Correlation effects in core and valence photoelectron spectra of alkene molecules

Chemical

Physics ELSEVIER

Chemical Physics 195 (1995) 171 - 193

Correlation effects in core and valence photoelectron spectra of alkene molecules G. Fronzoni, G. De Alti, P. Decleva, A. Lisini Dipartimento di Scienze Chimiche, Via L. Giorgieri l, 34127 Trieste, Italy

Receivcd 3 November 1994

Abstract The core, the inner and outer valence ionization spectra of propene, 1-butene, l-pentene, cis-butene, trans-butene and iso-butene have been calculated at the ab initio configuration interaction (CI) level, in order to analyze the influence of different substitutions on the double bond on the appearance of the spectra. The CI schemes adopted, i.e. 3h-2v('rr) + 2h - lp CI for the core part, 2 h - l v CI for the valence part and 2h lp CI for core and valence, have proven to be adequate for the description of correlation effects which cause the appearance of complex structures in the spectra. Satisfactory reproduction of the experimental features has been achieved and for their simplicity the CI schemes adopted can be put forward for the calculation of the spectra of larger molecules of the same type which allows a clearer insight of the evolution of correlation effects with the increasing complexity of the systems.

1. I n t r o d u c t i o n

Photoelectron spectroscopy (PES) represents one of the most direct and important probes of the electronic structure and bonding properties of molecules, particularly when high resolution experimental results are coupled to accurate calculations. Of particular interest is the study of correlation effects which, as is well known, are responsible for the appearance of complex structures in the spectra. These effects can be particularly strong in the inner valence region of the spectrum where a progressive fragmentation of the main lines into several lines of lower intensity is observed on going to higher energies, often revealing a complete breakdown of the one-particle picture [1]. The situation in the core region is in general simpler than in the valence region because of the decoupling between the core hole and the valence excitations, so that the shake-up structure is clearly

associated with a well defined core level. However the theoretical description of core spectra is not easy due to the presence of strong relaxation effects, which are usually small in the valence region and dominate instead the core ionizations, substantially determining the intensity of the satellite peaks. The interplay between these effects and the correlation effects renders therefore the calculation of these structures notably complex. From a theoretical standpoint a proper treatment of the many-body effects, both in the valence and in the core region, is essential to reproduce accurately the energies and intensities of the satellite structures. In this context the ab initio configuration interaction (CI) approach appears to be adequate to treat the various spectral regions at the same level of accuracy and to employ different orbital bases for the ground and the ionized states including at the outset a large part of the relaxation contribution. On the other hand

0301-0104/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 1 - 0 1 0 4 ( 9 5 ) 0 0 0 6 7 - 4

172

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

it is well known that in the CI approach the increase of the computational effort associated both with the enlargement of the basis set and with the inclusion of higher excitations soon becomes explosive, and it appears therefore sensible to employ limited schemes which are capable of giving an interpretation of the data of interest. To test the adequacy of such models it is very important to have the possibility of comparing the theoretical results with high resolution experimental data. In this respect several X-ray photoemission data have appeared recently, offering a rich ground for the study of various series of molecules [3-9]. Among these investigations, particularly interesting are the systematic studies of related compounds with electronic structures of increasing complexity, which can be used to anticipate the electronic structure of extended systems, such as polymer chains. Approaches of this kind have proven to be very useful to understand the evolution of many-body effects along series of molecules which can be the basis to anticipate the spectral behaviour of larger systems (see for example Refs. [10-14]). As an example, in a recent experimental work the X-ray core and valence spectra of polyacetylene have been assigned on the basis of a systematic study of the spectra of ethylene, trans-butadiene and trans-hexatriene model molecules, representing the monomer, dimer and trimer subunits of the polymer [4]. A parallel investigation [15-17] at the ab initio level, which has been extended up to decapentene for the valence ionizations, has pointed out the theoretical interest of this study for the strong correlation effects which dominate the core and the valence spectra and the adequacy of the (n + 1)h - n p CI schemes, which comprise the configurations with up to n + 1 holes in the occupied orbitals and 0 up to n particles in the empty orbitals. For the core region the simplest of these schemes, i.e. 2 h - l p CI, has given a qualitative description of the core satellite structures still mantaining a tractable dimension of the problem, provided due care is paid to an accurate choice of the basis set and an explicit inclusion of the relaxation effects by the use of relaxed orbitals relative to the core hole. More accurate results can be reached employing the (n + 1)hn v - m p CI schemes, where higher excitations are generated within a valence v-space of strongly interacting orbitals, while at most double excitations are

