J. Phys. Chem.
3518
1982,86,3518-3521
Calculation of SF,-/SF, and CI-/CFC13 Electron Attachment Cross Sections in the Energy Range 0-100 meV Ara Chutjlan Jet Propulsion Laboratory, California Institute of Technobgy,Pasadena, California 9 I109 (Received: January 22, 1982; I n Final Form: March 11, 1982)
Electron attachment cross sections for the processes SF{/SF6 and C1-/CFC13 are calculated in a local theory using a model in which diatomic-likepotential energy curves for the normal modes are constructed from available spectroscopic data. Thermally populated vibrational and rotational levels are included. Good agreement is found with experimental cross sections in the energy range 5-100 meV for a particular choice of potential energy curve parameters.
consistent with such an onset. Introduction Recent experiments using the technique of threshold Theoretical Considerations photoelectron spectroscopy by electron attachment In order to treat the complex SF6 and CFC13molecules, (TPSA) have provided, a t high electron energy resolution, a model was chosen in which each normal mode was new information on the shapes' and magnitudes2 of electreated independently, and a separate harmonic, diatomic tron attachment resonances which are located at essentially potential energy curve constructed for each mode. This zero electron energy. These data have provided an indiatomic approximation is probably satisfactory in the teresting tie-in with collisional ionization cross s e ~ t i o n s , ~ ? ~sense than only very low vibrational levels of the neutral swarm-unfolded cross s e ~ t i o n sand , ~ beam-gas cross sectarget are involved in the thermal attachment process. tiom6 Thus, the vibrational modes will be very nearly harmonic In the present work we attempt to calculate the observed and independent, and there will be little "cross-talk" becross sections in terms of a local electron attachment tween modes arising from anharmonic coupling. Naturally, theory derived by O'Malley.'t8 The goal is to account for the model does not consider the multidimensional nature the shapes and magnitudes of the experiments in terms of the neutral and ionic surfaces and their crossings. of potential energy curves for the neutral target and its Potential energy curves for the bound states SF6(X1Au), negative ion, and their point of crossing. Qualitative poSF((X2Alg), and CFC13(X1A1)were taken as Lennardtential energy curves have been sketched by various Jones 6-12 potentials, with parameters set either by known workers, configuration-interaction calculations of CFC13 spectroscopic and thermodynamic data on these molecules and CFC13- states have been carried out by Peyerimhoff or by the present calculations (see Table I). The and Buenker? and SCF calculations of SF6and SF, states CFC1 R,. In practice, it was found that values of p(t) calculated for appropriate r,(R) and v(R) in eq 2 were of the order SlO"', so that the exp[-p(c)] survival probability in eq 1 was taken as unity for all uw,J. To take into account the thermal population of uw,J levels at 300 K (temperature at which experimental data were reported), one must calculate the fraction of molecules in each state of the system and then sum over all "significantly populated" states. A particular state S consists of the set of excitations of one or more of the normal modes w, with u quanta of excitation in each mode. If we denote the Boltzmann population of each state by' the fraction fuw,J,then the cross section for each state S may be written as
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+
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a U
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and the final cross section at energy t as
In practice, it became unwieldy to carry the sum in eq 3b over all populated states of the system. Rather, the 11 most populated states in SF6and 15 in CFC1, were chosen, accounting for 80% of the vibrational partition function for each molecule at 300 K. (This increased to 100% for calculations at 100 K.) For example, the highest vibrational excitations involved were 3we in SF6 and 4w6 in CFC1, at 300 K. Also, CFC13 was treated as a spherical top for purposes of calculating the rotational partition
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Flgure 1. Rotational population In SFBat temperatures of 100 (top) and 300 K (bottom). Vertical bars indicate the sampllng Intervals in J used in the calculation.
