Photodissociation to Several Atomic Terms Bull. Korean Chem. Soc. 2001, Vol. 22, No. 12 1333
Photodissociation to Several Atomic Terms: Near-threshold Resonance for Production of O(3 P) and O(1D) in OH Photodissociation
SungyulLee
CollegeofEnvironmentalScienceand Applied Chemistry, Kyunghee University, Kyungki-do 449-701, Korea Received July 13,2001
A theoretical analysis is presented for the multichannel type resonance at energies above the dissociation threshold toO(1D)inthephotodissociation ofOH. Dissociationstoboth oxygenic termsO(3P)andO(1D) are treated. Total cross sections for producing these oxygen terms display asymmetric resonance due to the quantum interference resulting from complicated interplay of electronic states correlating to these two oxygenicterms. The branchingratios of O(3Pj, j = 0, 1, 2), and the vector properties of O(3Pj, j = 0,1, 2)and O(1D) display extensive changes nearthe threshold resonance as the result of the interactions among the electronicstatescorrelatedwithO(3P) and O(1D).
Keywords: Photodissociation,Resonance,OH.
Introduction
Photodissociation1 is a fundamentalprocess thatcan pro vide ampledynamic information. Variouskinds ofinteractions between theelectronic states and quantum interferencebet weenthe dynamicpathways may give extremely intriguing dynamic phenomena. In some simple situations, such as in direct dissociation, in which all the molecular electronic states correlated only with a single atomic term, measure ments of the properties of photofragments such as the branching ratios and angulardistributions may reveal direct information onthe photoexcitation pathways and the sym
metriesof the electronically excitedstates.2,3In general situ ations, however, interplay of different kinds of interactions may complicate direct link between experimental observations andthe mechanismofdynamicprocesses.Photodissociation tomorethanone atomic limit is such a case, because elec tronicstatescorrelatedwith different atomictermlimitsmay cross or experience avoidedcrossing intheFranck-Condon region. Loosely speaking,two kinds of non-Born-Oppenhei merinteractions(first,theinteractions, such as thespin-orbit coupling,betweenthecrossing statescorrelated with differ entatomic terms intheFranck-Condonregion, and second, the interactions inthe asymptotic region between the elec tronic states correlating with the same atomic term) may influencethephotodissociation processes in this situation. In this case,dynamicsofphotodissociationwouldbe verydif ferent, depending on the energy regime considered. At ener
gies belowthethresholdtothe upper atomic term (O(1D) in the present case), only lower term (O(3P))wouldbe produc edaswehaveshowninaseries ofpublications,4-7 sincethe electronic states correlating with the upper atomic term are closed channels. In many other studies on the predissoci
ation processes, these latter states were neglected for good reasons.8,9 At energies above the threshold to the upper atomic term, however, these molecular electronic states correlating with the upper atomic term must be explicitly included inthe calculation, because these areopen channels
now. Anyapproximations for these stateswould fail totreat theproductionof theupper atomic term. Therefore,theore tical framework to dealwith this general and complicated situation must certainly beneeded to analyze experimental observations at energies above the threshold to the upper atomic term. Thistypeofapproachmay also be a preludeto treating morecomplicated polyatomicprocesses,suchasthe photodissociation of CH2BrCl10orCF2Br211 inenergyregime from which two different atoms can be produced. To our best knowledge no investigations treated this interesting situation, properly including all the interactions discussed above to account for thecomplicateddynamics.
We describe in this work theoreticalformalismtotreat the productionof two atomic terms in the photodissociation of diatomic molecules, and present calculations onthe photo
dissociation of the OH molecule at energies above the dissociation threshold to O(1D). We show that thetheoretical method totreatthephotodissociation processof OH below thethreshold to O(1D)mayalso be employed to computefor thismore generalsituations. Productionsof both O(1D) and O(3P) are theoreticallytreated. We predictthemultichannel type threshold resonance at these energies due to compli
cated interactions between the electronic states correlated with the two oxygenic terms, O(1D) and O(3P). Total cross sections for producingtheseoxygenic termsdisplay theasym metric resonance12-17peak duetothe quantum interference, and theproperties of O(1D) and O(3P) exhibitrapidchanges near theresonance energies.
