Vibrational deactivation of DF

Chemical Physics 46 (1980) 287-296 0 North-Holland Publishing Company

VIBRATIONAL DEACTIVATION OF DF Lise Lotte POULSEN

and Gcrt Due BILLING

Iustirrrfefor Cltemi3try. Unicersity of Copenhagen. Randmmdsgude 71, DK-2200 Copenhagen N, Dennmk Received 6 August

1979

of DF in vibrationat states n = I to 7 in collisions with DF(0) are calculated range from 300 K to 3000 K. The variation with the temperature agrees quite wei! with experiments for n = 1, although the theoretica rates are 30 % rower than the experimental values for temperatures above IZCQ K and 75% lower at 300 K. This difkrence is discussed. Single quantum transitions dominate. At 300 K the mechanism is predominantly a V-V transfer for II.= 2 and a V-T/R transfer for R = 7, while both mechanisms contribute for )I = 3-6. Collision complexes are important for both V-V and V-T/R energy transfer. Rotational relaxation times are calculated for HF and DE Rate constants

for deactivation

semiclassically in the temperature

1. Introduction The information about the deactivation of vibrationally excited hydrogen fluoride and deutcrium fluoride is increasing rapidly both experimentally and theoretically. We have recently calculated the rate constants for deactivation of HF(rz) by HF(0) [ 1,2], for deactivation of HF(n) by DF(0) 133 and for deactivation of DF(n) by HF(0) [3]_ The vibrational quantum number II varies from I to 7. We have found good agreement with experiments with regard to the scaling of the rate constants with )I and also with regard to the temperature dependence, which has the characteristic minimum between 600 K and 900 K. The absolute theoretical values tend, however, to be lower than the experimental values, thus the theoretical rate constants are 40%. 60% and 10% lower, respectively, than the experimenta rate constants for II = I at 300 K for the isotopes mentioned_ The present work completes the list of isotope combinations by reporting calculated rate constants for the deactivation of DF(n) by DF(O). The aim of this work is to perform a further test of the potential and calculation method by a comparison with

available experimental results. Furthermore, rate constants are calculated for the upper vibrational levels, which have not yet been measured due to experimental difficulties. Information about these rates is necessary both for the modelling of the chemical DF laser and for the analysis and planning of experimental studies-of the vibrational deactivation rates.

2. Theory

The theory has been reported in previous work [l--4]. We shall, therefore, give only a brief description and define the concepts, which will be used later in the discussion of the results. The potential is a fit to 323 ab initio (SCF) points calculated by Yarkony et al. [IS]. The SCF calculation does not account for dispersion forces, and we have, therefore, added an isotropic dispersion potential, which was calculated from experiments by Zeleznik and Svehla [S]. The attractive well depth of this potential is 6.9 kcal/ mole while the experimental value is reported to be 6.0 f 1.5 kcal/mole [7]. The minimum is in a linear configuration, while experiments [8] and the SCF-

285

LL. Pouken. G.D. Bi!ling/Vibmrionol

calculation [s] indicate a minimum in a planar conliguration with the end hydrogen bend an angle of Xl-70” from the F-F axis. The potential parameters have not been adjusted to improve the agreement with the experimental deactivation rates. The deactivation rate constants are calculated semi-classically.

Rotation

and translation

are treated

classically by running rigid rotator trajectories over the potential surface. The forces perturbing the vibrational degrees of freedom are caIculated along the trajectories. For each trajectory, this time dependent perturbation is used in the time dependent Schrijdinger equation for the vibrational degrees of freedom. which are. in this way, treated quantum mechanically. When solving the Schriidinger equation, two further approximations are introduced in order to cut the computer time down to a realistic level (about 30 hours on a Univac 11 IO): (I) The potential is expanded to second order in the oscillator coordinates. (2) The diatomic molecules are approximated with two harmonic oscillators. However, for each molecule we use an oscillator frequency corresponding to the transition considered. In this way energy mismatch is accounted for. This approach is of course approximate but the anharmonic correction factors which have been estimated previously [4] for H, and Nz show corrections between 10 and 30 %_ We have therefore not included these correction factors in the present or previous HF(DF) calculations. The solution of the Schrddinger equation, which gives the vibrational transition probabilities, is carried to inlinite order using the approach described in previous publications [l-l]. The cross section for a vibrational transition rrrnz - n;n;, abbreviated II + n’, may be calculated for a lixed initial relative kinetic energy, Eki,, and lixed initial rotational energies of the two molecules, E rot1and Ero12,by using ~,,-n.(E~in. E,,, , >-LtJ

