INTERPRETATION OF X-RAY EMISSION SPECTRA OF MOLECULES

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INTERPRETATION OF X-RAY EMISSION SPECTRA OF MOLECULES

R. Manne

To cite this version:

R. Manne. INTERPRETATION OF X-RAY EMISSION SPECTRA OF MOLECULES. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-151-C4-153. �10.1051/jphyscol:1971427�. �jpa-00214628�

JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-151

INTERPRETATION OF X-RAY EMIS §ION SPECTRA OF MOLECULE S

R. MANNE

Department of Quantum Chemistry, Uppsala University, Uppsala, Sweden

R6surne. - Nous exposons une methode d'interprktation de 1'6mission X des mol6cules. La plus grmde partie du spectre d'emission X est en rapport avec les etats simplement ionises, egalement observable par spectroscopie des photoklectrons. Des calculs effectues avec une orbitale molkculaire simplifike donnent dans beaucoup de cas, de f a ~ o n satisfaisante, les probabilitks de transition relatives, ce qui est utile pour determiner la symetrie de l'etat observe. Des structures de haute kner- gie, non relikes aux ktats observks par spectroscopie des photoklectrons, sont attribukes tides tran- sitions entre etats doublement ionises.

Abstract. - A review is given of a method for the interpretation of X-ray emission from mole cules. The main part of the X-ray emission spectra is related to the singly ionized states also obser- vable by photoelectron spectroscopy. Simplified molecular orbital calculations give in most cases satisfactory relative transition probabilities which are useful for the symmetry assignment of the states observed. High-energy structures not relating to states observed by photoelectron spectroscopy are attributed to transitions between doubly ionized states.

This report concerns the interpretation of X-ray emission spectra of gaseous molecules where the final states can be described as missing one or several valence electrons. Spectra of this kind have been recorded by LaVilla and Deslattes [l, 21, by Mattson and Ehlert 13, 41, by Gilberg 151 and by Sadovskii et al. [6].

Numerous spectra of complex anions in ionic crystals belong also to the category considered here as well as those of sulfur-containing compounds presented by Meisel et al. [7] at this conference.

The understanding of molecular spectra requires some simple molecular theory. The extension to molecules of the well-known shell description of the electronic structure of atoms leads to the molecular orbital approximation. The electrons in a molecule are thus described as moving independently of each other with molecular orbital wavefunctions exten- ding throughout the molecule. Each of these mole- cular orbitals belongs to one of the irreducible represen- tations of the molecular point group. Several approxi- mations are involved in this description. What is important for X-ray spectroscopy is that singly ionized states are described in this way by the wavefunction of the parent neutral molecule minus one molecular orbital.

In some recent papers we have made use of mole- cplar orbital theory to interpret soft X-ray emission spectra of molecules in the gas phase [8, 91. A syste- matic procedure was developed for the construction of semitheoretical K emission spectra for comparison

with those observed experimentally [8]. The extension to other kinds of X-ray emission spectra is straight- forward.

Relative intensities. - For dipole-allowed transi- tions, the spontaneous emission probability I is related to the transition energy E and the transition moment R,, through

I N E ~ I R , , , ~ ~ ~ (1)

where R,,,, ⁼

< +, ^{I C}

^I +, ^>

+,

1

are the wavefunctions for the two states involved in the transition. These wavefunctions are approximated by the molecular orbital wavefunctions for the ground state of the neutral molecule, each with one electron missing. Under this condition Rm, reduces to the one-electron dipole element between the two vacated molecular orbitals. For K spectra one of these is a l S orbital, and the other a delocalized molecular orbital which is expressed in terms of the available valence molecular orbitals as

This gives the result

In the summation in eq. (3) all, but the dominant

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971427

C4-152 R. MANNE valence-shell one-center terms

<

I

I

>

may be neglected. If we further drop the slowly varying energy dependent factor we obtain the approximate expression

I

C ckZi

k = n p

i. e., the relative emission probability is considered to depend only on the amount of p character in the molecular orbital describing the final state vacancy.

In molecules with several equivalent atoms emitting X-radiation, instead of using localized l s orbitals one might consider symmetry adapted molecular orbitals constructed from these and apply the group theoretical selection rules. However, the interaction energies between l S orbitals are much smaller than the natural linewidths, and no splitting of the l s levels has been observed for the molecules so far considered. All l s hole states could therefore be treated as degenerate which made the simpler treatment with localized 1 s states equivalent to a full molecular orbital treatment.

