Threshold Photoelectron Spectroscopy of the A 2.PI. state of CO+

Feb 1, 1995 - ... states of N[sub 2][sup +] in the 15.5 eV to 17.7 eV photon energy range. J. W. Hepburn. The Journal of Chemical Physics 1997 107 (18...
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J. Phys. Chem. 1995,99,1643-1648

1643

Threshold Photoelectron Spectroscopy of the A 211State of CO+ Kwanghsi Wang* and V. McKoy Arthur Amos Noyes Laboratory of Chemical Physics, f Califomia Institute of Technology, Pasadena, Califomia 91125 Received: August IS, 1994;In Final Form: October 31, 1994@

Results of calculations of single-photon pulsed-field ionization of the ln orbital of the X (v" = 0) ground I (v+ = 0-2) excited ionic state are reported. Agreement between the calculated state of CO leading to the A T and measured specta is reasonable except for the A T I 1 / 2 (v+ = 0) level which shows strong autoionization at larger positive AJ transitions. Our studies show that the direct photoionization of the In orbital is very atomiclike.

Introduction

Theory and Numerical Details

Rotationally resolved photoelectron spectra can clearly provide much insight into the dynamics of molecular photoionization, one of the simplest of molecular fragmentation processes.'S2 With the recent development of zero-kineticenergy (ZEKE) photoelectron techniques,' based on delayed pulsed-field ionization (PFI) of high Rydberg states, such studies have been extended to a wide range of systems.' To date, these studies, either by resonance-enhanced multiphoton ionization (REMPI) of Rydberg states or single-photon ionization of ground states, have generally dealt with ions in their ground electronic states. Recently, however, Kong et aL3 have reported ZEKE photoelectron spectra for the a 3E+excited state of NO+ resulting from single-photon ionization of the I n orbital of the X 211 ground state of NO by coherent extreme vacuum ultraviolet ( X W ) radiation. Such studies can be expected to provide new and valuable insight into the dynamical behavior of electronically excited states of molecular ion^.^,^ Kong et aL5 have recently studied the ZEKE-PFI photoelectron spectra for the ground electronic states of CO+ and N2+ produced by single-photon ionization of rotationally cold molecules by coherent extreme ultraviolet radiation. These threshold spectra were interpreted on the basis of ab initio calculations of the ion rotational distributions and illustrated some striking differences expected in the ion distributions of these two molecules due to their heteronuclear and homonuclear characters. For these spectra both neutral and ionic system can be well described by Hund's case (b) coupling scheme. In this paper we report calculated ZEKE photoelectron spectra for the A 2113/2 and A 2 1 1 ~ / 2excited electronic states of CO+. These calculations represent the first application of our computational procedure to studies of rotationally resolved photoelectron spectra for an excited electronic ion state. The results of these calculations are compared with the measured spectra of Kong and Hepbum6 which were obtained by single-photon ionization of jet-cooled CO molecules using coherent extreme ultraviolet r a d i a t i ~ n .Comparison ~ of the measured and calculated ion rotational distributions provides useful insight into the underlying dynamics of these spectra, including the role of autoionization.

The formulation of molecular photoionization processes used in the present studies has been described Here we present just a very brief outline of some essential features of our procedure as it is used to obtain the rotational ion distributions of interest here. For linearly polarized light the differential photoionization cross section can be expressed in terms of Legendre polynomials as

where o is the total cross section, p 2 the asymmetry parameter, P2(cos 0) the Legendre polynomial, and 8 the angle between the direction of photoelectron and the electric vector of the polarized light. Under collision-free conditions, ionization 1) magnetic sublevels of originating from each of the (2J the initial state forms an independent channel. Therefore, the total cross section o of interest here for ionization of a J level of the initial state can be written as

+

lm

M J W

where QM,,M/ is the population of the MJ sublevel of the initial state. The coefficients Clm(Mj,Mp)are related to the probability for photoionization of the MJ level of the initial state leading to the MJ+ level of the ion. An expression for Clm (MJ,MJ+) 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 both the initial and target states has been given by Wang and McKoy.* Crm (Mj,Mp) has the form8

' Contribution No. 8972. @

Abstract published in Advance ACS Abstracts, January 15, 1995.