generated in the remaining virtual space. As concerns the choice of the v-space, the space obtained by projecting the minimal basis set (MBS) onto the extended basis set (EBS) [18,19] has been repeatedly employed [7,20-25]; for the unsaturated hydrocarbons this valence space can be restricted to the set of the valence "rr orbitals, which are low-lying and strongly interacting, and in fact the 3 h - 2 v ( ' r r ) - l p CI scheme has proven to be adequate to treat the core spectra of ethylene, propene, trans-butadiene and trans-hexatriene [15]. The satellite structures have instead different origins in the valence region, since nondynamical correlation effects, in particular of the quasidegenerate type, are dominant and tend to increase on going from the outer to the inner valence part of the spectrum. Here the 2 h - l p configurations are the most important for the description of these effects and both the 2 h - l p and the more restricted 2 h - l v CI scheme, in which excitations are generated only within the valence space, have proven to be very advantageous when treating large molecules. On the basis of the preceding studies on hydrocarbons with alternating double bonds [15-17], in the present work we undertake a systematic analysis of the core and valence spectra of a series of unsaturated organic compounds containing one carboncarbon double bond and different aliphatic substituents, i.e. -CH3, - C z H 5 and -C3H7, so the molecules examined are propene, 1-butene, 1-pentene and the three isomers of 2-butene (cis-, trans- and iso-butene). For these compounds highly resolved C1~ shake-up spectra have appeared recently [5] showing interesting variations of the shake-up structures along the series which suggest that different many-body effects are active depending on the carbon atom which is ionized within each molecule. The present CI calculations can give a further insight in the assignment of the transitions and in the understanding of the mechanisms involved in the shake-up processes of this kind of systems. In addition through the comparison with the accurate experimental data available it is possible to test the capability of the CI schemes proposed to deal with this class of compounds. As concerns the valence region, there are several experimental data for the three isomers of 2-butene [26-31]. There are also some ab initio calculations

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

[26,27,32,33], which however do not cover the inner valence region. For propene, 1-butene and 1-pentene among the various experiments [28,30-35] the most detailed experimental data, which cover the entire valence region, are the XPS spectra of Liegener et al. [36] which have appeared recently together with Green's function (GF) calculations. The present analysis covers the entire valence region, included the inner valence part where prominent many-body structures are anticipated and for the three isomers of 2-butene have not been analyzed theoretically. This will allow to explore possible variations of correlation effects along the series and their connection with the various substituents.

2. Computational details Due to the different many-body mechanisms associated with the core and the valence ionizations, different choices both of the basis set and the CI schemes have been made for the core and the valence spectra calculations. For the core part, where shake-up structures are associated with transitions towards empty valence or Rydberg orbitals, some diffuse orbitals have to be included in the EBS. Previous tests on the ethylene [15] have indicated that the influence of polarization functions on carbon atoms is modest, and therefore they can be excluded from the basis set. The MBS has been obtained from the general contraction scheme of the 9s5p (5s for H) set of Huzinaga [37]. The EBS has been obtained by decontracting the same set to 5s3p (3s for H), by leaving the most diffuse primitives uncontracted and two sets of s,p Rydberg functions with exponent obtained by the even tempered criterion (factor 3.0) have been added on the centre of mass. A localized description of the core hole has been adopted, since it has been found that better results are generally obtained for low excitation level in the CI [38]. For the ions the SCF orbitals of the doubly ionized species are employed, i.e. with the holes in the core and in the highest orbital. The CI schemes employed are: - 2 h - l p CI, which comprises 1 or 2 holes in the occupied orbitals and 0 or 1 particle in the empty orbitals;

