Photoionization of ammonia

2 May 1997

CHEMICAL PHYSICS LETTERS

ELSEVIER

Chemical Physics Letters 269 (1997) 222-226

Photoionization of ammonia A.E. Orel a, T.N. Rescigno b a Department of Applied Science. University of California, Davis, Livermore, CA 94550, USA b Physics and Space Technology Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550. USA

Received 31 December 1996; in final form 29 January 1997

Abstract

We report the results of separated-channel, frozen core calculations of partial and total photoionization cross sections and asymmetry parameters for NH 3. The calculations were performed using the complex Kohn variational method. The results for the total and partial cross sections agree well with experiment as well as previous theoretical calculations. The asymmetry parameters are found to be a more sensitive test of the accuracy of the wave function.

1. Introduction

Though substantial progress has been made in the theoretical study molecular photoionization, most work has been restricted to diatomic or linear targets. This is partially due to the complexity of the underlying matrix elements required and, in particular, the difficulties associated with calculating accurate continuum wave functions for the final state of the electron in the field of a residual polyatomic molecular ion. However, photoionization of various polyatomic species, such as short-lived radicals, can play an important role in combustion [1], and the development of reliable theoretical methods is especially important because of the extreme difficulty of experiments in this area. The situation with respect to theoretical studies of molecular photoionization is somewhat mixed. Detailed calculations, which can provide total and partial cross sections as well as vibrationally resolved branching ratios and asymmetry parameters, have been based on multichannel scattering techniques such as the iterative Schwinger [2] and linear alge-

braic methods [3]. These rigorous approaches have, with a few exceptions [4,5], only been applied to linear targets. On the other hand, LZ-methods, based on either moment theory [6] or complex rotation [7], have been used to study photoionization of polyatomic molecules. However, these latter methods do not readily provide the detailed phase information necessary to calculate angular distributions, and generally rely on decoupling approximations to compute partial photoionization cross sections. The complex Kohn variational method [8] has been extensively applied to the study of elastic and electronically inelastic electron scattering by neutral and ionic molecular targets. Since the method does not rely on single-center expansions of the electrontarget interaction and uses partial waves only to describe the asymptotic part of the trial wave function, it can readily be applied to polyatomic systems. Moreover, properties such as the transition dipole moment in Eq. 6 below have been shown [9] to be variationally stable when computed from Kohn trial wave functions. We have recently applied the complex Kohn method to the photoionization of CO [10].

000%2614/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0009-261 4(97)00283-2

A.E. Orel, T.N. Rescigno/ Chemical Physics Letters 269 (1997) 222-226 In this paper, we present preliminary results on the application of the complex Kohn method to the photoionization of a polyatomic, NH 3.

223

{q~g} are a set of square-integrable (Cartesian-Gaussian) functions. The matrix elements needed to construct photoionization sections can be expressed in terms of the body-frame amplitudes [13]:

2. Theory The complex Kohn method has been used to describe electron scattering by both neutral and ionic molecular targets. Technical details of this method have been discussed in several recent review papers [11,12] and will not be repeated here. Details on the adaptation of this method to the study of molecular photoionization has been presented in Refs. [9] and [10]. We present a brief summary of the method here. The final-state wave function for production of photoions in a specific state F 0 is written as

atrro = E A ( XrFrro) + E d i r o o i - Prl~o + Qtlt~o , F

i

(1) where the first sum runs over energetically open ionic states, which are described by N - 1 electron wave functions Xr, and the functions F~or are channel functions that describe the photoionized electron. The superscript ' - ' is used in Eq. 1 to denote incoming wave boundary conditions on the scattered wave function. The O i are N-electron configuration-state functions (CSF's) used to introduce polarization and correlation effects into the trial wave function [12]. We use the label F to denote a specific state of the molecular ion, as well as the angular momentum of the corresponding electron. In a separated-channel, frozen-core calculation, the sum over target states is truncated to a single term and the only N-electron CSF's included are those needed to relax strong orthogonality constraints [ 12]. In the Kohn method, the functions F~or(r-') are further expanded, in the molecular body-fixed frame, as

Frro(F)

=

E cfFo~oi( F) + E [ ft( kF r ) alloammoaFFo i lm

+ Ttrord,.oh; ( krr)]Ytm( ? ) / r ,

(2)

where ft are h~- partial-wave continuum basis functions which behave asymptotically as regular and incoming Coulomb functions, respectively, and the

