ion-molecule

reacrions

V/cm electric field and detection is restricted to electrons having nominally zero (i.e. ( 50 mev) initial kinetic energy “threshold electrons” on the basis of angular and temporal discrimination [7]. The electron time-of-flight (TOP) is measured with respect to the AC0 photon pulses (73.5 ns period) as described in previous publications [5-71. The threshold electron signal triggers an electric pulse producing a field of 12.8 V/cm during 5 ps. The ions are accelerated over 0.3 cm out of the ionization chamber and refocused by a simple immersion three elements electrostatic lens onto an effusive jet of neutral Ar target gas. The latter emerged from a 0.4 mm i-d. hypodermic needle directed at the center of the reaction region defined by two gold-mesh covered diaphragms which are spaced by 3 mm and have 2 mm apertures_ A field of 20 V/cm was established between these diaphragms. The median potential was applied to the hypodermic needle to define (within a halfwidth of = 3 eV) the average laboratory collision energy. The latter was verified to agree within 0.2 eV with its nominal value by retarding potential measurements_ The potential of the field-free ion drift region was adjusted according to those in the reaction region in order to ensure first-order space focusing conditions [8], while those applied to the -

DOUBLE

ELECTRON

ION TIME OF FLIGHT

SPECTROMETER

TO PUMP Ar

t

PHOTON

PULSES

I 2 Rs (FWHM)

ELECTRON SIGNAL

Fig. 1 Schematicdiagram(to scale)of the dual electron-iontime-of-flight spectrometer.

ION SIGNAL

-_

-

T. R Goners et al. / Srate-select& ton - moiecde reactions

remaining electrodes were adjusted to &ptim&the primary ion signal. Parent ions of selected internal energy (equal to the nominal photon energy) or their products are detected in delayed coincidence with threshold electrons. The vacuum chamber containing the dual TOF spectrometer is evacuated by two turbomolecular pumps with a combined effective pumping speed of = 1600 &J/sand a base pressure of = 5 X lo-’ Torr. Operating pressures in the photoionization and reaction regions were maintained sufficiently low to ensure linear pressure dependencies of the primary and product ion signals, and were typically estimated at 2 x 10d4 and 3 X 10d3 Torr, respectively, for a vacuum-chamber pressure of <4x lo- 5 Torr, consisting essentially of Ar. Under the above conditions we find that = 5-10% of the primary ions react in the collision region. We estimate that, for a cross section of 20 p , = 1% of the parent ions react with background gas in the 5 cm long acceleration region and that j= 2% are lost in the drift region. The Ari products from these reactions are not time correlated with the parent ions and contribute only to the background in the ion TOF spectrum. As a result one observes a decrease in the summed intensities of the NT and Art‘ TOF peaks as the collision gas is introduced_ This decrease was measured and found to be typically 5% therefore verifying the above estimates. A possible problem may be encountered by inelastic non-reactive collisions occurring in the acceleration region which may change the Nz state from that specified by the threshold electron signal. Cross sections for such vibrational and/or electronic energy-transfer reactions are scarce. Recent SIFT dsta indicate that the vibrational quenching cross section of NT (X, u” =- 0) is 10 & or less 19,101. Even for cross sections of 100 A2 we estimate that the fraction of N,f ions quenched before reaction with Ar would only be 5%. We conclude therefore that intemalenergy-changing collisions of N; can be ignored.

3.

Results

Fig. 2 shows the threshold-photoelectron spectrum (TPES) of N, obtained at the resolution used

700

110

375

1.0

PHOTON

1*0

780

WAVELENGTH

(A)

800

-

Fig. 2. Threshold photoelectron spectrum of N, obtained under the expenmental photoion

conditions

coincidence

rate on the NC (X. u”=

employed

experiments_

for the photoekctron-

The

1) peak is typically

time-averaged

count

2000 c/s.

in the present coincidence experiments. The levels = O-4 of the N,+ ground state and levels u” = O-6 of the long-lived A’II, can be easily distinguished. The peak energetically just above u = 0 of the X state results from a strong autoionization process of NZ decaying into N,t (X, u” = 0) while emitting 50 meV electrons, which are detected through the wings of the TOF transmission window. The fixe<-wavelength photoelectron spectra at 584 or 304 A [11] show a negligibIe intensity for X-state levels U” 2 2, and also a quite different intensity distribution for the A-state levels. The modifications observed in the TPES are due to resonant autoionization [7,12,13] and/or autoionization from Rydberg levels to ion states 5 50 meV lower in energy. The possibility to study “ uncommon”, often high-lying, vibrational levels because of this phenomenon, makes the threshold coincidence technique particularly attractive for the study of relaxation and reactivity of molecular ions. V”

3.1. N,+(X,

u” = O-4) + Ar

Fig. 3 illustrates a typical coincidence spectrum, corresponding to charge transfer from Ng(X, u” = 2) to Ar at a collision energy E,_, = 8 eV_ The abscissa shows the time interval between the threshold electron signal and the corresponding ion signal, as measured by means of a LeCroy QVT time-to-digital analyzei whose 256 channels span 4.5 ps (the electron signal was delayed by 10.3 ps). The ordinate shows the number of coincidences per channel, ob$ained during a_ 6.7 min.

T.R. Go&errei al. / State-selecred ran -molecule

Yfc

r II

I

.

ION

Fg. NT

.

11

*

13

TIME

OF

=

*

the reaction

measure of the corresponding relative chargetransfer cross section. These data permit a direct evaluation of the variation of the charge-transfer probability from one X-state vibrational level to the other and of its dependence on the collision energy. ECm . The intensity ratios are transformed to ahsolute cross sections by calibrating them against the Ar+/Ar charge-transfer reaction (see section 3.3). The resulting cross sections obtained at the three collision energies investigated are listed in table 1 and displayed graphically in fig. 4.