where (P,,_,.> is the average value of the transition probabilities from trajectories with Monte Carlo selected initial orientations. The rate constant is

denctinntion of DF

obtained by averaging c~_“. over a Boltzmann distribution of ELin, E,,, 1 and Erolz. The calculation of the detailed cross sections in eq. (I) requires, however, a wealth of computer time. When the goal is thermal rate constants, considerable computer time is saved by Boltzmann averaping over initial rotational and kinetic energies from the beginning. This is done by calculating a cross section for a fixed torn! energy E. The sum of the initial rotational and kinetic energies is U = E -

En = E - (En, + E,,&

(2)

where I?. is the sum of the initial vibrational energies of the molecules. Ci is resolved in initial rotational and relative kinetic energies by selecting the initial molecular rotational angular momentaj, and j2 randomly in ranges given by [I] E rOll,nux = 0’1mT.x+ f)w;(zl)

= u,

E rolI.mv: = 0’2mx f

= u -

yhy(l(21,)

(3) E,,, 1.

(4)

A “rotationally Boltzmann averaged- cross section for a fixed total energy is delined by [I]’ G~_,.(E - En, To) = G&U,

To) im.. 0

I:

jha dj2(2j2 + 1)

X s

0

d/(21 + 1)
(5)

s 0

where p is the reduced collision mass, Q,=2l,kT,A-‘, Ii is the moment of inertia of molecule i, and 1 is given by b = (1 t $h(2PEki”)_ I/z.

(6)

To is an arbitrary temperature defming the Boltzmann distribution. In the present study To = 300 K. The rate constant is finally calculated at any temperature using [l]

The only dil’lerence between this detinition of the rotationally averaged cross section and the delinition used by Melton and Gordon in ref. [9] is, that they include (Q,Q2)-r in the subsequent calculation of the rate constant. eq. (7), while we keep it together averaging ofa over j, and jl in eq. (5).

with the

L.L. PouLsen, G.D. Billing/Vibrational

&.(T) X

=

deoctiuation

of DF

289

(skT/ltp)“‘(T,lT)3

s

d(U/kT)

exp (- llJ/kT)~,,,.(lJ,

Incsemiclassical classical trajectory the oscillators.

(classical

path)

T,).

calculations,

(7) the

does not gain the energy

Microscopic

lost by must, there-

reversibility

fore, be forced to be fulfilled. When this is done with the use of the three-dimensional generalization of the collinear arithmetic velocity symmetrization, u for a given total energy, E, is calcuiated with the following energy in the classical trajectory [I] Usc = f[(E - 15~)“~+ (E - E,.)““]. For an exoergic transition valent to

(8)

II --* PI’,eq. (8) is equi-

U = E - En = (II,, - AE/4)‘/U,c,

(9!

where AE = E, - En. > 0.

(10)

The lower limit for USC is seen to be AE/4. Thus we have calculated G,_,.( Us,, T,) for a number of Us,-values. The variation of these cross sections with n and Use is discussed in section 4. Rate constants are obtained from eq. (7) using the substitution in eq. (9).

Table

Fig. 1. Temperature dependence of the rate constants for transfer ofvibrational energy out of DF(I). The experiments are:0 Lucht and Cool [lO],x Bott and Cohen [ll, 12],U Ernst, Osgood and Javan [13],A Hinchen [14], line B-C Bott and Cohen [IS], line B Blauer, Solomon and Owens [ 161. I are error bars (sd.).