0022-3654/95/2099- 1643$09.QQ/Q 0 1995 American Chemical Society

Wang and McKoy

1644 J. Phys. Chem., Vol. 99, No. 6,1995

Q = A J + AS

+ 2S, + Ap + 1 + 1

(6)

0

for e states (7) forfstates where AJ = Ji - J , AS = S+ - S, Ap = p+ - p . In these equations, SZ denotes the total electronic angular momentum, including spin, along the internuclear axis, A the projection of electronic orbital angular momentum along the internuclear axis, S the total spin, Z its projection along the internuclear axis, S, the spin of the photoelectron, & its projection along the internuclear axis, J the total angular momentum, and MJ its projection along the laboratory z axis. Parity selection rules,*-" governing changes of rotational angular momentum upon ionization, can be obtained from eqs 3 and 6 and rue of the form

{

P= 1

A J + AS

+ Ap + I = even + +

where VklA is the partial wave component of the photoelectron with momentum k and q is the Coulomb phase shift.7 There are three dipole-allowed final-state wave functions IA&) for photoionization of the I n orbital of the X IZ+ state of CO leading to the A 211excited ionic state. The corresponding fmalstate wave functions are

$('IT>= (1/Jz)[l(core>ln2+ 1 n 5 - 1(core)1n2+G-/call

I(core)lJz,G_h-I

(10)

+ I(core)ldlx+G+l I (core) 1dG+h+ I1 ( 11

~ ( ' I I )= (1/2/2)[1(core)&

~n+ks+ 1-

2

I

I

(

I

I

I

134880

core) 1 d G + / c d + l l

(12) where (core) = lo22u23u24u2502 and the bars over the orbitals indicate opposite spin. The ground-state wave function of CO used here is obtained at the self-consistent-field (SCF) level. We use the same Gaussian basis as in ref 5. The total SCF energy in this basis was -112.777 839 au at the equilibrium intemuclear distance of Re = 2.1322~0.'~The single-center expansion of the In orbital around the center-of-mass shows 80.96% p, 5.72% d, 11.07% f, 0.73% g (lo = 4), and 1.13% h (lo = 5 ) character at Re. The angular momentum composition of the I n orbital evolves gradually from its predominant 2p character at smaller internuclear distance to a p, d, and f admixture at larger R . For example, the ln orbital has 91.20% p, 2.67% d, 5.49% f, 0.18% g (10 = 4), and 0.37% h (10 = 5) character at R = 1.5ao and

,

I

I

134900

I

I

,

,

1341920

,

,

134940

I T = l o K

(8)

Since the intermediate coupling scheme uses the case (a) basis, these parity selection rules can also be applied to pure Hund's case (a) coupling. However, for a 2-2 photoionization process, the parity selection rules become U Ap 1 = odd for the Hund's case (b) coupling.8-" A central quantity in these studies is the photoelectron matrix elements Zlip(A&) of eq 5 for photoejection of an electron from a bound molecular orbital lyi into a photoelectron continuum orbital. In a one-electron approximation, the photoelectron matrix element Z~A~(A&) for each dipole-allowed final-state wave function lA&) can be written as

$('E+) = (1/2)[l(core>ln2+1n-kn-l-

I

134880

2G

M h

D

-jk n

9 1

m

1

'

~

'

1

"

'

1

'

'

~

1

'

46.41% p, 18.57% d, 20.92% f, 5.60% g (lo = 4), and 4.78% h (lo = 5) character at R = 3.5~0.The vibrational wave functions for the X state of CO and the A 211state of CO+ were obtained by numerical integration over a range of 1.0 5 R 5 5.0 ao. We used the Rydberg-Klein-Rees (RKR) potential curves of Tobias et al.I3 for the X state of CO and those of Singh and Rail4 for the A 211state of CO+. The photoelectron matrix elements for each vibrational transition are further averaged over 12 internuclear distances between 1.5 and 3.5 ao. Further details of the calculations can be obtained from ref 5. Results and Discussion