*

r* FLIGHT

3 Typical ion time-of-flight spectrum ions (left-hand peak) and Ar’-product

peak) resulting from Ar+ at EL, =8 eV.

.

(f~ SC)

showing unreacred tons (right-hand

NT (X. o”=

Z)+Ar

reacttons

-

N, f

collection time. The large peak on the left-hand slds IS due to NT parent tons, that on the righthand side results from Ar’ ions produced by charge transfer. The arrival time of the latter. 13.1 ps. is the sum of the flight of the NT ions to the reaction region (6.2 ys) and that of the daughter ions Ar’ from the reaction zone to the detector (6.9 ps) and is rhus characteristic not only for the Ar+ mass. but also for this ion being a charge-exchange product with very low initial velocity (Art Ions when produced in the photoiomzation region arrive 0.26 ps earlier). The background between the two peaks results mainly from false coincidences. typical of pulsed-extraction experiments. As the extraction pulse is applied. there is a finite probability (proportional to the total ionizntion rate) of detecting an ion produced by an earlier. uncorrelated. ionization event [14.15]. False coincidence spectra were obtained by applying extraction pulses randomly distributed in time with respect to the ionizing photons_ They were scaled to the appropriate number of extraction pulses and to the ionization rate, and subtracted from the coincidence spectrum of interest_ The main effect of this correction is to “flatten” the background signal in the coincidence spectra. so as to facihtate the evaluation of the true ion-peak integrals. The latter were typically reduced by l--10% by the false coincidence subtraction. At a given Ar-target pressure, the ratio of the Arf to the sum of the Art -I- NT peak areas, is a

3.2. N,+(A. u’ = O-6) + Ar For the A-state levels. the above procedure yields apparent cross sections which have to be corrected for the fact that the A state decays radiatively to the X state on a time scale comparable to the flight time, t, from the ionization region to the reaction region. Denoting the apparent and true A-state cross sections by u,,,(A, u’) and a(A, u’), respectively, and those for the X-state by a(X. 0”). one obtains u,,,(A,

u’) = exp( -r/q.)u(A, + [l - exp( -f/7,,)]

u’) Cb,.,,,u(X. u”

u”). (2)

where 7, is the lifetime of the (A, u’) level, and bI.L- the ermssion branching ratio to the various u” levels of the X state. The second term on the right-hand side of eq. (2) represents the contributlons from charge-transfer reactions of X-state ions resulting from A-X emission. This term increases with t/r,. and is most important when there is substantial emission (i.e., bt,.,..) to highly reactive X-state levels_ Having measured u(X, u” G 4), we corrected our apparent u(A, u’) by means of eq. (2), using the Q from Cartwright [16] (see table 1). based on measurements by Peterson and Moseley 1171 and the bL,stsI from Maier and Holland [18]. The flight time t was obtained by subtracting from the measured total Nf TOF to the detector, its computed TOF from the center of the reaction zone to the detector.‘The latter can be calculated accurately because the relevant potential configuration is sim-

.TX_ Goners ez ai. / State -selected ion -molecule reacJi0n.s

_

377 .

.

.Table 1 _. Cross sections, a (A*). for N; (X, 0”) and N;(A. u’)+Ar + N, + Ar+. The A-state-data in parentheses are the- ap&en; cross secti0113 obtained before ~9rre~tion for A 4-X emission. The uncertainty kits are conservative zrstimat~~based on the reproducrbiity of the experimental data. Those for the A state include the uncertainty due tothe choke of the u&k and lower bounds to a(X, I”) in

the cocre&ori for A -B X‘emission. The lifetimes r(A, 0’) indicated in ps just below the;(A, u’) column headings. u&e taken from -_ Cartwright (161 E cm N;(X. J’)+Ar “0’ = 0 8 118” 14 20

Q” = 1

GO9 0.9&06”’ 6 0.9 16+0.2 N:

““C

18.7~16 15.7+2 1 a) 15 6~1.2 14 3k2.4

u” = 3

2

23.1 f 1.9 23.9 c 3.3 =’ 243f2.8 17 8t29

0” = 4

30.0 + 1.6 30 3k4.4”’ 30.3 _c4.4 34.6+3 6

26.8 f: 09 26.5 +- 3.1 300*3.1

(A. u’)+Ar

lJ’=O

d=l

o’= 2

v’= 3

c?‘= 4

d = 5

or=6

T( u’) = 16.6

13.9

12.0

10.7

9.68

8.89

8 25

(9.7) 11.6~1.0

(13.1)

(14.7)

(15 6) 15.0&-3.1 (13.1)

(11.2)

(112) 65 (9.7) =S2 (18.3) 16.0 +4.1

G2 (10 3) =Sl (16.9) 9 0*4.4

8

172&25

14

(10 0) 122* 1.2

(9.7) 11.9&1.2

20

(8 6) 10.1 f 1.2

(14 8) 18.95 19

166+28 (13.1) 15.0+22 (16.4) 19Sc2

3.1 f 3.1 (11.5)

11.9f2.2 5

5 9k2.2 (15.8) 15.3 -i_3.1

(345) 47.1+62

*’ Relative data from Kato et al. [4] which were adjusted to our absolute 0(X, u”= 3) for E,,

The flight times to the reaction zone were t = 6.2, 5.4 and 5.2 ps for the E cm = 8,14 and 20 eV experiments, respectively_

N-J(X,A,v) +Ar E em=8

eV

E em=14

= 14 eV.

The effect of the correction procedure can be seen by comparing the a(A, 0’) and (in parentheses) u,,,(A, u’) in table 1. For the low vibrational

ple.

