Quantum Mechanical Calculation of Maximum Electron Impact Single

calculated cross section has been found to follow systematic trends. Introduction. Electron impact ionization was first used in mass spectrometry by D...
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J. Phys. Chem. 1996, 100, 15021-15026

15021

Quantum Mechanical Calculation of Maximum Electron Impact Single Ionization Cross Sections for the Inert Gases and Small Molecules Claire Vallance, Peter W. Harland,* and Robert G. A. R. Maclagan Chemistry Department, UniVersity of Canterbury, Christchurch, New Zealand ReceiVed: February 19, 1996; In Final Form: May 24, 1996X

Quantum mechanical calculations based on a simple concept of electron impact single ionization have been carried out for the inert gases and several molecules in order to determine maximum electron impact ionization cross sections. For molecular targets, cross sections are calculated as a function of the electron-molecule approach geometry and then averaged over all orientations for the total ionization cross section. These have shown promising agreement with experimentally measured cross sections for randomly oriented molecules and also with existing theoretical methods. The effect of a quantum mechanical method and basis set on the calculated cross section has been found to follow systematic trends.

Introduction Electron impact ionization was first used in mass spectrometry by Dempster1 in an attempt to generate reproducible mass spectra for use in analytical chemistry, an application of mass spectrometry suggested by J. J. Thomson.2 After 80 years of experience in electron impact ionization, a relatively small number of absolute ionization cross sections have been measured, and fragmentation patterns are not always predictable using theoretical models or chemical intuition. Although the experimentally measured ionization cross sections for the inert gases determined by several independent groups lie in a narrow range, this is not always the case for molecules where the range of values reported can be substantial. For example, recent values reported for the maximum ionization cross section for O2 lie in the range from 2.622 3 to 2.978 Å2 4 and for NH3 from 2 to 3.19 Å2. 5-7 A recent measurement for NH3 using a crossed molecular beam time-of-flight mass spectrometer gave a value of 2.4 Å2, in agreement with several earlier measurements.7 For most molecules only one measurement is available, and for many simple molecules there are no experimental values. We have recently explored the effect of projectile electron-target molecule orientation on the ionization cross section and product distribution using crossed particle beams and found significant differences between electron impact ionization cross sections for collisions at the positive and negative ends of the molecular dipole for a number of symmetric top molecules.8 A simple classical model, in which the electron-molecule separation satisfying the condition that the Coulomb potential equals the ionization potential, qualitatively reproduced the experimental results.8 We now report a quantum mechanical extension of this model for the ab initio calculation of electron impact single ionization cross sections for atoms and small molecules. Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence; they are divided into quantum, semiclassical, and semiempirical. The theoretical treatment of the ionization process has been seen as a complex problem with the involvement of three charged particles in the exit channel.9 Even for atomic hydrogen, the simplest ionization case, the longrange Coulomb force restricts free movement of the particles even at very large interparticle separations.10 Quantum methods use a partial wave approximation. The Born approximation11 X

Abstract published in AdVance ACS Abstracts, August 1, 1996.

S0022-3654(96)00491-1 CCC: $12.00

considers the incident electron as a plane wave with limited interaction with the molecule.9 A series of higher order approximations, including distorted wave theories,11,12 have found some success in describing the absolute electron ionization cross section and the energy dependence for light neutral atoms such as H, He, and Ne and light ion targets such as He+, Be+, Na+, and Mg2+. One of the most successful methods for the calculation of electron impact ionization cross sections is the semiempirical additivity method developed by Deutsch and Ma¨rk (DM) and their co-workers.13-16 In its original form, the method was used to calculate atomic cross-sections and was then extended to molecules using the additivity rule first described by Fitch and Sauter.17 According to the DM theory a molecular electron impact ionization cross section is given by j σ ) ∑ πrA,nl2 ∑ (gA,nl ξA,nl )f(uj) j

