Theoretical investigation of the energy dependence of photoionization cross-sections and angular distributions of photoemission of CH4 and CF4

Journal of Electron Spectroscopy

41 (1888) 43942 Printed in The Netherlands

and Related Phenomena,

Elsevier Science Publishers B.V., Amsterdam -

THEORETICAL INVESTIGATION OF THE ENERGY DEPENDENCE OF PHOTOIONIZATION CROSS-SECTIONS AND ANGULAR DISTRIBUTIONS OF PHOTOEMISSION OF CH, AND CF, MOLECULES*

M. ROSI, A. SGAMELLO’ITI, F. TARANTELLI Department of Chemistry, University of Perugia, 06100 Perugia (Italy)

V.A. ANDREEV Far-East State University,

Vladivostok

(U.S.S.R.)

M.M. GOFMAN and V.I. NEFEDOV Institute of General and Znorganic Chemistry, Academy of Sciences of the U.S.S.R, Moscow (U.S.S.R.)

(First received 17 June 1986, in final form 18 August 1886)

ABSTRACT This paper reports a theoretical investigation of the energy dependence8 of the partial photoionisation cross-sections and angular distributions of photoemission for the molecules CH, and CF,. Two theoretical approaches are used for the calculation of the cross-sections. In the first, the multiple scattering Xa method (MS-Xc) is adopted, and in the latter, an extension of the additive scheme (multiple scattering with atomic amplitudes, MSAA) is employed to provide a description of the resonance structure taking into account multiple scattering of photoelectrons by the molecular potential. The main aim is to compare the results of the two theoretical approaches with the experimental data obtained using synchrotron radiation and dipole (e, 2e) measurements in a wide photon energy range. INTRODUCTION

The molecules of methane and tetrafluoromethane have been investigated thoroughly from both experimental and theoretical points of view [l-9]. Recently, experimental data on the partial photoionization cross-sections and the photoelectron angular distributions over a wide photon energy range have been reported [9]. These are very useful as an aid to the assignment of photoelectron spectra and as a probe for the molecular electronic structure, provided that there is a suitable theoretical model for the data interpretation. This paper reports a complete theoretical investigation of the energy dependences of the partial photoionixation cross-sections and the angular distributions of photoemission for the CH, and CF, molecules. *Dedicated to Prof. E. Heilbronner on the occasion of his 88th birthday.

0888.2048/es/$08.59

0 1988 Elsevier Science Publishers B.V.

440

While the atomic photoionization is well understood theoretically, with almost quantitative agreement between theory and experiment [lo], for molecules the situation is less satisfactory. In the latter case the main problem is the construction of reliable continuum wave functions for the ejected electron [ll]. In the present work, two theoretical approaches have been used for the calculation of the photoionization cross-sections. In the first, the continuum orbitals have been calculated by the multiple scattering Xa method [B-15] employing a multi-centre potential of the “muflln-tin” type, which reflects the singularities of the nuclei and shows a correct asymptotic behaviour [16]. (Hereafter it will be referred to as the MS-Xa method.) In the second approach, proposed in ref. 17, the photoionization cross-sections of molecular orbitals have been calculated using the amplitudes of photoionization of atomic shells and the multiple scattering formalism. This method, which is hereafter indicated as MSAA (multiple scattering with atomic amplitudes) gives a description of the near-threshold behaviour of the cross-sections in terms of deviations from the additive scheme of Gelius and Siegbahn [18]. The main aim of this paper is to compare the results of the two theoretical approaches with the experimental data obtained from synchrotron radiation and dipole (e, 2e) measurements in a wide photon energy range [9, B-211. Some preliminary results were presented at the X-64 Conference [22]. COMPUTATIONAL

