Vibrational Energy Transfer in Ozone Excited to the (101) State

J. Phys. Chem. 1996, 100, 15015-15020

15015

ARTICLES Vibrational Energy Transfer in Ozone Excited to the (101) State: Double-Resonance Measurements and Semiclassical Calculations in the 200-300 K Temperature Range F. Menard-Bourcin,* C. Boursier, L. Doyennette, and J. Menard Laboratoire de Physique Mole´ culaire et Applications,1 CNRS, UniVersite´ Pierre et Marie Curie, Tour 13, Bte 76, 4 Place Jussieu, 75252 Paris Cedex 05, France ReceiVed: May 1, 1996; In Final Form: June 26, 1996X

The relaxation of ozone excited into the (101) vibrational state is studied in O3-O2 and O3-N2 gas mixtures over the 200-300 K temperature range using a laser double-resonance (DR) technique. Rate coefficients for V-V transfer processes occurring in O3-O3 collisions are experimentally determined and theoretically calculated. The temperature exponent n obtained by fitting the calculated values with a law of the form k(T) ) k(T0)(T0/T)n is in very good agreement with the experimental values. To model the vibrational energy deactivation processes occurring upon O3-foreign gas collisions, the rate coefficients for levels higher than the first dyad are deduced from the rate coefficients for the lowest states using simple scaling. The simulated DR signals obtained by a kinetic model using these values are in good agreement with the corresponding experimental DR signals over the entire temperature range.

I. Introduction In recent years, we have carried out a series of experiments on vibrational energy transfer in ozone. The collisional relaxation of O3 following excitation into the (100) or (001) state was studied first.1-6 The vibrational deexcitation and energy transfer processes between the lower vibrational states in the 200-300 K temperature range, in O3-O2 and O3-N2 mixtures, were investigated by means of a time-resolved doubleresonance (DR) technique using two CO2 lasers. These experiments yielded rate coefficients for the major relaxation processes occurring upon collisions with the main atmospheric constituents, in the temperature range of the upper atmosphere. Such measurements are of interest for modeling the atmospheric ozone concentration. Indeed, it is now well established that, in the upper atmosphere, the collisional processes are not efficient enough to allow complete relaxation, to local thermodynamic equilibrium, of ozone produced in excited vibrational states of the stretching modes. The major process producing the atmospheric ozone, the three-body recombination of atomic and molecular oxygen, is known to significantly populate vibrational states higher than the first dyad ((001) and (100) states).7 In order to determine the rate coefficients for the transfer processes that arise in higher vibrational states and to see how they relate to those of the lower states, we extended our investigations to processes involving vibrational states up to the {(200), (101), (002)} triad by laser-exciting O3 molecules in the (101) state with the frequency-doubled 9P8 CO2 laser line.8 These measurements, performed at room temperature, showed that, subsequent to pumping the (101) state, a fast equilibration of the populations of the triad occurs via Coriolis-assisted intermode transfers as is the case for the {(100), (001)} dyad. Subsequently, the near-resonant V-V transfer processes resulting from O3-O3 collisions tend to establish a quasi-steady vibrational distribution and the vibrational energy spills over * To whom correspondence should be addressed. Fax: 33 1 44 27 70 33. Email: [email protected]. 1 Laboratoire associe ´ aux Universite´s P. et M. Curie et Paris-Sud. X Abstract published in AdVance ACS Abstracts, August 15, 1996.