I

Experimental and theoretical rate constants for various processes removing DF(1) and HF(l) at 300 K. The energy transfer in collisions between two excited molecules is more important for pure DF than for the other isotope combinations Process

Experiments k(lO-“cm”s-I)

Present theory k(IO-” cm’s_‘)

DF(I) + DF(0) -+ 2DF(O) 2DF(1) -c DF(2) -f- DF(0)

0.60[10],0.64[11],0.49[13],0.71[14] 29[13], 31[12]

0.16” 13”’

DF(I) f HF(0) + DF(0) + HF(0) DF( I) •t HF(0) + DF(0) f HF(1) 2DF( 1) + DF(2) + DF(0)

0.83[10],0.96[10],

HF( I) f HF(0) + 2HF(O) ZHF(I) --t HF(2) + HF(0)

1.8[20]

29[13], 31[12]

HF(I) + DF(0) -+ HF(0) + DF(0) HF(I) f DF(0) + HF(0) i- DF(I) 2HF(l) --) HF(2) i HF(0) a’ Present work.

1.1[14, 17],2.0[18],

w Sum of the rate constants.

2.S~10],2.4~17],2.1~14]b’

1.6[19]

0.9 I[33 0.004[3] 13”’ 1.1[1,2] 8.6[1,2]

L.L. Poulstw, G.D. BillitrgfVibrutionu! decrcricurion of DF

290 3. Results

3.1. Comparison with experinzents Fig. I. shows, that the temperature dependence of the theoretical rate constants agrees quite well with available experiinental results. The theoretical vibration to translation/rotation (V-T/R) rate constant for n = 1 amounts to about 70’;/, of the experimental value above 1200 K. At 300 K, the theoretical rate constant is, however, only about 25% of the experimental result. At present we cannot explain, why the theoretical result is so much lower than the experimental results for this particular isotope combination considering that the agreement is significantly better for the other isotopes, which collide on the same potential surface, see table 1. The property measured experimentally is the rate of disappearance of DF( l), and the result is, therefore. the sum of the rates ofall processes causing a removal of DF( I). The experimental re!axation time is attributed solely to the V-T/R process DF( 1) -I- DF(0) --f ZDF(0).

1 I

my10

1600 1;00 2000 2500

(12)

contributions from this process can hardly explain the difference between the theoretical and experimental rate constants. 3.2. V-T/R

rate ~~n~futzt~

Fig. 2 shows the temperature dependence single quantum V-T/R energy transfers

II = 1-7.

(13) scaling of

HF is shown

[Z] DF(u) i

DF(0) -

T = 300 K

DF(rr -

I) f

DF(CtJ

HF(rrJ + HF(OJ + HF(rt -

T = 1000 K

?‘=NOOK

z

24

3 4 5

4.9 8.3 20

2.6 5.6 9.5 18

2.6 5.0 8.1 13

6 7

ZS 50

27 43

17 24

of the

DF(n) + DF(0) - DF(n - 1) i DF(O),

Table 1 is shown. The Scaling of the V-T/R rates with II 31 three temperatures. The ratio Ic~~_~_,~O/kIO_OO II

I

(11)

has a rate constant. which we find to be of the order 13jO.16 = 80 times larger than process (I I), see table 1. Thus process (13) contributes to the measured rate unless the concentration of DF(1) is significantly less than 1 T/,_Experimentalists seem. however, confident that they see a single exponential decay of [DF(l)]-undisturbed by process (12), SO

for comparison

l(K)

Fig 2. Temperature dependence of the theoretical rate constants for transfer of vibrational energy from DF(n) into translation/rotation. I is the error bar (s.d.).@indicate the analytical rate constants (eq. (22)) based on a fit of G = IIIU,,-.JB)’to the theoretical cross sections.