A,nl

j

where rA,nl2 is the mean square radius of the n,l atomic shell, j is the occupation number of the n,l atomic shell, and gnl is ξA,nl a weighting factor which is given to a first approximation by 3.0 for s electrons and 0.5 for other electrons.15 A Mulliken population analysis or an equivalent method is required in order j . The energy dependent term, f(u), where uj ) to obtain ξA,nl E/Ej and Ej is the ionization potential from the nth subshell, is given by

f(u) )

){

2 1 1 u - 1 3/2 1+ 1ln(2.7 + (u - 1)1/2) uu+1 3 2u

(

(

)

}

Recent experimental data16 suggest that this term should be slightly different for s, p, d, and f electrons.15 The value of the cross section calculated from the DM equation depends on the method and basis set used for the generation of the atomic orbital coefficients. For example, the maximum cross section for H2O calculated by Margreiter et al.14 using atomic orbital data from Terrisol et al.18 or from Berkowitz19 was 1.1 Å2. Using the same equation and atomic orbital coefficients calculated at Hartree-Fock level, we calculate a value of 1.89 Å2, which is in better agreement with the experimental value20 of 2.05 Å2. While the additivity rules reproduce the general shape of ionization efficiency curves for molecules, the electron energy at the maximum cross section is not uniformly reproduced and the discrepancy between the © 1996 American Chemical Society

15022 J. Phys. Chem., Vol. 100, No. 37, 1996 experimental and calculated values for the maximum cross section can vary from a few percent up to ∼100%.14 Since there is a variation in reported experimental results, it is not readily apparent whether the discrepancies are in the experiments, the calculation, or a combination of both. Kim and Rudd21 have developed a method called the binaryencounter dipole (BED) theory for calculating energy-dependent cross sections. The BED method gives good agreement with experimental cross sections for a large number of atomic and molecular species. They have used a combination of Mott scattering theory augmented by the binary encounter theory22 for low impact parameter (low energy) collisions and the Bethe theory23 for high impact parameter (high energy) collisions. The application of the BED model requires dipole oscillator strengths, df(w)/dw, where w ) W/B, W is the ejected electron energy, and B is the orbital binding energy. Since these are not easily calculated, a modified version of the theory, called the binaryencounter Bethe or BEB theory, employs a simple form for the dipole oscillator strength based on the approximate shape of this function for ionization of ground-state hydrogen. The quantities required for each orbital in order to carry out a BEB calculation are the orbital occupation number, the orbital kinetic energy, and the orbital binding energy, all easily calculated. The total molecular cross section is found by summing over the occupied orbitals. Bobeldijk et al.24 recognized that “the 100% additivity rule” overestimated the cross section. The molecular orbitals are better described by valence orbitals of bonded rather than isolated atoms. Similarly, ionization energies of the molecular orbitals differ from the atomic values. In general, the inner atoms will be shielded from an approaching electron by the outer atoms and will not contribute to the ionization cross section. This last effect will be orientation dependent. They developed a “geometric additivity model” in which the sum in the additivity rule is over molecular subunits for which experimental or theoretical cross sections have been determined. The method was applied to a large number of organic compounds, giving much better agreement with experiment than the original additivity rule. For example, in the case of linear hydrocarbons, the cross sections required are those of the CH, CH2, and CH3 subunits, available from measured ionization cross sections of small molecules. The model assumes that for end-on approach the cross section will be that of a CH3 subunit, while for broadside approach, it will be the sum of the cross section of the methyl and methylene units in the molecule. This approach is not applicable to the small molecules considered here. The quantum mechanical approach introduced here is easily applied to atoms and small molecules, although it is currently restricted to the calculation of the maximum total ionization cross section. The calculations were carried out using Gaussian 9225 and 94.26 The electron energy corresponding to the maximum has been calculated for the inert gases with some success, and the approach used could probably be extended to molecules. Method for the Calculation of Cross Sections The model assumes that ionization occurs when the Coulomb potential experienced by the molecule due to the projectile electron is equal to the ionization potential of the molecule. The calculations determine the critical separation between the molecule and the electron for which this condition is satisfied, for a specified relative orientation. Since at smaller separations the Coulomb potential produced by the electron will be higher, this critical separation corresponds to the maximum impact parameter for the ionization process.

