Table Of ContentDissociative electron attachment and electron-impact resonant dissociation of
vibrationally excited O molecules
2
V. Laporta,1,2,∗ R. Celiberto,3,1 and J. Tennyson2
1Istituto di Metodologie Inorganiche e dei Plasmi, CNR, Bari, Italy
2Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
3Dipartimento di Ingegneria Civile, Ambientale, del Territorio, Edile e di Chimica, Politecnico di Bari, Italy
State-by-statecrosssectionsfordissociativeelectronattachmentandelectron-impactdissociation
for molecular oxygen are computed using ab initio resonance curves calculated with the R-matrix
5
1 method. WhenO2 isinitsvibrationalgroundstate,themaincontributionforbothprocessescomes
0 fromthe2ΠuresonancestateofO−2 butwithasignificantcontributionfromthe4Σ−u resonantstate.
2 Vibrational excitation leads toan increased contribution from thelow-lying 2Πg resonance, greatly
increasedcrosssectionsforbothprocessesandthethresholdmovingtolowerenergies. Theseresults
n
provideimportant inputfor models of O2-containing plasmas in non-equilibrium conditions.
a
J
PACSnumbers: 34.80.Ht,34.80.Gs,52.20.Fs
8
] I. INTRODUCTION in kinetics models of oxygen-containing non-equilibrium
h
p plasmas,where high-lying vibrationallevels of molecules
- Molecularoxygenisamajorcomponentofthe Earth’s can be hugely populated.
m
atmosphere and is fundamental for life. It plays an im- The paper is organized as follow: In the Section II we
s portantroleinmanynaturalandtechnologicalprocesses. will give a brief account and numerical details on the
a
l In this paper we focus on the ability of low-energy elec- adopted theoreticalmodels for the calculation of the po-
p trons to dissociate molecular oxygen, in its fundamental tentialenergycurvesandonthedescriptionofthenuclear
s. electronicstate,bymeansofresonantscattering. Inpar- dynamics. TheresultsareillustratedinSectionIII while
c ticular we consider the state-by-state processes of disso- the concluding remarks are given in Section IV.
i
s ciative electron attachment (DEA),
y
ph e−+O2(X3Σ−g;v)→O−2∗ →O−(2P)+O(3P), (1) II. THEORETICAL MODEL
[
and electron impact dissociation (EID),
Many low-energy electron-molecule scattering pro-
1
v e−+O (X3Σ−;v) O−∗ e−+2O(3P), (2) cesses are dominated by resonances. For molecular
1 2 g → 2 → oxygen these processes can be quantitatively under-
7 stood in term of four low-lying O− resonances of sym-
for each oxygen vibrational level v. The threshold for 2
7 metry 2Π , 2Π , 4Σ− and 2Σ−. First calculations
the process (1) is 3.64 eV, corresponding to the asymp- g u u u
1 − were made by Noble et al. [2] who used the R-matrix
0 toticenergyofOandO fragmentsfromthelevelv =0,
method [3] to determine the positions and widths for
. whereas for process (2) corresponds to the oxygendisso-
1 these four resonances. The O target was represented
ciation of 5.11 eV. 2
0
usingnine states,correspondingtothe orbitalconfigura-
Such collisions are important to study phenomena oc-
5 tions: [core]1π41π2 and[core]1π31π3. The scatteringT-
1 curring in the upper atmosphere, re-entry physics, elec- u g u g
matrixwascalculated,inthefixed-nucleiapproximation,
: tricaldischargesandplasmachemistry. DEAistheprin-
v for internuclear distance range [1.85, 3.5]a , using the
cipalmechanisms,inmolecularplasmas,forformingneg- 0
Xi ative ions from neutral molecules; the inverse process configurations: [core]1πu41πg3(2Πg), [core]1πu31πg4(2Πu),
r represents associative detachment. Although significant [core]1πu41πg23σu(4Σ−u) and [core]1πu41πg23σu(2Σ−u), for
a theoretical and experimental effort has been invested in energies up to 15 eV.