The V-V process involving fwo excited DF molecules 2DFII) -+ DF(2) f DF(0)

*o-‘3

T=3ooK 3.3 7.8 19 31

52

100

1) + HW

L.L. Poulse:L G.D. Billing/Vibrational deacticarion ofDF

The rate constant for 10 --f 00 increases more with the temperature than the rate constant for 70 + 60, reflecting that the vibrational .energy mismatch is larger for n = 1 then for n = 7, a&, being -2906.8 cm-’ and -2358.3 cm-l, respectively+. Consequently, the scaling of the rate constants with II varies with the temperature, see table 2. This scaling is usually assumed to be independent of the temperature due to lack of betrer information [22]. The scaling is faster than a harmonic oscillator scaling, which is linear in n. Since we have used harmonic oscillator wavefunctions, the faster increase with II is due to the use of a frequency for each oscillator corresponding to the transition considered. This has two efTects: the ener,g mismatch decreases with n, and the matrix-element increases with II. In laser modelling, the V-T/R rate constants for DF have usually been assumed to scale with II like in HF [22]. Table 2 shows, however, that the rate constants increase more slowly with 11for DF than for HF. This result was expected qualitatively because

DF is less anharmonic

than

HF.

r, I

300500

1000

1500

2000

2500

TCKI

Fig. 3. Temperature dependence of the theoretical rate constants for transfer of vibrational energy from DF(n) to DF(0). I is the error bar (s.d.). The analytical rate constants (eq. (22)) based on a fit of d = n(USJB)’ to the theoretical cross sections deviate less than 10% from the curves shown.

about 307/, (s.d.): Although the rate constants in fig. 3 vary in a complicated fashion, a systematic analysis is possible for the cross sections, see section 4. 3.4. Tile relative irnportarwe of V-V and V-T/R energy transfer

3.3. V-V rute coutanrs

Fig. 3 shows the temperature dependence of the rate constants for the single quantum V-V transitions DF(n) + DF(0) + DF(n - 1) + DF(l), 1, = 2-7.

(14)

The scaling of these rate constants with n is much more complicated than the scaling of the V-T/R rate constants. The reason is that the V-V rates are determined by two properties, which have opposite effects when II varies. The endoergicity, which increases with n, is most important at low temperature, and 70 + 61 has, therefore, the lowest rate constant at low temperature. Energy mismatch is less important at high temperature, where 70 + 61 becomes the fastest transition because the matrix element I<701 V 161>1increases with n. The relative positions of the rates for n = 3,4,5 are hardly significant at 300 K as the statistical uncertainty is * The energies of using

the

vibrational levels are calculated

the values listed in ref. [21].

Many thoughts have been given to the question whether the deactivation of DF(rz) in collisions with DF(0) occurs via a V-V or a V-T/R mechanism. Table 3 shows that at 300 K the V-V mechanism dominates for n = 2, and V-T/R dominates for )I = 7, while both mechanism are important for n = 34. The importance of the V-T/R mechanism Table 3 The relative importance of V-T/R and V-V deactivation of DF(n) by DF(0) at three temperatures. The fi&ures shown are the percent V-T/R transfer, i.e. 100% x k.,_.._,J(k.,_._,., + k,,_,_,.,).Thestatistica! uncertainty of these rates is about 30 % (s.d.) n

2 3 4 5 6 7

Pe:cent

V-T/R transfer

T=3OOk

T=

4.2 21 24 39 54 87

7.7 23 25 32 44 66

IOOOK

T= 30 48 53 58 65 74

2000K

increases with tz because the energy mismatch decreases with n for the V-T/R energy transfer, while the mismatch increases with II for the V-V energy transfer (see table 4.). Furthermore, V-V is endoergic while V-T/R is exoegic. The V-T/R mechanism contributes even more in the Iower IeveIs when the temperature is high, because the energy mismatch is less important when energy is plentiful.

Two multiquantum V-V energy transfers were considered: the nearest resonance transition which is endoergic DF(3) -t DF(0) + DF(I) + DF(2), A&,

= lS2.84 cm- t.

(15)

and the exoergic process

= -2054.05

cm-‘.