S0022-3654(96)01253-1 CCC: $12.00

through nonresonant intermode transfer to the bending mode (ν2) and vibrational deexcitation upon O3-foreign gas collisions. At the smallest O3 molar fraction attained in these experiments (0.5%), the near-resonant V-V transfer processes are still effective in populating the {(100), (001)} dyad levels, but the stretching to bending mode transfer occurring in O3-M collisions becomes the major process in populating the states of the {(110), (011)} dyad. From comparisons of the experimental DR signals to kinetic model simulation the room temperature rate coefficients of these processes were deduced. The present work is devoted to the investigation of the same energy transfer processes over the 200-300 K temperature range. A review of the kinetic scheme for the vibrational relaxation of ozone mixed with O2 or N2 is first given in section II, and then a brief description of the experimental setup is given in section III. Section IV deals with the temperature dependence of the near-resonant V-V transfer. We present first the results of the double-resonance experiments and then results calculated using a theory based on long-range multipolar interaction. The processes involved in the vibrational energy deactivation of O3 in collision with O2 or N2 are investigated in section V, and the experimental DR signals are compared to simulations from a kinetic model. II. Kinetic Scheme Subsequent to the excitation of O3 molecules in the (101) state, a rapid equilibration of population occurs between the states (101) and (200) and the states (101) and (002) through very efficient Coriolis-assisted intermode transfer upon both O3-O3 and O3-O2/N2 collisions. Near-resonant V-V transfer processes tend to spread the vibrational energy among the states of the triad and those of the {(100), (001)} and {(110), (011)} dyads. Since these processes occur only through O3-O3 collisions, in gas mixtures with sufficiently small O3 molar fraction, the resulting transfer rates can be more than 1 order of magnitude smaller than the rates corresponding to Coriolis-assisted intermode transfers. Thus, the populations of the states in each polyad may be considered as permanently equilibrated with each other and the © 1996 American Chemical Society

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Menard-Bourcin et al.

near-resonant transfer processes can be represented by “global” processes involving polyads rather than individual states:

O3(001, 100) + O3(001, 100) a O3(002, 101, 200) + O3(000) (1) O3(001, 100) + O3(011, 110) a O3(002, 101, 200) + O3(010) (2) O3(010) + O3(001, 100) a O3(011, 110) + O3(000) (3) When the global approach cannot be used, as is the case for neat ozone, the detailed state-to-state processes have to be considered.8 For example, the main contribution to the global process 1 is due to the following detailed processes involving dipole-dipole interactions:

O3(100) + O3(001) a O3(101) + O3(000) + 34 cm-1 (1a) O3(001) + O3(001)a O3(002) + O3(000) + 26 cm-1

(1b)

Next, other less efficient processes allow the vibrational energy to spill over from the stretching modes to the bending mode:

O3(002, 101, 200) + M a O3(011, 110) + M

(4)

O3(011, 110) + M a O3(020) + M

(5)

O3(001, 100) + M a O3(010) + M

(6)

Figure 1. Diagram of ozone vibrational energy levels showing the pump (9P8*2) and probe (10R16, 10R18, and 9P20) transitions.

equations, DR signals can be calculated and compared to the observed signals for various experimental conditions. III. Experimental Section

Process 4 contributes to population of the states of the {(110), (011)} dyad from the states of the triad. In neat ozone, this contribution is negligible compared to that of the near-resonant process 1, but it is no longer the case in gas mixtures with very small ozone molar fraction, as shown by previous measurements at room temperature.8 In the upper atmosphere, where the ozone molar fraction is in the range 10-5 to 10-7, these processes certainly play a major part in the ozone relaxation. Finally, vibrational energy transfer to translation and rotation occurs via the following processes:

O3(011, 110) + M a O3(001, 100) + M

(7)

O3(020) + M a O3(010) + M

(8)

O3(010) + M a O3(000) + M

(9)

O3(002, 101, 200) + M a O3(001, 100) + M

(10)

O3(001, 100) + M a O3(000) + M

(11)

The experimental arrangement has been fully described in previous papers.4,8 Below we give only an overview of the experimental apparatus. Essentially, the O3 molecules are pumped into the (101) vibrational state with the frequencydoubled 9P8 line from a transverse pulsed CO2 laser. The probing beam is produced by a stable CW CO2 laser. The laser lines used as pump or probes are shown in Figure 1, representing the ozone vibrational energy levels. The pump and probe beams have a counterpropagating geometry in the sample cell. At the exit of the cell, the probe beam is reflected onto a AuGe detector, which detects the temporal variation of the transmitted CW beam intensity. The corresponding double-resonance signal is then sampled and averaged by a digitizing signal analyzer DSA601 from Tektronix. The measurements were performed in O3O2 and O3-N2 mixtures. The ozone is prepared in a HF discharge, and the gases are introduced into a variable temperature Pyrex cell cooled by flowing ethanol from a cryostat. IV. Near-Resonant V-V Transfers

The values of the rate coefficients for processes 3, 6, 9, and 11 have been previously determined in the 200-300 K temperature range.4,6 For the other processes, only the room temperature values of the rate coefficients were measured.8 Rate equations describing the temporal variations in populations of the vibrational states are obtained by taking into account processes 1-11. The laser excitation process is modeled by adding to the rate equations terms accounting for the increase of population in the triad and the corresponding decrease in the ground state. By numerical integration of this set of