Vallance et al. Initially, a geometry optimization is performed for the neutral molecule and the energy of the positive ion is calculated at the neutral geometry. A frequency calculation for the neutral molecule is carried out in order to determine the zero-point vibrational energy. The vertical ionization potential is then calculated from

IPV ) Ei - (En + E0) where Ei is the energy of the ion, En is the energy of the neutral, and E0 is the zero-point energy. To calculate ionization cross sections, the target energy, T, is taken to be the energy of the electron-molecule system at which ionization occurs, which is the energy of the neutral molecule plus the Coulomb potential due to the electron, Φ. Since the Coulomb potential is taken to be equal to the ionization potential, the target energy is the energy of the neutral molecule minus the ionization potential of the molecule (minus because the Coulomb potential is negative).

T ) En + Φ ) En - IPV A series of energy calculations are carried out on the neutral molecule in the presence of a charge distribution consisting of a single electron. The energy of the system is calculated for a starting set of electron coordinates, and the coordinates are then adjusted systematically in order to converge to the target energy in subsequent energy calculations. The coordinates of the electron with respect to the molecule when the system is at the target energy gives the separation, r, between the electron and the center of mass of the molecule at ionization. The cross section for electron impact ionization for the specified relative geometry of the molecule and electron is then given by

σ ) πr2 The total single ionization cross section, the average over all orientations, can be approximated by carrying out the above calculations with the electron approaching along each of the positive and negative Cartesian axes and averaging

σ ) 1/6(σ+x + σ-x + σ+y + σ-y + σ+z + σ-z) To estimate the electron energy of maximum cross section, it is assumed that the electron is ionized from the highest lying atomic orbital. This electron is treated as a particle in a classical orbit for which an orbital frequency can be calculated. The inbound electron is treated as a wave, and it is assumed that coupling between the orbital electron and the projectile electron, leading to energy transfer and ionization, is most likely to occur when the frequency of the projectile electron wave is equal to the orbital frequency of the atomic electron. It is further assumed that the energy of the orbital, E, is made up of kinetic and potential energy contributions27

E)K+V The kinetic energy, K, is due to the classical orbital motion. The potential energy, V, is the Coulomb potential due to the interaction between the electronic charge and the effective nuclear charge. The effective nuclear charge is given by

Zeff ) Z - S where Z is the nuclear charge and S is the screening factor.28 The potential energy contribution is then given by

Quantum Mechanics of Single Ionization Cross Sections

J. Phys. Chem., Vol. 100, No. 37, 1996 15023

TABLE 1: Maximum Electron Impact Ionization Cross Sections for the Inert Gases cross section/Å2

IP/eV atom He

Ne

Ar

Kr

Xe

theory

calcd

HF/6-31G* HF/6-311G** MP4/6-311G** CCSD(T)/6-311G** QCISD(T)/6-311G** HF/6-31G* HF/6-311G** MP4/6-311G** CCSD(T)/6-311G** QCISD(T)/6-311G** QCISD(T)/6-311G**(2df) QCISD(T)/6-311G(3df) HF/6-31G* HF/6-311G** MP4/6-311G** CCSD(T)/6-311G** QCISD(T)/6-311G** HF/6-31G* HF/6-311G** MP4/6-311G** CCSD(T)/6-311G** QCISD(T)/6-311G** HF/6-31G*