“4

(11.2)

N, + Ar’ ,

eV

E .,=2oeV 3

1

2

3

4

h

1

5 6

0 >,&

16

0 N; tX.v) A N< (4~) l Kato et. al.

17

18

16

N;

17

18

16

17

18

INTERNAL ENERGY (eV)

Fig. 4. Ilhtstration of the vibrational- and kinetic-energy dependences of charge exchange between-N; and Ar. The present (X, 0”) data are indicated by circles, those for N,C (A, u’) by triangles. The solid squares are relatiie (X, o”) &subs from Kato et ah [4] at = 14 eV_ The solid lines connecting the data points are drawn to = 11.8 eV, adjusted to our absolute value for Nz (X, 3) at E_ Eguide the eye.

-

-

378

T R Goters et al. / Srate-selecxed ton -molecule reacriom

IeveIs of the A state, emission occurs mainly to the unreactive (X. t”’ = 0) level. so that the apparent A-state cross section is lower than the true one. For the higher (A, u’) levels. emission increasingly populates X-state levels with high charge-transfer cross sections and these ultimately account for most. if not all, of the observed reaction products_ The corresponding correction to oapp(A, u’) involves the subtraction of two numbers of comparable magnitude, so that the statistical uncertainty on the measured cross sections results in a large relative uncertainty of a(A. u’), as indicated in table 1. An additional source of error resides in the unknown reactivity of the levels X. u” 2 5. For A, o’ < 4 this is not a serious problem, as the sum of the emlsslon branching ratios to these high klbratlonal levels of thz ground state amounts only to 5 2%_ But for A, u‘ = 5 and 6 these add up to 7.8 and 8.5%. respectively [lS]. In correcting the apparent A-state cross sections. those for X, U” > 5 were assumed to be equal to the maximum a(X, u”) measured. If the actual o(X. u” 2 5) are smaller (which is probably the case. given the trend observed for u” G 4), the true a(A, u’) will be somewhat larger than those reported in table 1. but even if a(X, 0” 2 5) = 0, the result falls well within the quoted uncertainty limits. This is also true if one allows for as much as 20% variation in the flight time. I_ Table 1 summarizes our results for the three collision energies investigated. All cross sections are dlspldyed graphlcally in fig_ 4.

AS indicated earlier, our relative cross sections were placed on an absolute basis by comparing them to those obtained for charge transfer Ar+(zP3/2)+Ar*Ar+Ar+ at the same Artarget pressure and at the same laboratory ion translational energies as those for NT + Ar. Our test measurements on the ArC/Ar system conflmled the finding of Campbell et al. [14], that the Ar’ ‘PJ,z and zP,,z charge-transfer cross sections differ by - 10% or less at these collision energies. The state-unresolved absolute measurements of Mahadevan and Magnuson [19] could therefore be used for calibration purposes. Their data show that a(Ar+/Ar) varies by 5 7% between EIPb = 14

and 34 eV, and our relative measurements agree with this finding. We used the corresponding average Ar+/Ar charge-transfer cross section of 39 A’, to calibrate the Ar effusive beam effective thickness, thereby allowing the N,t /Ar data to be placed on an absolute basis.

4. Discussion The major features observed in charge exchange between state-selected NT and Ar are: (a) the slightly endothermic (by 0.18 eV) charge transfer from N:(X, u” = 0) remains an order of magnitude slower than that from the other X-state levels studied, even at E,, = 20 eV; (b) the charge-exchange cross section drops precipitously in going from N2f(X, u” = 4) to the nearly isoenergetic Nzf(A, u’ = 0) state; (c) the reaction probabiiities for NT(A, u’ 2 3) depend strongly on relative collision energy, in contrast to the behavior of the lower-lying levels. These observations are discussed further in sections 4.1 and 4.2. 4.1. N,‘(X,

u” = O-4) + Ar

4.1. I. Comparison with other experlmentai data Examination of the data shown in table 1 and fig. 4 confirms earlier conclusions [l-4] that the cross section for reaction (1) is strongly enhanced by vibrational excitation of N’(X). When the relative cross sections of Kato et al. [4] for u” = O-3 to our data at at Ecm = 11.8 eV are adjusted = 14 eV, we note (see fig. 4) an excellent E. air:ement between the two sets of results. Com= 11.8 and 14 eV data is justified paring E,, because the present results (fig. 4) show that the X-state charge-transfer cross sections are relatively insensitive to the translational energy Ecm between S and 20 eV. Lindinger et al. [l] have measured the kineticenergy dependence of the rate constant for reaction (1) in a drift apparatus in the range E,,_ = O-3-6 eV. Their data indicate that two reactions with different rates contribute to Ar+ production_ The slowest process was attributed to charge transfer from N,‘(X, u” = 0) and the faster to that from