function. The rotational B values used were 1.101 X (SF,) and 9.919 X lo* eV (CFCl,)." Because of the very high S s involved, a sampling of the rotational distribution was taken, as shown in Figure 1. The cross section uA"J(t) at 300 K was calculated in groups of 20 S s , from J = 0 to 140. This was reduced to 10 S s from J = 0 to 80 at 100 K. The sampling took into account 100% of the rotational partition functions. Halving the group size had less than a 1% effect on the final cross section. A summary of the spectroscopic data used in the calculation is given in Table I and ref 11 and 12. (11)(a) Vibrational frequencies for SF8 were the average of data reported by: R. S.McDowell, J. P. Aldridge, and R. F. Holland, J. Phys. Chem., 80, 1203 (1976);W.V. F. Brooke, M. Eshaque, C. Lau, and J. Parsmore, Can. J. Chem.,54,817(1976);G. Henberg, "ElectronicSpectra and Electronic Structure of Polyatomic Molecules", Van Nostrand, Princeton, NJ, 1967, p 644. Vibrational frequenciea in CFC13were taken from S. T. King, J. Chem. Phys., 49,1321 (1968). The rotational B value of SF8 was taken from V. C. Ewing and L. E. Sutton, Tram. Faraday Soc., 59,1241 (1963)(see also McDowell et al.,referencedabove), and that in CFC&from M. W. Long, Q. Williams, and T. L. Weatherly, J.Chem. Phys., 33,508(1960).(b) The equilibrium S-F internuclear distance in SF6is from Ewing and Sutton (reference above) and the C-Cl distance in CFC13 from R. B. Bernstain, J. P. Zietlow, and F. C. Cleveland, J. Chem. Phys., 21, 1778 (1953). The electron affinity for SFBia from C. Lifshitz, T. 0. Tiernan, and B. M. Hughes, J. Chem. Phys., 59, 3182 (1973)and for C1 from H. Hotop and W. C. Lineberger, J. Phys. Chem. Ref. Data, 4,639(1975). The diaeociation energy of CFC13ia from ref 12. (12)E. Illenberger, Chem. Phys. Lett., 80,153(1980);E. Illenberger, H.-U. Scheunemann, and H. Baumgirtl, Chem. Phys., 37,21(1979);R. Foon and K. B. Tait, J. Chem. Soc., Faraday Tram. 1 , 6 8 , 104 (1972).
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Chutjian
The Journal of Physical Chemistry, Vol. 86, No. 18, 1982 I
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Figure 2. Experimental and theoretical electron attachment cross sections for the process SF,-/SF,. The solid line within the shaded area represents TPSA results of ref 2, open circles (0)represent swarm unfolded data of ref 5, and solid squares (W) represent collisional ionization cross sections derived from ref 4. The heavy soli line (-) and the long-short dashed line (---) are results of the calculation at temperaturesof 300 and 100 K, respectively. The s-wave capture cross section (d2) is given by the short dashed (- - -) line, and resolution of the TPSA experiments’ is shown.
Results and Discussion A large range of values of the SF6equilibrium internuclear distance R*, n,and Fa0 was varied in SF6and CFC13. In addition, for CFC13 the dissociation energy DeCFc13and the exponential factor x in the R“ repulsive state for CFC1, were varied. Results of these variations are, for SF6 R* = 1.7122 f 0.0005 A n = 2.0 f 0.5 F: = 3.08 X eV
and for CFC1, DeCFC13 = 3.02 x = 25 f 1
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0.05 eV R, = 1.7625 f 0.0005 A n = 3.0 f 0.5 I?: = 0.210 eV
The degeneracy factor g in eq 1was taken to be the spin degeneracy,8and it was g = 2 for both molecules. The errors above represent the sensitivity of the overall fit to the individual parameters rather than to any absolute errors. For example, if better spectroscopic data such as dissociation energy, equilibrium internuclear distance, or electron affinity should become available, then the calculated parameters above would readjust to give comparable or better agreement with experiment. With the present set of data, calculated results were found to be quite sensitive to the equilibrium internuclear distance of SF6-, or to the CFC13- curve’s point of crossing with the neutral state. The equilibrium internuclear distance R* for SF6from this calculation (1.7122 A) was found to be gratifyingly close to results in an SCF calculation of Haylo (1.710 A). The dissociation energy of CFC1, is within errors of several experimental results.12 From the relationship n = I + 1/2,one has over the energy range 0-100 meV an average value of angular momentum of 1.5 and 2.5 for SF6 and CFCl,, respectively. In general, it was found from the fitting procedure that the higher n tended to raise the high-energy part of the attachment cross section ( E 2 50 meV), while leaving the region E < 50 meV unaffected in
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Figure 3. Experimental and theoretical electron attachment cross sections for the process CI-XFCI,. Identification of curves and data is the same as in Figure 2.
