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X-RAY EMISSION PROCESSES FOR MOLECULES : AN AB INITIO STUDY FOR THE N2O MOLECULE
F. Larkins, R. Phillips
To cite this version:
F. Larkins, R. Phillips. X-RAY EMISSION PROCESSES FOR MOLECULES : AN AB INITIO
STUDY FOR THE N2O MOLECULE. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-729-C9-
732. �10.1051/jphyscol:19879124�. �jpa-00227233�
X-RAY EMISSION PROCESSES FOR MOLECULES : AN AB INITIO STUDY FOR THE N, 0 MOLECULE
F.P. LARKINS and R.A. PHILLIPS
Department o f C h e m i s t r y , U n i v e r s i t y o f Tasmania, H o b a r t , 7001 Tasmania, A u s t r a l i a
Abstract
-
The oxygen and nitrogen X-ray spectra f o r the N20 molecule---
have been calculated using an ab i n i t i o molecular o r b i t a l method a t the relaxed Hartree Fock level. Transition r a t e s include interatomic contri- butions. Tne central and terminal nitrogen atom spectra a r e separately identified. Comparison with the experimental spectrum reveals the extent of s a t e l l i t e contamination i n the electron impact excited spectrum.1 INTRODUCTION
X-ray emission spectra (XES) of atoms and molecules are often complex, because of shake-up and multiple ionisation type phenomena. Energy s h i f t s between diagram and s a t e l l i t e lines are often small. In principle, the origin of the s a t e l l i t e structure i s understood / I / , resulting from electron correlation and multiple vacancy effects. For molecules, multicentre interatomic /2/ and vibrational effects further contribute t o the complexity. We have recently undertaken theoretical investigations up to the relaxed Hartree Fock level for t h e molecules CO, HCN, C02 /3/, HC1 and CH3Cl (unpublished). In t h i s paper we report our findings t o date for the N20 molecule. This molecule i s of especial i n t e r e s t because of the chemically d i s t i n c t environments f o r the two nitrogen atoms. High resolution XES spectra f o r N20 obtained following electron impact have been reported 141. A selective excitation experiment i s required t o separate the contributions from the two nitrogens.
I I THEORETICAL CONSIDERATIONS
Details of the ab i n i t i o molecular o r b i t a l procedures used t o calculate the transition energies and transition r a t e s using a relaxed Hartree Fock method and non-orthogonal o r b i t a l s e t s have been reported elsewhere 131. N20 i s a linear molecule with a ground s t a t e electronic configuration lo22023024025u21n4602
7 0 2 2 ~ 4 . NOrmal XES f ~ l l o w s core ionisation from the oxygen ( l o , 541.2 eV), central nitrogen NC (20, 412.5 eV) o r terminal nitrogen NT (30, 408.5 eV)
.
Therelaxed Hartree Fock calculations reported here were carried out in the C2,
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879124
JOURNAL DE PHYSIQUE
subgroup of the C, point group with the neutral molecule geometry ( q N = 1.155 A, NO = 1.185 A). Both the nitrogen and oxygen Gaussian basis s e t s were taken from t h e (9s5p) + [5s3p] contraction of Dunning / 5 / , t o which were added d functions with exponent 0.80 (N) and 0.85 (0) 161. The transition probabilities have been calculated using both the length and velocity form of the dipole operator and a multicentre model which includes intermolecular contributions.
For a molecule such a s N20 the one-centre intra-atomic approximation i s not adequate 131.
I11 RESULTS
The oxygen K X-ray energies and relative intensities a r e presented i n Table 1 along with the experimental energies /4/. The calculated energies a r e a l l within 1.5 eV of the experimental values, hmever the ordering of t h e 1 n and 60
transitions i s the reverse of the experimental observation. The discrepancy i s due t o t h e neglect of some electron correlation contributions. The relative i n t e n s i t i e s are presented only f o r the length form since there i s a close agreement with the relative intensities using t h e velocity form. Absolute rates a r e not presented i n d e t a i l here. They can be deduced from data i n the footnote.
Based upon previous experience / 3 / the absolute rates with the relaxed HF model a r e expected t o be larger than the frozen o r b i t a l o r one centre rates. The calculated spectrum is compared with the experimental s p e c t m /4/ i n fig. 1. In t h e synthesis of the calculated spectrum Lorentzian l i n e shapes were used with F W values taken from the experiment / 4 / , 2n (0.42 eV), I n (1.5 eV), 6a (0.22 eV) along with the experimental positions of the lines.
The nitrogen K results are also sham i n table 1. The calculated transition energies are within 3 eV of the experimental values. The relative intensities a r e referenced t o the strongest l i n e i n t h e spectrum, namely NC[3u ] - [ I n ] . They are determined assming that the branching r a t i o i s equal f o r each nitrogen such t h a t the t o t a l spectral area associated with NT i s equal t o that associated with Nc. The calculated XES spectrum f o r NC i s sham i n fig. 2a and the
corresponding spectrum f o r NT i n fig. 2b. Lorentzian l i n e shapes with FhhIM taken from t h e experimental observation /4/ namely, 1.0 eV f o r NC I n and 2n and NT In, 60 and 2n, 0.5 eV f o r NC 60 and 70 and 0.3 eV for NT 70 and experimental
transition energies have been used. The t o t a l nitrogen s p e c t m i s sham i n fig.
2c assuning equal ionisation cross-sections and branching r a t i o s f o r the two nitrogen centres. The experimental spectrum i s also presented 141.