characterizingelectron-O crosssections [1], information In our previous paper on state-to-state cross sections
2
is only available for the vibrational ground state of O for resonant vibrational excitation (RVE) for electron-
2
forwhichbothprocesseshaverathersmallcrosssections. oxygen scattering [4], we extended Noble et al.’s cal-
Here, we willshow thatDEA andEID processesbecome culations toward larger internuclear distances using the
much more important for vibrationally excited oxygen, quantumchemistrycodeMOLPRO[5]. Weusedamulti-
asthe correspondingcrosssectionsincreasesbyordersof referenceconfigurationinteraction(MRCI)modelandan
magnitude with the excitation of the molecule. These aug-cc-pVQZ basis set. For the neutral ground-state of
−
cross sections represent fundamental input quantities O2 as well as for the real part of its anionic state O2,
the active space included the first 2 core orbitals (1σ ,
g
2σ ) and 8 valence orbitals (2σ , 3σ , 2σ , 3σ , 1π ,
g g g u u u
1π )plus 150externalorbitalsfora totalof160contrac-
g
∗Electronicaddress: [email protected] tions. TheMRCIorbitalsweretakenfromaground-state
2
multi-configuration self-consistent field (MCSCF) calcu- 7
lation in which 4 electrons were kept frozen in the core 6 HaL
owrebrietaclosnasinddereexdciftoartitohnes1a2m- aonndg 1a3ll-etlhecetrvoanlesnocfetohrebniteauls- LeV 5 2S- OH3PL+OH3PL
H u
tral and ionic state respectively. gy 4 OH3PL+O-H2PL
er 2P
In the presentworkwe update Noble et al.’s R-matrix en 3 u
ctthiaoelncusstlwaatteierosenispnevinroflovorermddeeirdntutohsiehnagsvcteahtateerbUienKtgtReprMroroeclpecsroseesdsee.nstCa[6ta]il.ocnuOlaor--f Potential 12 X3S-g 4Su-
bitalsfortheO2weregeneratedusingconfigurationinter- 0 2Pg
action (CI) calculations using a cc-pVTZ Gaussian-type
2 3 4 5 6 7 8
orbital (GTO) basis set. The electrons in the lowest 3 InternucleardistanceHa.u.L
coreorbitals,(1σg,2σg,1σu)6,werefrozenandanactive 12
space was constructed from 9 valence orbitals (3σg, 2σu, HbL
3σ , 1π , 2π , 1π )10. The scattering calculations with 10
u u u g
17 electrons also used a GTO basis [7] to represent the
8
continuum electron. The calculations were based on use
LV
of a complete active space CI representation which in- e 6
H
volvesplacingtheextraelectroninbothacontinuumor- G
bitalandtargetorbitalsusingthe followingperscription: 4 4S- 2Su-
u
(1σg, 2σg, 1σu)6 (3σg, 2σu, 3σu, 1πu, 2πu, 1πg)11 and 2 2Pu
(1σg, 2σg, 1σu)6 (3σg, 2σu, 3σu, 1πu, 2πu, 1πg)10 (4σg, 2P
5σ ,3π ,4σ ,2π , 3π , 1δ , 1δ )1, wherethe secondset 0 g
g u u g g g u 2.0 2.5 3.0 3.5
ofconfigurationsinvolvesplacingtheextraelectroninan
InternucleardistanceHa.u.L
uncontracted[8]targetvirtualorbital. Calculationsused
anR-matrixradiusof10a0. Boththe MOLPROandR- FIG.1: (Coloronline)(a)Potentialenergycurvesforground
matrixcalculationswereperformedusingD2h symmetry. stateX3Σ−g ofO2 andforthefourlowestresonantstatesO−2;
ThepotentialcurvescalculatedwiththeR-matrixand (b)The corresponding resonance widths, Γ(R),asa function
MOLPRO codes use different basis-sets, different theo- of the internucleardistance.
