460
J. Phys. Chem. 1994,98, 460-466
Studies of Photoionization Dynamics of CH, NH, and OH Radicals at Near-Threshold Photoelectron Kinetic Energies Kwanghsi Wang,’ J. A. Stepheris,’ and V. McKoy Arthur Amos Noyes Laboratory of Chemical Physics,$ California Institute of Technology, Pasadena, California 91 125 Received: August 5, 1993; In Final Form: October 20, 19930 W e discuss results of theoretical studies of rotationally resolved photoelectron spectra of the CH, NH,and OH radicals, including predictions of zero-kinetic-energy (ZEKE) spectra for molecular ions produced via resonance enhanced multiphoton ionization. The influence of dynamical features such as Cooper minima, orbital evolution, and 1 mixing are examined for photoionization of the 3pu Rydberg orbital in these radicals. We also make specific predictions for the photoelectron spectra for each molecule within the context of current experimental capabilities.
I. Introduction Recently there have been several theoretical and experimental studies of the photoelectron spectra for resonance enhanced multiphoton ionization (REMPI) of the low Rydberg states of some first-row diatomic hydrides.’“ These studies have probed previously and recently identified Rydberg states of these molecules, particularly through the rotationally resolved photoelectron spectra of these Rydberg states. Such rotationally resolved spectra provide significant insight into the underlying dynamics of molecular photoionization at a state-selectivelevel. In this paper we present the results of some further studies and a comparison of the dynamical effects due to Cooper minima, Rydberg orbital evolution, and 1 mixing for REMPI of the E ’ W (3pu) state of CH, the f I l l (3pu) state of NH, and the D 22(3pu) Rydberg state of OH. Motivated by recent developments and refinementsof the zero-kinetic-energypulsed-field-ionization (ZEKE-PFI) we also report the ZEKE spectra for these molecules for realistic experimental conditions. Measurements of these ZEKE spectra are currently quite feasible, and we hope the present studies will stimulate such investigations. The remainder of this paper is organized as follows. In section I1 we briefly discuss the theoretical formulation and numerical details of the calculations. In section I11 we discuss and compare the fundamental body-frame dynamical quantities which govern the photoionization dynamics of these three systems and present rotationally resolved spectra which illustrate the systematics of these spectra. 11. Formulation and Numerical Details
and 20
OH[X211(u”,J’?]-OH*[D2Z-(u’,J’,”)]
2 OH+[X’ Z - ( u + , f , N + ) ]
(IC)
The photon energies of the excitation and ionization steps may differ from each other in such two-color experiments. Under collision-free conditions, ionization out of each My level can be treated as an independent channel for linearly polarized light. The integrated cross section and asymmetry parameters for photoionization of a J’ rotational level of the resonant state leading to a J+ level of the ion can then be written aslo
where
4L+ 1
P2L
=-
(-1)m(21+ 1)(21’+
l)UMPM,
x
Mr&+
a. Rotatio~llyResolved (2+1’) REMPI. The (2+1’) REMPI processes via the E’2Z+ (3pu) state of CH, the f I l l (3pu) state of NH, and the D 22- (3pu) state of OH can be summarized as follows:
20
C H [ X 211(u”,J’’)]
-
CH*[E’2Z+(u’,J’,N’)]
20
NH[a’A(v’:J’’)]
NH*Lf’Z+(v’,J’= N’)]
Present address: Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder, CO 80309-0440. t Contribution No. 8836. *Abstract published in Advance ACS Abstracts, December IS, 1993.