(16)

Furthermore, three multiquantum tions were considered:

4. Analytical

of DF(n) by HF(0)

V-V and V-T/R rate constants

A log-log plot of the rotationally averaged cross sections a( USC, To) against the semiclassical (rotational + kinetic) energy Us, is almost linear. A positive curvature at low energies is seen for the other isotope combinations, but it is less pronounced for DFfn) f DF(0). A small negative curvature is found at high energies, where multiquantum transitions become likely, which decreases the probability for single quantum transitions. A similar behaviour has previously been noticed for H, i He [23,24]. The linear log-log relationship is here expressed in the form (IS)

G”aWn-,.m(usc, T,) = ~r(&/W,

DF(6) + DF(0) + DF(4) + DF(1). A&

be insigniiicant for deactivation and of HF(n) by DF(0) [3].

V-T/R dsactiva-

DF(n) •t- DF(0) --* DF(rr - 2) t DI=(O,. it = 2.3.6,

(17)

for which A& = -5722.2 cm- I, - 5539.4 cm- ’ and -4990.9 cm-‘. respectively. All of these processes vverc found to be insignificant giving contributions less than IO?< of the single quantum V-V and V-T/R transitions (13) and (14). Multiquantum transiiions have previously been found to

where III = 0 for V-T/R and nt = 1 for V-V energy transfer. At temperatures, where this power law is followed for the most contributing energies, analytical rate constants may be obtained. Thus, when eqs. (9), (IO) and (IS) are inserted into eq. (7) together with the substitution s = Us,-/AE_ we obtain for the exoergic direction 1~-+ II’ ky::,“,.= (SkTj~~l)“‘(T,!T)‘(AE~~) x exp (AEjXT)n(AEjB)“I,

(19)

where I is the integral

Table 4

The semi&ssicJ

cross sections are fitted to cz = ~r(tJs,-/B)~_ The statisticA

uncertainty

on the semiclassical

cross sections is

about 30 7; (s.d.). The unit of G is A’ and of AE cm- '

DFW t DF(0) + DFtrt - 1) + DF(0)

-

DF(n) t

DF(0) -+ DF(u - 1) + DF(I)

7

6

A.&,,

i’

B

ALi,

2.16 2.57 2.45

356 658 584

1828

1

5.53

2

5.45

2875 2725

3

5.30

2535

4

5.15

2370

-2906.8 -2815.4 - 2724.0 -2632.6

5 6

4.84 4.72

2080 1970

- 2541.2 - 2449.7

2.36 2.41

531 581

274.3 365.7 457.1

7

4.47

1730

-2358.3

2.63

so1

548.1

91.4

L.L. Podsen,

s m

I=

dx[l

- (16x’)-‘]

l/4 x

exp { - [xAE/kT + AE/(16kTx)]}xy.

(20)

This integral can be evaluated analytically when the lower limit is approximated with 0 [25]. Using also WI K,_,(z)- K,+,(z)= ZK,(z)/z

(21)

we obtain keX’”. = (SkT/~n)“‘(Ta/7)~ n-n

(79)

where K, is thr modified Bessel function. Table 4 gives the values obtained when eq. (18) is titted to the cross sections calculated in the range Us, = 200-25000 cm- I. The resulting analytical V-T/R rate constants are shown as fi!led circles in fig. 2. The analytical V-V i-ate constants are not shown because they can hardly be distinguished from the plots in tig. 3, the deviation being at most IO:/, and generally much smaller. Table 4 demonstrates a systematic variation in y and 5 which is difticult to realize from figs. 2 and 3. A large AE implies large values of y and B. The apparent deviation from this tendency for the V-V processes is not significant but due to the fact, that the increase in y is small when going from tr = 1 to 11= 7, while the statistical uncertainty on the calculated cross sections is about 30 T{ (s.d.). This systematic variation may be expressed in the following way for the single quantum V-T/R energy transfers (eq. (13)) =

for level n. The rate constants obtained with eqs. (24) and (25) for all levels n = l-7 differ insignificantly from the values obtained when using B and y from table 4, where the cross sections for each level were fitted individually_ The variation in 7 with n is not so systematic for the V-V energy transfer, see table 4. It is, therefore, more diflicult to construct a general expression, which gives the rate constants for all levels. The best result we have been able to obtain is g”no-n- I.1 = A(Us&D’H~Em,

exp (AE/ZkT)

x rra~(AE/4B~~,(AE/2kT),

G”Cl-“- 1.0

293

G.D. Billing/Vibrational deadcation of DF

DnAE,‘(LI,CF/AE~)4”“G,

(23)

(26)

where A = 24.75, C = 1!86.2, D = 2.068 and H = 0.00103. These values give G in A’ when Us, and C are inserted in cm-‘. Furthermore AE, = 1~~~~~1 = IE, + E, - E,_,

- E,I.

