Table Of ContentVolume107,Number1,January–February2002
Journal of Research of the National Institute of Standards and Technology
[J.Res.Natl.Inst.Stand.Technol.107,63–67(2002)]
Electron-Impact Total Ionization Cross Sections
of Hydrocarbon Ions
Volume 107 Number 1 January–February 2002
KarlK.IrikuraandYong-KiKim TheBinary-Encounter-Bethe(BEB)model Keywords: CH+;CH+;CH+;CH+;
2 3 4 2 2
forelectron-impacttotalionizationcross CH+;CH+;andHO+;electron-impaction-
2 4 2 6 3
National Institute of Standards and sectionshasbeenappliedtoCH+,CH+, ization;molecularions.
2 3
Technology, CH+,CH+,CH+,CH+,andHO+.The
4 2 2 2 4 2 6 3
Gaithersburg, MD 20899-0001 crosssectionsforthehydrocarbonionsare
neededformodelingcoolplasmasinfu-
and siondevices.Noexperimentaldataare
availablefordirectcomparison.Molecu-
larconstantstogeneratetotalionization Accepted: December18,2001
M. A. Ali
crosssectionsatarbitraryincidentelec-
Department of Chemistry, tronenergiesusingtheBEBformulaare
presented.Arecentexperimentalresult
Howard University,
ontheionizationofHO+isfoundtobeal-
3
Washington, DC 20059 most1/20ofthepresenttheoryatthe
crosssectionpeak. Availableonline: http://www.nist.gov/jres
[email protected]
[email protected]
1. Introduction
Ionization cross sections for atomic and molecular tionofHO++byelectronimpact[8]iscomparedtothe
3
ions are among the critical data needed in modeling present theory in Sec. 3.
plasmas in fusion devices. Hydrocarbon molecules and
theirionfragmentsareformedinsideatokamakinedge
2. Outline of Theory
plasmas and near a divertor. The Binary-Encounter-
Bethe(BEB)model[1]hassuccessfullygeneratedreli-
The BEB formula for ionizing an electron from a
able total ionization cross sections of small as well as
molecularorbitalofaneutralmoleculebyelectronim-
largemolecules[2-6].TheBEBmodelcombinesamod-
pact is [1]:
ifiedformoftheMottcrosssectionwiththeasymptotic
(cid:1) (cid:2) (cid:3) (cid:4)
form of the Bethe theory (i.e., high incident energy T) S lnt 1 1 lnt
for electron-impact ionization of a neutral atom or (cid:1)BEB=t+u+1 2 1(cid:2)t2 +1(cid:2) t (cid:2)t+1 , (1)
molecule. The original BEB model was slightly modi-
fied for applications to atomic and molecular ions [7]. where t=T/B, u=U/B, S=4(cid:3)a2NR2/B2, a is the
0 0
InthisarticleweapplythemodifiedBEBformulafor Bohr radius (=0.5292 Å), R is the Rydberg energy
ionstohydrocarbonionsofinteresttomagneticfusion: (=13.6057eV),Tistheincidentelectronenergy,andN,
CH+, CH+, CH+, CH+, CH+, CH+, and HO+. We out- B,andU aretheelectronoccupationnumber,thebind-
2 3 4 2 2 2 4 2 6 3
linethetheoryinSec.2,andourtheoreticalresultsare ingenergy,andtheaveragekineticenergyoftheorbital,
presentedinSec.3.Arecentexperimentontheforma- respectively.
63
Volume107,Number1,January–February2002
Journal of Research of the National Institute of Standards and Technology
InEq.(1),thetermsinthesquarebracketsarebased 3. Theoretical Results
on the Mott theory and the Bethe theory. However, the
denominator t+u+1 is based on a plausible, but less We present the BEB cross sections from Eq. (2) for
rigorous argument, i.e., the effective kinetic energy of CH+, CH+, CH+, CH+, CH+, CH+, and HO+ in Figs.