0022~3654/94/2098-0460S04.50/0 , , . . . ..-.... -, . ~
~
~
with u the total cross section, BZLthe asymmetry parameter, P ~ ( c 00)s a Legendre polynominal, and 0 the angle between the photoelectron and the polarization vector of the laser. For the branching ratios of interest here, the constant implied in eq 3 is unimportant and will be suppressed. In eq 3, ~ M , N , is the population of a specific iUf level of the intermediate state created by two-photon excitation. For rotational branches other than Q branches, pn,& given by a product of a 3-j symbol and a rotational line strength B,ll
where N is a normalization constant. The rotational strengths Ca 1994 American Chemical Society
Photoionization Dynamics of CH, NH, and OH Radicals
B for two- and threc-photon excitation of diatomic molecules have been tabulated by Halpem e? al.l1 However, in the case of Q branches, p ~ , f ibecomes12 ~
The evaluation of the factors B2 and BO of eq 6’requires a summation over all possible paths and dipole-allowed virtual states in the twephoton excitation step. An expression for Ci,,,(My,MI+) of eqs 3 and 4 which explicitly considers the spin coupling associated with multiplet-specific final state wave functions and an intermediate coupling scheme between Hund’s cases (a) and (b) for the resonant and ionic states has been given by Wang and McKoylO for photoionization of linear molecules. A central quantity in these studies is the matrix element for photoionization of an electron from a bound molecular orbital 4, into a continuum orbital $j$). Here kis the momentum of the photoelectron and (-) denotes incoming-wave boundary conditions. The partial wave components t&L of q(-)(r)are defined by an expansion in spherical harmonics aboutk of the photoelectron
Single-center expansions of &&(r) and &(r’), e.g.,
define partial wave photoelectron matrix elements #’(It) in the molecular frame for ionization out of orbital 4,(r’), i.e.,
= where R denotes a dependence on internuclear distance, p the photon polarization index in the molecular frame, m and X the projection of 1 in the laboratoryand molecular frames, respectively, and a rotational matrix in Edmonds’ notation.13 Equation 9 reveals an important underlying dynamical aspect of molecular photoelectron wave functions. Whereas only 1 = I’ terms are allowed in eq 9 for the central fields of atomic systems, where the angular momentum of the photoelectron must be conserved, 1 # I’ terms arise in eq 9 due to the nonspherical potential fields of molecular ions. Such angular momentum coupling in the photoelectron wave function plays a crucial role in rotationally resolved molecular photoelectron spectra. This is particularly true when these angular momentum components are influenced by Cooper minima and shape resonances. The use of molecular photoelectron orbitals which correctly incorporate such angular momentum coupling is essential at the low photoelectron energies of interest here. Parity selection governing changes of rotational angular momentum upon ionization, have been derived previously and are of the form
AJ+
-
a+Ap+ I =even
(10) for Hund‘s case (a) coupling scheme, where AJ = J+ - J’, AS = S+ - S’,and Ap p+ - p’, In eq 10, p is the parity index for e/flevels.10 For the cases of CH and O H , whose Rydberg and ionic states are beat described by the Hund’s case (b) coupling, eq 10 reduces toloJ4-16
AN+l=odd (1 1) where AN = N+ - N’. b. Numerical Dewla In applications of our procedure to REMPI of Rydberg states, we use the improved virtual orbital
The Journal of Physical Chemistry, Vol. 98, No.2, 1994 461