T. R Gooers et al. / State -selected ton -molecule

NT(X, d’ 2 1). The results of Lindinger et ;?. indicate- that - the -ch-&ge-ekchange cross section - for (X, u” z 1) equals = 20 A2, and is essentially independent of collision energy between 0.3 and 6 eV. The present data are in good agreement with this finding; since our cross section, averaged over the levels (X, Y” = l-4) amounts to 25 2, constant within a few % between E,,_ = 8 and 20 eV. For (X, u” = 0). however, &here is an apparent discrepancy, since the present experiments, in agreement with those of Kato et al. [4], show no measurable reactivity at EC_,_= 8 eV: o(X, D” = 0) ( 1 A2, while the cross section derived from the experimental rate constant at 6 eV of Lindinger et al. [l] amounts to = 7 li’. Furthermore, the cross section derived from the drift-tube data shows an increase with translational energy. We thus agree with the sugestion of Kato et al. [4] that the slower of the rate constants reported by Lindinger et al. and attributed to NT(X, v” = 0) actually incorporates a contribution from N’(X, u”) excited states produced by vibrational excitation prior to the charge-exchange reaction. When the excitation rate becomes comparable with or faster than the charge exchange from (X, u” > l), the drift-tube constant for (X, u” = 0) is then expected to converge to that for vibrationally excited ions. Extrapolation of the data by Lindinger et al. suggests that this indeed occurs at EC,,_ = 20 eV, indicating a vibrational excitation cross section of = 20 ;i’ in this energy range. A 1.2. Theoretical considerations In an attempt to rationalize the strong vibrational dependence of the total N,f(X, u”) + Ar charge-exchange cross sections, Kato et al. [4] calculated vibronic state-to-state cross sections using the formulation of Rapp and Francis [20] and obtained the total cross sections from a Franck-Condon-weighted sum over the N?( u G 10) product states. This procedure assigns a major contribution, modulated by the Franck-Condon factors, to energetically near-resonant channels. We wilI in the following suggest an alternative framework for discussion of the dynamics which attempts to investigate the influence of the relevant potentials and their interactions on the charge-transfer probabilities.

reacttons -

379

. Apa+ fro% spin, three different &iectronic states are to. be considered, which correlate at- infinite R(N,-&)+ separBti& to _NF(X ‘2,‘) + Ar(%), tid N,(‘B,f) -+ Ar+(‘P), ‘reN,*(A’II,) + Ar(‘Sj sp&tively. A cut along the r(N-N) coordinate through these surfaces tit R = & is shown in fig. 5. The additional surface correlating to N2(‘Zc,‘) f Ar’(‘P& is not represented for clarity but must be taken into account for a quantitative theoretical analysis. In the absence of ab initio or semi-empirical calculations of these surfaces at finite R, which would allow studies of the dynamics by trajectory surface-hopping calculations for instance, we have adopted a simpler model which employs diabatic vibronic potential curves [22-241. The long-range part of these potentials is determined by the positions of the vibronic levels of the separated collision partners (fig. 5) and the (N2-Ar) +

POTENTIAL ENERGY CURYES

INTERNUCLEAR Rg.

5. Cross-cut

lowest

DlSTANCf

along the r(N-N)

(i)

coordinate of the three

potentialsurfacesof the (N,-Ar)+

These curves are smply [26], of N,(X

‘2,’

system at R = CQ the diatomic potentials taken from ref.

), Nz(X

‘Ep’)

and N2(A21T,).

the first

bag positionedalong the energy axis to account for the internalenew of Ar+(2P3fl). ix. the zero of energy corresponds to ground-gate N,+Ar. spondq to N2(X)+Ar+(*P,,)

N2
An additional curve, corre-

lies 176 meV above that for and has beeti omitted for clarity_

380

T-R GOLUSet al. / Stare-selected

ton

-

moleculereactions

charge-induced dipole and permanent quadrupole interactions_ The induced dipole term, -aa/R4. is obtained with a = 1.6 A3 for NC + Ar f253. In the case of Art + N,, the polarizability a varies with the angle 9 between r and R, with a = 2.38 A3 for Q = 0” and a = 1.45 A3 for Q = 90” [25]. In addi-

tions and criteria of appIicabiIiity of which have been discussed in several recent publications [23,24,27-291. In the present situation, the NZ vibrational period, = 1.4 X lo-l4 s, is of the same order as the time spent by the collision partners in exploring

tion, the latter potential comprises an angle-dependent permanent quadrupole term. /3(3 co& 1)/2 with p = -1.1 au. which is attractive for + = 0 O and repulsive for + = 90 o 1251. Fig. 6 illustrates how the differences in the respective long-range potentials just mentioned gve rise to crossings between the [N,‘(X, u”) + Ar] and [N,(X, u) + ArC] vibronic diabates. with crossmgs. where u = u” - 1, situated in the region R = 5-8 au when + = O”. This situation remains qualitatively the sa_me for 9 = 90 O. except that the [NC(O) + Ar] level does no longer cross any [Nz + Ar+] state. Because only long-range attractions are included in these potentials, their shapes and the locations of the resulting crossings should not be considered as quantitatively correct, particularly for R 5 5 au, where repulsive interactions are likely to become important. Nevertheless, by means of a dynamics model outlined below, these curves do allow us to obtain illustrative numerical results which offer relevant insight and which may serve to stimulate further theoretical work. The appropriate theoretical treatment of charge-exchange dynamics on the vibronic potential curves of fig. 6 depends strongly on the regime of collision energies. In the high-energy limit, one considers the N-N vibration as frozen during the collision, and the transition probability from one vibronic level ma of the [NT + Ar] manifold to a level tzfi of [N, + .4r+] is proportional to the Franck-Condon factor FCF (a. j3) = {a I/3)*_ On the basis of criteria outlined in refs. [24,27] this regime 1s expected to apply at relative velocities much larger than the =: lo6 cm/s range explored here. The other extreme is the low-energy limit in which numerous N-N vibrations are performed in the time needed to explore the network of crossings between the various (ma, nfl) vibronic curves. Bauer, Fisher and Gilmore developed a model applicable in these conditions [22], the implica-

the interaction region (i.e. 5 s R ,( 8 au). Thus a rigorous treatment of the dynamics will call for a coupled-channel treatment as outlined by Klomp and co-workers [27,29]. Kato et al_ [4], however, did investigate low-energy (EC, = 0.3 eV) collisions where the criteria [23,24.27-291 of applicability of the BFG model are satisfied. The vibrational dependence for NT(X, 0”) + Ar charge transfer observed m that case is rather similar to that observed here, the non-activity of u” = 0 being the most striking feature over the whole 0.3-20 eV energy range. It is therefore tempting to examine the salient features of this charge-exchange reaction using the BFG model. The curves in fig. 6 are thus interpreted as the attractive part of diabatic potential curves which govern the R motion at fixed $.LIn the BFG model charge exchange is considered as resulting from transitions between vibronic potential curves, where the transition probabilities pas may be calculated using the Landau-Zener formalism [24] P,s = 1 - exp( -A,,),