(A) Experimental Results. The near-resonant V-V transfer process 1 has been studied by using the 10R16 CO2 laser line as a probe. Typical DR signals obtained by pumping the ozone molecules into the (101) state and by probing a (002) r (001) transition with the 10R16 CO2 laser line are shown in Figures 2 and 3. After an initial peak corresponding to the equilibration of the Coriolis-coupled states of the triad, the signals exhibit a fast decay in transmission as the triad levels are depleted and the dyad levels are populated. The DR signals observed in 0.5 Torr neat ozone at 220 and at 296 K are compared in Figure 2, and it can be seen that the process becomes faster as the temperature decreases. In gas mixtures with O2 or N2 added to 0.5 Torr O3, the decreasing part of the DR signals remains nearly unchanged, as can be seen by comparing the signal obtained in neat ozone (Figure 3a) to those observed with 5 Torr total pressure (parts b and c of Figure 3) at 200 K. It is clear that in these time ×

Energy Transfer in Ozone

J. Phys. Chem., Vol. 100, No. 37, 1996 15017

Figure 2. Double-resonance signals observed in 0.5 Torr neat ozone at 296 K (upper) and at 220 K (lower) by probing a (002) r (001) transition after excitation into the (101) state.

pressure conditions the most efficient process involves O3-O3 collisions. As expected, the initial peak is higher in parts b and c of Figure 3 because of the faster equilibration among the Coriolis-coupled levels, and the slow part of the signal that corresponds to the deexcitation from the first dyad through O3O3 and O3-O2/N2 collisions is slightly more rapid. When the foreign gas pressure is further increased, no significant change is observed in the initial peak, indicating that the Corioliscoupled states of the triad can be assumed to be equilibrated during the pumping pulse. Such measurements have been performed at 200, 220, 240, and 270 K in O3-O2 and O3-N2 mixtures with O3 molar fraction ranging from 0.1 to 0.01, and from each DR signal a decay rate was deduced. In order to determine the values of the rate coefficient for process 1 from the experimental signals, we have calculated DR signals corresponding to the various experimental conditions by numerically solving the set of differential equations describing the temporal variations in populations of the considered states. For mixtures with 10% or less O3 molar fraction, the Coriolis-coupled states are assumed to be equilibrated; it is then possible to treat the system with the global approach as described in section II. The rate coefficients introduced in these calculations are varied, and the decay rates are determined in a way similar to that for the experimental signals. As expected, the decay rate is essentially dependent on the rate coefficient of process 1, which is then well determined by comparing experimental and calculated results. Calculated DR signals obtained with such values are in quite good agreement with the experimental ones, as shown in parts b and c of Figure 3 for T ) 200 K. In Figure 3a, corresponding to neat ozone, the solid line is the DR signal computed by taking into account the detailed processes. The rate coefficients of the Coriolis-assisted intermode transfers are taken to be equal to that measured for the

Figure 3. Double-resonance signals obtained at 200 K by probing a (002) r (001) transition after excitation into the (101) state for (a) 0.5 Torr neat ozone, (b) a mixture of 0.5 Torr ozone with 4.5 Torr oxygen, and (c) a mixture of 0.5 Torr ozone with 4.5 Torr nitrogen. The experimental DR signals are compared to the simulated ones obtained with (D) the detailed kinetic model or (G) the global kinetic model.

(100) T (001) transfer, and for the detailed near-resonant transfers, the rate coefficients are deduced from the global ones by assuming that they are related to each other as the ratio of the squares of transition dipole moments. In parts b and c of Figure 3, the DR signals computed in the same way are compared to those obtained with the global approach, thus attesting that the assumption of a permanent equilibrium among the Coriolis-coupled states is justified for such an ozone molar fraction. The temperature dependence obtained for the rate coefficient of process 1, in the 200-300 K temperature range, is shown in Figure 4. Another near-resonant process involving the triad levels occurs, namely process 2, but it only has a nonnegligible effect upon the populations of (011, 110). That means it can be observed only by probing the (012) r (011) transition with the 10R18 CO2 laser line, and it competes with the cumulative processes 1 and 3. It is then not possible to accurately determine the rate coefficient of process 2 and to obtain its temperature dependence, but by considering the similarity with process 3