(IVO) method” to obtain the wave functions of the resonant state. The core orbitals of these Rydberg states are taken to be those of the fully relaxed ion. The SCF wave function for the E ’ W Rydberg state of CH was obtained with a [9sSp/Ss3p] basis set of Dunning18 augmented with two d functions (a= 0.92 and 0.256) on the carbon atom, a [5s/3s] basis setI9 augmented with two p functions (a = 1.4 and 0.25) on the hydrogen atom, and a diffuse basis set of five s (a = 0.07, 0.0253, 0.011 41, 0.005 89, and O.OOlS), five p (a = 0.054, 0.0257, 0.011 13, 0.004 49, and 0.0013), and three d (a = 0.0569, 0.0289, and 0.008 46) functions at the center of mass. With this basis, the SCF energy for the E ’ W Rydberg state of CH was-37.992 993 au at the equilibrium internuclear distance of & = 2 . 2 5 ~ ~ . ~ O Note that this basis set is essentially the same as that used in ref 1 except that the diffuse d functions at the center of mass were not included previously.21 Inclusion of these diffuse d functions at the center of mass leads to some important changes in the angular momentum compositionof the 3paorbital of CH obtained with a basis which did not include these functions. For example, with these d functions, the 3pa orbital has 19.65% s, 68.07% p, 12.12%d,andO.l1%fcharacterat theReof2.25uowhilewithout them thecorrespondingcompositionis 18.19%s,78.27%p, 3.40% d, and 0.12% f character. In section 111 we will see that these differences lead to some significant changes in the calculated rotationally resolved photoelectron spectra for REMPI of this orbital. The basis set for the SCF wave function of the f Rydberg state of N H was given in ref 5. The basis set for the D 2 2 - state of OH was that of ref 22 augmented with two d diffuse functions (a = 0.036 and 0.008) at the center of mass. For the final state we assume a frozen-coreHartree-Fockmodel in which the core orbitals are taken to be those of the ion and the photoelectron orbital is obtained as a solution of a one-electron SchrMinger equation containing the Hartree-Fock potential of the molecular ion, Von(r,R),Le.,
I&;,
To obtain the partial wave photoelectron orbitals we use an iterative procedure, based on the Schwinger variational principle, to solve the LippmannSchwinger equation associated with eq 12?3 This procedure begins by approximating the static-exchange potential of the relaxed ionic core by a separable form
where the matrix V1is the inverseof thematrix with the elements ( U ) , j = (ai(Ula,),the a’s are discrete basis functions such as Cartesian or spherical Gaussian functions, and U is twice the static-exchange potential in eq 12 with the long-term Coulomb potential removed. The LippmannSchwinger equation with this separable potential Us(r,r’) can be readily solved and provides an approximate photoelectron orbital @&. These’solutionscan be iterativelyimproved to yield convergedsolutionsto the LippmannSchwingerequation containing the exact static-exchangepotential USE.In this study, two iterations provided converged solutions of eq 12. The basis set used in the expansion of the separable potential of eq 13 and other details of the calculations can be found in ref 1 for CH, ref 5 for NH, and refs 6 and 22 for OH.
III. Results and Discussion a. Body-Frame D y ~ m i Quantities. ~d To illustrate possible differences in the photoionization dynamics of the 3pu Rydberg orbitals of CH (E’22+),NH (fin), and OH (DZZ-), it is useful to compare the dependence of the quantum defects p ( R ) of these orbitals and their partial wave photoionization amplitudes on internuclear distance. In Figure 1 we show quantum defects p(R) obtained from our IVO calculations. These are
462 The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
Wang et al.
0.0 0.0
,
1.o
3.0
2.0
2.0
4.0
6.0
6.0
10.0
40
60
BO
100
4.0
R (Bohr) Figure 1. Calculated quantum defects p(R) for the E ' W (3pu) state of CH, the f I l l (3pu) state of NH, and the D ZE- (3pu) state of OH.
1
a
--
w
-q
a01 iiw P=O
wsss P = l
u "P=2
w P=3 QoQoD P = 4
00 00
20
Kinetic Energy (eV)
Figure 3. Magnitude pf)I of the partial wave components of the photoelectron matrix element for photoionization of the D Q-(3pu) Rydberg state of OH for the (a) 3pu ku and (b) 3pu kr ionization channels. The inset shows the principal-valuedipole amplitude 0;'for the I = 2 component.
-
0.0; 0.0 0.2
I
I
I
I
I
,
I
,
I
-
I
