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VALENCE CORRELATION EFFECTS IN THE CORE IONIZATION OF MOLECULES
A. Lisini, P. Decleva
To cite this version:
A. Lisini, P. Decleva. VALENCE CORRELATION EFFECTS IN THE CORE IONIZA- TION OF MOLECULES. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-715-C9-718.
�10.1051/jphyscol:19879121�. �jpa-00227230�
JOURNAL DE PHYSIQUE
Colloque C9, supplkment au n 0 1 2 , Tome 48, dkcembre 1987
VALENCE CORRELATION EFFECTS IN THE CORE IONIZATION OF MOLECULES
A . LISINI and P. DECLEVA
Dipartimento di Scienze Chimiche, ~niversita di Trieste, Piazzale Europa 1, I-34127 Trieste, Italy
A b s t r a c t
C o r r e l a t i o n e f f e c t s a s s o c i a t e d w i t h e x c i t a t i o n s w i t h i n t h e v a l e n c e s h e l l , and t h e c o u p l i n g w i t h s i n g l e e x c i t a t i o n s i n t h e v i r t u a l s p a c e , a r e examined by C I c a l c u l a t i o n s w i t h v i r t u a l o r b i t a l s d e f i n e d by a pro- j e c t i o n o r t h e I V O scheme. A r e a s o n a b l e d e s c r i p t i o n i s o b t a i n e d by a minimal model combining double e x c i t a t i o n s i n t h e v a l e n c e w i t h s i n ~ l e e x c i t a t i o n s i n t h e v i r t u a l s p a c e .
The p r e s e n c e of s a t e l l i t e s t r u c t u r e s i n c o r e p h o t o e l e c t r o n s p e c t r a h a s been l o n g r e c o g n i z e d . A t v a r i a n c e w i t h t h e i n n e r v a l e n c e r e g i o n , t h e g e n e r a l i n t e r p r e t a t i o n i s however s t i l l based on t h e s i m p l e shake t h e o r y , a l t h o u g h t h e importance of h i g h e r o r d e r c o r r e l a t i o n e f f e c t s h a s been s t r e s s e d i n i n d i v i d u a l . s y s t e m s . I n t h e v a l e n c e r e g i o n o f molecules t h e dominant c o r r e l a t i o n e f f e c t s a r e a s s o c i a t e d w i t h f l u c t u a t i o n s of e l e c t r o n s w i t h i n t h e v a l e n c e s h e l l ( 1 , 2 , 3 ) . A C I s t u d y o f t h e c o r e r e - g i o n w i t h i n a minimal b a s i s s e t h a s i n d i c a t e d t h a t b e s i d e s r e l a x a t i o n s a t e l l i t e s t h e most i m p o r t a n t s t a t e s a r e g i v e n by double e x c i t a t i o n s t o low-lying empty o r b i t a l s , w h i l e no f l u c t u a t i o n s o f t h e c o r e h o l e a r e r e l e v a n t , e x c e p t i n t h e c a s e o f e q u i v a l e n t atomic s i t e s . T h i s i s i n marked c o n t r a s t w i t h t h e s i t u a t i o n found i n t h e v a l e n c e r e g i o n , where t h e s t r o n g e s t e f f e c t s a r e a s s o c i a t e d w i t h s u c h e x c i t a t i o n s , t h a t i s t h e 2h-lp c o n f i g u r a t i o n s . D e s p i t e t h e l i m i t a t i o n s due t o t h e u s e o f a mini- mal b a s i s s e t , i t i s e x p e c t e d t h a t a c o r r e c t p i c t u r e i s achieved. I t i s however obvious t h a t an e x t e n d e d b a s i s must be employed f o r a q u a n t i t a - t i v e d e s c r i p t i o n . I n o r d e r t o r e t a i n t h e c o n c e p t u a l and c o m p u t a t i o n a l s i m p l i c i t y a s s o c i a t e d w i t h t h e u s e of a v a l e n c e s p a c e , i t i s however n e c e s s a r y t o e x t r a c t a v a l e n c e complement of t h e occupied o r b i t a l s from t h e f u l l v i r t u a l s p a c e . We have h e r e a n a l y z e d two p o s s i b i l i t i e s , namely a p r o j e c t i o n scheme ( 4 ) , s u c c e s s f u l l y employgcllin t h e v a l e n c e r e g i o n , and t h e improved v i r t u a l o r b i t a l ( I V O )
,
o r V scheme ( 5 ) .C a l c u l a t i o n s were performed a s i n p r e v i o u s work ( 3 ) . The b a s i s em- ployed i s ( 9 s r 5 p / 5 s , 3 p ) f o r C , 0 , N and ( 5 s / 3 s ) f o r H , p l u s ( 2 s , 2 p ) Rydberg o r b i t a l s i n t h e c e n t e r o f mass ( 6 ) . S e p a r a t e SCF calculations were performed f o r t h e qround and i o n i z e d systems. I n t e n s i t i e s were c a l c u i a t e d a c c o r d i n g t o - t h e u s u a l e x p r e s s i o n
N 2 I ( % ) = 100xR./R
1 0
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879121
C9-716 JOURNAL DE PHYSIQUE
between the individual peaks is lacking in the higher energy part, Fig. 1. 0 1s satellite structure and the overall intensity appears in H 0. to be underestimated. A similar de- A: 24-lv, B: 2h-lp, C: 3h-2v+2h-lp, scription is however given by pre- E: 3h-2v-lp, all with projected vious investigations (11).
orbitals. D: 3h-2v+2h-lp with IVO Only the projection scheme has orbitals. All energies are relati- been employedfor the 2al (C 1s) ve to the main 0 Is peak. spectrum of CO. The relevant re- where k is the core orbital considered.