When the cross sections follow eq. (26), the rate constant may be calculated from eq. (22) using y,, = D + HAE,,

(27)

B, = C(,Z/A)‘~“.

(28)

The rate constants obiained using eqs. (27) and (28) are in very good agreement with the curves shown in fig. 3 for II = 2,4 and 7. The systematic variation forced upon the result by eq. (26) places the rate constants for II = 3,5 and 6 between the others, i.e. the rate constants increase monotonically in the order II = 2-7 above 1200 K, while they decrease in the same order below 1200 K. 5. Rotational relaxation of HF and DF The rotational relaxation time rro, is according to the Wang Chang-Uhlenbeck theory [27] related to the second moment of the change in rotational energy [28,29]: ou

where D = 9486, F = 2328.1, G = 519.81, and

4BWe-P”

AE, = [AErib] = E,, - E,_,,

(AEfJ,

(29)

0 where E,, is the vibrational energy of DF(n). These values give G in A’ when AE,, and Us, are inserted in cm- ‘_ When the cross sections follow eq. (23), the rate constants may be calculated from eq. (22) using Y, = ALG

(24)

B, = (AEJD)G“=EnAE;/F,

(25)

where II is the number density, k Boltzmann’s constant, tint the internal heat capacity, ~71the mass of HF(DF) and = [rcR6/nf rIa(ctT)‘]

L.L. Pordsm, G.D. Billing/

294

Here N is the number of trajectories at a given energy U and AE,,, = E;,, , c E&, 2 - E,,, , - E,,, z _ The rotational collision number Z,,, is defined by

c301 where oL, and cU are the Lennard-Jones parameters for HF(DF) [6]_ The Q*(“.” integrals are taken from the tables in reT. [31]_ The second moment was determined at eight energies in the energy range 250 cm-’ to 4000 cm-’ using about 1200 trajectories. The rotational collision numbers were obtained with an accuracy of about 5 yO.The numbers are shown-in table 5 at temperatures between 150 and 500 K. We notice that the temperature dependence is small and that a slight minimum is predicted around 3-400 K. Experimental information is hardly available but a completely different theoretical calculation gave results which for HF are close to the present findings [28]. The Z,,, for DF was in ret [2S] found to be around 1.5 but this value is probably foe low and the small number might as mentioned in ref. [28] be due to uncertainties in the experimental value for the thermal conductivity used in ref. [2S]. The values found here show very littie isotopic dependence which is consistent with previous tindings for HCI(DC1) in :ef. [zS] and the high temperature results for HJD,) in rel. [29]_ 6. Comparison with other calculations Wilkins has recently published two classical trajectory studies of the deactivation in HF [32] and DF [33]_ His rcjults differ from ours in several respects.

Table 5 Rotational collision numbers for HF and DF as a hnction of tcmpatturc T(K)

-UHF)

L&W

I50 YJJ 3al 350 Jo0 450 500 .___

5.1 4.9 4.6 4.7 1.9 5.5 5.4

4.4 4.5 4.4 4.3 4.3 4.5 4.3

Vibmrioml

deucrication

of

DF

(1) Contrary to our calculations, Wilkins sees no formation of collision complexes. The main reason for this difference is probably that the well depth of his potential is 2.6 kcal compared with our 6.9 kcal (see section 1). (2) Although we lind the most eflicient energy