3pu- ka (Figure 2b) channels for photoionization of the E ' W Rydberg state of C H at the R, of 2.25a0. Note that Df)here 1 is one of the 1.1 components of the photoelectron matrix element 2 3 of eq 9. Interesting features of Figure 2 include (i) strong 4 [mixing among the s, p, d, and f partial waves of the photoelectron a t low photoelectron energies in the ku channel, (ii) unusually strongf waves in both ku and ka continua, and (iii) a minimum in the d (I = 2) wave in the 3pu ka channel around -0.15 eV (Figure 2b). However, the corresponding principal-value dipole amplitude which actually determmes the position of the Cooper zero>* does not show a distinct sign change within theenergyrange studied (not shown). TheCooper zeroassociated 0.0 with the minimum in the d wave of the ka channel must occur 0.0 2.0 4.0 6.0 6.0 10.0 just below threshold in the discrete region of the ~pectrum.s.~~ Kinetic Energy (eV) The 1Df)I's for the 3pu ka and 3pu ku channels for Figure 2. Magnitude @-'I of the partial wave components of the photoionization of the f I I I (3pu) Rydberg state of NH have been photoelectron matrix element for photoionization of the E' Q+(3pu) reported elsewhere.5 Briefly, Cooper minima were predicted in Rydberg state of CH for the (a) 3pu ku and (b) 3pu kr ionization channels. the 1 = 2 (d wave) components around the minimum in IDf'I at a kinetic energy of about 0.5 eV for the ku(ln) and kr('Z-) derived from the relation E(R) - E+(R) = -l/[2(n - I . ~ ( R ) ) ~ ] , channels and about 1.8 eV for the ku(12+)and ka(lA) channels. The actual sign changes associated with these minima are seen where E(R)and E+(R)are the total electronic energies in atomic in the principal-value form of the dipole matrix element $. The units of the Rydberg and associated ionic states, respectively, position of these zeroes may differ from the location of the and n is the principal quantum number. Figure 1 clearly shows that the quantum defects increase sharply around R = 2 . 5 ~ 0 minimum in I D ! - ) [ , particularly in cases of strong I mixing. particularly for CH and less so for OH. This behavior reflects In Figure 3 we show the IDf)I for the 3pu ku (Figure 3a) the rapid change in the angular momentum composition of these and 3pu kr (Figure 3b) channels for photoionization of the 3pu orbitals with internuclear distance from predominant 3p D 2 2 - Rydberg state of OH at the &of 2.043~0.Cooper minima character a t smaller R to 3s character a t larger R. For example, are clearly seen in the I = 2 (d wave) components around 3.0 eV a single-center expansion about the center of mass shows that the in both the ka and ku continuum channels. The corresponding 3pu orbital of CH has 13.26% s, 8 1SO% p, and 5.24% d character dipole amplitudes f l are shown in the insets of Figure 3. This at R = l.8ao and 79.53% s, 4.88% p, 14.22% d, and 0.83% f Cooper minimum in the ka channel has been identified previously character at R = 3.2~0.The 3pu orbitals of N H and OH show by Stephens and M c K o Y . ~ ~ , ~ ~ a similar behavior with R.5~2~ b. Vibrational and Rotational Ion Distributions of CH. In Figure 2 we show the magnitude IDi:I of the (incomingRudolph et a1.l previously reported the vibrational-state depenwave normalized) partial wave dipole amplitude as a function of dence of the ion rotational branching ratios in (2+1') REMPI photoelectron kinetic energy for the 3pu ku (Figure 2a) and of the E ' W (3pu) Rydberg state of CH. In these studies, the 2.0
4.0
8.0
6.0
10.0
I
+y
-
g,
-
-
-
-
-
-
-
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 463
Photoionization Dynamics of CH, NH, and OH Radicals 1.0 0 A .d
(4
1.0
18
18
18
0-0 20
20
1-1
d M .s 0.5 % 9
&i 0.0 350
550
750
950
350
550
750
950
Rotational Energy (mev) Rotational Energy (mev)
Figure 4. Ionic rotational branching ratios for (2+1’) REMPI via the Oll(20.5) branch of the E ’ W (3pa) state of CH for various vibrational levels. The value of u’and u+ are shown in the upper right corner of each frame, and the value of N+ is shown over each peak. The photoelectron kinetic energy is 100 meV, and the spectraare convoluted with a Gaussian detection function having an FWHM of 6 meV.