Within the valence space, single, single+double (hereafter refer- red as 2h-lv and 3h-2v respectively) and full CI were employed both for the neutral and ionized system. In the latter a hole was localized in the relevant core orbital, or delocalized over equivalent orbitals in the case of N2. Additionally single excitations were allowed in the rest of the vlrtual space by combining 3h-2v in the valence plus the complete 2h-lp space (referred as 3h-2v+2h-lp), or by employing a maxi- mum excitation level of 2 in the valence space and 1 in the remaining virtuals (3h-2v-lp)
.
The results for H20 are reported in figure 1. The 2h-lv results show few lines, with most of the intensity concentrated at -28 eV.
This intensity is reduced by a factor of 3 from the value computed in a minimal basis, showing the large effect of relaxation in this case.
If961
2
2
-
2
-
2
-
2
-
although a detailed correspondence While the inclusion of higher exci- tations within the valence shell does not lead to significant varia- tions, the extension to the whole
E
virtual space (2h-lp) gives rise to-
I,
I
a splitting of this single line in-
I
further given by the more extended schemes and also by the use of the
D
IVO orbitals. The results so obtai-ned are in good agreement with the experimental data and those of pre- vious extensive calculations (7,8,
I I
l j I,, !,, , 9 ) .
In N a larger difference is afforded !$y the use of IVO orbitals,
C
especially apparent in the CI wi-thin the valence shell. In this ca- se single excitations are unable to give a correct description of the spectrum. The 3h-2v results repor- ted in figure 2 give a reasonable description of the first two peaks,
B
while the structure at the higherenergy side in the experimental to a multiplet of closely spaced
,l,l,.,
states, possibly because of Rydberq1
-valence mixing. Small changes are
spectrum (10) is concentrated in few lines, and also the spacings
1 1
are underestimeted. This structurespreads into several low intensity lines in the 3h-2vi-2h-lp and 3 h - 2 ~ -
A
x 2 lp schemes. At the same excitation level the use of projected orbitals gives fewer lines carrying similar intensity over the same energy re- gion. The agreement with the expe-20 3 0 E(eV) rimental spectrum is reasonable,
Pig. 2. N 1s satellite structure in N2. A: 3h-2v, B: 3h-2v+2h-lp, C:
3h-2v-lp, all with IVO orbitals. D: 3h-2v-lp with projected orbitals.
E: experimental spectrum (ref. 10). All energies are relative to the main N 1s peak.
levant results are reported in figure 3. Again the coupling to the sin- gle excitations in the virtual space gives rise to several lines in the higher energy side. A greater change is apparent in this case in going from the 3h-2v+2h-lp to the 3h-2v-lp scheme. The agreement with the experimental data (10) is less satisfactory. There is still one to one correspondence for the first two peaks (and the results of previous calculations (12)) but the enerqies are overestimeted and the intensity is calculated much lower. This deficiency is much improved in the va- lence full CI calculations, indicating the importance of higher excita- tions in this case. An overall qualitative agreement, like in N2, is instead obtained for the higher energy part.
From the results reported it appears that the major deficiency associated with the use of a minimal basis set, namely the concentra- tion of the intensity in few lines and the absence of structure, which is most apparent in the water molecule, is rec3vered by the schemes em- ployed. Correlations associated with higher excitations are reasonably taken into account by double excitations in the valence shell, even in the simpler 3h-2v+2h-lp scheme. This is particularly convenient for the small dimension of the relevant CI matrices, which allows an easy ex- tension to larger systems.
JOURNAL DE PHYSIQUE
Fig. 3. C is satellite,structure in CO. A: 3h-2v, B: 3h-2v+2h-lp, C:
3h-2v-lp, all with projected orbitals. D: experimental spectrum (ref.
10). All energies are relative to the main C Is peak.
References
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Chem. Phys.1 65 (1986) 115.
2. P. Decleva and A. Lisini, Chem. Phys. 106 (1986) 39.
3. P. Decleva and A. Lisini, Chem. Phys. 112 (1987) 339.
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Phys. 90 (1984) 271.
5. W. J. Hunt and W. A. Goddard 111, Chem. Phys. Letters 3 (1969) 414.
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Pireaux, U. Gelius and K. Siegbahn, Nouv. J. Chim. 1 (1977) 191.
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9. D. Moncrieff, I. H. Hillier, S. A. Pope and M. F. Guest, Chem. P h ~ s . 82 (1983) 139.
10. U. Gelius, J. Electron Spectry. 5 (1974) 985.
11. W. R. Rodwell, M. F. Guest, T. Darko, I. H. Hillier and J. endr rick, Chem. Phys. 22 (1977) 467.
12. M. F. Guest, W. R. Rodwell, T. Darko, I. H. Hillier and J. r end rick, J. Chem. Phys. 66 (1977) 5447.