23.43 23.44 24.28 24.28 24.28 19.65 19.75 21.13 21.06 21.06 21.29 21.34 14.66 14.63 15.28 15.12 15.22 13.18 13.16 13.82 13.80 13.80 11.44

expt36 24.59

21.56

15.76

14.00

12.13

calcda 0.38 0.44 0.43 0.43 0.43 1.05 1.03 1.01 1.09 1.01 1.05 1.09 2.62 2.66 2.60 2.61 2.60 3.52 3.61 3.50 3.51 3.50 4.24

calcdb 0.37 0.44 0.43 0.43 0.43 1.00 0.99 1.00 1.08 0.99 1.04 1.08 2.53 2.56 2.56 2.56 2.56 3.42 3.50 3.48 3.48 3.47 4.13

expt 0.37,

30-32

0.3833

0.72,31 0.74,33 0.7830

2.54,31 2.70,33,34 2.8630

3.70,33 3.72,31 4.2630

4.59,35 4.98,33 5.4630

a Cross sections calculated using the ionization potential calculated by theory. b Cross sections calculated using experimental values for the ionization potential.

V)-

Zeffq 4π0r

where q is the electronic charge and 0 is the permittivity of free space. The kinetic energy can then be found from K ) E - V. For a particle in a classical circular orbit we have

K ) 1/2Iω2 ) 1/2mer2ω2 where I is the moment of inertia, ω is the angular velocity, me is the electron mass, and r is the orbital radius.28 The orbital frequency is then given by

ν)

x

2K mer2

w 1 ) 2π 2π

The electron energy at the maximum, Emax, corresponds to the strongest coupling between the incoming electron and the orbiting electron which occurs when the frequency of the incoming electron wave is equal to the orbital frequency

Emax ) hν )

x

h 2π

2K mer2

Results and Discussion Inert Gases. Since the cross section is independent of the approach geometry for the atomic species, the effect of the method and basis set on the calculation of the ionization cross section could be readily explored. Table 1 lists the calculated and experimental ionization potentials and ionization cross sections for the inert gases calculated using Hartree-Fock (HF), Mo¨ller-Plesset perturbation theory (MP), coupled cluster (CCSD(T)), and quadratic configuration interaction (QCISD(T)) methods with a range of basis sets. In general, expanding the basis set leads to an increase in calculated cross section, while moving to a higher level of theory (with the same basis set) leads to a decrease, though both of these effects are small. The lowest level calculations, HF/6-31G*, return values close

to those calculated with the more sophisticated methods, so that improving the level of theory and basis set has little effect on improving agreement with experiment. Cross sections were calculated using both the calculated and the experimental ionization potentials in the determination of the “target” energy. As expected, for cases where the calculated ionization potential is less than the experimental value, the calculated cross section is higher since the Coulomb potential reaches the ionization energy at a larger interparticle separation. With the exception of Ne, there is good agreement between calculation and experiment. In Figure 1, the results of the HF/6-31G* level quantum calculation of the cross section for the inert gases from He to Kr are compared with the DM and BEB calculations and with the range of reported experimental values for the maximum cross section. For He all three methods give the same maximum cross section of around 0.4 Å2 at ∼100 eV, in agreement with experiment (Table 1). For Ne, Ar, and Kr, the three methods agree well on the position of the maximum although there is some variation in the value of the predicted maximum cross section between methods. In the case of Ne, the quantum and BEB methods give a value of about 1.0 Å2, while the DM theory predicts a lower value of 0.69 Å2. For Ar and Kr the situation is reversed, with the quantum and DM calculations in agreement, but the BEB calculations giving a lower result. The experimental measurements in the literature13,29-34 show considerable variation in the shape of the experimental ionization efficiency curves (Table 2). These include plateaus covering a wide range of electron energy about the maximum, double maxima in some cases, and distinct peaks with well-defined maxima. In all cases the experimental trend in the position of the maximum is qualitatively reproduced, and also the experimental values seem to lie within the range bracketed by the three theories. We conclude that the model works well for predicting maximum inert gas ionization cross sections, with the exception of Ne, and also for predicting the electron energy at the maximum. Since the method is relatively insensitive to basis set effects and level of theory used in the calculations, we

15024 J. Phys. Chem., Vol. 100, No. 37, 1996

Vallance et al.