rotational branching ratios were seen to be very dependent on the vibrational level accessed in the intermediate state, with a strong AN = odd (Le., 1 = even) propensity rule apparent in lower vibrational levels and a AN = even (Le., 1 = odd) propensity rule for higher levels. This vibrational-state dependence of these rotational distributions was further explained on the basis of the evolutionof the 3pu Rydberg orbital from 3pu character at smaller R to mainly 3su at larger R. However, such a vibrational-state dependence of the ion rotational distributions was not predicted for (2+1’)REMPIofthe3puorbitalsofNH andOH (not shown), although these 3pu Rydberg orbitals also evolve from 3pa character at smaller R to 3su at larger R. Further study of these differencesin the behavior of the ion rotational distributions for photoionization of the 3pu orbitals of CH, NH, and OH seems necessary. We have reexamined the vibrational-state dependence of the ion rotational branching ratios for (2+1’) REMPI of the E’22+ state of CH using the larger Gaussian basis set with diffuse d functionsat the center of mass, discussed in section IIb, todescribe the Rydberg orbital. Figure 4 shows our calculated rotational branching ratios for (2+1’) REMPI of the E ’ W state of CH via the 011 (20.5)branch for the u+ = Cb3 levels of the ion and Av = u+ - u’ = 0. The photoelectron energy in these spectra, which are convoluted with a Gaussian detection function having a full width at half-maximum (FWHM) of 6 meV, is 100 meV. The value of N+ is shown over each photoelectron peak, and the values of u‘ and u+ are given in the upper right corner of each frame. In contrast to the strong AN= odd propensityfor the 0-0 and 1-1 vibrational bands predicted previously,’ these calculated spectra now show dominant AN = even transitions and relatively weaker AN = odd peaks. Although a AN= even propensity was also predicted for the ion rotational distributions for the 2-2 and 3-3 vibrational transitions previously,’ our present results show much stronger AN = a2 and much weaker AN = 1 rotational transitions for these higher levels. These differencesbetween the present ion rotational distributions of Figure 4 with a AN = even propensity from those obtained previously by Rudolph et a/.’ with their AN = odd propensity can be shown to arise from a Cooper minimum which was not adequately accounted for due to a lack of diffuse d functions in the basis used in ref 1 to obtain the Rydberg orbital of the E’ 22+(3pu) state. This Cooper minimum in the kr continuum depletes the 1 = 2 continuum and, hence, due to the parity selection rule of eq 11, reduces the odd
*
Figure 5. Calculated photoelectron angular distributions for the ion rotational distributionsof Figure 4 for the A h 2 0 transitions. Asymmetry parameters up to 6.5 are included, and @ = 0 is vertical.
AN rotational peaks in the photoelectron spectra. The relative importance of the odd partial waves ( I = 1 and 3) of the photoelectron continuum and, hence, of the even AN rotational peaks is subsequently enhanced. Such behavior arising from Cooper minima has been seen previously in (2+1) REMPI of the D 2Z+(3pu) state of the f I l l (3pu) state of NH,33 and the D 22-(3pu) state of OH.6 The inclusion of diffused functions at the center of mass in the description of the Rydberg orbital proves to be important for a correct description of the position of the Cooper minimum and of the magnitude of the photoelectron matrix elements. Calculations with several different basis sets with diffuse d functions at the center of mass of the molecule confirmed this behavior. To provide further insight into the photoionization dynamics of these rotationaldistributions, Figure 5 shows the photoelectron angular distributions for AN L 0 transitions of each vibrational band of Figure 4. With its high Jvalue, the angular distributions for the AN < 0 transitions are seen to be the same as those for the corresponding AN > 0 transitions for the 011(20.5) branch. On the basis of the parity selection rule AN 1 = odd of eq 1 1, these AN = odd transitions arise from 1 = even components of the photoelectron matrix element whereas the AN = even transitions arise from 1 = odd contributions. Due to the changing 1 character of the 3pu orbital with internuclear distance and the parity selection rule of eq 1 1 , the rotational distributions must alsodepend on thevibrational levels. This behavior can be readily seen in the angular distributions for the AN = 1 transitions of Figure 5 where the s (1 = 0) wave is predicted to be dominant for the 0-0 vibrational band and the d (I = 2) wave character is expected to increase for higher vibrational transitions. c. ZEKE Photoelectron Spectra. It is also of interest to compare the ZEKE photoelectron spectra and associated photoelectron angular distributions for photoionization of the N’ = 2 levels of the E’22+,the f I l l , and the D 22-Rydberg states of CH, NH, and OH, respectively. Figure 6 shows the calculated ZEKE photoelectronspectrum and correspondingphotoelectron angular distributions for (2+1’) REMPI via the S’’(0.5)+ R21(0.5)rotational branch of the E ’ 2 2 + ( u ’ = 0, N ’ = 2) Rydberg state of CH leading to the X ‘E+(u+ = 0) state of the ion. A photoelectron kinetic energy of 50 meV is assumed in these calculations, and the photoelectron spectrum is convoluted with a Gaussian detection function having an FWHM of 2 meV. This ZEKE spectrum with its dominant AN = even peaks is similar to that for the 0-0 vibrational transition of Figure 4a. This behavior again mainly reflects the influence of the Cooper minimum since a dominant AN = odd propensity would be expected in an atomiclike picture for photoionization of a 3pu orbital with its strong p wave character. However, smaller contributions to these AN = even peaks would be also expected
+
464
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994
Wang et al. 1.o
1.0
3
2
.4 w 0.5 0.5
! E
11/2
c9
0.D
00
5
25
45
65
65
Rotational Energy (mev) 20
40
--
0'
I
20
.