TheoryandComputation지 Methods
We employ the theory4 that can treat the very general situationsinwhichthere can be more thanone atomicterm limit involved and wheretherecan be allkinds of crossings and avoided crossings among the electronic states. The theorywas described in detailin Ref. 4, and we only briefly summarize ithere tohelp present the results in Section III.
Two basis sets are employed to describe the dissociation
1334 Bull. Korean Chem. Soc. 2001, Vol. 22, No. 12 Sungyul Lee dynamics in the molecular andasymptotic region, respec
tively. The first basis (ABObasis set) is a space-fixedone derived fromHund’s coupling cases. Hund'scase (a) basisis used here, although other coupling cases may also be em ployed as long asall theinteractionsare included toevaluate the total Hamiltonian. The second basis set | JFMljojH >, which is called the ‘asymptotic’ molecular basis, diagona lizes the total Hamiltonian at infinite internucleardistances.
This basis is employed to properly describe the transition amplitudes for thedissociationto eachatomic fine structure state of the oxygenic and hydrogenic terms with total elec tronicangular momentumquantum numbers Joandj'h,respec tively. Here, l is the orbital angular momentum quantum number, j = j +
J
h,andJ
f(= j + l) isthe total final angular momentum quantum number. M is thezcomponentofJ
fin the space-fixedcoordinate system. Thesetwo basis sets are related to each other by the r-independent transformation matrix <JIJ
oJ
h | CASSp>j. Thescatteringequation,[E-H] | k,询而仙=0, (1)
is solved, where H is thefull Hamiltonian which describes motion onthe excited states andk is the wave vector. The scattering wave function |k, jOmOjHm'H} isexpanded interms of energy-normalized continuum eigenfunction |
EJ
fMI
o-
mOHm") of thetotalangularmomentumoperator
J
f| k, jomojHmH)=
X
|EF
fMJIJ
oJ^)〈J
fM
Ijlmp) xJplm 卩
〈Jm \jo'HmomH)i"* (2) Close-coupled equations are solvedtoobtain thecontinuum wave function | EJFMjljomojHm("). Transition amplitudes to a specificfine structure componentof the oxygen atom are computed bythe Golden Rule, and canbe factoredusing the Wigner-Eckart theorem toseparatethedependenceon Mi, M
T(k,
J
oJ
h| i) =X
〈EJ
fMJIJ
o/
hH\£ - Aj-Mtn^)J^jlm卩
defined by
0
ksqs(£
s) =X
(-1 广 q〈KsQs|11q - q)游. (5)The integral cross section for dissociation to a particular spin-orbitcomponentofthefragmentatom is obtained as
4 兀2 aw 1
—3 2Ji+ 1
Ooo, 00 =
X
( 2 Jf +1)1 T( JfJIJoJ'hI Jn )12.JFjl
(6) Thefragmentanisotropyparameter(for theangulardistribu tions) and thealignmentparameter are obtained as the ratio ofthepartial cross sections
P
d= O00;20--- O00;00
and
c O02；00
P
s= O—o00;00(7)
(8) respectively (the definitions ofb's included in these equa tions are given in Ref. 3).
Thepropagationofthescatteringwave function is carried out by the Renormalized Numerov method,18 and appro priateboundary conditions are imposed atthe end of propa
gation(up to 25bohr).Convergence of thecomputedresults is confirmed by increasingthe number of integration steps upto 2500. Thepotentialcurves, transitiondipole moments and the spin-orbit couplingsemployed inthe present calcu
lationsweredescribedinRef.4.