DETAILS

All the parameters needed in the MS-Xa calculations, i.e. molecular geometries, a values, and radii of the non-overlapping spheres, have been taken from refs. 4 and 23. Particular attention was paid to the truncation of the partial waves entering in the multiple scattering expansion of the wave functions of both final and initial states. The convergence of the expansions was checked in preliminary calculations of the cross-sections and asymmetry parameters. For the initial state, the expansions were truncated at Z_ = 4 for outer spheres, 1 = 3 for the carbon and fluorine spheres, and 1_ = 2 for the hydrogen siieres. For the final state, the value of Z,_ = 7 was adopted for both the outer and all the atomic spheres. All the continuum channels allowed by the dipole selection rules were considered. To compute the initial state potential, the transition state formalism was used. In the MSAA calculations, the photoionization cross-section was determined within the stationary approach as the flux of the photoelectron wave through the atomic spheres [17]. The initial (“seeding”) electron waves are described using the atomic amplitudes of photoionization, and the propagation of these waves in a “muffin-tin” potential of a molecule is treated using the formalism of Green’s functions of the multiple scattering method. The amplitudes of photoionization of atomic orbtials were taken from calculations of the photoionization of atoms within the random phase approximation with exchange [24,25]. The MO-LCAO coefficients were taken from the ab initio calculations using double zeta quality basis sets [26]. The scattering phaseshifts of the partial waves on the atomic centres (involved in the determination of Green’s functions) were computed for the “muffin-tin”

441

. . * * Q&., -x-xx-

~sca1 a, e

hv (eV)

Fig. 1. Partial photoionization croes-eections of the It, orbital of CH, versus the photon energy. Experimental data are taken from [21]. MS-Xa and MSAA denote the valuea calculated using the corresponding methods, uGELand USCATare the contributione due to the additive scheme and interference effects to the total MSAA crow-section; al, e, t, , h are the contributions from different channels of the final state to the ascAT value.

potential obtained by the Xa calculation of the ground state using the parameters of ref. 4. The photoionization cross-section in the MSAA approach is represented as the sum of two contributions d = aGEL + aSCAT where cezL corresponds to the additive scheme of Gelius and Siegbahn, while t~scAr takes into account the influence of molecular potential on the photoelectron [17]. The contributions of individual channels of the final state to ascAr were also calculated. RESULTS AND DISCUSSION

Partial photoionization

cross-sections

Figures 1 and 2 show the partial cross-sections of the valence orbitals ltp and 2a, of the CH, molecule as a function of the photon energy in the range from the ionization threshold to 60 eV. The experimental data are taken from the (e, 2e) measurements and are in good agreement with the results of complementary electron-ion coincidence measurements [21]. The MS-Xa cross-sections have been multiplied by a factor of two in order to be in the same scale as the other data, hence permitting a closer comparison. The MS-Xa theoretical results reproduced the experimental trend for the (2~~)~’ state reasonably well, al-

20, (IP=23.05 x - -

eV)

Experiment MS-X. MSAA

. . . f QGe, - .- Qtcat

60

50

40

30

hv (eV)

Fig. 2. Partial photoionization cross-sections of the 2a, orbital of CH, versus the photon energy. For notations see Fig. 1. captions.

though the calculated values are lower than the measured ones. At the same time, the MSAA method yields strongly decreasing values of cross-section in the low energy region. Both the theoretical patterns computed for the (lLJT1 state are very similar to the experimental dependence, but the MS-Xa and

20

IO

6

5 b 0 --

15

e

IO 5 0 20

30

40

50

60

I

hv(eV)

Fig. 3. Partial photoionization cross-sections of the lh orbital of CF, versus the photon energy. Experimental data are taken from [9]. Notations as in Fig. 1.

443

4t2

(IP= 17.4 eV) Experlmeni MS-X, MSAA Gelius

l

-. .

It I

20 I

d,

I _I I

..

-

Qscat a, e

-x--

‘.bg._:,;;_ 20

30

40

50

hv (eV)

Fig. 4. Partial photoionization cross-sections of the 4% orbital of CF, veraua the photon energy. Experimental data are taken from [9]. Notations aa in Fig. 1. le (IP= 18.5 eV) l

-

-

Experiment MS-X, MSAA

* . . . Gelw

L

I

.