IV DISCUSSION
The 0-K experimental spectrum obtained by electron impact (fig. 1) contains a significant s a t e l l i t e contribution. The dominant diagram lines result from transitions involving the In, 60 and 2n orbitals. The XES spectrum i s consistent with the Auger electron spectrum i n t h i s regard. The l r transition i s the most vibrationally broadened since t h i s o r b i t a l i s a n banding o r b i t a l f o r both N-N and N-0 bonding. The I n peak i n the photoelectron spectrum also shdvs the most vibrational structure of any of the outer valence orbitals. It i s predicted that t h e intensity cgntributions from the 40, 50 and 70 are small, We have noted a significant electron population redistribution, in a Mulliken population sense, f r m using the grcund s t a t e t o t h e specific hole s t a t e wavehctions. This partly explains the difference between our ab i n i t i o intensities and the e a r l i e r one centre estimates 141. On the basis of the theoretical intensity i t i s evident that s a t e l l i t e c o n t r i h t i o n s t o the experimental spectrum a r e very important. There a r e many sources of s a t e l l i t e lines / I / principally i n i t i a l s t a t e correlation s a t e l l i t e s , f i n a l s t a t e correlation s a t e l l i t e and multiple excited correlation s a t e l l i t e s . While such calculations have been attempted f o r a t m i c argon / I / , the additional ccmplexi t y f o r molecules has precluded exten- s i v e s a t e l l i t e calculations t o date. An experiment with selective ionisation of t h e l o o r b i t a l near threshold (541.2 eV) would minimize the s a t e l l i t e contri- bution t o yield a near 0-K diagram l i n e spectrum.
F i n a l Hole Eif (eVIa R.I. Final Hole Eif (eVIa R.I.
S t a t e theor. expt/4/ S t a t e theor. exp t/4/
Nitrogen NC-K
4a 372.6
-
0.0 60 395.7 392.4 19.250 378.0
-
4.9 7 0 398.2 396.1 8.4l r 395.1 394.6
looc
2r 402.5 399.5 0.2Nitrogen NTK
40 368.0
-
1.5 60 391.1 388.5 5.350 373.4
-
0.6 7 0 393.6 392.1 45.21 n 390.5 390.2 29.6 2n 397.9 395.5 50.5
a Reference energies [ l o ] -163.8305 h, [2u] -168.4895 h, [3u] -168.6582 h ,
[ - I
-183.7145 h.b For 0-K, Rel. Int. 100 = Abs. Rate (L) 34.07 x au, (V) 29.62 x au.
For NC-K, Rel. Int. 100 = Abs. Rate (L) 13.87 x au, (V) 11.93 x au. For NTK 2a Rel. Int. 50.5 = Abs. Rate (L) 5.92 x 10-6 au, (V) 5.09 x au. Total NC and NT i n t e n s i t i e s scaled t o be equal (see t e x t ) .
The experimental and t h e o r e t i c a l t o t a l N-K spectra a r e s h a m i n fig. 2c. The agreement between t h e two i s most encouraging. There is a l s o c l e a r evidence f o r a significant contribution of s a t e l l i t e s t o t h e experimental spectrum. The separate nitrogen spectra f o r t h e c e n t r a l (fig. 2a) and terminal (fig. 2b) nitrogens a r e very d i f f e r e n t r e f l e c t i n g t h e electron d i s t r i b u t i o n within t h e molecule. The NC spectrum i s dominated by t h e l r , 60 and 70 o r b i t a l
contributions, while t h e NT spectrum i s dominated by t h e l r , 70 and 2r o r b i t a l contributions. Synchrotron radiation may be i n principle used t o separate t h e two spectra, through s e l e c t i v e excitation of t h e NT 30 o r b i t a l (408.5 eV) and then t h e NC 20 o r b i t a l (412.5 eV). The l a t t e r w i l l yield a NT
+
NC spectrum from which t h e NT can be subtracted. The two nitrogen contributions of t h e Auger spectrum f o r N20 molecule have recently been separated using synchrotron r a d i a t i o n and resonant excitation from t h e core t o t h e f i r s t unoccupied molecular o r b i t a l NT 30 + 3r (401.2 eV), NC 20 + 3r (404.9 eV). Related t r a n s i t i o n s i n t h e resonant Auger and t h e normal Auger spectra appear t o have s imilar non-radiative t r a n s i t i o n r a t e s . Such a s i t u a t i o n may not p r e v a i l f o r r a d i a t i v e t r a n s i t i o n s , therefore t h e resonant X-ray s p e c t r a l p r o f i l e s may not be a fingerprint f o r t h e nonnal X-ray s p e c t r a l profile. For example, a s e r i e s of ab i n i t i o calculations f o r spectator X-ray t r a n s i t i o n s NC[20](3n)-
[no](3r) have revealed t h a t while t h e t r a n s i t i o n energies a r e l m e r by 2-3 eV compared with t h e corresponding diagram l i n e s there i s no systematic trend f o r t h e t r a n s i t i o n r a t e s . Absolute values increased by 104 per cent, 56 per cent and 8 per cent f o r n equal t o 5, 6 and 7 respectively. The participator t r a n s i t i o n s [na](3n)-[-I where ~2 f o r NC and n=3 f o r NT a r e predicted t o occur near 405 eV and 401 eV respectively with a greater i n t e n s i t y than t h e [no](31r) spectator s e r i e s of 1 ines.
JOURNAL DE PHYSIQUE
0 518 520 522 524 526 528 530 532 534 ENERGY N
Fig. 1. Theoretical and Experimental m g e n K XES spectra f o r n i t r o u s oxide.
20
00
80
60
40
20
0 388 390 392 394 396 398 400 402 404 ENERGY EV
Fig. 2. Theoretical and Experimental Nitrogen K XES spectra f o r n i t r o u s oxide, a) c e n t r a l nitrogen, b) terminal nitrogen, and c) t o t a l nitrogen theory and experiment.
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