ab
,
40
Rotational Energy ( m e v )
60
Rotational E n e r g y (mev)
F'igure 6. Calculated (a) ZEKE photoelectron spectrum and (b)
Figure 7. Calculatod ZEKE photoelectron spectra for (a) the X 2113/2 and (b) theX2Ill12 ionic states along with (c) the photoelectron angular distributions resulting from (2+1') REMPI via the S(0) branch of the f I l l (3pu) Rydberg state of NH. The value of J+ is shown over each photoelectron peak, and the AN = 0 transitions correspond to J+ = 3/2 and '/2 for the X '&/2 and X 2111/2 ions, respectively. Terms up to fl6 (with BO = 1) are included in the photoelectron angular distributions, and 0 = 0 is vertical.
from the s (20%) and d (12%) components of the initial 3pu orbital. Finally, it is worth noting that the relative intensities of the AN = -1 peaks in Figures 6 and 4a, where N+ has values of Oand 16,respectively,aredue to thenatureofangularmomentum transfer for a low J state with its small number of MJ levels. Figures 4-6 also illustrate an interesting difference in photoionizationof lower and higher Nlevels of the E'Rydberg state of CH. In contrast to the behavior seen in Figure 4 for a high N level, the photoelectron angular distributions of Figure 6b are no longer symmetricalwith respect to AN = 0. For example, the photoelectron angular distribution for the AN = -1 (N+ = 1) peak for the N = 2 level has more s character than that of the AN = 1 (N+ = 3) peak. Similar behavior is also seen for AN = f 2 transitions where the AN = -2 (N+ = 0) peak shows stronger f wave character. This asymmetrical behavior for lower N(N+) levels has also been predicted for other systems.28 On the other hand, for higher N levels, the partial wave components of the photoelectron matrix element contribute equally to the positive and negative AN transitions. Figure 7 shows calculated ZEKE photoelectron spectra for photoionization of the f III (3pu) Rydberg state leading to (a) the X 2113/2 and (b) the X 2111/2 spin-orbit components of the ion along with (c) the corresponding photoelectron angular distributions for two-photon excitation of the f In resonant state from the a IA statess via the S(0) branch. This S(0) line results in extreme alignment where only the MI. = 0 component of the J' = 2 level of the f I l l state is populated. A photoelectron kinetic energy of 50 meV is assumed in these calculations, and the photoelectron spectra are convoluted with a Gaussian detection function having an FWHM of 2 meV. Note that the parity components of the a 1A and the f 1II states of NH and the X 2n state of the ion are not resolved in these photoelectron spectra. On the basis of the parity selection rules of eq 10, each spectral peak hence arises from contributions from both even and odd partial wave components of the photoelectron matrix element. Figure 7c shows that the photoelectron angular distributions for the J+ = 3 / 2 (AN = -1) and the J+ = I / z (AN = -1') levels of the X 2II112 ion have almost pure d,i character. Note that the
prime distinguishes a rotational level with N+ = 1 and J+ = from that with N+ = 1 and J+ = 3/2. The asymmetry parameters for the AN = -1' peak are 8 2 = 1.247, 84 = 1.480, and fl6 = -0.555, and those for AN = -1 are 82 = 1.354,84 = 1.120, and 86 = -0.386 with 80= 1. Close examination of the (incomingwave normalized) partial wave dipole amplitudes for photoionization of the f In (3pu) Rydberg state of NH, shown in Figure 1 of ref 5, reveals strong 1 mixing in the continua near threshold. The angular distributions of Figure 7c clearly show that there must be significant interferenceamong the partial wave amplitudes associated with these AN = -1 and AN = -1' transitions. Figure 8 shows our (a) calculated ZEKE photoelectron spectrum and (b) corresponding photoelectron angular distributions resulting from (2+1') REMPI via the R11(1.5) Qzl(1.5) rotational branch of the D 22- (N' = 2) Rydberg state of OH leading to the X 3Z-state of the ion. The photoelectron kinetic energy is 50 meV, and the spectrum is convoluted with a Gaussian detection function having an FWHM of 2 meV. In these calculations, the alignment of the D state