Figure 1. Ionization efficiency curves for the inert gases He through Kr calculated by the BEB method (open circles) and the DM method using atomic orbital coefficients calculated at the HF level of theory (closed circles). The crosses show the magnitude and electron energy for the maximum cross-sections calculated by HF and the horizontal lines show the range of experimental values for the maximum cross section.

TABLE 2: Experimental Maximum Electron Impact Ionization Cross Sections for the Inert Gases atom

maximum cross section/Å2

electron energy range/eV

He Ne Ar Kr

0.37 1.00 2.53 3.41

50-120 150-200 50-120 50-100

TABLE 3: Maximum Electron Impact Ionization Cross Sections for Small Molecules Averaged over the Cartesian Coordinates ionization potential/eV molecule H2 N2 O2 CO NO H2O CO2 NH3 CH4 CH3Cl

calcd 15.30 18.06 12.88 12.86 9.75 10.25 12.16 8.25 12.11 9.27

expt36 15.43 15.58 12.07 14.01 9.26 12.61 13.77 10.16 12.51 11.22

cross section σ/Å2 calcda 0.95 2.40 2.87 2.91 3.42 2.42 5.62 3.58 3.90 5.89

calcdb 0.94 2.61 2.97 2.84 3.52 2.11 5.35 3.17 3.83 5.27

expt 0.9730 2.5330 2.62-2.983,4,30,37 2.05-2.6630,38-40 3.1530 2.0524 2.05,38 3.5530 2.4-3.00767,41-44 3.7030

a Cross sections calculated using the ionization potential calculated by theory. b Cross sections calculated using experimental values for the ionization potential.

conclude that the HF/6-31G* level calculations suffice to give good agreement with experimental results. Small Molecules. Ionization potentials and cross sections calculated at the HF/6-31G* level of theory using the calculated and reported experimental ionization potentials are listed in Table 3. The cross sections are determined by averaging over the Cartesian coordinates at the center of mass, as described above. Except for CO2, and possibly CO and NH3, depending on the experimental value chosen for the cross section, there is good agreement between the cross section calculated using the experimental ionization potential and the values reported in the literature. We cannot readily explain the large overestimation

TABLE 4: Comparison of Maximum Total Ionization Cross Section for Molecules between This Method, the Additivity Method, and Experimental Results (In Units of Å2) species

HFa

DM14

H2 N2 O2 CO NO H 2O CO2 NH3 CH4 CH3Cl

0.94 2.61 2.97 2.84 3.52 2.11 5.35 3.17 3.83 5.27

1.15 1.7 1.6 2.0 1.8 1.1 2.8 2.4 3.4

DM (our calcn)b

2.03 1.81 1.89 2.40 5.56

BEB

exptd

0.93 2.52 2.38 2.52 2.54 2.25 3.57 2.96 3.30 5.06

0.97 2.53 2.62-2.98 2.05-2.66 3.15 2.05 2.05, 3.55 2.4-3.00 3.70

a

Calculated at the HF/6-31G* level of theory and averaged over Cartesian coordinates. b Calculated at the HF/6-31G* level of theory and calculated from radius of ionization volume. c Using atomic orbital coefficients calculated at the HF/6-31G* level of theory. d See Table 3 for references.

of the calculated cross section in the case of CO2. A comparison among the HF, BEB, and the DM methods is made in Table 4. It is noted that the additivity rules generally underestimate the cross section. Assuming this to be the case, then the value of 2.8 Å2 calculated for the CO2 cross section13 using the additivity rules would tend to favor the higher experimental value of 3.55 Å2. With the exception of CO2, the molecules in Table 3 are either diatomic or near spherical polyatomic. An alternative method for calculating the orientation-averaged cross section is from the volume constructed from the calculated ionization surface. If the maximum separation of electron and molecule for which ionization can occur is determined for a large number of different relative geometries, it is possible to extend the concept of ionization cross section into three dimensions to give a volume of ionization where ionization occurs when the electron penetrates the surface enclosing the volume.45 With the exception of CO2, the averaged ionization cross sections calculated from the radius of the ionization volume for diatomics and polyatomics are within 10% of the values calculated using