N

=E f

~o(rl . . . . . ru)r~

i=l

X ~ , ( r I . . . . . rN)dSrl . . . . . d3rN,

(6)

where r t' is the dipole operator which, in the length form, is defined as r~=

z,

/z=0

T-(x+_iy)/¢-2,

tx = +_1

,

(7)

and W0 is the wave function that describes the initial state of the target molecule. In order to construct an amplitude that re_presents an ejected photoelectron with momentum kro associated with a particular ion channel, the matrix elements defined in Eq. (6) must be combined in a partial wave series

lrro.~=

Y'. i'oe-it,olfoYt~(e)Ytomo(kro), lomolZ

(8) where ~¢ro specifies the direction of the ejected electron and ~ is the direction of polarization of light. The doubly differential cross section for a hypothetical space-fixed target molecule is then given as d2o"r°

8'rr to

dO~ dO~

3c

2

l~ro.~ ,

(9)

where to is the photon energy and c is the speed of light. In order to compute a cross section defined in the typical experiment where the target orientation is not resolved, the quantity defined in Eq. (9) must be averaged over all orientations of the target molecule in the laboratory frame. The resulting differential cross section has the form [14]

do F° = {

da

\da

/

dad."

= or ° [l+

roe

(cosO)],

(10)

A,E. Orel, T.N. Rescigno / Chemical Physics Letters 269 (1997) 222-226

224

where P2 is the Legendre polynomial of order 2, 0 is the angle between ~ and k and fir° is the so-called symmetry parameter. The quantity tr r0 is the total photoionization cross section averaged over all polarizations and photoelectron directions and is given by 8"rrto °'r°=~

3c

E

IlPo12.

Table l Gaussian basis sets used in NH 3 photoionization calculations Center

Type

Exponent

Coefficient a

N

s s s s s s

5909.44 887.451 204.749 59.8376 19.9981 2.686

0.006240 0.047669 0.231317 0.788869 0.792912 0.323609

s s s s p p p p p p d d

7.1927 0.7 0.2133 0.048 26.7860 5.9564 1.7074 0.5314 0.1654 0.048 1.4 0.4

1.0 1.0 1.0 1.0 0.038244 0.243846 0.817193 1.0 1.0 1.0 1.0 1.0

s s s s p d

19.2406 2.8992 0.6534 0.1776 0.75 1.0

0.130844 0.921539 1.0 1.0 1.0 1.0

(11)

loreo IX

3. Results We have computed partial photoionization cross sections and asymmetry parameters for NH 3 within the fixed-nuclei approximation. The calculations were performed at the equilibrium geometry ( N - H bond distance 1.014 A and H - N - H bond angle 67o58') [15] and provide vertical electronic profiles that give an approximation to the photoionization cross sections summed over the vibrational and rotational states of the final ion. Although the NH 3 molecule in its equilibrium geometry has C3~ symmetry, the calculations were performed in the reduced symmetry C s because of code restrictions. We computed a Hartree-Fock wave function for the ground-state of NH 3 in a basis of Gaussian functions described in Table 1. The SCF energy in this basis is -56.21509 hartree. To complete the basis for constructing the Kohn trial function, we included continuum functions of appropriate symmetry up to l = 4 and Iml--4. The radial continuum functions, which satisfy asymptotic Coulomb boundary conditions, were constructed by the numerical procedures described in Ref. [16], which provides an implementation of a general procedure described in Ref, [ 17]. We have considered photoionization of NH 3 leading to the three lowest states of NH~-: the 2A l(3a~- l ) state, which has an experimental ionization potential (IP) of 10.9 eV, the 2E(e-1) state with an IP of 15.8 eV and the 2A l(2a~- ~) state which has an IP of 27.7 eV [18]. We carried out separated channel, frozencore Hartree-Fock (FCHF) calculations. At this level of approximation, the initial state is described by a single configuration SCF wave function and the ion states used in the Kohn trial function were single configuration state functions constructed from the

H

a Underlined values separate contracted basis functions.