(3)

where h

=

43

2WL,l*(aI P)’ hRIA.FI

-

(4)

The electromc matrix element, H,,, the radial velocity, i? = 6R/6t, and the difference in slopes of the vibronic curves h F = 6( H,, - H,+)/i5R are all evaluated at the crossing radius R = R,. Because the transitions are localized, the transition probabilities will be sensitive to the variation of these parameters with R,, which is particularly strong (exponential behaviour) for H,,(R,). Together with the differences between the respective FCFs, this results in substantial variations in the probabilities pas for transitions from any particular initial ma to the various accessible channels nSThe selectivity which results from these effects

T.R Gowrs er aI_ / State-selected ton -molecule reacttons

DIABATIC ‘7

c

VIBRONIC N-N

POTENTIAL

ANGLE

---Ar

= 0'

ENERGY

N;

(-$,vj+Ar

381

CURVES N,'(X.vi

__;)

+Ar+

.

_____ ..._.... . .. ... ...... .. .-....._..f 0 .

a 3

1

6

7

9

R (N2----Ar)

13

distance

(a u)

DIABATIC VIBRONIC POTENTIAL ENERGY CURVES

.__.*

.

___...

. . . .

.

L”............

0

_._........“.

154 _

15,

x

7

1

I 3

5

R

(N2

I

7

----AI) distance

I 9

I

, 11

,

Ib , 13

(a-u)

Fig. 6. Attractive parts of the vibronic diabatic potentials peming to N$(X, u”)+AT * N~(X.V)-~-A~*(*P). as a function of R tN,-Ar) for a fied angle + = 0 o (a), and + = 90 o (b). The dotted curves refer to Nz (X, u”) tAr, with the values of u” indicated at the right-hand side of the drawing. The full curves pertain to the potential pairs N2(X, u)+Ar* (zP3fi,,.J with the higher curve referring to zP 1m At R = 01 these curves coincide with the vibrational leveh of N,(X) and N: (X) (211, the former being displaced by rhe internal energies of Ar+(*PSn) and (zPI/2)_

3S2

T R. Govers et ai / Srare-selected ran - molecule reactions

can be illustrated considering the successive crossmgs explored with decreasing R for Nc(X. L”’ = 3) + Ar at an angle $J = 0 O. for instance (fig. 6a and table 2). The first of these can populate NJ u = 2) + Ar’( ‘P,,l) and occurs at R, = 6.4 au. Because the charge-transfer cross section for N1+( u” = 3) is large (= 30 2) and relatively insensitive to kinetic energy. it is reasonable to expect that this outer crossing is efficient in promoting charge exchange, with p3 2 = 0.5 at E, “, = 20 eV (see below). Using eqs. (3) and (4) with the assumption of a straightlme trajectory for a representative impact parameter b = 3.2 au. and with FCF (3.2)= 0.19 from table Z and AF = 2.5X 10-l au from fig. 6. we obtain H,,,,, ( RL = 6.4 au. Q = 0 “) = 3.0 X lo-’ au = 82 meV. We can now evaluate the interaction element for the (3.3) crossmg at 5.3 au. using 120.301 K,,, ( R, ) a R,I

exp [ - (21)“‘RJ.

(5)

where both R, and the average ionisation potentral I are expressed in au. We thus obtain H,,,,,(5.3 au, + = 0 o ) = 14 x lo-’ au = 380 meV_ Not only H,,,,,. but also the FCF is iarger for the 5.3 than for the 6.4 au crossing. FCF (3,3)= 0.51 (table 2). and takmg EL *,, = 20 eV and h = 3 2 au as before. with AF = 4.9 X lo-” au from fig. 6a. we now find p3 ;( ‘P,,,) > 0.999. In other words. thts crossing ~111 be traversed adiabattcally (transition between diabates) both in the approaching and recedmg part of the trajectory. and ~111 not contribute to charge transfer_ Because of the strong increase of

H,, with decreasing R,, transition probabilities at smaller R, will also be close to 1. This numerical example and analogous results for the other N+(X, u”) levels summarized in table 2 illustrate the following point: if the outer crossings for NZ+(u” 2 1) in fig. 6 are efficient in promoting charge exchange. as suggested by the relatively large cross sections, the inner crossings are like!y to be traversed adiabatically (p = 1) and will therefore not contribute to charge transfer. which requires the system to “hesitate” between diabatic ( p = 0) and adiabatic ( p = 1) behaviour. Thus the total charge-transfer probability P, for a given reactant channel is likely to be governed by a single - presumably the (u”, u” - 1) - vibronic crossing (cy. fl) P, = K/3 = 2PJI

-Pap)-

(6)

In such a picture, the relative invariance of the total cross section reflects the invariance of the transition probabihty for the dominant crossing. This feature is self-consistent with our interpretation of the relative invariance of o(X. 3) with kinetic energy. and the magnitude of this cross section (- 30 A’) as implying pj2 = 0.5 in the numerical example above: p = 0.5 maximizes P and minimizes its dependence on p [eq. (6)]. Such an analysis also makes clear that P, will be proportional to a particular FCF (a, /3) only if charge exchange is dominated by a single crossing and if the corresponding transition probability is suffrciently small for (6) to reduce to [see eqs. (3) and