Quantum Mechanics of Single Ionization Cross Sections TABLE 5: Calculated Maximum Electron Impact Ionization Cross Sections for CO at Various Levels of Theory theory

IP/eV

cross section/Å2 a

expt HF/6-31G* HF/6-311G** MP2/6-31G* MP2/6-311G** b MP4/6-311G** b QCISD(T)/6-311G** b

14.01 12.86 12.88 14.02 14.16 14.16 13.69

2.05-2.66 2.91 (2.84) 2.93 2.79 2.82 2.81 2.88 (2.76)

a Values in parentheses were calculated using the experimental value for the ionization potential. b Using the MP2/6-31G* geometry.

TABLE 6: Calculated Maximum Electron Impact Ionization Cross Section for H2O at Various Levels of Theory theory

IP/eV

cross section/Å2 a

expt HF/6-31G* HF/6-311G** MP4/6-311G** CCSD(T)/6-311G** QCISD(T)/6-311G** QCISD(T)/6-311G**(2df) QCISD(T)/6-311G(3df)

12.61 10.25 10.29 11.60 11.57 11.57 11.77 11.77

2.05 2.42 (2.11) 2.48 2.34 2.34 2.34 2.35 2.34 (1.97)

a Values in parentheses were calculated using the experimental value for the ionization potential.

experimental ionization potentials shown in Table 3. For example, the ionization cross sections calculated in this way for N2, H2O, and CH3Cl are 2.82, 2.09, and 5.57 Å2, respectively. These values are +8.0%, -0.9%, and +5.7% different from the values determined by averaging over Cartesian coordinates. The value determined from the ionization volume for CO2 is 4.00 Å2 which is 25% lower and in better agreement with the experimentally reported value of 3.55 Å2. The effect of method and basis set on calculated cross section is illustrated in Tables 5 and 6 for CO and H2O, respectively. For both CO and H2O, there is a significant increase in the ionization potential and decrease in calculated cross section on increasing the level of theory above Hartree-Fock. The HF calculations using the 6-31G* and 6-311G** basis sets show again the increase in calculated cross section obtained on expansion of the basis set. This is not an effect of a change in the vertical ionization potential, since for CO the HF/6-311G** ionization potential is larger than the HF/6-31G* value, while for H2O it is smaller. The same trend is reproduced in the MP2/ 6-31G* and MP2/6-311G** calculations. For the H2O molecule, once the level of theory is increased above Hartree-Fock, any further improvements seem to have little affect on the cross section. The absolute cross sections are virtually identical when calculated using fourth-order perturbation theory (MP4), coupled cluster methods (CCSD(T)), and quadratic configuration interaction (QCISD(T)), even with several different basis sets. Though significant variation over the critical distances for each axial direction was apparent, these effects seem to cancel each other, giving a calculated absolute cross section of 2.34 Å2 for any calculation above Hartree-Fock level (2.35 Å2 for QCISD(T)/6-311G**(2df)). Though expanding the basis set by inclusion of additional polarization functions in the QCISD(T) calculations had no effect on the calculated cross section, it did affect the calculated ionization potential, with an increase of around 0.2 eV (19 kJ mol-1). The ionization cross section for CO is much more sensitive to change in the level of theory used. Moving from HF to MP2 causes a decrease of 0.12 Å2 for the 6-31G* and 0.11 Å2 for the 6-311G** basis sets, an effect similar to that seen earlier