The measured PFI-ZEKE threshold photoelectron spectra of Kong and H e p b u d for the Y+ = 1 level of the A 2111/2 and A 2n3/2states of CO+ produced by single-photon ionization of rotationally cold CO in the v" = 0 level of its X IZ+ground state by coherent extreme ultraviolet radiation are shown in Figure l a and 2a, respectively. In both the spectra the AJ = '/z peak, which arises from several rotational transitions, is the most intense due to a band head located in that region and similar rotational constants for both neutral and target states. Since the lowest J+ for the 2113/2 component is 3/2 (the spinorbit splitting of the A 211state is -120 cm-'), transitions to the J+ = l/2 rotational level are only present in the spectrum of the *lI1,2 component. The observed maximum change in rotational angular momentum AJ is 7/2, which is consistent with the conservation of angular momentum. On the basis of conservation of angular momentum for single-photon ionization, the maximum change in angular momentum would be AJ = f(l 3/2) with 1 an angular momentum component of the

+

The A 213 State of COS

l

~

134880

'

I

I

J. Phys. Chem., Vol. 99,No. 6, 1995 1645

I

I

134880

I

I

I

I

134900

1

(

!

'

134b20

I

I

134b40

l l l l 3/2

(b)

o

l

30

I

135000

(b)

s

I

(

l

-

A

I

(

134880

J

I

1

I

134900

1

1

1

1

I

~

135bBO

calculated

d

T = 5 0 K

612

AJ = 11'2

10

~

135040

A, = 1,2

calculated T = 1 0 K

J

135020

0

I

I

1

I

2

I

134920

3

I

I

4

-,w

O

134940

Photon Energy (cm-') Figure 2. (a) Measured and (b) calculated PFI threshold photoelectron spectra for ionization of the In orbital of the X 'X+ (v" = 0) ground state of CO leading to the A 2113,2 (v' = 1) spin-orbit component of CO+. A photoelectron kinetic energy of 50 meV and a rotational temperature of 10 K are assumed in the calculation.

photoelectron. With its strong p character and on the basis of an atomiclike propensity rule, a dominant d ( I = 2 ) partial wave component is expected for the photoelectron for photoionization of the 1 n orbital. The maximum change in angular momentum should then be '12. In Figures l b and 2b we show the calculated rotationally resolved PFI-ZEKE photoelectron spectra for photoionization of the In orbital of the X 'E+(v" = 0) state of CO leading to the v+ = 1 level of the A 2111/2 and A 2n3/2ions, respectively, for a temperature of 10 K. A temperature of 10 K was assumed on the basis of the cooling expected in the beam and on our earlier studies of the ZEKE! photoelectron spectra for groundin which the same apparatus was used under state CO+ (X *Z+) similar condition^.^ The spectra were calculated for a photoelectron kinetic energy of 50 meV and convoluted with a Gaussian detector function with a full width at half-maximum (fwhm) of 2 cm-I. In this figure and elsewhere, the calculated spectra are normalized to the most intense peak of the measured spectra. The same dynamical matrix elements were used in obtaining the photoelectron spectra for both spin-orbit components. There clearly are significant differences between the measured and calculated spectra at this temperature, particularly for the A 2&2 component. For example, the higher negative AJ transitions are weak in the calculated spectra of both spinorbit components due to the lack of population in higher s' levels at this temperature (10 K). One may argue that this discrepancy between the calculated and measured intensities for these negative AJ transitions arises from rotational autoionization which is not accounted for in our calculated spectra. However, the most intense peak of the calculated spectrum (Figure 2b) f o r the A 21T3/2 component is due to the AJ = 3/2

30

135000

135020

135040

135080

Photon Energy (cm-') Figure 3. (a) Measured and (b) calculated PFI threshold photoelectron spectra for ionization of the I n orbital of the X 'X+ (Y" = 0) ground state of CO leading to the A 2111/2 (v+ = 1) spin-orbit component of CO+. A photoelectron kinetic energy of 50 meV and a rotational temperature of 50 K are assumed in the calculation.