20

30

40

50

60

hv (eV)

I!ig. 6. Partial photoionization crow-w&ions of the le orbital of CF, veraua the photon energy. Experimental data are taken from [9]. Notations aa in Fig. 1.

444

MSAA values are always smaller than those measured. However, a better quantitative agreement is provided by the MSAA method. This is not surprising since the latter technique is in fact parametrized due to the use of the atomic cross-sections. It is worthwhile noting that the results obtained are more satisfactory than those reported by Dewar et al. [27], calculated using the ab initio wave functions for the initial state and the plane wave approximation for the final state. Figures 3-7 show the partial cross-sections of the valence orbitals ltl, 4&, le, 3t,, and 4a, of the CF, molecule as a function of the photon energy in the range from the ionization threshold to - 70 eV. The experimental data [9] are from angle-resolved photoemission measurements carried out using a variable energy photon source with synchrotron radiation [28]. Reference 9 also gives the results of MS-Xa calculations carried out by Stephens, et al., the general trend being analogous to our results, with the exception of the threshold region. The reason for this difference is not clear but the theoretical results for the threshold region seem to be incorrect. The MS-Xa values in Figs. 3-7 have once again been multiplied by a factor of two. The general pattern for the energy dependence of the calculated cross-sections are rather similar for the two approaches

312 (IP=ZZ.l l

-. . .

-x--e

i \

: ‘\ . *\XI. /----

-5

.

-.-

‘._,’

ew

Experiment MS-X. MSAA Gehus

clcoI cl1

t1 * 12

. 20

30’

40

50

60

hv W)

6. Partial photoionization cross-sections of the 3& orbital Experimental data are taken from [9]. Notations as in Fig. 1.

Fig.

of CF, versus

the photon

energy.

4a, . . . .

4-

(IP=25.1 l

--

. . ..

0 /

.’

.’

-*--._.

30

40

eV)

Expenment MS-X, MSAA Gelius

-*--._._.-.-

50

60

J

hv (eV)

Fig. 7. Partial photoionization cross-sections of the 4a, orbital of CF, versus the photon energy. Experimental data are taken from [9]. Notations aa i_nFig. 1.

used. The two methods give comparable results, the main difference being the higher values obtained by the MSAA scheme. For the photoionization of the ItI orbital, the broad resonance at - 30 eV which is present in the experimental curve is also predicted by both theoretical methods, although at a somewhat lower energy (- 26 ev). The feature is due to the continuum channel of e symmetry. According to the MSAA calculations, the & channel of the final state leads to a strong maximum in ~~8cA.r and, hence, in c, near the ionization threshold. Still sharper maxima are found for the photoionization of the 4h, le, and 3t, orbitals. The same peaks were also obtained by the MS-Xz method [9]. These maxima have not been observed experimentally and emerged from our calculations, apparently, because the phaseshifts were calculated using the molecular ground state potential. Application of the potential of an ionized state or a transition state should lead to the shift of the virtual 4 level to the discrete spectrum. For the (4&)-l state, both theoretical approaches predict a flat minimum at low photon energies and a broad maximum at higher energies (- 40 eV). An analysis of deviations from the additive scheme (represented as the contribution of dscAzin Fig. 4) shows that the structure of the photoionization cross-section obtained (with a local minimum) is due to a negative contribution of the interference effects, which has already been noted [22]. Similar conclusions are obtained from the results of the MSAA calculations of the photoionization cross-sections of valence levels of the SiF, molecule [29]. Thus, the manifestation of the resonance shapes in the form of quasi-forbidden bands (negative minima in ascAr;see [29]) is quite a widespread phenomenon, together with the well known manifestations in the form of quasi-stationary states (positive maxima in cscAz)_The negative interference effects are also characteristic of the energy dependence8

448

CH4

0

20

30

40

50

60

hv (eV)

Fig. 8. Total crces-sections of CH, versus the photon energy. (-) MSAA calculation, (---) experimental data from [30].