J. Phys. Chem., Vol. 100, No. 37, 1996 15025 for neon. Changing from second- to fourth-order perturbation theory caused a small decrease (0.01 Å2) in the calculated cross section. In contrast to H2O, calculations at MP4 and QCISD(T) levels gave significantly different results, with the QCISD(T) value almost equal to that obtained in the Hartree-Fock calculations. In conclusion, we have found that higher level theory tends to decrease the calculated cross section for molecules, particularly on moving above the Hartree-Fock level, while expanding the basis set causes an increase in most cases. The best agreement between calculation and experimentally determined cross sections occurs where the experimental value for the ionization potential has been used in the calculation. Both calculated and experimental cross sections are strongly dependent on the relative orientation of the electron and the molecule with the values reported here representing averages over the Cartesian approach geometries (z, (y, (x. If the maximum separation of electron and molecule for which ionization can occur is determined for a large number of different relative geometries, it is possible to extend the concept of ionization cross section into three dimensions to give a volume of ionization where ionization occurs when the electron penetrates the surface enclosing the volume.45 Acknowledgment. We would like to acknowledge the Foundation for Research, Science and Technology for financial support and the University of Canterbury for the provision of a doctoral fellowship to C.V. References and Notes (1) Dempster, A. J. Phys. ReV., 1918, 11, 316. (2) Thomson, J. J. Philos. Mag. 1912, 23, 449. Thomson, J. J. Rays of PositiVe Electricity and Their Application to Chemical Analyses; Longmans, Green and Co.: London, 1913. (3) Schram, B. L.; De Heer, F. J.; van der Wiel, M. J.; Kistemaker, J. Physica 1965, 31, 94. (4) Srivastava, S. K.; Krishnakumar, E. Int. J. Mass Spectrom. Ion Processes 1992, 113, 1. (5) Ma¨rk, T. D.; Egger, F.; Cheret, M. J. Chem. Phys. 1977, 67, 3795. (6) Djuric, N.; Belic, D.; Kurepa, M. V.; Mack, J. U.; Rothleitner, J.; Ma¨rk, T. D. Proc. 12th ICPEAC, Gatinburg, 1981; p 384. (7) Syage, J. A., J. Chem. Phys. 1992, 97, 6085. (8) Aitken, C. G.; Blunt, D. A.; Harland, P. W. J. Chem. Phys. 1994, 101, 11074. Aitken, C. G.; Blunt, D. A.; Harland, P. W. Int. J. Mass Spectrom. Ion Processes 1995, 149/150, 279. (9) (9) Ehrhardt, H.; Jung, K.; Knoth, G.; Schlemmer, P. Z. Phys. D 1986, 1, 3. (10) (10) Brauner, M.; Briggs, J. S.; Klar, H. J. Phys. B 1989, 22, 2265. (11) Ma¨rk, T. D., Dunn, G .H., Eds. Electron Impact Ionization; Springer-Verlag: Wein and New York, 1985. (12) Jones, S.; Madison, D. H.; Franz, A.; Altick, P. L. Phys. ReV. A 1993, 48, R22. (13) Deutsch, H.; Ma¨rk, T. D. Int. J. Mass Spectrom. Ion Processes 1987, 79, R1. (14) Margreiter, D.; Deutsch, H.; Schmidt, M.; Ma¨rk, T. D. Int. J. Mass Spectrom. Ion Processes 1990, 100, 157. (15) Margreiter, D.; Deutsch, H.; Schmidt, M.; Ma¨rk, T. D. Int. J. Mass Spectrom. Ion Processes 1994, 139, 127. (16) Deutsch, H.; Ma¨rk, T. D.; Margreiter, D. Z. Phys. 1994, D29, 31. Deutsch, H.; Ma¨rk, T. D. Contrib. Plasma Phys. 1994, 34, 19. (17) Fitch, W. L.; Sauter, A. D. Anal. Chem. 1983, 55, 832. (18) Terrisol, M.; Bordage, M. C.; Caudrelier, V.; Segur, P. IAEA Technol. Doc. 1988, 506, 218. (19) Berkowitz, A. Photoabsorption, Photoionization, and Photoelectron Spectroscopy; Academic: Orlando, FL, 1979. (20) Djuric, N. L.; Cadez. I. M.; Kurepa, M. V. Int. J. Mass Spectrom. Ion Processes 1988, 83, R7. (21) Kim, Y. K.; Rudd, M. E. Phys. ReV. A. 1994, 50, 3954. Hwang, W.; Kim, Y. K.; Rudd, M. E. J. Chem. Phys. 1996, 104, 2956. (22) Vriens, L. Case Studies in Atomic Physics; McDonald, E. W., McDowell, M. R. C., Eds.; North-Holland: Amsterdam, 1969; Vol. 1, p 335. (23) Bethe, H. Ann. Phys. 1930, 5, 325. (24) Bobeldijk, M.; Van der Zande, W. J.; Kistemaker, P. G. Chem. Phys. 1994, 179, 125.