retical models and computational methods. This means
thatthe resultingcurvesdidnotjoinanda mergingpro- a smaller contribution coming from the 2Σ− state. In
cedure was required. First of all the O neutral ground- u
2 the case of DEA and EID processes we show that they
statepotentialwascalculatedusingMOLPROandallthe
are dominated, at least for low vibrational levels v of
subsequent results were referred to this curve. The real
O , by the 2Π resonance. Although electron attach-
part of the resonance potentials, computed as a bound 2 u
ment from oxygen molecules has been widely studied [9]
scattering state in the R-matrix calculations, were fixed
there are only a few, rather old, papers reporting cross
at large internucleardistances beyondthe crossingpoint
section measurements of the DEA process as a function
to the MOLPRO curve which precisely reproduces the
of the incident electron energy. We cite here Rapp and
experimental oxygen atom electron affinity of 1.46 eV.
Briglia [10], Schulz [11] and Christophorou et al. [12].
At shorter internuclear distances, the R-matrix resonant
DEAfromthe1∆ stateofO hasalsobeenobserved[13]
curves, are simply a smooth continuation of these large g 2
andfoundtohaveacrosssectionofsimilarmagnitudeto
R curves and therefore their positions are fixed by the
process (1). Cross sections for EID only appear to have
corresponding MOLPRO curve. Potential energy curves
for the O (X3Σ−) ground state, which supports 42 vi- been measured for electronically excited states of O2 by
2 g Cosby [14].
brational states, and the four resonance states, plus the
In Born-Oppenheimer approximation, the dynamics
corresponding widths, are reported in Fig. 1. We note
of the oxygen nuclei in DEA is treated within the
that the new calculated potentials are slightly changed
local-complex-potential model [15], already satisfactory
withrespecttothoseofourpreviouspaper[4], inpartic-
adopted for resonant calculations in other diatomic
ularforthe2Π symmetry,andthiscouldaffecttheRVE
u molecules (see Refs. [4, 19] and references therein). The
cross section values. To check this aspect, we performed
corresponding cross section from the vibrational level v
new calculations for RVE processes, observing however
of oxygen and for electron energy ǫ is given by:
no significant changes in the cross sections with respect
to the corresponding results in [4]. m K
σ (ǫ)=2π2 e lim ξ(R)2 , (3)
Previously[4]weshowedthatforenergiesuptoabout v
k µ R→∞| |
4 eV the RVE crosssections arecharacterizedby narrow
spikes dominated by the 2Π resonance. For energies whereK istheasymptoticmomentumofthedissociating
g
−
about 10 eV, the cross sections showed a broad maxi- fragments O and O with reduced mass µ; m and k =
e
mum due to enhancement by the 4Σ− resonance with √2m ǫ are the incoming electron mass and momentum
u e
3
respectively and ξ(R) is the solution of the Schrodinger-
0.015 HaL
likeequationfortheresonantstateandtotalenergyE =
Presentwork
ǫv+ǫ: 2L Rapp&Briglia
Þ 0.010
H
~2 d2 − i cs Schulz
−2µdR2 +V + 2Γ−E ξ(R)=−V χv(R), (4) EA Christophorouetal.
(cid:18) (cid:19) D 0.005
whereV−+ iΓisthecomplexpotentialoftheresonance
2
reported in Fig. 1, V2 = Γ/(2πk) is the discrete-to- 0.000
4 6 8 10 12 14
0.015 HbL
continuum potential coupling and χ is the vibrational
v H L
wavefunctionofO correspondingtothevibrationallevel Sum
2 L
v. Rrepresentstheinternucleardistance. Thereisnotin- Þ2 0.010 2Pg
H
terference among the resonantstates with different sym- cs 2Pu
metries and for the two Σ−u states the interference can EA 4Su-
be considered negligible as they have different spin mul- D 0.005
2S-
u
tiplicity.