MS-Xcr calculation; (-.-.--)

of the photoionization cross-sections of the le and 3h levels (Figs. 5 and 6) where the calculated values agree qualitatively with experiment. We have also calculated the energy dependences of the photoionixation cross-sections of the CF, molecule inner valence orbitals.The cross-sections obtained are small and weakly dependent on the photon energy. Total cross-sections There are experimental data for the total cross-sections of photoabsorption of the CH, and CF, molecules [30]. These results have been obtained within a

01

20

30

40 hv (eV)

50

60

Fig. 9. Total cross-sections of CF, versus the photon energy. (MSAA calculation, (---) experimental data from [30].

) MS-Xa calculation; (-s-s-)

wide photon energy range using synchrotron radiation as a continuous source and a double ionization chamber. Theoretical values of the total cross-sections have been obtained by summing the partial cross-sections discussed above. The results of the two approaches are compared with experimental data in Figs. 8 and 9. However, a straightforward comparison is not possible since the calculated values take into account only the ionization channels, whilst the experimental data include all the possible channels, corresponding, for example, to the excitation of the Rydberg states, to dissociation, and to other phenomena. The cross-sections calculated by the MS-Xcr method have been multiplied by a factor of two in order to be in the same scale as the other data, to permit a closer comparison. Figure 8 shows the total cross-sections for the CH, molecule. The trends of the theoretical curves are rather similar and in reasonable agreement with experiment. Both the computed curves exhibit a discontinuity in the range of 22-24eV. This feature, which is not as well pronounced in the experimental curve, can be attributed to the ionization of the 2a, orbital. All the curves show a decrease in the cross-section as the photon energy grows; constant values are assumed at 46 and 49eV for the theoretical and experimental dependences, respectively. There is no clear experimental evidence for the Rydberg transitions, which may explain the satisfactory agreement between theory and experiment. On the other hand, fluorescence measurements indicate fragmentation processes with the formation of CH groups. These processes may be responsible for an increase of the background at low photon energies on the experimental curves when compared with the theoretical ones. The measured total cross-sections of CF, present a much more articulated structure in the interval 1622eV. In this energy region, the Rydberg transitions assigned at It, + 39,3p; 4t2 + 3s,3d; le + 3p, 3d; 3t, -P 39,3p, 3d have been measured using the electron impact spectroscopic techniques [6]. These Rydberg processes seem to become more important in the description of the total cross-section with increasing complexity of the molecular system studied, e.g. with substitution of hydrogen by fluorine. Angular distribution

parameter fi

The Xa formalism allows the calculation of the asymmetry parameter j?. This quantity characterizes the angular distribution of photoemission and reflects to a large extent the symmetry of an ionized orbital, especially at high kinetic energies of photoelectrons. At low and intermediate energies, resonances and interchannel interactions may affect the B value. Nevertheless, the dependence of j? on the photon energy in a wide range is an invaluable tool in obtaining symmetry and dynamical information. Figures 16-15 show the calculated energy dependences of B values for the CH, and CF, molecules, together with the experimental data [9, 291 obtained using synchrotron radiation as a continuum source. These figures reveal a complex and articulated trend of fi values, a general tendency being the in-

448

0.8.

0.6 -

-. r /”

P 0.4 I 0.2 r

20

24

28

32

36

40

hv (eV)

Fig. 10. Asymmetry parameters for the It, and 2a, orbitale of CH, versus the photon energy. (---) MS-Xa calculation for the lb orbital; ( x x ) experimental data for the 1% orbital taken from [19]; (---) MS-Xa calculation for the 2a, orbital.

crease of the angular distribution parameters with the photon energy. In the first energy range, clear maxima and minima are present, which cannot, however, be explained in general terms. Thus, in the case of minima, atomic considerations on the nature of the Cooper minima [31,32] are not valid, since

0.6

/----_

-\

Q

--

0.2 -

-0.6

16

24

32

40

48

---_

56

64

hu bV)

Fig. 11. Asymmetry parameters for the 11*orbital of CF, versus the photon energy (---) calculation; (-) experimental data taken from [9].