Results
Figure 1 depicts the potential curves of the electronic statesincluded in the present calculations.Zeroof theenergy is defined as thestatistical average of theenergysplittings of O(3Pj, j =0,1,2) in Figure 1. The X2n, 4Z-, 2S- and4nstates correlate with O(3P), while the A2X+, 2A and 22n states
=
X
〈J
fM
| 1J.qM》爲TjFjjjojHJini),(2)
q
where| JMin > is thewavefunction for theinitial state, and
tW |Jn) is called the reduced transition amplitude.
The double differential cross section for the coincidence detection of photofragments and fluorescence is obtained as
---do dQedQk
(爲,k)=
X
ksqs；kdqd
O
KsQsKQd©
KsQs(£
s)CKdQdD(
k), (4) where £S is the polarization vector, relative tothespace-fixed (SF) z-axis, of the emitted light from an excited photofragment. The vector properties of the photodissociation processes are given in terms of the ratios ofO s, whichare describedin Ref. 3 in termsof the geometrical factor and the dynamical T factor.
C
kq is the renormalized spherical harmonics, and 0 is the photon polarizationdensity matrixFigure 1. Ab initio Potential energy curves of OH. Zero of the energy is defined as the baricenter of the energies of O(3Pj, j =0,1, 2).
Photodissociation to Several Atomic Terms Bull. Korean Chem. Soc. 2001, Vol. 22, No. 12 1335 correlate with O(1D). At energies between thresholds to
O(3P) andO(1D), the dynamics is described as predissoci ation ofthe A2X+ state by thethreedissociative 4X-, 2X- and 4n states,4-7 resulting from the spin-orbit couplings of this state with the three repulsive 4X-, 2X- and4n states. Since both of the bound A2X+ and dissociative 2X- state are opticallycoupled with the ground X2n state, and sincethese two excited states interact by spin-orbit couplings, absorp tionspectruminthis energy regime may exhibitasymmetric resonancelineshapesas a result of the quantuminterference betweentwo indistinguishable pathways: that is, between the three indirect dissociationpaths via the A2X+state and thedirectpath via the 2X- state.
At energies above the threshold todissociation to O(1D), the photodissociation dynamics may become much more complicated for several reasons. First, the channels for the O(1D) term are now open, and dissociations both to O(3P) and O(1D) compete atthese energies. Second, the electronic states (A2X+, 2A and 22n)correlating with O(1D) play a significant role in the dynamics, and interactions among them would affect theproperties of O(1D) produced. Third, interactions amongthese states correlatingwith O(1D) and those(X2n,也-,2S" and4n) correlating with O(3P)mayalso affect the outcomes of photodissociation in a complicated fashion. Forexample, these interactionsmaygiverise to the multichannel-type resonance at energies nearthe threshold to O(1D). The effects of quantuminterferencemayinfluence theresonances for productionof O(3P) and O(1D) in differ entways. Morespecifically,the degreeofasymmetry of the resonances would be different. In this work, we show that theinteractionsamongtheelectronic statescorrelatingwith O(3P) or O(1D) can yield threshold resonances at energies abovethedissociation limitto O(1D) bothfor dissociation to O(3P) and O(1D).
Figure 2 shows suchresonances reached from the initial groundX2n+2/3 state J = 15.5and v = 0). In the total cross section for producing O(3Pj, j = 0, 1, 2), two resonances are observed atE = 15880 and 15908 cm-1. These resonances
Figure 3. Anisotropy parameters
P
d of angular distributions of O(3Pj, j =0,1,2).o
은 으 )
ou
=
응 OT留 。」°
0.52.0
0.6 0.5 0.4 0.3 0.2 0.1 15910 159200.0 0.0 15870 15880 15890 15900
Energy (cm-1)
Figure 2. Multichannel threshold resonances lying above the threshold to O(1D), reached from the initial ground X2n+2/3 state J
= 1 1.5 and vi = 0). Total cross section and branching ratios for production of O(3Pj, j = 0, 1,2).