transition from the s' = 0 level while the AJ = '12 peak is dominant in the measured spectra, suggesting that the assumed temperature of 10 K may not adequately describe the initial rotational population. To explore possible reasons for the differences between the calculated and measured spectra of Figures 1 and 2, we have calculated these spectra at different rotational temperatures. Previous experiments have found rotational temperatures ranging from 10 to 20 K, suggesting some uncertainty in the actual temperature.6 An assumed temperature of 50 K leads to the most satisfactory agreement between the calculated and measured photoelectron spectra. In Figures 3b and 4b we show the calculated rotationally resolved PFI-ZEKE photoelectron spectra for photoionization of the I n orbital of the X IX+ (v" = 0) state of CO leading to the v+ = 1 level of the A 2 r I l / 2 and A 2&2 ions, respectively, for a temperature of 50 K. Again, these spectra were calculated with the same dynamical matrix elements for both spin-orbit components of the ion, assuming a photoelectron kinetic energy of 50 meV, and were convoluted with a Gaussian detector function with a fwhm of 2 cm-I. Agreement between the calculated and measured spectra is quite reasonable. Both calculated and measured spectra show AJ = to be the most intense peak and display transitions arising from higher rotational levels. Since the calculated spectra of Figures 3 and 4 for the A 21T3/2 and A 21T1/2 components of the ion assume the same initial rotational populations and dynamical matrix elements, differences in these ion distributions must arise from the spin-orbit interaction, Le., the projection of total electronic angular momentum on the internuclear axis, Q+, in eq 3. Figures 3 and 4 also show that the measured negative AJ transitions are

1646 J. Phys. Chem., Vol. 99, No. 6, 1995

(4

Wang and McKoy

measured

0.0

-

0

h

2

I 4

l

0

o-

.- o -

8

1

0

A 0

t

~

134660

~

134880

134900

~

l

~

134920

~

134940

1O 6 F T

lI

i

~

~

~

8

10

"c Energy (eV)

l

~

l

'

0.0

calculated

AJ = 1/2

~

0

4

2 *-'

0

2

0

4

10

8

Kinetic Energy (eV)

=

I

612

Figure 5. Magnitude of the partial wave components of the photoelectron matrix element lD!-)l for photoionization of the X IZ+ground state of NO leading to the A 217excited ionic state: la) In ko; (b) In kn; (c) In kd ionization channels.

-

-

-

(4

measured

-~ t

"

34860

~

i

l

134880

!

~

1

8

134900

'

1

(

1341920

(

1

1

1

134b40

Photon Energy (cm-') Figure 4. (a) Measured and (b) calculated PFI threshold photoelectron (v" = 0) ground spectra for ionization of the In orbital of the X state of CO leading to the A 2113/2 (v' = 1) spin-orbit component of CO+. A photoelectron kinetic energy of 50 meV and a rotational temperature of 50 K are assumed in the calculation. I

30

somewhat more intense than those of calculated spectra, while the positive AJ transitions have similar intensities for both calculated and measured spectra. This behavior is quite common in rotational intensity profiles of PFI spectra for a wide range of system^.'^-'^ Field-induced autoionization has been used to explain such anomalous spectral profiles. This mechanism involves the interaction of high-n Rydberg states ( 2150) with nearly degenerate low-n Rydberg states converging to higher cation rovibronic ionization threshold. Application of the pulsed electric field lowers the ionization potential by an amount equal to the Stark shift and allows the low-n Rydberg states to autoionize. Parity selection rules of eq 8 govem angular momentum transfer between the photoelectron and ion core upon ionization. Since the A doublets (e/f) of the A 213excited state rotational levels are not resolved, it is not possible to assign a specific parity (even or odd 1) to individual rotational transitions. Both parities can contribute to each rotational transition. Since the I n orbital has almost pure odd (81% p and 11% f) character, dominant even (s and d) partial wave components would be expected for the photoelectron on the basis of atomiclike propensity rule. The magnitude of the photoelectron matrix elements lDj-)l of Figure 5 shows that this is indeed the case is the for photoionization of the lx orbital. Note that 1@-'1 magnitude of only one of the p components of I),+ (see eq 9). Since the X state of neutral CO has only an e component, we would predict that the e component of the rotational levels of the A state is dominant for the even AJ f AS (AJ = - 5 / 2 , -l/2, 3/2, and ' 1 2 ) transitions and the f component is dominant for the odd AJ AS (AJ = -3/2, I/*, and V2) transitions. Note that this is not true for larger photoelectron energies where the