15018 J. Phys. Chem., Vol. 100, No. 37, 1996

Menard-Bourcin et al. where V2′ is the vibrational ground state (000) and F(VJτ) is the Boltzmann state density normalized to unity for the rovibrational level |VJτ〉 of the dyad. The Coriolis interaction has been taken into account in the calculation of the D(1)(VJτ, V′J′τ′) provided by Flaud and Camy-Peyret.11 For example, the D(1)(V1J1τ1, V1′J1′τ1′) are related to the transition dipole moments by

D(1)(V1J1τ1, V1′J1′τ1′) ) 1

(-1)q〈Vi|M1q|Vf〉∑CVV KJ τ CVV′K′J′ τ′ C(J11J1′, KqK′) ∑ ∑ q)-1 V ∈D KK′ 1 1 1

i

1 1 1

f

i

Vf∈T

with

|V1J1τ1〉 )

CVV KJ τ |ViJK〉 ∑ V ∈D 1 1 1

i

i

K

Figure 4. Calculated and experimental values of the rate coefficient of process 1 are plotted vs temperature. The solid lines are the fits obtained by a law of the form k(T) ) k(300) × (300/T)n with n ) 1.33.

that has been studied previously,6 we can assume the same temperature dependence. (B) Theoretical Results. It is now well-known that nearresonant V-V energy transfer can be accounted for on the basis of long-range multipolar interactions between the colliding molecules, at least at low temperature. In order to calculate the rate coefficient of process 1, we have used a semiclassical model based upon dipole-dipole interactions. The method is similar to that described in ref 6 and will be only briefly presented. For the sake of clarity, the {(100), (001)} dyad and the triad will be denoted D and T, respectively. The rate coefficient of the direct process 1 is given by

k(1) ) Vj∫R

∞ min

2πrc(Vc′/Vj)2P(rc) drc

V. Nonresonant Intermode Transfers and Deactivation

where Vj is the average velocity, rc the distance of closest approach, and Vc′ the equivalent straight trajectory velocity. Rmin is the value of rc for head-on collisions. Vc′ is a function of rc and is calculated following the Robert and Bonamy formalism9 from the parameters σ and  of the isotropic 6-12 LennardJones interaction potential. The Lennard-Jones parameters as well as the molecular parameters are taken from ref 10. P(rc), giving the probability of transfer for a given distance of closest approach rc, is obtained by averaging the elementary probability over the initial rovibrational levels of the dyad and summing over the final levels of the triad and of the ground state:

P(rc) )

8

∑

9(pVc′rc2)2 V1J1τ1∈D

F(V1J1τ1)F(V2J2τ2)

V2J2τ2∈D

|D(1)(V1J1τ1, V1′J1′τ1′)|2 ×

Mlq is the qth component of the dipole moment operator and C(J1J′, KqK′) is a Clebsch-Gordan coefficient. Finally, f1(x), with x ) ∆Erc/(pVc′), is a resonance function,12 and the factor exp(∆E/(2kBT)), ∆E being the elementary energy gap, is artificially introduced in order to be consistent with detailed balancing. The rate coefficient k(1) has been calculated at different temperatures by taking into account, for each (100) and (001) vibrational state, the rotational levels having a population higher than 10% of the most populated level. The calculated values are plotted vs temperature in Figure 4 along with the experimental values. The calculated values are lower than the experimental ones, which is not very surprising, since the interaction potential is limited by lack of data to the dipoledipole term as it was outlined in ref 6. However, the experimental temperature dependence is very well reproduced by the calculations. Indeed, in Figure 4 where the calculated values have been fitted by a law of the form k(T) ) k(300) × (300/T)n, leading to a temperature exponent n of 1.33, the fit of the experimental values obtained with the same temperature exponent shows good prediction of the temperature dependence. These fits yield k(T) ) 370(300/T)1.33 ms-1 Torr-1 for the calculated values and k(T) ) 690(300/T)1.33 ms-1 Torr-1 for the experimental values.