0.7
exhibitasymmetric features.12-17The asymmetry of thetwo resonances can be seen more clearly by noticing that the branchingratios for production ofO(3Pj, j =0, 1, 2) changes considerably near the resonances in Figure 2. Figure 3 depictstheangulardistributionanisotropyparameters19-21
P
dofO(3Pj, j =0, 1, 2)near theresonance. Thevalues of
P
d are differentfrom each other, and they changerapidly near the resonance. Different values of pD's for O(3Pj, j = 0, 1,2) near the resonance suggests thatangular resolutionof photofrag ments maybepossiblenearthe multichannelresonance. It is noteworthy to observethatthevalues ofP
d of about0.5 are different from the high-energy recoil limit value (-1) for perpendicular (| AQ | = 1, n — X) electronic transition at off-resonance energies. It seems that both of the perpendi culartransitions (A2X+ — X2n and2X- —X2n) may interfere to affect the angulardistributions ofO(3Pj, j =0, 1,2).
The fluorescence anisotropy parameters2,3
P
s of O(3Pj, j = 0, 1, 2) shown in Figure 4 alsoexhibitsimilarbehaviors near theresonance.The dissociation to O(1D) is alsoopenat energiesnear these resonances, and thespectrum fordissociation tothis state of the oxygen atomis given in Figure 5 along with the valuesof
P
dandP
s. ThecrosssectionattheFigure 4. Fluorescence anisotropy parameters ps of O(3Pj, j = 0, 1, 2).
1336 Bull. Korean Chem. Soc. 2001, Vol. 22, No. 12 Sungyul Lee
Figure 5. Total cross section and anisotropy parameters &)and ps
for production of O(1D).
resonance at E = 15880 cm-1 is so much smallerthanthatat E = 15908 cm-1 that it isincluded as inset. Both anisotropy parameters
P
dand Psdisplay rapid changesnearthereson ances. The asymmetry of the resonance E = 15880 cm-1is now veryevident. The computed asymmetry of theresonance and the rapid changes of the vector properties near the resonancecouldgiveusefulinformation when theyarecom paredwith theexperimentally measured values. Specifically, the interactions between the bound and the dissociative states, and the relative oscillator strengths from the initial state to the bound and the dissociativestatescouldbe determined by direct computation ofthe asymmetry parameters as shownin our previous work.24
SincetheresonancesshowninFigure2-Figure 5 lie above the threshold to O(1D), they do not correspond to the rovibrational levels of the A2X+ state. They rather seem to correspond to the shaperesonanceattributable tothecentri fugal barrier of thedissociative states.Sincetheheightof the centrifugal barrier depends on the magnitude of the orbital angular momentumquantum number l for therelativemotion of the two nuclei,and since
J
f = j +l, there would hardly be resonances observed for lowJ
f, ifthe multichannelreson ances are due tothe centrifugal barrier. Thereforewe carry out the computations for lowJ
f, sayJ
f = 1.5, and confirm that indeed no multichannel-type resonance is computed.These resonances are, however, different from ordinary shape resonance, since the effects ofthe asymptotic inter actions are also seen. For example, it shouldbe noted that theresonancesare seen both in the cross section fordissoci
ation to O(3P) and to O(1D) in Figure 2. Iftheresonance is duetothecentrifugal barrier ofonly oneofthedissociative states, cross sections for dissociation to O(3P) or to O(1D) wouldexhibitresonance. Therefore, itseems to be ofmulti channel character,asshown byFreed and co-workers for the threshold resonances in thephotodissociation of CH+.2
Since these resonances are predicted tobe observedjust
above the thresholdto the upper atomic term O(1D), the kinetic energy of the atoms produced is small. Thus, these resonances would correspond to those observed in the collision of ultracold atoms.22,23 The multichannel reson
ances predicted in this work in thephotodissociationof OH, therefore, mayalsobe observed in thecollisionof ultracold O(1D) and H(2S) atoms. Experimental study onthis type of multichannel threshold resonanceswill beveryintriguing.
Acknowledgment. This work was supported by Korea Science and EngineeringFoundationGrant(1999-1-121-001 5).
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