+

I

I

136510

'

I

(

136530

(b)

I

J

l

'

J

I

I

136570

(

I

131 590

calculated

A J = l,a

-112

(

136550

3/2

rirrn

1 - 8

0

3

* 512

6

s

-312 4

3

2

0

1

2

3

4

5

l " l , , , , , , , , " , , , , l

30

136510

136530

136550

136570

136590

Photon Energy (cm-') Figure 6. (a) Measured and (b) calculated PFI threshold photoelectron spectra for ionization of the In orbital of the X '2' (v" = 0) ground state of CO leading to the A 21T1/2 (v+ = 2) spin-orbit component of CO+. A photoelectron kmetic energy of 50 meV and a rotational temperature of 50 K are assumed in the calculation. even and odd partial wave components have comparable intensities, Le., nonatomiclike photoionization dynamics would occur at these kinetic energies. Figure 6 shows the (a) measured and (b) calculated PFI threshold photoelectron spectra for photoionization of the 1 x orbital of the X (VI' = 0) ground-state CO leading to the A 21-11/2 (v+ = 2) spin-orbit component of the ion. For reasons discussed above, the calculated spectra again assume a temperature of 50 K. The maximum value of the FranckCondon integral between the ground state of CO and the A 21-1 state of CO+ occurs for v+ = 2,20 but the PFI signal for this

~

i

The A 211 State of CO+

J. Phys. Chem., Vol. 99,No. 6, 1995 1647

(4

measured

Ilk I 40

,

,

,

I

,

,

I

,

(b)

I

,

133970

133550

30

,

,

13: 410

133b90

calculated

A J = 112 3/2

m

0

1

I

-

1

j0

I

I

133480

1

I

I

1

133500

I

'

"

"

133520

8

6

1

13 40

Photon Energy (cm-')

Figure 7. (a) Measured and (b) calculated PFI threshold photoelectron spectra for ionization of the In orbital of the X '2' (v" = 0) ground state of CO leading to the A 2 1 T ~ / 2(v+ = 0) spin-orbit component of CO+. A photoelectron kinetic energy of 50 meV and a rotational temperature of 50 K are assumed in the calculation.

vibrational level was barely observable6(see Figure 6a). In fact, the relative intensities of the v+ = 0, 1, and 2 vibrational bands of the 2111/2 ion are quite non-Franck-Condon.6,2' However, agreement between the calculated and measured rotational branching ratios is still good. The (a) measured and (b) calculated PFI threshold photoelectron spectra for photoionization of the In orbital of the X (v" = 0) ground state CO leading to the A * l l 1 / 2 (vf = 0) and A * l l 3 / 2 (v+ = 0) spin-orbit components of CO+ are shown in Figures 7 and 8, respectively. Strong peaks arising from autoionization are clearly seen in the measured spectrum for the A *II1/2 component. These autoionization peaks have been identified through high-resolution spectroscopic studies2*as due to perturbation of the A 2111/2 v+ = 0 level by the v' = 10 level of the X *E+ground state of CO'. Mechanisms involving coupling of Rydberg series of two perturbing ionic states have been proposed to account for the spectral intensity profile.6s21 The present calculations can be helpful in unravelling the roles of autoionization and direct photoionization in these spectra. Agreement between the calculated and measured spectra for the A 2113/2 (v+ = 0) component, which is not perturbed, is again good. Finally we note that our calculated PFI threshold photoionization spectra are essentially identical for all vibrational levels of a given spin-orbit component of the ion. The same is true for the other component. This is expected since the photoionization transition moment does not have a significant dependence on internuclear distance. Vibrational averaging of the photoelectron matrix elements, hence, leads only to small changes in relative vibrational intensities but not in rotational intensities. This is the case for unperturbed spin-orbit components.