2 3 4 2 2 2 4 2 6 3
the incident electron seen by the bound target electron 1-4. The molecular constants B, U, andN for the
shouldbetheincidentelectronenergyTplusthepoten- molecules are listed in Table 1. For all molecular ions
tialenergyU+Bofthetargetelectron[9].HencetheT exceptCH+,moleculargeometrieswerecomputedusing
4
inthedenominatoroftheoriginalMottandBethetheo- a hybrid density functional (B3LYP) [10,11] with 6-
rieswasreplacedbyT+U+B,ort +u+1inEq.(1), 31G(d) basis sets. For CH+, B3LYP/6-31G(d) gave an
4
where B is used as the energy unit. incorrect molecular symmetry (C point group instead
2
The net effect of using t+u+1 instead of t in the of C ), so the geometry was computed using frozen-
2v
denominator of Eq. (1) is to reduce substantially the core, second-order perturbation (MP2) theory with 6-
crosssectionneartheionizationthreshold.Thismodifi- 31G(d)basissets.TheB3LYPorMP2geometrieswere
cationwasfoundnotonlytobeeffectivebutalsoabso- usedforallsubsequentcalculationsofBandU.Kinetic
lutely necessary to have the theory agree with reliable energiesUforallorbitals,andbindingenergiesBforthe
experimentalionizationcrosssectionsnearthethreshold innerorbitals,werecalculatedattheHartree-Fock(HF)
for many neutral atoms and molecules. level using 6-311G(d,p) basis sets. More accurate, cor-
Inapreviousarticle[7]forsinglychargedmolecular related values of B were obtained for the outer-valence
ions, we have shown that the denominator t+u+1 is orbitalsbyusingfrozen-coreGreen’sfunction(OVGF)
replaced by t+(u+1)/2 to generate ionization cross methods [12,13] and 6-311+G(d,p) basis sets. For the
sectionsingoodagreementwithavailableexperimental important threshold ionization, B values were obtained
data. The modified BEB equation for singly charged byusingfrozen-corecoupledclustertheory[CCSD(T)],
ions is: withthesingleanddoubleexcitationoperatorsincluded
(cid:1) (cid:2) (cid:3) (cid:4) iteratively [14] and the contribution from connected
S lnt 1 1 lnt triplesestimatedperturbatively[15].Dunning’scorrela-
(cid:1) = 1(cid:2) +1(cid:2) (cid:2) . (2)
ion t+(u+1)/2 2 t2 t t+1 tion-consistent valence-triple-zeta (cc-pVTZ) basis sets
[16] were used for the CCSD(T) calculations. The HF
Equation(2)isassimpleastheBEBformulaforneutral calculations were performed using the GAMESS [17]
targets, Eq. (1), and does not require any more input programpackage;allothercalculationsemployedGaus-
data than the original BEB formula. sian 981 [18].
Fig.1. Electron-impactionizationcrosssectionsforCH+andCH+.
2 2 2
1Certaincommercialequipment,instruments,ormaterialsareidentified
inthispapertofosterunderstanding.Suchidentificationdoesnotimply
recommendationorendorsementbytheNationalInstituteofStandards
andTechnology,nordoesitimplythatthematerialsorequipmentiden-
tifiedarenecessarilythebestavailableforthepurpose.
64
Volume107,Number1,January–February2002
Journal of Research of the National Institute of Standards and Technology
Fig.2. Electron-impactionizationcrosssectionsforCH+andCH+.
3 2 4
Fig.3. Electron-impactionizationcrosssectionforCH+andCH+.
4 2 6
Fig.4. Electron-impactionizationcrosssectionforHO+.
3
65
Volume107,Number1,January–February2002
Journal of Research of the National Institute of Standards and Technology
Table1. Molecularpointgroup,molecularorbitals(MO),electron or A+++B+2e(cid:4), (7)
bindingenergyB,kineticenergyU,andelectronoccupationnumber
NforCH2+,CH3+,CH4+,C2H2+,C2H4+,C2H6+,andH3O+ or A+B+++2e(cid:4). (8)
Molecule(pointgroup) MO B(eV) U(eV) N
Processes(3)and(4)aredissociationwithoutioniza-
CH+(C ) 1a 319.07 436.58 2 tion, while processes (5) through (8) are the ionizing
2 2v 1
2a 33.16 38.98 2 eventsdescribedbytheBEBmodel.Themodelcalcu-
1
1b2 27.04 29.90 2 lates the sum of all processes (5) through (8) that lead
3a1 22.17 37.74 1 totheejectionofaboundelectron.Moreover,themodel
also assumes—erroneously—that all energy transfers
CH+(D ) 1a' 317.93 436.46 2
3 3h 1
from the incident electron to the target molecule that
2a' 33.55 37.57 2
1
1e' 25.59 29.56 4 exceed the ionization energy of a given molecular or-
bitalresultinionization.Thisisanassumptioncommon
CH4+(C2v) 1a1 315.92 436.20 2 toallbinary-encountertypetheories.Althoughsuchan
2a 33.67 33.40 2
1 assumption may be valid for atoms, molecules may
3a 25.87 27.79 2
1
dissociatewithoutionizingevenifenergytransfersex-
1b 24.48 28.73 2
2
1b 22.08 29.42 1 ceed the orbital binding energies. If processes (3) and
1
(4) are significant for energy transfers above orbital
C2H2+(D(cid:1)h) 1(cid:2)g 316.56 435.87 2 bindingenergies,thentheBEBmodelwilloverestimate
1(cid:2) 316.48 436.63 2
u ionizationcrosssections.Morediscussionsonthispoint
2(cid:2) 34.59 49.00 2
g
2(cid:2) 27.96 35.66 2 can be found in Ref. [5].