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shape. The average n is a compromise between the limit E 0 where (by the symmetry of the states involved) the cross section should be s-wave, and E 2 50 meV where apparently waves higher than s-wave are already contributing to the attachment. Results of the calculation for SF6-/SF6and C1-/CFC13 are shown in Figures 2 and 3, respectively, at temperatures of 300 and 100 K. The corresponding potential energy curves for u = 0, J = 0 are given in Figure 4, with the experimental and calculated parameters given in Table I. (In regard to the experimentalresults of Figure 3, we point out that the data of ref 2 were multiplied by a factor 20.1 to take into account the correct value of the thermal electron attachment rate I Z ( ( E ) ) against which the line shapes were normalized to an absolute cross section.13J4 The previously used value reported by McCorkle et al.5 was incorrect.) One notes that ~ A ( Edecreases ) with decreasing temperature because of the “freezing out” of excited vibrational states into regions of R correspondingto smaller widths Fa(R). Such temperature effects have been noted for CFC13 by Wentworth et al.15 The gentle undulation between 10 and 70 meV in the calculation is a result of the energy dependence in the product c-lFa(R) X vibrational overlap factor. The steady decrease in aA(e)with E is balanced by its increase with attachment width Fa@), and with overlap up to E 40 meV, after which both E and the overlap factor tend to decrease ~ A ( E ) . In each case the undulation can be essentially removed by a small reduction (-O.OOO5 A) in the crossing point. As noted in ref 1, there appears to be experimental evidence for such an undulation in the cross section (see Figure 2 of ref l), so that this effect in the calculation was allowed to remain. Of further interest is the extremely sharp rise in the cross section below 8 meV. This increase arises essentially from a playoff between the autoionization width and the e-1 energy dependence. From eq 1one has, in terms of the
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(13) A value of k ( ( ~ of ) ) 2.43 X cm3/s was used, as measured by D. L. McCorkle et al. (erratum in ref 5). (14) A. Chutjian, Phys. Rev. Lett., 48, 289 (1982) (erratum). (15) W. E. Wentworth, R. George, and H. Keith, J . Chem. Phys., 51, 1791 (1969).