30

4

1

3

1

133350

2

1

,

I

I

133370

J

J

I

I

133390

(

J

13:410

Photon Energy (cm-')

Figure 8. (a) Measured and (b) calculated PFI threshold photoelectron spectra for ionization of the In orbital of the X 'Zf (v" = 0) ground state of CO leading to the A * I I 3 / 2 (v+ = 0) spin-orbit component of CO'. A photoelectron kinetic energy of 50 meV and a rotational temperature of 50 K are assumed in the calculation.

Acknowledgment. Work at the California Institute of Technology 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 also acknowledge use of the resources of the Jet Propulsion LaboratoryKalifomia Institute of Technology CRAY Y-MP2E/232 supercomputer. References and Notes (1) Muller-Dethlefs, K.; Schlag, E. W. Annu. Rev. Phys. Chem. 1991, 42, 109. (2) Wang, K.; McKoy, V. In Highly Resolved Laser Photoionization and Photoelectron Studies; Powis, I., Ed., John Wiley & Sons: New York, 1995. (3) Kong, W.; Rodgers, D.; Hepbum, J. W. 1.Chem. Phys. 1993, 99, 857 1. (4) Wang, K.; McKoy, V.; Kong, W.; Rodgers, D.; Hepbum, J. W. J . Chem. Phys., to be published. (5) Kong, W.; Rodgers, D.; Hepbum, J. W.; Wang, K.; McKoy, V. J . Chem. Phys. 1993, 99, 3159. (6) Kong, W.; Hepbum, J. W. J . Phys. Chem. 1995, 99, 1637. (7) Lucchese, R. R.; Raseev, G.; McKoy, V. Phys. Rev. A 1982, 25, 2572. (8) Wang, K.; McKoy, V. J . Chem. Phys. 1991, 95, 4977. (9) Dixit, S. N.; McKoy, V. Chem. Phys. Lett. 1986, 128, 49. (10) Xie, J.; Zare, R. N. J . Chem. Phys. 1990, 93, 3033. (11) Raseev, G . ; Cherepkov, N. Phys. Rev. A 1990, 42, 3948. (12) Huber, K. P.;Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules; Van Nostrand; New York, 1979. (13) Tobias, I.; Fallon, R. J.; Vanderslice, J. T. J . Chem. Phys. 1960, 33, 1638. (14) Singh, R.; Rai, D. K. J . Mol. Spectrosc. 1966, 19, 424. (15) Wiedmann, R. T.; Grant, E. R.; Tonkyn, R. G.; White, M. G. J . Chem. Phys. 1991, 95, 746.

Wang and McKoy

1648 J. Phys. Chem., Vol. 99, No. 6, 1995 (16) Wiedmann, R. T.; Tonkyn, R. G.; White, M. G.; Wang, K.; McKoy, V. J. Chem. Phys. 1992, 97, 768. (17) Tonkyn, R. G.; Wiedmann, R. T.; White, M. G.J . Chem. PhYS. 1992, 96, 3696. (18) Wiedmann, R. T.; White, M. G.; Wang, K.; McKoy, V. J. Chem. Phvs. 1993. 98. 7613. (19) Lee, M.-T.; Wang, K.; McKoy, V.; Tonkyn, R. G.; Wiedmann, R. T.; Grant, E. R.; White, M. G. J. Chem. Phys. 1992, 96, 7848.

(20) Nicholls, R. W. J . Phys. B, Ser. 2 1968, 1, 1193. (21) Kong, W. Photoionization Spectroscopy of Small Molecules Using Coherent Extreme Ultraviolet Radiation. Ph.D. Thesis, Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada. (22) Katayama, D. H.; Welsh, J. A. J. Chem. Phys. 1981, 75, 4224.

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