0.000
4 6 8 10 12 14
ElectronenergyHeVL
III. RESULTS AND DISCUSSION
FIG. 2: (Color online) (a) Calculated dissociative electron
Figure2(a)showsourresultsfortheDEAcrosssection
attachment cross section for v = 0 compared with exper-
for O (v =0) comparedwith the experimentalresults of
2 imental results of Rapp and Briglia [10], Schulz [11] and
Rapp and Briglia [10], Schulz [11] and Christophorou et
Christophorou et al. [12]. (b) Contributions from the four
al. [12]. The agreement is excellent, within the experi-
resonances tothe total cross section.
mental error of 15%: the peak is positioned at 6.43 eV
with an absolut±e value of 0.0154 ˚A2 and the FWHM
of about 2 eV. Fig. 2(b) reports cross sections coming the interplay between the neutral vibrationalwave func-
from all four resonances and their sum. As found exper- tion and the resonant continuum wave function. Anal-
imentally, the main contribution to DEA cross section ysis of the resonance contributions to the cross section
comes fromthe 2Π state ofO−. We also note, atabout at v = 20 shows a complicated picture with both Π res-
u 2
8.5 eV, the presence of a significant contribution due to onances making significant contributions at low energy
the4Σ− symmetrywhich,addedtothemain2Π contri- and important contributions from the Σ resonances at
u u
bution, reproduces the high-energy tail observed exper- higher energies.
imentally. The non-negligible contribution of 4Σ− res- Figure 3 also shows the cross sections for v =30. The
u
onance to DEA cross section has already been deduced increasing trend of the maxima is now inverted. The
fromthe measuredangulardistributionofO− ions[16]. eigenvalueforthis vibrationallevel[4],infact,lies above
Figure 3 shows our DEA cross sections calculated for the energy of the O−(2P)+O(3P) asymptotic state (see
higher vibrational levels of O , v = 10,20 and 30, com- Fig. 1), so that the DEA process becomes exothermic
2
pared with the result v = 0. All cross sections are with a threshold at zero-energy. For this case Rc > Re
summedoverallfourresonancestates. As expected[17], sothatthe exponentρinEq.(5)vanishes (Γ(R>Rc)=
the threshold of the process shifts to lower energies as 0) and the magnitude of the cross section is no longer
the vibrational level increases; the is due to the reduced governedby the survival factor. The decreasing trend of
threshold for dissociation limit. At same time the maxi- the cross section maxima is maintained for v >30.
mumvalueofthecrosssectionforv <30growsbyofsev- The corresponding EID cross section from
eralordersofmagnitude atlowenergies. This behaviour O2(X3Σ−g;v) and electron energy ǫ is given by [19]:
is due to the survival factor e−ρ [18], given approxima-
tively by: EID 64π5m2 ′k′ 2
σv (ǫ)= ~4 dǫ k |hχǫ′(R)|V|ξ(R)i| , (6)
Z
Rc Γ(R)dR
e−ρ exp , (5) where means integration over the internuclear dis-
≃ "−ZRe ~v(R) # tance Rh·,·ξ·i(R) is the resonant wave function solution of
theEq.(4)andχǫ′ isthecontinuumwavefunctionofO2
′ −
whereintegrationisextendedovertheregionbetweenthe with energyǫ representingthe 2O + e fragments. The
′
classical turning point (R ) and the stabilization point continuumenergyǫ wasintegratedfromO dissociation
e 2
(R ) and v(R) is the classical velocity of dissociation. threshold up to 10 eV.