transfer in collision complexes, Wilkins obtains much iarger V-T/R rate constants for An = - 1 in HF (comparison can only be made with Wilkins’ rotationally Boltzmann averaged rate constants). (3) His Boltzmann averaged V-T/R rate constants for AU = - 1 decrease with II, while ours increase as a result of decreasing energy mismatch and increasing quantum number (matrix element), see tig. 2. (4) Wilkins finds large rate constants for multiquantum V-T/R energy transfer in both DF and HF. We found about 90% An = - 1 deexcitation. Our result agrees with recent experiments by Douglas and Moore [34] who found, that when HF(4) is deactivated by HF. 95 + 15 y: of the deactivated molecules appear as HF(3). Wilkins and Kwok have obtained very good agreement with the experimental rate constants for the deactivaticn of HF( 1) by HF by assuming a nonequilibrium rotational population [35]. Shin has published an analytical method for the calculation of the rate constants for vibrational deexcitation of HF(I) by HF and of DF(1) by DF [36]_ Being analytical, this method must necessarily simplify both the interaction and the trajectories. The resulting rate constants agree quite well with experiments at high temperature, but the inverse temperature dependence at low temperature is much too steep rl4]. Bott has modilied Shin’s model using a different-effect of the attractive potential [37]. By adjusting the potential parameters, Bott has obtained good agreement with experiments at 300 K and above 1400 K1 but the rate constant is half of the experimental value at 600 K [14]. Shin has later [3S] obtained a better agreement with the experiments using an entirely different model at low temperature. Shin [39] has calculated the V-V rate constants for DF(tl) i- DF(0) + DF(n - 1) i DF(1) with II = 2-5. His results look very different from fig. 3 in the present work. He found, that the rate constants have a sharp minimum around 350 K for )I = 3-5. All rate conslants, n = 2-5, have a steep inverse

L.L. Podsen,

G.D. Billit~g/Vibrarionul

temperature dependence below 350 K. The rate constants increase monotonically with II at all temperatures, i.e. he does not find the dominating effect of the endoergic energy mismatch, which makes 70 -t 61 the slowest at 300 K in fig. 3 in the .present work. Berend and Thommasson [40] have performed a two-dimensional classical trajectory study of the deactivation of DF(1) by DF and of HF(l) by HF. This work has been thoroughly discussed by Hinchen [ 143. The most serious assumption in the present work is probably not a part of the calculation procedure. It is a lack of knowledge about how the potential varies with the lengths of the oscillators, because all the SCF points on the potential surface were calculated for equilibrium bond lengths in both diatomic molecules. The best method of extrapolation to other bond lengths was to use a dumbbell expression in the analytic fit to the SCF points [I].

dtwcriuation of DF

[S] T.R. Dyke, B.J. Howard and W. Klemperer, J. Chem. Phys. 56 (I 972) 2442. [9] L.A. Melton and R.G. Gordon, J. Chem. Phys. 51 (1969) 5449. [IO] R.A. Lucht and T.A. Cool, J. &hem. Phys. 63 (1975) 3962. [I 1] J.F. Bott and N. Cohen, J. Chem. Phys. 59 (1973) 447. [12] J.F. Bott, Chem. Phys. Letters 23 (1973) 335. [13] K. Ernst. R.M.Osaood and A. Javan. Chem. Phvs. Letters 23 (1973) 553. J.J. Hinchen, J. Chem. Phys. 59 (1973) 233; 2224. J.F. Bott and N. Cohen, J. Chem. Phys. 5S (1973) 934. J.A. Blauer, WC. Solomon and T.W.-Owens, Intern. J. Chem. Kinetics 4 (1972) 293. J.F. Bott and N. Cohen, J. Chem. Phys. 58 (1973) 4539. J.R. Airey and J.W.M. Smith, J. Chem. Phys. 57 (1972) 1669; P.R. Poole and I.W.M. Smith, J.C.S. Faraday II 73 (1977) 1434. r191 M.A. Kwok and R.L. Wilkins, J. Chem. Phys. 63 (1975) 2453. [20] J.F. Bott, J. Chem. Phys. 61 (1974) 3414, references therein. G. Heraberg, Spectra of diatomic molecules, 2nd Ed. PI (Van Nostrand,

Acknowledgement This work was supported Science Research Council.

by the Danish Natural

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