was determined by including eight 22- and six 211virtual states (obtained from IVO calculations) in evaluating the BOand B2 factors of eq 6. Inclusion of ten 22- and eight 2 I I virtual states leads to no significant changes in these photoelectron spectra. Important features associated with the ZEKE spectrum of Figure 8 are that (1) AN = 0 and AN = f l are the dominant transitions, (2) the AN = f l branching ratios are asymmetrical with respect to the AN = 0 peak, and (3) the AN = even (odd) peaks arise from odd (even) partial wave components of the photoelectron matrix element (see eq 11). It is interesting to compare the ZEKE spectra of Figure 8 with the measured photoelectron spectrum for (2+1) REMPI via the OI1(1.5)rotational branch of the D 22- state of OH (Figure la of ref 6 ) . Note that in ref 6 this branch was designated by its "'quantum number, Le., 01 I (1 1). These measured spectra show a dominant AN = 0 peak and much weaker AN = f l peaks at a photoelectron kinetic energy of about 2.1 eV in contrast to the dominant AN = odd transitions expected for photoionization of a 3pu orbital on an atomiclike basis. Analysis of the spectra of ref 6 revealed that Cooper minima in the d ( I = 2) wave of the photoelectronmatrix element at a photoelectronenergy of 2.1 eV are responsible for such behavior. These Cooper minima (see Figure 3) lead to a depletion of the d continuum wave and, hence,
corresponding photoelectron angular distributionsresulting from (2+ 1') REMPI via the S11(0.5) + Rzl(0.5)branch of the F 2 2 +(3pu) Rydberg state of CH. N+ is shown over each photoelectron peak, and the AN = 0 transition corresponds to N+ = 2. Terms up to B6 (with BO = 1) are included in the photoelectron angular distributions, and 0 = 0 is vertical.
+
Photoionization Dynamics of CH, NH, and OH Radicals 1.0
-m
The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 465 AN=l
I
1.0
b
3
60
40
20
Rotational E n e r g y ( m e v )
E. 8
N’= 1
N‘=O
c3
N+=2
400
560
860
’
760
’
860 ’ 9
Rotational E n e r g y ( m e v )
Figure 8. Calculated (a) ZEKE photoelectron spectra and (b) photoelectronangular distributionsresultingfrom (2+1’) REMPI via the R11(1 5 ) + Q21( 1.5) branch of the D 28 (3pu) Rydberg state of OH. N+ is shown over each photoelectron peak, and the AN = 0 transition corresponds to N+ = 2. Terms up to fl6 (with flo = 1) are included in the photoelectron angular distributions, and 8 = 0 is vertical.
Figure 9. Photoelectron spectra at several kineticenergiesresultingfrom (2+1’) REMPI via the 011(20.5) branch of the E ’ W (3pu) Rydberg state of CH. The AN = 0 transition corresponds to N+ = 18. Photoelectron angular distributions for the AN = 1 transition are also shown. Terms up to fl6 are included, and 8 = 0 is vertical. AN=l
IO
to an enhancement of the p and f (I = odd) components of the photoelectron matrix element. In the case of Figure 7,since the photoelectron energy is near threshold and away from both minima, the d wave contribution is essentially comparable to that of the I = odd waves. d. Energy Dependence of Photoelectron Spectra. Recently, Wang et a1.27 have identified and systematically investigated the role of Cooper minima in photoelectron spectra for (2+ 1’) REMPI of the D22+ (3pu) and C2II (3pa) Rydberg states of NO. These minima result in a strong dependence of the ion rotational distributions and photoelectron angular distributions on photoelectron energy.27~29To explore how these previously identified Cooper minima may influence the ion rotational distributions resulting from photoionization of the E’ 22+state of CH, the f l nstate of NH, and the D 2 2 - state of OH, we examine the ion rotational branching ratios and photoelectron angular distributions (AN = 1 transition only) at photoelectron kinetic energies of 0.1, 1.0, 2.5, and 4.0 eV. To facilitate comparison with previous studies, we have studied these spectra for REMPI via the 011(20.5)branch of the E’Q+ state of C H (ref l), the R(12) branch of the f I l l state of N H (ref 5), and the OI1(11.5) branch of the D 22-state of O H (ref 6). In these studies, the ion rotational branching ratios at each