c
As the vibrational level increases, R increases and the Figure 4(a) shows the calculated EID cross sections
e
−
survival probability grows like the cross section. The os- for v = 0. Contributions coming from the four O res-
2
cillations, visible at high vibrational levels, results from onances are shown. Like DEA, the main contribution
4
1
HaL
v=0 Sum
Þ2L 0.1 vv==1200 Þ2HLcs 0.006 22PPgu
HDEAcs 0.01 v=30 sociation 0.004 42SSu-u-
0.001 Dis 0.002
10-40 2 4 6 8 10 12 14 0.0000 5 10 15 20
ElectronenergyHeVL ElectronenergyHeVL
HbL
FIG. 3: (Color online) Calculated dissociative electron at- 0.1 v = 30
etalschvm=en1t0,cr2o0ssansdec3ti0o,ncsofmorpavriebdrawtiiotnhatllhyeegxrcoiutenddOle2v,elfovr=lev0-. Þ2HL v = 20
s 0.01
Thecrosssectionsincludeallthefourresonantcontributions. c
n v = 10
o
ati 0.001
ci
o
s
s
comes from the 2Π symmetry, which gives a maximum Di 10-4 v = 0
u
at6.93eVwithanabsolutevalueof0.0072˚A2,andasig-
nificantcontributionfromthe4Σ−at9.47eVwithacross 10-50 5 10 15 20
u
section of 0.0026 ˚A2. The contribution from the other ElectronenergyHeVL
symmetries is negligible. Figure 4(b) shows the cross
sectionsforexcitedvibrationallevelsofoxygencompared FIG. 4: (Color online) (a) Calculated cross sections for reso-
withthoseforthegroundlevel. Crosssectionsincludeall nant electron impact dissociation of oxygen for v = 0. Con-
−
tributions from the four O resonances are shown; the black
four resonance contributions. As expected [17] the EID 2
curve is the sum. (b) Dissociating cross sections for vibra-
crosssectionincreasesrapidlywithvibrationalexcitation
tionally excited oxygen at v = 10, 20 and 30 compared with
and the threshold moves to lower energy. The cross sec-
theresults for v=0.
tion for v =30, for example, reaches a value comparable
with that of the well-known Shuman-Runge dissociative
transitions for the same vibrationallevel[20], whose dis- tionalgroundstateandinitsv =20state. Forthev =0
sociative cross sections decrease with increasing the vi- level vibrational excitation is the dominant low-energy
brationalexcitationofthemolecule. WenotethatEIDis process. However for vibrationally excited molecules the
known to occur efficiently via electron impact excitation DEA increases rapidly and becomes much the most im-
of O2 [1, 9]. However the threshold for electronic exci- portant process at low energies. We expect that the in-
tation processes lie significantly higher than those con- clusionoftheseresults willhaveimportantconsequences
sideredhere, makingthem relativelyunimportantin low in models of plasmas containing molecular oxygen and,
temperature plasmas. inparticular,willleadto asignificantincreaseinO− ion
production in these models.
Recently, we have calculated also the rate coefficients
IV. CONCLUSIONS fortheprocesses(1)and(2)asafunctionoftheelectronic
temperature and for all the vibrational levels. Details of
thecalculationsandresultswillbereportedin[21]. DEA
Inconclusion,wepresentnewcalculationsfordissocia-
tive electron attachment for oxygen using ab initio po- and EID cross sections as a function of electron energy
and O vibrational state, along with the corresponding
tential energy curves and the first calculations for reso- 2
rate coefficients, have been made freely available in the
nantelectron-impactdissociationof oxygen. We confirm
thedominantcontributionof2Π symmetryinbothpro- Phys4Entry database [22].
u
cesses starting from v = 0. Both cross sections however
increase rapidly with increase in the vibrational excita-
tion of the molecule and for these vibrationally excited Acknowledgements
states it is necessary to consider the contributions from
−
all four of the low-lying O resonance states. TheauthorsaregratefultoProf. M.Capitelli(Univer-
2
Finally, Fig. 5 compares cross sections for different sit`adiBariandIMIP-CNRBari,Italy)forusefuldiscus-
resonant processes involving electron-O (X3Σ−,v) scat- sion and comments on the manuscript. This work was
2 g
tering: our previous results for v v +1 vibrational- performed as part of the Phys4Entry project under EU
→
excitation [4], with the present cross sections for DEA FP7 grant agreement 242311. One of the authors, RC,
andEIDforthecaseswhentheO isinitiallyinitsvibra- wouldliketoacknowledgefinancialsupportfromMIUR-
2
5
PRIN 2010-11,grant no. 2010ERFKXL.