MS-Xu

449

_----_

0.6 .

-0.6 16

24

32

40

48

56

64

hv (eV) Fig. 12. Asymmetry parameters for the 4h orbital of CF, versus the photon energy. (---) calculation; (-) experimental data taken from [9].

MS-Xa

the lone pair orbitale in the molecules studied are formed by the 2p drbitals of fluorine and exhibit no nodes, which are an essential condition for the presence of minimal in the case of atoms [33]. On analysis of the results forthe angular distribution parameters of the CH,

1.0

0.6 9 0.2

-0.2

-0.6

24

32

40

48 hv

56

64

k.V)

Fig. 13. Asymmetry parametera for the le orbital of CF, versus the photon energy. (---) calculation; (-) experimental data taken from [9].

MS-Xa

-0.61

16

24

32

40

48

56

64

hu (eV) Fig. 14. Asymmetry parameters for the 3b orbital of CF, versus the photon energy. (---) calculation; () experimental data taken from [9].

MS-Xa

molecule, note that the (2~~)~’ state always shows positive and rather high initial B values (greater than 0.6). These exhibit a broad maximum at low energies and then start decreasing. A similar behaviour is observed for the ionization of the 4a, orbital of CF,, which correlates with the 2a, orbital of methane. The (It&’ state of CH, shows a strong dependence of the angular distribution parameter on the photon energy, with a sharp maximum observed at - 25 eV. It is worthwhile noting that our calculations are in a much better agreement with the experimental data [20] than the orthogonal planewave predictions of [34-36]. A general feature of the results obtained for the CF, molecule is that the asymmetry parameter is underestimated at high photon energies. For the (ltl)-’ and (le)-’ states the calculations do not exhibit the minimum near the ionization threshold, which is present in the experimental curves [9]t. However, the minimum at approximately 26 eV in the (4&)-l state is well predicted. For the (4&)-l state, the experimental maximum and minimum at -27 and 33eV, respectively, appear at lower energies in the calculated curves (20 and 25 eV). Finally, the minimum observed at 32 eV, in the (4a,)-l state is predicted theoretically at - 30 eV while the calculated maximum at - 27 eV is not found experimentally. The calculations of the ionization of the 4ul orbital exhibit poor agreement with the experimental data. This fact has already been noticed [37] for the deeper valence orbitals and may be attributed to the presence of configuration interaction, or to the strong relaxation effects. +The minimum near the (IQ- ’ threehold is preeent in the theoretical B-curvea of ref. 9.

451

-0.6

I

16

24

32

40

48 hu

56

64

(ev)

Fig. 15. Asymmetry parameters for the 4a, orbital of CF, vereue the photon energy. (---) calculation; (-) experimental data taken from [9].

MS-Xa

CONCLUSION The results of both MS-Xa and MSAA calculations of the photoionization cross-sections of the CH, and CF, molecules agree qualitatively with experiment. An analysis of deviations from the additive scheme suggests that the minima observed in the energy dependences of the photoionization crosssections are due to negative interference effects. In the evaluation of the asymmetry parameter j3,the MS-X& method seems to be able to provide a reliable prediction of the experimental values, at least for the ionization of the outer valence orbitals. For the inner valence orbitals, this technique is obviously less adequate due to the presence of strong relaxation and electronic correlation effects, which is explained by the inherent one-electron nature of the MS-Xa method. ACKNOWLEDGEMENT

One of us (A.S.) is grateful for the hospitality provided by the N.S. Kurnakov Institute of General and Inorganic Chemistry during their visit to Moscow within the agreement of the USSR Academy of Sciences and the CNR of Italy. REFERENCES 1 2 3

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