The Journal of Physical Chemistty, Vol. 66,No. 16, 1962 3521
Electron Attachment Cross Sections 1.01
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W 4. LennardJOne~potential energy CUTV~Sfor SFe, SFe- (lower, CFCI,- (upper, b) corresponding to the calculated cross Sections In Figures 2 and 3, respecthrely. Curves are shown for no vlbratbn or rotation In the ground target states. LennardJones parameters are given in Table I. F
a) and CFCI,,
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strong energy-dependentfactors, uALwJ(e) c-lr,,"(R, - R,)". For e approaching zero, R, approaches R,. However, the first factor dominates, as R, is greater than R, even at zero energy by virtue of the fact that the crossing point R, lies below the lowest vibrational level in energy. Hence, the cross section increases with decreasing e, regardless of the power n. Experimentally there are three pieces of evidence which point to such a rise at threshold: (1)In our own work, a rise in the first 6 meV or so was noted in ref 2 in the sense that a twepiece exponential fit to the line shape of ref 1 fell below the data by -10% in the first 6 meV. This rise in the data would be consistent with a steep cross section folded into the 7-meV (fwhm) resolution in that experiment. However, in light of other experimental errors (grating calibration, assumption of photoionization line shapes, and stray fields) this could not be taken as conclusive evidence for a steep threshold. (2) Alp0 plotted in Figures 2 and 3 are results of collisional ionization experiments of West et ala3and Foltz et alS4These cross sections were obtained by dividing the reported collisional ionization rate constants by the average electron velocity in the Xe(n1) orbital. One sees a definite upward trend in the cross sections, with approximately a factor of 2-3 increase between 20 and 8 meV. (3) Reference has been made to results in which a sharp onset of width 3 meV or less was noted.16 The details of this experiment are un-
published, but the indirect reference lends some credibility to the present calculation which gives a width of less than 1.5 meV at onset. It would be desirable to confirm this sharp onset by measurements at higher resolution (-3meV fwhm). Such experiments are currently in progress in this laboratory. At energies greater than about 100 meV, the calculations fall below experimental data. Within the present local approximation factors which can raise the high-energy portion of the cross section are use of higher partial waves (larger n) and a steeper repulsive wall of the negative ion at smaller17 R. In view of the nature of the theoretical approximation, the diatomic-like model, and the loss of simplicity involved, these remedies were not explored further. The potential energy curves for SF,, CFCl,, and their negative ions are given in Figure 4 for u = 0 and J = 0. One should note that the parameters given in Table I were those actually used in the calculation to give the observed experimental peak in gA(e) at 0 eV. Because of the energy dependence in uA(e)arising from the factors 6-l X vibrational overlap factor X exp[-p(c)], the observed peak (0 eV) and the actual location of the negative-ion state in the Franck-Condon region are slightly displaced. This displacement A is given by the condition7 daA(c)/dt= 0, or A = (I'd2/8)[dp(e)/de + l / e ] . It is -0.15 eV for SF6 and CFC13. If greater accuracy in the curves is desired, the energy difference between the neutral and its negative ion in the relevant R region17should be increased by 0.15 eV. One way is, for example, to increase the dissociation energy of the neutral by this amount. For both SF, and CFCl,, this increase is again within the experimental error in the dissociation energy of each molecule. Also, the curves of Figure 4 differ from those of ref 9 (Figure 2) and 10 (Figure 1)for CFC13 and SF6,respectively. Results of these molecular-orbital calculations give both crossing points and Franckxondon (vertical) energies which are not consistent with the experimental observation and present calculation that the attachment process has a zero-energy threshold. It is interesting to note that the good agreement for the process SF6-/SF6was obtained in a theory developed for dissociative attachment. The excess electron energy in the dissociative attachment C1-/CFCl3 appears as translational energy in the fragments. In SF6it must appear as internal vibration of SF,. One can argue that by virtue of the high density of vibrational states (in excess of 105/meV) the SF6- States form a quasi-continuum analogous to a translational continuum in dissociative attachment. One would expect any differences in the theory probably to arise in the normalization of the cross section (determined here by ,):'I rather than in the description of the capture process and energy dependence of uA(t). Acknowledgment. We thank Dr. T. F. O'Malley (General Electric Co.) and Professor H. Weinberg (California Institute of Technology) for helpful discussions. This work was supported by the National Aeronautics and Space Administration under Contract NAS7-100 to the Jet Propulsion Laboratory, California Institute of Technology, and by the Air Force Office of Scientific Research. (16) R. W. Odom, D. L. Smith, and J. H. Futrell, J.Phys. E, 8, 1349 (1975) (see p 1364); W. A. Chupka, private communication, 1981. (17) In this regard, we note that the portion of the repulsive, negative-ion wall explored in these calculations is small because of the small range of electron energies involved. The range of R is 1.531 5 R 5 1.567 A for SF,-, and 1.722 5 R 5 1.761 %, for CFCl,-.