French-Condon factora (FCF) crorsmg rddu R, (III au) and tr~ns:tlon probabdltws p, .L for rlu = 0.1 crossmgs between the [X>* (X t”)~Ar] and [N,(_Y. u)+Ar+ ] btbromc tunes of fig. 6n (6 = 0 O) and fig. 6b (+ = 90 O) situated between S-S au. The FCFs \\erecalculated for hiorbe potentuls fitted to the spectroscopic data surnm~nzed m ref. [Zl]. The crossing probablhties uere obtamed b, Jssuming ~(3.2) = 0 5, rls aplaned m the text. for both angles A slmllar result would have been obtluncd by making this as\umptlon .I[ 9 = 0 O. e S . and raLmg H,,, to be angle-Independent N,(v)

FCF R,-P,,,,

( 1“‘)

0

1

2

3

4

L’= ‘*I

0.9’ 5s; 1 00

0.77 5.6; 1 00

063 5.5; 1 00

0.51 5.3. 1 00

0.41 5.1. 1.00

t.l=LY--_l

-

0 076 7 5 *‘; 0 02 5.7: 0.98

0 14 6.7 =); 0.24 6.3; 0.94

0.19 6 4 a)-. 0 50 6.9: 0 50

022 6 2 =‘: 0.74 7.7: 0.20

(O”)

FCF R,. P,,,, (0 o ) R,; P., c 6’0 o 1

Nf

-

u’ Crossmgs whlch populate [N,( rr)+Ar+ (‘P,,,)];

the other crossmg radn refer to ArC ( ‘PJ,z)

T_R Covers et al. / State-selected ion_- molecule reactions

(411 P, = 2P& = 2&3 a (a f lQ2:

(7)

We recognize that the actual values of R, and the corresponding parameters in eqs. (3) and (4) are subject to the approximate nature of our vibronic curves and to variations due to the dependence on the angle +_ The effective crossing radii can be estimated if one interpretes the cross sections in the impact parameter approximation, e.g., a(X,

3) = ~(3,

2) = P,.,?rR$

Taking P3.r= 0.5, the observed yields R, = 8.6 au, as compared

(8) o(X, 3) = 30 A’

to the values of 6.4 and 6.9 au in fig. 6 and table 2. Also if we take element which we the %I = 82 meV interaction estimated above for the (3, 2) crossing and deduce R, from the semi-empirical relation of Olson et al. [30]. we obtain R, = 8 au. It thus appears that the actual crossings occur at somewhat larger distances than those deduced from fig. 6. We believe, however, that a more precise theoretical treatment is likely to maintain the conclusion reached above, namely that among the many possible vibronic crossings as illustrated by fig. 6, only a few will be effective in promoting charge transfer, largely because of the strong variation of H,,, with R, and the relative magnitude of the respective FCFs. A simrlar selectivity has been observed experimentally and interpreted by means of the BFG model in the case of thermal charge transfer into specific product states for the system He+ + Nz + He + N’(C, u) 1311. The preceding arguments readily account for the observed non-reactivity of N$(X, 0). As fig. 6 indicates, the only crossing available to this reactant involves transfer to N,(O) at $I = 0 O. Using eqs. (3)-(S) and the value H,,,, (R, = 6.4 au, $I = 0 “) = 3.0 X 10e3 au employed above, the corresponding interaction element is found to be I-I,,,, (R,=5.8 au, cp=O”)=6.9x-10-3 au=190 meV. The FCF for this transition is large, 0.92 (table 2), and if we now calculate P for E,,- = 20 eV and a typical b = 3.2 au, we find poo > 0.999 and P, = 1 X 10m5. In other words, the (0,O) crossing is passed completeIy adiabatically and does not allow for charge transfer from (X, v” = 0). It is interesting

383

to note that if the FCF for the (0,O) crossing would have been small, say 0.1, we would have found po,o = 0.17 and PO = 0.14, illustr&ing I the possible enhancement of charge transfer_ by small FCFs [32]. The present analysis is also consistent with the finding of Lindinger et al. [l] that charge exchange at E = 0.12 eV between ArC(‘P3,,) and Nz yields almost exclusively N,f(X, u” = 1) rather than proceeding exothermically to N,f(X, 0” = 0). A sin+ lar result was recently obtained by Futrell and Friederich [33] from a crossed-beams experiment between Arf and Nz_ Smith and Adams [2] found 60-70s of the N+ products to be produced in o.” = 1 in their 300 K SIFT experiment. These findings substantiate the ineffectiveness of the (0,O) crossing outlined above. The population of N,i(X, 1) presumably proceeds via a N,(O)/N,+(l) crossing such as the one observed at + = 90 O in fig. 6. It is possible that a more accurate representation of the diabatic potentials will result in more nearly parallel curves, in which case the Demkov treatment [34] of the transition probabilities may be more appropriate. The corresponding transitions will remain localized however, and it is probable that the main result of the present analysis wiil remain the same: N,C(X, 0) is non-reactive because the [N,+(X,O) + Ar]/[Nz(X,O) + ArC( “P3,,)] interaction region is explored adiabatically. 4.2. &‘(A,

u’ = d-6) + Ar

The first observation that can be made -wrth regard to charge exchange between N:(A, u’) ions and Ar concerns the magnitude of the (A, u’ = 0) cross section relative to that for the quasi-isoergic Nc(X, v” = 4) state. These states are separated by only 65 meV, yet they differ in reactivity by a factor of 2.5, and it is the electronically excited state which is the less reactive_ This contrasts, e.g., with the reaction 0: -I- H, + HOT + H or --, 0, + HZ, where the electronically excited a411,(u) levels of 0: are more reactrve than the quasi-isoergic vibrationally - excited levels of the X ‘IIs ground-state[35].We have examined the decreased reactivity of