orbitals of the neutral molecule by placing a vacancy in the appropriate valence orbital. Coupling between different ionic channels was ignored. Partial cross sections are shown in Fig. 1 and compared to the results of Cacelli et al. [19,20] which were calculated using the Stieltjes moment theory technique [6]. The agreement is seen to be reasonably good, with slight discrepancies which are presumably attributable to differences in the target basis sets used in the two calculations. The partial cross sections are compared with measured values [21,22] in Fig. 2. For the 2Al(2a~- l) and 2E(le~-l) partial cross sections, the agreement between our theoretical values and experiment is reasonably good. For the 2A 1(3a~- ~) cross section, however, there is substantial disagreement in the magnitude of the cross section near threshold. The major discrepancies between theory and experiment in the 21-24 eV range are no doubt attributable to interchannel coupling and configuration interaction effects that are neglected in our calculations.

A.E. Orel, T.N. Rescigno / Chemical Physics Letters 269 (1997) 222-226 14 E u b

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225

metry parameter is more sensitive than the partial cross section to approximations made in the trial wave function. In summary, we have reported the first use of the complex Kohn variational method to study photoionization of a polyatomic molecule. In the case of NH 3, we have found good agreement with experiment for two of the three channels studied. The asymmetry parameter is a more sensitive test of the accuracy of the wave function. For the lowest energy channel, it appears that it will be necessary to combine the effects of final channel coupling with a correlated initial target state to achieve quantitatively

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40 50 Energy (eV)

....

i ....

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E J~ 1.5 'o

i ....

u ....

i ....

60

u ....

u ....

u ....

I ....

3a

I ....

I ....

i ....

E u

I

70

80

b

..--.%

r, 0

1

1o

6 4 2 o 40

9

(.J

...m

0

....

I0

m ....

ZO

m ....

n ....

n ....

30 40 50 Energy (eV)

i ....

60

I.IL

70

E

n

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~

10 "''1

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30 40 50 Energy (eV) I ....

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,~..~..~... 60

70

I ....

80

I ....

•

35 30

2s

,§ 20

Fig. 1. Photoionization cross sections for NH 3 in the frozen-core Hartree-Fock (FCHF) approximation. Solid curves, present results; dashed curves, results of Caceili et al. (Ref. [ 17,18]) Panel a: cross sections for production of 2Al(3a ~-i) state of NH~. Panel b: cross sections for production of 2 E ( e - l ) state of NH~-. Panel c: cross sections for production of 2A 1(2a~- l ) state of NH~.

g 15 0

~

s o

................ 0

2

10 • ''l

d-" E

One of the major advantages of the complex Kohn method is it allows the calculation of asymmetry parameters. These parameters are compared to the experimental results of Banna et al. [22] in Fig. 3. The agreement between theory and experiment for the asymmetry parameters is again quite good for the 2Al(2a~-l) and 2E(le~-l). The 2Al(3a~-I) channel does not agree with experiment even at energies above 30 eV. Significantly, this is also the channel where the partial cross section is in poor agreement with experiment below 30 eV. Evidently, the asym-

A

............................

o

0

I ....

i ....

2a 1

(..)

g,

....

5

....

20 u ....

•,..'~"~'~..~ 30 40 50 Energy (eV) I ....

I ....

i ....

.,. a .A... 60

70

I ....

80

u'''

2a 1.s

v

×

o

&

o.5

U 0

o,om

0

....

10

! ....

20

! ....

I ....

u ....

30 40 50 Energy (eV)

! ....

60

n,,,

70

80

Fig. 2. Comparison of present partial cross sections for photoionization of NH 3 with experiment. Crosses: results of Brion et al. (Ref. [19]), triangles: results of Banna et al. (Ref. [20]). Panel designations as in Fig. I.

226

A.E. Orel, T.N. Rescigno / Chemical Physics Letters 269 (1997) 222-226 2

. . . .

I

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Grant No. PHY-93-22067. Computer time was supplied by the National Energy Research Scientific Computing Center.

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References

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n , n n n l n n

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Fig. 3. Comparison of present photoelectron asymmetry parameters for NH 3 with experimental results of Banna et al. (Ref. [20]). Panel designations as in Fig. 1.

correct cross sections and asymmetry parameters. We intend to examine these effects in a future study.

Acknowledgements This work was performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48. AEO acknowledges support provided by the National Science Foundation under

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