∑

V1′J1′τ1′∈T J2′τ2′

( )

|D(1)(V2J2τ2, V2′J2′τ2′)|2f1(x) exp

∆E

2kBT

The nonresonant intermode transfers 4-6 and the V-T/R deexcitation processes 7-11 that involve O3-N2/O2 collisions arise in mixtures with small O3 molar fractions. It was shown from our previous measurements at room temperature8 that the dominant channel for depleting the triad states through O3foreign gas collisions is the transfer from the triad to the {(011), (110)} dyad involving the change of a ν1 or ν3 stretching quantum into a ν2 bending quantum (process 4). This dyad is then depleted by either another stretching to bending mode transfer (process 5) or the loss of a ν2 quantum (process 7). These processes particularly affect the (011) and (110) levels and are best observed on DR signals obtained by probing the (012) r (011) transition with the 10R18 CO2 laser line. Measurements were performed with O3 molar fractions down to 0.005, at various temperatures, by probing not only the (012) r (011) but also the (002) r (001) transitions with the 10R16 laser line and the (011) r (010) transition with the 9P20 laser line. Experimental DR signals obtained with the (012) r (011) probe transition in O3-O2 and O3-N2 mixtures at 200 K are shown in Figure 5 for 0.1 Torr O3 in 20 Torr total pressure. At this low O3 molar fraction the O3-O3 collisions are still

Energy Transfer in Ozone

Figure 5. Double-resonance signals obtained at 200 K by probing a (012) r (011) transition in O3-O2 and O3-N2 mixtures with 0.1 Torr ozone for 20 Torr total pressure.

competing with the investigated O3-foreign gas collisions to populate and deplete the {(100), (001)} dyad. Several processes play a large part, particularly the very efficient near-resonant V-V transfer 1 coupled to process 3. It is worth noting that as the temperature decreases, the near-resonant V-V transfer probabilities increase as shown above whereas the nonresonant intermode transfer anddeexcitation probabilities decrease. Thus, it is necessary to consider all the processes to account for the observed time evolution of the population for each state, and it is essential to observe the evolution of all the states. DR signals obtained by probing the other transitions in O3-O2 mixtures at the same pressures and the same temperature as in Figure 5 are shown in Figure 6. It can be seen that as the (011) population decreases, resulting in the rising part of the signals in Figure 5, the signals in Figure 6 are still decaying, showing that the (001) and (010) populations are increasing. TABLE 1: Processes Taken into Account in the Kinetic Model

O3-O3 Collisions (1) O3(001, 100) + O3(001, 100) a O3(002, 101, 200) + O3(000) (2) O3(001, 100) + O3(011, 110) a O3(002, 101, 200) + O3(010) (3) O3(010) + O3(001, 100) a O3(011, 110) + O3(000)

O3-M Collisions (4) O3(002, 101, 200) + M a O3(011, 110) + M (5) O3(011, 110) + M a O3(020) + M (6) O3(001, 100) + M a O3(010) + M (7) O3(011, 110) + M a O3(001, 100) + M (8) O3(020) + M a O3(010) + M (9) O3(010) + M a O3(000) + M (10) O3(002, 101, 200) + M a O3(001, 100) + M (11) O3(001, 100) + M a O3(000) + M

J. Phys. Chem., Vol. 100, No. 37, 1996 15019

Figure 6. Double-resonance signals obtained at 200 K in a O3-O2 mixture with 0.1 Torr ozone for 20 Torr total pressure by probing a (002) r (001) transition (upper signal) or a (011) r (010) transition.

In order to estimate the efficiency of the processes involving O3-foreign gas collisions, all the experimental DR signals were compared to the signals simulated by means of the numerical model, taking into account all the processes indicated in Table 1, as in the work at room temperature.8 The values of the rate coefficients relevant to the lowest levels have been determined in ref 4 for each temperature. The rate coefficients for vibrational energy deexcitation processes concerning levels higher than the first dyad are assumed to be related to the rate coefficients for the lowest states in the following way. For processes 4 and 5 involving a transfer from stretching to bending mode, the rate coefficients are related to the rate coefficient kD2 of process 6 by the expression

k(Vs, V2 f Vs - 1, V2 + 1) ) Vs(V2 + 1)kD2 For processes 7 and 8 involving the loss of a bending quantum, the rate coefficients are related to the rate coefficient k2 of process 9 by

k(Vs, V2 f Vs, V2 - 1) ) V2k2 and for process 10 involving the loss of a stretching quantum, the rate coefficient is related to the rate coefficient kD of process 11 by

k(Vs, V2 f Vs - 1, V2) ) VskD where V2 is the number of bending quanta (ν2) and Vs is the number of stretching quanta (Vs ) V1 + V3). These relations have proven to yield the best results at room temperature.8 In the present work, we took the values of kD2