Relative transition energies. - Energies of the final states involved in X-ray emission of singly ionized molecules can be obtained from photoelectron spectra.

For several small and moderately large molecules the lowest ionized states are well known both as regards energy and as regards symmetry. In other cases the symmetry of the states has not yet been elucidated.

For bigger molecules with low symmetry the vibra- tional progressions of the various electronic states overlap making the interpretation of the photoelectron spectrum difficult if not impossible.

As an approximation to the energies of the ionized states calculated molecular orbital energies are quite useful. However, even for rigorous calculations with large basis sets there are errors of at least 2 eV and in some cases not even the order of the calculated molecular orbital energies is correct. This inherent inaccuracy of the molecular orbital approximation and the great amount of computer time needed for accurate ab initio calculations make the application of simplified computational schemes convenient.

The loss of accuracy introduced by the simplifications is in fact rather limited for ionization energies. Devia- tions are observed for X-ray intensities but are in most cases insignificant for the interpretation of the spectra.

Construction of semi-theoretical spectrum. - Kno- wing the energies of the final states and the relative transition probabilities one can construct a line spec- trum with the zero of energy undetermined. In order to guide the eye in the comparison with the experi- mental spectrum we found in convenient to convolute this line spectrum with a smearing function, e. g., a Lorentzian with suitable width.

If the energies of the final states are determined experimentally one can determine the energy of the initial state from the fit of the experimental and cal- culated X-ray spectra. In some instances the inner- shell ionization energies have been determined by X-ray photoelectron spectroscopy (ESCA) and then a check of the consistency of the experiments is possible.

Applications. - The above procedure has been applied to carbon K spectra of a series of hydrocarbons and carbon oxides [8]. In most of these compounds the energies of the final states were well-known from photoelectron spectroscopy. For carbon tetra- fluoride [g] there was an uncertainty in the assignment of the 2 a, and 2 t, molecular orbital levels (T, symme- try). Since carbon K emission in that molecule is allowed only to states of t, symmetry it was possible to make an assignment of these states using the X-ray emission spectrum. The 1 t, level could be determined from intensity considerations in the photoelectron spectrum and the energy difference between the l t, and 2 t, states was known from the X-ray emission leading to a unique assignment of the 2 t, level in the photoelectron spectrum. The 2 a, level could then be determined by exclusion.

Calculations have also been made of C1 and S KP spectra of some inorganic anions [10, 111. In that case tests were made with several different approximate molecular orbital methods on the ions SO:-, SO$-, S0,F-, SCN-, C104 and C10.T. The X-ray emission spectra of some of these compounds have also been discussed by others using the molecular orbital inter- pretation [12-151. It was found that the one-center approximation of the transition dipole elements produces no serious errors in the calculation of K emission probabilities. For SCN- calculations werc done also with the ab initio wavefunction produced by McLean and Yoshimine [16]. In all cases satisfac- tory results were obtained for the molecular orbital energies while the K/3 emission probabilities showed some deviations from experiment. This was true particularly for the C N D 0 calculations while the methods not neglecting differential overlap generally gave better results. For SCN- the ab initio calculation gave results in closest agreement with experiment.

In the carbon K spectra there are intense high- energy structures which cannot be explained from the molecular orbital description of singly ionized states.

We have attributed these structures to transitions between doubly ionized states, i. e. to Wentzel- IDruyvesteyn satellites. Intense satellites of this type have been observed also in the X-ray emission spectra of other light elements [17, 181, Moreover, the double ionization process is well documented from the inner- shell photoelectron spectra of light atoms in several small molecules as well as in the noble gases [19, 201.

INTERPRETATION OF X-RAY EMISSION SPECTRA OF MOLECULES C4-153

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ABERG

SIEGBAHN (K.), NORDLING (C.), JOHANSSON (G.), HEDMAN (J.), HEDEN (P. F.), HA= (K.), GELIUS (U.), BERGMARK (T.), WERME (L. O.), MANNE (R.) and BAER W.), ESCA Applied to Free Molecules (North-Holland, Amsterdam, 1969).

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