15026 J. Phys. Chem., Vol. 100, No. 37, 1996 (25) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomberts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart J. J. P.; Pople, J. A. GAUSSIAN 92, Revision C; Gaussian Inc.: Pittsburgh, PA, 1992. (26) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomberts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzales, C.; Pople, J. A. GAUSSIAN 94, Revision A.1; Gaussian Inc.: Pittsburgh, PA, 1995. (27) Lotz, W. J. Opt. Soc. Am. 1970, 60, 206. (28) Fraga, S.; Karwowski, J.; Saxena, K. M. S. Handbook of Atomic Data; Elsevier: New York, 1976. (29) Kieffer, L. J.; Dunn, G. H. ReV. Mod. Phys. 1966, 38, 1. (30) Rapp, D.; Englander-Golden, P. J. Chem. Phys. 1965, 43, 1464. (31) Stephan, K.; Helm, H.; Ma¨rk, T. D. J. Chem. Phys. 1980, 73, 3763. (32) Montague, R. G.; Harrison, M. F. A.; Smith, A. C. H. J. Phys. B 1984, 17, 3295. (33) Wetzel, R. C.; Baiocchi, F. A.; Hayes, T. R.; Freund, R. S. Phys. ReV. A 1987, 35, 559. (34) Straub, H. C.; Renault, B. G.; Lindsay, B. G.; Smith, K. A.; Stebbings, R. F. Phys. ReV. A 1995, 52, 1115 and references therein.

Vallance et al. (35) Stephan, K.; Ma¨rk, T. D. J. Chem. Phys. 1984, 81, 3116. (36) (a) Franklin, J. L.; Dillard, J. G.; Rosenstock, H. M.; Heron, J. T.; Draxl, K.; Field, F. H. Ionization Potentials, Appearance Potentials, and Heats of Formation of Gaseous Positive Ions. Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.) 1969. (b) Levin, R. D.; Lias, S. G. Ionization Potential and Appearance Potential Measurements, 1971-1981. Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.) 1982. (c) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. Gas-Phase Ion and Neutral Thermochemistry. Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.) 1988. (37) Tate, J. T; Smith, P. T. Phys. ReV. 1932, 39, 270. (38) Freund, R. S.; Wetzel, R. C. Phys. ReV. A 1990, 41, 5861. (39) Hille, E.; Ma¨rk, T. D. J. Chem. Phys. 1978, 69, 4600. (40) Orient, O. J.; Srivastava, S. K. J. Phys. B 1987, 20, 3923. (41) Srivastava, S. K.; Rao, M. V. V. S. J. Geophys. Res. 1991, 96 (E2), 17563. (42) Khare, S. P.; Meath, W. J. J. Phys. B 1987, 20, 2101. (43) Bedereski, K.; Wo´jcik, L.; Adamczyk, B. Int. J. Mass Spectrom. Ion Phys. 1980, 35, 171. (44) Crowe, A.; McConkey, J. W. Int. J. Mass Spectrom. Ion Phys. 1977, 24, 181. (45) Vallance, C.; Harland, P. W.; Maclagan, R. G. A. R. To be published.

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