photoelectron energy have been normalized to the most intense transition and each spectrum is convoluted with a Gaussian detection function having an FWHM of 6 meV. Furthermore, the parity components of the a ‘A and f In states of N H and the X 211 state of NH+ are not resolved in these calculated spectra. Figures 9-1 1 show our calculated ion rotational branching ratios and photoelectron angular distributions(0= 1 transition only) at several kinetic energies for these (2+1’) REMPI spectra of CH, NH, and OH, respectively. Important features associated with these spectra include the following: (1) dominant AN = even transitions are predicted for all three molecules for photoelectron energies in the vicinity of the Cooper minima. This behavior is in distinct contrast to that based on atomiclike selection rules for photoionization of a 3pa orbital. Note that the 0 = f 1 peaks for photoionization of OH (Figure 11) at a photoelectron
0.5
-
0.1 eV
AN= 1
-1 -2
-3 A
i:
8
0
3
0.5
2 B
3 0.0
2
0.5
0.0
2.5 eV
1
n
4.0 eV
1 I
n
Figure 10. Photoelectron spectra at several kinetic energies resulting from (2+1’) REMPI via the R(12) branch of the f In (3pu) Rydbcrg state of NH. The spin-orbit (X zI13/2, X 2111/2) and parity (c/o components of the ion are not resolved. The AN = 0 transitioncorresponds to N+ = 13. Photoelectronangular distributionsforthe AN = 1 transition are also shown. Terms up to fl6 are included, and 0 = 0 is vertical.
energy of 0.1 eV are evident here since this energy is not in the vicinity of the Cooper minima. (2) The effects of these Cooper minima are also strongly reflected in the kinetic energy dependence of the photoelectron angular distributions. For example, the angular distributionsfor the AN = 1 peaks in Figures 9-1 1 change dramatically with photoelectron energy in the vicinity of the Cooper minima. Note that the AN = 1 transition arises from even partial wave componentsof the photoelectron matrix element. (3) Photoionization of the D 22-state of OH (Figure 11) best illustrates the dependence of the ion rotational branching ratios on kinetic energy with the relative intensities of the AN = f l
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The Journal of Physical Chemistry, Vol. 98, No. 2, 1994 AN=l
Wang et al. are quite feasible and could provide very valuable insight into the role of Cooper minima in these spectra. Acknowledgment. This work was supported by grants from the Air Force Office of Scientific Research and the Office of Health and Environmental Research of the U.S.Department of Energy. We acknowledge the use of resources of the Jet Propulsion Laboratory/California Institute Technology CRAY Y-MPZE/116 Supercomputer. References and Notes
Figure 11. Photoelectron spectra at several kinetic energies for (2+1’) REMPI via the 011(11.5) branch of the D Q- (3pu) Rydbcrg state of OH. The AN = 0 transition corresponds to N+ = 9. Photoelectron angular distributions for the h V = 1 transition are also shown. Terms up to @5, are included, and 0 = 0 is vertical.
peaks decreasing in the region of the Cooper minima. (4) The ion rotational branching ratios for photoionizationof the E’ 22+ state of CH (Figure 9) depend only slightly on energy since the Cooper minimum only occurs in the k~ continuum and the s and d waves of the ku continuum are responsible for the AIV = odd transitions at near-threshold energies (see Figure 2). However, the effect of this Cooper minimum is quite evident in the photoelectron angular distributions.
IV. Conclusions In this paper we have presented the resultsof theoretical studies of rotationally resolved photoelectron spectra and photoelectron angular distributions for photoionization of the 3pu Rydberg orbitalsofCH,NH,andOH hydrides. Due tothecorepenetration by this 3pu orbital and the formation of Cooper minima in the d waves of the photoelectron continua, the photoionization dynamics of these spectra is quite nonatomiclike in nature. Measurements of these rotationally resolved spectra for these hydride systems over the relevant range of photoelectronenergies
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