173

- 3h-2v('rr) + 2 h - l p CI, which comprises 1, 2 or 3 holes in the occupied orbitals with a maximum excitation level of 2 in the w-space and 1 in the remaining virtuals, excluding the configurations with one particle in the "rr valence space and one particle in the virtual orbitals. In both schemes one core orbital is kept singly occupied and the others doubly occupied. The 2 h - l p CI calculations are coupled to a single determinant description of the ground state. For the more extended scheme, the ground state has been obtained as follows: natural orbitals have been obtained from a 2h-2p CI with a perturbative selection of configurations and with these orbitals a 2h-2p CI has been performed with another perturbative selection of configurations. For the valence calculations the MBS was obtained in the same way as for the core calculations. The EBS has been obtained by decontracting the same set of Huzinaga to 3s2p (2s for H), by leaving the most diffuse primitives uncontracted and adding one d polarization function with exponent 0.75 on the carbon atoms. Polarization functions are necessary especially for the description of the inner valence part, where different results have been previously obtained with and without these kind of functions on the carbon atoms [16]. For the ions the SCF orbitals relative to the doubly ionized species, i.e. with both holes in the highest "rr orbital, have been employed. The following CI schemes have been employed: - 2 h - l p CI; - 2 h - l v CI, which comprises I or 2 holes in the occupied orbitals and 0 or 1 particle in the empty valence orbitals. Both these schemes have been coupled to a onedeterminant description of the ground state. The valence space has been obtained, both in the core and in the valence region, by a projection scheme of the MBS onto the EBS, as previously described [18,19]. The MELDF set of programs [39] has been employed and the intensities have been calculated in the sudden approximation according to the usual expression:

Rik = I(q', N ', a,~o ~) I =, where k is the orbital annihilated.

174

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

E x p e r i m e n t a l g e o m e t r i e s h a v e b e e n e m p l o y e d for all m o l e c u l e s [40]. O n l y in the case o f 1-pentene, for w h i c h n o e x p e r i m e n t a l data are available, w e h a v e used the structural p a r a m e t e r s o f 1 - b u t e n e substituting the i n - p l a n e h y d r o g e n a t o m o f the t e r m i n a l carb o n a t o m o f the alkyl g r o u p w i t h a m e t h y l group.

3. Results and discussion 3.1. C I s s h a k e - u p s p e c t r a A s already m e n t i o n e d , fine e x p e r i m e n t a l core s h a k e - u p spectra are a v a i l a b l e for the m o l e c u l e s

e x a m i n e d here, f u r t h e r m o r e I N D O - C I c a l c u l a t i o n s h a v e b e e n p e r f o r m e d [5] w h i c h are in q u a l i t a t i v e a g r e e m e n t w i t h the e x p e r i m e n t . In the p r e s e n t paper, b e s i d e s p r e s e n t i n g the first c a l c u l a t i o n for 1-pentene, w e a i m at g i v i n g a m o r e detailed a n a l y s i s of the s p e c t r a in particular as c o n c e r n s the h i g h e r e n e r g y part b e l o w the shake-off. C o n s i d e r first p r o p e n e , 1 - b u t e n e a n d 1 - p e n t e n e w h i c h a l l o w to study the effects o f the i n c r e a s i n g l e n g t h o f the alkyi g r o u p a t t a c h e d to the d o u b l e b o n d ( - C H 3 , - C 2 H 5 a n d - C 3 H 7) o n the s h a k e - u p structures. A s h a s b e e n e v i d e n c e d in the e x p e r i m e n t a l study, in the s h a k e - u p spectra of these s y s t e m s the i n t e n s i t y o f the l o w e s t - l y i n g structure s h o w s a pro-

Table 1 Calculated shape-up energies (eV) and intensitics for propene ~ 3h-2v(v) + 2 h - l p CI E

Composition h

l

Exp. c E

I

line no.

C1

C2

C3

- 0.45

31.53

9.57 12.61

3.80 0.34

14.25

0.05

17.36

0.05

0.06 7.17 9.54 12.95

32.50 0.05 2.82 0.09

15.80 15.99

0.07 0.05

16.45 18.12 18.86

0.05 0.08 0.05

0.12 10.66 18.30 18.57

35.97 0.35 0.09 0.06

0.899 10.- 1 0.32610" L2ar 13'rr 0.912 10" 12'rr-]3w 0.594 let 12~- ln'rr 0.482 lcr-12"n 15'rr 0.34210"-12'rr 1nat 0.314 10. t2rr 'n'rr 0.555 10" ] 2rr- ln'rr 0.54410" 12~ ~5v 0.313 10. 12'rr-ln'n mixed 10.-t30. in0" 0.917 20.- 1 0.961 20" ] 2vr- 13"n 0.90420" 12"rr L3rr 0.677 20. 12"rr- In'rr 0.56020. 12rr 15"rr 0.367 20. 190.- ln0" 0.413 2o" 12"rr- t4'rr 0.36920. ' l'rr- ]3'rr 0.369 20. L9cr lno" mixed 20.-130" In0" mixed 20" ]l'rr- tn,rr 0.945 30" 0.824 30" 0.532 30" mixed 3o-

7.2 '~ 9.75

7.2 2.25

1 2

7.2 o

7.2

1

1 12rr- 137r 12'rr-23"rr2 18o-- 'no.