15020 J. Phys. Chem., Vol. 100, No. 37, 1996 and k2 from the following expressions as given in ref 4

kDN22 ) 1.2T-1/2 exp (-26.8/T1/3) µs-1 Torr-1 kDO22 ) 0.5T-1/2 exp (-22.8/T1/3) µs-1 Torr-1 kN2 2 ) 7T-1/2 exp (-40/T1/3) µs-1 Torr-1 kO2 2 ) 60T-1/2 exp (-53.8/T1/3) µs-1 Torr-1 As can be seen in Figures 3, 5, and 6, the kinetic scheme and these simple formulas lead to results in very good agreement with the experimental signals, and that is true for all the probe transitions used, as well as for all the investigated mixtures and temperatures. VI. Conclusion The very efficient near-resonant transfer process that occurs upon O3-O3 collisions

O3(001, 100) + O3(001, 100) a O3(002, 101, 200) + O3(000) has been investigated from double-resonance measurements by laser-exciting the states of the {(200), (101), (002)} triad. The temperature dependence of its rate coefficient has been found to be in good agreement with the dependence calculated by using a theory based on long-range dipolar interaction in the 200300 K temperature range. We have also investigated the processes involved in the vibrational energy deexcitation of ozone in collision with O2 or N2, namely the energy transfers from stretching to bending mode and vibrational deactivation with energy transfer to translation and rotation. At small molar fraction these processes compete with near-resonant processes to relax the gas. Thus, the knowledge of the near-resonant transfer rate coefficients is essential for deducing the rate coefficients of vibrational

Menard-Bourcin et al. relaxation through O3-O2/N2 collisions from laboratory measurements, particularly at low temperature. Finally, we have verified that in the 200-300 K temperature range, the rate coefficients of the processes involving the states of the triad and the second dyad can be deduced from those of the corresponding processes involving the lowest states by simple relations established in the case of harmonic vibration. These results should be useful in atmospheric physics, bringing a simplification in the modeling of the atmospheric ozone altitude profile. References and Notes (1) Me´nard-Bourcin, F.; Doyennette, L.; Me´nard, J. J. Chem. Phys. 1990, 92, 4212. (2) Doyennette, L.; Me´nard, J.; Me´nard-Bourcin, F. Chem. Phys. Lett. 1990, 170, 197. (3) Me´nard-Bourcin, F.; Me´nard, J.; Doyennette, L. J. Chem. Phys. 1991, 94, 1875. (4) Me´nard, J.; Doyennette, L.; Me´nard-Bourcin, F. J. Chem. Phys. 1992, 96, 5773. (5) Doyennette, L.; Boursier, C.; Me´nard, J.; Me´nard-Bourcin, F. Chem. Phys. Lett. 1992, 197, 157. (6) Boursier, C.; Me´nard-Bourcin, F.; Me´nard, J.; Doyennette, L. J. Chem. Phys. 1993, 99, 5905. (7) Rawlins, W. T.; Caledonia, G. E.; Kennealy, J. P. J. Geophys. Res. 1981, 86, 5247. (8) Me´nard-Bourcin, F.; Doyennette, L.; Me´nard, J. J. Chem. Phys. 1994, 101, 8636. (9) Bonamy, J.; Bonamy, L.; Robert, D. J. Chem. Phys. 1977, 67, 4441. (10) Bouazza, S.; Barbe, A.; Plateaux, J.-J.; Rosenmann, L.; Hartmann, J.-M.; Camy-Peyret, C.; Flaud, J.-M.; Gamache, R. R. J. Mol. Spectrosc. 1993, 157, 271. (11) Flaud, J.-M.; Camy-Peyret, C.; Rinsland, C. P.; Smith, M. A. H.; Malathy Devi, V. Atlas of Ozone Spectral Parameters From MicrowaVe to Medium Infrared; Academic: New York, 1990. Flaud, J.-M.; Camy-Peyret, C. Private communication. (12) Messer, J. K.; Khoobehi, B.; Roberts, J. A. J. Chem. Phys. 1982, 76, 2914.

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