u
3(cid:2) 26.06 34.23 2 Experimentally, the production of doubly charged
g
1(cid:3)u 21.00 31.42 3 ions can be detected directly when the doubly charged
ions have reasonably long lifetimes. In reality, most
CH+(D) 1a 315.15 436.08 2
2 4 2 doubly charged molecular ions quickly dissociate into
1b 315.12 436.44 2
1
twosinglychargedfragments,makingitalmostimpos-
2a 33.52 40.73 2
2b 28.22 36.01 2 sibletodistinguishprocesses(3)and(4)fromthedisso-
1
1b2 24.41 27.06 2 ciation of doubly charged ions by Coulomb repulsion,
3a 23.30 35.07 2 i.e.,process(6).Forthisreason,itisdifficulttodistin-
1b 21.81 29.99 2
3 guishprocesses(3)and(4)fromprocess(6)simplyby
2b 19.21 29.54 1
3
detecting singly charged ions unless coincidence mea-
CH+(D ) 1a 314.28 436.27 2 surementsofallproductsareperformed.Theusualex-
2 6 3d 1g
1a2u 314.28 436.30 2 perimentalprocedureistomeasurethecrosssectionfor
2a1g 31.76 33.19 2 producinganyion,i.e.,(3)through(8).Then,processes
2a 29.16 38.10 2
2u (3) and (4) are measured separately, and subtracted
1e 23.07 26.29 4
u
from the total ion production cross section. This sub-
1e 21.38 30.07 4
g
3a 19.04 30.07 1 traction introduces large uncertainties in the resulting
1g
experimental ionization cross sections.
H3O+(C3v) 1a1 571.51 794.48 2 The direct measurement of only the doubly charged
2a 45.59 72.42 2
1 ions—processes (5), (7), and (8)—tends to produce
1e 29.90 52.11 4
3a 24.7a 65.41 2 small cross sections compared to the total ionization
1
cross section because of the high probability for the
aExperimentalvaluefromRef.[8]. rapidbreak-upofthedoublychargedionsasshownin
Ref.[7]forCO+.Asanotherexample,Bahatietal.[8]
Ingeneral,whenanelectroncollideswithamolecu- recently reported experimental cross sections for the
lar ion we get process of
e(cid:4)+AB+→A+B++e(cid:4), (3) e(cid:4)+HO+→HO+++2e(cid:4) (9)
3 3
or A++B+e(cid:4). (4) Theirmeasurementcorrespondstoprocess(5)only,and
theirpeakcrosssectionis0.049Å2atT(cid:1)125eV.The
e(cid:4)+AB+→AB+++2e(cid:4), (5) positionofthepeakisinagreementwiththeBEBcross
sectioninFig.4,butthemagnitudeisalmost1/20ofthe
or A++B++2e(cid:4), (6) BEB cross section. This discrepancy and the similar
66
Volume107,Number1,January–February2002
Journal of Research of the National Institute of Standards and Technology
discrepancy in CO+ (experiment is lower by a factor of C.Y.Peng,A.Nanayakkara,C.Gonzalez,M.Challacombe,P.
1/12atthepeak)measuredbythesamegroup[19]isa M.W.Gill,B.Johnson,W.Chen,M.W.Wong,J.L.Andres,
strongindicationthateitherdissociativeionizationisthe C.Gonzalez,M.Head-Gordon,E.S.Replogle,andJ.A.Pople,
Gaussian,Inc.,Pittsburgh,PA(1998).
dominantprocess,orthebreak-upofthedoublycharged
[19] D.S.Belic,D.J.Yu,A.Siari,andP.Defrance,J.Phys.B30,
ionsisfasterthantheexperimentalcapabilitytodetect.
5535(1997).
Acknowledgments Abouttheauthors: KarlK.Irikuraisachemistinthe
PhysicalandChemicalPropertiesDivisionintheNIST
We gratefully acknowledge partial financial support Chemical Science and Technology Laboratory. Yong-
by the Office of Fusion Energy Sciences of the U.S. KiKimisaphysicistintheAtomicPhysicsDivisionin
DepartmentofEnergyandbytheAdvancedTechnology theNISTPhysicsLaboratory.M.AsgarAliisaprofes-
Program of NIST. sorintheDepartmentofChemistryatHowardUniver-
sity,andaguestresearcherintheAtomicPhysicsDivi-
sion at NIST. The National Institute of Standards and
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