384

T R. Gorers et ai / Sate-selecred

Table 3 Fnnck-Condon [N,(X.

u)+Ar*

ton -nrolecuIe

reactions

factors (first entry) and crossmg radn (second and third entries in au) for crossmgs between [Nf(A d)+Ar] and beween 5-9 au, when + = O” or 90 O. The FCFs uere calculated for Morse potentials

1 Llbronic ctmes obtained

fitted to the specrroscopicconstants of ref. (211

FCF R,(O”)

N,(o)

N; (11’) 0

0=0*-i-2

0.24 -

R,(90°)

1

2

3

4

5

6

0.28

0 18 -

0.065 -

0.006 -

5.0 =’

5 5 J’

7.1 =’

-

0007 s.9 =’ 52

0.043 7.13’ 6.1

FCF R,(O”) R,(90°)

u=o’+3

00s 7.6 a’ 5.7

0 19 6.7 a’ 67

024 6 1 =’ -

024 5 6 a’ -

0 19 5 2 J’. 7 4 -

0 12 5 0 =I, 6 5

0.053 55 -

FCF R,(OO)

L =e’+4

0 018 61

0 060 55

0 12 53

0 17 50

021 -

0.23

0.23 -

-

-

R&(90”)

J’ Crossings whvzh populate [N,(o)+Ar’(

‘P,,:!)].

the other crossing radii refer to 4r+ ( ‘Px,z)_

Ng(A, 0) using the BFG model as outlined tn section 4.1.2. The vibronic curves were constructed using the same long-range interactions as for NT(X)+ Ar, resulting in networks of crossings analogous to those of fig. 6. The corresponding crossing radti and FCFs are listed in table 3. In our calculations, we assumed the electronic coupling element at a given R, to be the same as for N’(X) + Ar: since the 1~” and 3~~ orbitals in N,. the ionization of which yields N’(A) and NT(X) respectively, have nearby energies, one does expect similar H,,,, for charge exchange from these two ion states [30]. In contrast to the situation pertaining to N’(X) +Ar, we find that charge exchange from the N+(A. u’) levels is likely to involve several participating vibronic crossings, because smaller FCFs are often compensated by smaller R, (i.e. larger H,,), as may be seen in table 3. Using the same analysis as for NT(X) above, we find for NT(A, 0) with EC, =20 eV, b=3.3 au and +=O”, the values pus = 0.08 and po_4= 0.12, which yield a probability PO = 0.3 for reaction into either N2( c = 3) or (u = 4), sinular to the value PO = 0.4 resulting from the (0, 3) crossing for Q = 90 O_ While this numerical example does suggest a lower reactivity for N;(A, 0) than for NT(X, 4). where P = 0.5, the rather subtle interplay between the various parameters in eqs. (3) and (4) cautions that this agreement with our experimental findings

is possibly quite fortuitous_ This type of calculation is nevertheless useful tn illustrate that there is no reason to believe that an electronically excited state will have a larger charge-exchange cross section than a ground-state ion of comparable internal energy. A second possibility that comes to mind as a cause of lowering the A-state charge-transfer cross sections is competition by the sequence N,‘(A.

u’) + Ar + [N,(X.

--, N’(X,

u) + Arf]

L”‘) + Ar,

(9)

in which. during the course of a single collision, a transition from N’(A) to N?(X) is followed by one from N?(X) to NC(X). Such a collision, which amounts to a radiationless electronic transition via double charge-transfer can reduce the observed charge-exchange cross section as illustrated by the stmplified curve-crossing picture shown in fig. 7: we consider two energetically close vibronic levels [NT(A, a) + Ar] and [N,C(X, y) + Ar] which cross a single vibronic level [N,(X, j3) + Ar’] at R, and R x, respectively_ If pA and p x are the corresponding transition probabilities, the probability for charge transfer from NT(A, a) to N,(X, /3) becomes P, P = 2P.40

-P*)(l

-PA

for the case, illustrated in fig. 7, where R,

004 > R,,

T.&. Govers %I al. / Srare-selected ion ;- mo&ctde reactions

-

DOUBLE CHARGE

R

EXCHANGE

(N2 ---Ar)

DIAGRAM

distance

Fi_g 7. Simplified curve-crossing model dlustrating thr possible competition for charge transfer and electronically inelastic collis~ons from Nf (A)_

Nz (A, o’) + Ar + [N:

and

P_Jj= 2p*(l --P,)[l

--Pxo

341

-+N,(X,u)+Ar+,

0Ob)

in the analogous case where R, > R,. In particular in the first case, charge transfer can be effectively suppressed in favour of the radiationless electronic transition, since P, B -3 0 as px --) 1 in eq. (lOa). While the mechanism just invoked may affect the different NT(A, u’) levels to various degrees, a corresponding BFG treatment would result in relatively small variations with energy over the rather narrow relative-velocity range explored here: 8, (20 eV)/&, (8 eV)= 1.6. We are thus left to account for the second salient feature of the N:(A) data which is the pronounced variation with translational energy of the cross sections for u’ g 3_ Several of these vary by more than an order of magnitude as the relative velocity varies by only a factor of 1.6. This suggests that a phase relationship between the N-N and N,-Ar relative motions plays a role in the reaction and is particularly effective for A(3 < u’ f 6). In this case the averaging over the vibrational wavefunctions performed in the BFG model is no longer appropriate. The vibronic curve-crossing model‘ has been extended by Klomp et al. [27,29] to allow for this time dependence.