10
HaL
v=0
L 1
2
Þ
H
on 0.1 RVE
cti
e
s 0.01
s
s
Cro 0.001 EID
DEA
101-04
HbL
v=20
L 1
Þ2 DEA
H
on 0.1 EID
cti
e
s 0.01 RVE
s
s
o
Cr 0.001
10-4
0 5 10 15
ElectronenergyHeVL
FIG. 5: (Color online) Summary of the cross sections for
electron-O2 collisions: Resonant vibrational excitation for
∆v = 1 transition [4] (solid line), dissociative electron at-
tachment (dashedline) and resonant dissociation by electron
impact (dotted line) for (a) v =0 and (b) v =20. The cross
−
sections are thesum overthe four O resonances.
2
[1] Y.Itikawa, J. Phys.Chem. Ref. Data38, 1 (2009). [11] G. J. Schulz,Phys. Rev.128, 178 (1962).
[2] C. J. Noble, K. Higgins, G. W¨oste, P. Duddy, P. G. [12] L. G. Christophorou, R. N. Compton, G. S. Hurst, and
Burke, P. J. O. Teubner, A. G. Middleton, and M. J. P. W. Reinhardt,J. Chem. Phys.43, 4273 (1965).
Brunger, Phys.Rev. Lett.76, 3534 (1996). [13] T. Jaffke, M.Meinke, R.Hashemi, L.G. Christophorou,
[3] J. Tennyson,Phys. Rep.491, 29 (2010). and E. Illenberger, Chem. Phys.Lett. 193, 62 (1992).
[4] V. Laporta, R. Celiberto, and J. Tennyson, Plasma [14] P. C. Cosby,J. Chem. Phys. 98, 9560 (1993).
Sources Sci. Tech.22, 025001 (2013). [15] W. Domcke, Phys.Rep. 208, 97 (1991).
[5] H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, [16] V. S. Prabhudesai, D. Nandi, and E. Krishnakumar, J.
M. Schu¨tz, et al., MOLPRO, version 2012.1, a package Phys. B: At. Mol. Opt.Phys.39, L277 (2006).
of ab initio programs (2012). [17] D.T.StibbeandJ.Tennyson,NewJ.Phys.1,2(1998).
[6] J.M.Carr,P.G.Galiatsatos,J.D.Gorfinkiel,A.G.Har- [18] T. F. O’Malley, Phys.Rev.155, 59 (1967).
vey,M.A.Lysaght,D.Madden,Z.Masin, M.Plummer, [19] V. Laporta, D. Little, R. Celiberto, and J. Tennyson,
and J. Tennyson, Eur.Phys. J. D 66, 58 (2012). Plasma Sources Sci. Tech. 23, 065002 (2014).
[7] A. Faure, J. D. Gorfinkiel, L. A. Morgan, and J. Ten- [20] A. Laricchiuta, R. Celiberto, and M. Capitelli, Chem.
nyson,Computer Phys.Comms. 144, 224 (2002). Phys. Lett. 329, 526 (2000).
[8] J. Tennyson, J. Phys. B: At. Mol. Opt. Phys. 29, 6185 [21] V. Laporta, R. Celiberto, and J. Tennyson, AIP Conf.
(1996). Proc. 1628, 939 (2014).
[9] J. McConkey, C. Malone, P. Johnson, C. Winstead, [22] Database of the european union Phys4Entry project,
V.McKoy, and I. Kanik,Phys. Rep.466, 1 (2008). 2012–2014.
[10] D. Rapp and D. D. Briglia, J. Chem. Phys. 43, 1480 http://users.ba.cnr.it/imip/cscpal38/phys4entry/database.html
(1965).