-385

.; . Examinatiouof the cut through the potential surfaces at R _= co in fig. 5 suggests-a mecl@nisn; which involves direct Nz(A, 2 j --) NT-(X; u”) radi; ationless transitions. These--would occur for the d > 3 levels, as i\i,+a&l Ar approach and the NT(A) and N,‘(X) potentials are slightly displaced with respect to each other. In the surface-hopping trajectory model [23,24] one would picture this transition as occurring at the outer (right-hand) turning point of the N-N vibrational motion, where the [N:(A) +Ar] and [NC(X) + Ar] diabatic surfaces intersect. On the other hand, transitions between the [N,+(X)+Ar] and the [N2(X) + Ar+J surfaces will, if they do occur, take place at the left-hand turning points. This introduces a competition between collision-induced N:(A) + N:(X) transfer and charge transfer via a radiationless transition (X, u”) + Ar] (11)

which depends on the phases of the motions along the R and r coordinates. Such a mechanism may introduce energy-dependent oscillations in the charge-exchange cross section, if the NT(A) + NC(X) transition is favoured over direct A-state charge exchange. Interactions between N,f(A’II”) and Nzf (X ‘Z,‘) are forbidden in the isolated molecule because of the u c, g selection rule. Collisions can induce radiationless transitions between the two states, however, as evidenced by the work of Katayama et al. [36], who found that the deactivation of NC(A) by He proceeds as effectively as for heteronuclear molecules_ Ignoring the spin-orbit interactions, six surfaces are now to be considered, the symmetries of which are listed in table 4 for the linear C,,, perpendicular CzV, and planar C, geometries. One sees that the N:(A) --, N;(X) transition is induced by dynamic coupling of the (1) ‘A, and (3) ‘At states. It is clear that the possible interplay of four ‘At states is well beyond the scope of-the present paper, and that ab initio potential calculations will be necessary to set the basis for future dynamical calculations. From the experimental point of view, measuring the quenching of individual N$ (A, u’) levels

Table 4 Electromc-state correlations for (N, +Ar)+ symmetries States of the products

in C,,.

C,

and C,

States of the quasi-molecule

R=co

C Div

C2.

C,

Nf (X ‘IT; )+Ar(‘S) pJ,(X ‘Zc)+Ar*(‘P)

(1) ‘2’ (2) Ix+

(l)‘A, (2) ?A,

(I)% (2) ‘A’

(I)‘rI

(1) ‘B2

(I) ‘B,

(3) k’ (1) ‘A”

(3) ‘A, (Z)‘B,

(3) ‘A’ (2) ‘A”

N’(A’fI,,tAr(‘S)

(2) ‘n

with Ar would be useful to verify the that radiationless transitions NT(A) + Ar ---,N’(X) + Ar compete effectively with charge exchange from N;(24)_ An equivalent concluston was already reached by Comes and Speier [37,383. who examined the quenching of a number of excited molecular ions. among which the CO’(A) analogue of NC(A). and argued that quenching occurred mainly by collision-induced radiationless transitions rather than by charge transfer. even in the parent gas of the ion. Largely because the N’ (A - X) Memel bands are among the strongest emissions in normal auroras. a fair amount of data is available For quenching of N,‘(A) by NZ and O2 [39]. but we are not aware of results for quenching by Ar. in collisions

present

suggestion

5. Conclusion The total charge-transfer cross sections for the reaction of vibronic-state-selected N’(X, u”) and N’(A. u’) with Ar show a strong dependence on the internal energy of the reactant ion. The effect of the relative collision energy is rather small for N’(X. u” < 4) and Nlf(A, u’ < 2). whereas pronounced variations with kinetic energy are found for NL(A. u’ = 3-6). The Bauer-Fisher-Gilmore model which invoques transitions between pairs of vibronic diabatic potential curves accounts satisfactorily for the observed Iow reactivity of the N’(X, u” = 0) ion. It is ascribed to the fact that the only crossing accessible to NT(X, 0) is that populating N,(X, 0) + Arf and that this crossing is explored achabati-

tally, in contrast to the (X, u” = 1-4) levels for which effective charge exchange is possible via (o”, u = u” - 1) transitions. The model predicts that large Franck-Condon factors may actually reduce the charge-transfer probabilityThe sharp variations of the N$ (A, u’ >, 3) + Ar cress sections with kinetic energy are interpreted as resulting from a competition between charge exchange and collision-induced radiationless transitions. A theoretical treatment of this situation calls for the interaction of at least three electronic states. The present experiments are a good example of the flexibility of the threshold photoelectron-photoion coincidence technique in the study of unimolecular and bimolecular reaction dynamics of state-selected ions. in particular when monochromatized synchrotron radiation is used for photoionization_ The pulsed character of this source allows for well-resolved and effective selection of the threshold electrons by time-of-flight, and its wide tunability allows the access to a broad range of selected ion states.

Acknowledgement

We thank A. Abadta, G. Bellec and M. Soyez for their contributions to the constructron of the dual TOF spectrometer_ We are also thankful to Drs. V. Sidis. J. Durup, G. Parlant and E. Gislason for stimulating discussions and to Dr. B. Lassier-Govers for providing Franck-Condon factors. We appreciate the long hours of work offered by the staffs of the Orsay linear accelerator and of L.U.R.E. in operating the storage ring. This work was made possible by a contract from the French National Research Center (ATP-CNRS) and was partially financed by a joint CNRS-NSF grant as weIl as by grants from Universite Paris-Sud, NATO and the Physics Division of the US National Science Foundation_

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Phys. Rev. A23 (1981)

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1156. PI W. Dobler, F. Howorks and W. Lindmger. Plasma Chem. Process. 2 (1982) 353. WI E_ Ferguson, pnvate communication.

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[22] [23]

v41 [251

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WI DC. Cartwnght. J. Chem. Phys 58 (1973) 178. P71 J R. Peterson and J. Moseley. J. Chem. Phys. 58 (1973) 172.

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