The energies are shifted according to the experimental core binding cnergies [5]; the intensities are given in percentage with respect to thc calculated intensitics of the main peaks, values >~0.05 arc reported. Calculated ASCF shake-off limits: C1 17.37 cV, C2 17.33 eV, C3 14.74 eV. b Configurations with coefficients >~0.300 arc reported. c Ref. [5]. d Two calculated lines contribute to the intensity of this experimental peak.

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

gressive decrease on going along the series while its energy remains fairly constant [5]. This peak has been associated with a transition activated when a hole is created on a carbon atom attached to the double bond, and this assignment is also confirmed by a comparison with the shake-up spectrum of propane where this peak is instead absent [5,41]. The broad feature present in the spectra at higher energy shows instead increased intensity on going along the series, as the length of the aikyl group increases, and is attributed to transitions associated with core holes on alkyl carbons. The core shake-up of propene has been investigated at the ab initio CI level in a previous study [15] and good agreement with the experimental data has been obtained employing the 3 h - 2 v ( ' r r ) - l p CI scheme. Here we employ the 3 h - 2 v ( w ) + 2 h - l p CI scheme, which being more limited can be put forward for the calculation of larger systems and we will point out here only the differences between the results obtained with the two schemes, in order to state the capability of the latter. We indicate as C1 the terminal carbon atom on the double bond, C2 the inner carbon atom and C3 that on the CH3 moiety. As can be seen in Table 1 and in Fig. 1 the experimental spectrum is fairly reproduced at the 3 h 2v('rr) + 2 h - l p CI level, with only a general overestimate of the shake-up energies, as found also with the 3 h - 2 v ( w ) - l p CI scheme. This is not unexpected since in both schemes the core ionized state is better correlated than the shake-up states. Like in the previous calculation, most of the shake-up intensity is due to transitions relative to the C1 and C2 ionizations and the experimental band 1 (see Fig. 1) is originated by the H O M O - L U M O transitions between the rr and 'rr* orbitals associated with the C1C2 double bond (at 9.57 eV for the C1 ionization and at 9.54 eV for the C2 ionization). Low intensity is instead calculated in the region of the experimental band 2, where there is only one line of appreciable intensity, relative to the C1 ionization, at 12.61 eV, due to a 2rr --+ nrr transition (see Table 1). It should be noted that at the 2 h - l p CI level practically no intensity is calculated in this region, as can be seen in Fig. 1. The 3 h - 2 v ( r r ) - l p CI calculations instead indicate that line 2 is originated also by the l'rr -~ 3'rr shakeup relative to the C2 ionization, which is a charge transfer (CT) transition since the I rr orbital is mainly

175

ak PROPENE

exp

1

• .

3 ,,,~..;,

-

~.~

3h-2v(n)+2h-lp

2h-lp

5

15

25 E{eV)

Fig. 1. CalcuLated shakc-up spectra of propene; experimental spectrum from Ref. [5].

localized on the C H 3 moiety while 3rr is the 'rr* relative to the C1C2 double bond [15]. Instead in the 3h-2v(rr) + 2 h - l p CI scheme this transition is calculated with negligible intensity. This is the major discrepancy between the more accurate and the present CI scheme and we can conclude that the accuracy of the 3 h - 2 v ( T r ) + 2 h - l p CI scheme can be considered something in between that afforded by the 2 h - l p CI and the 3 h - 2 v ( ' r r ) - l p CI, as is apparent from Fig. 1. The results obtained for 1-butene are reported in Table 2 and in Fig. 2, together with the experimental spectrum. We start the numbering of the carbon atoms from the double bond as in propene. Fig. 2 shows that already at 2 h - l p CI level a qualitative description of the experimental spectrum is achieved, with a first intense band at low energy (band 1 in the experiment) followed by two less defined and very broad structures in the higher energy part of the spectrum (bands 2 and 3). The 3 h - 2 v ( r r ) + 2 h - l p CI calculation provides substantially a rearrangement

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

176

~2

i

i

b

i

b

i

~

i

b

i

b

i

~

i

b

i

~

b

d d d d d d d d d ' ~

es

s

~

~

~

¢d e-,

~.

~

~

o.

~ T

~ ~

~

~

.=_

eq "~

~ ~ ~

b b b b b b b b b b b b b b b b ....

e~

~ ~ ~ ~ ~

~

~

~

~

~

~

~

~

177

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

~>~ I

ii = I b

c5c5 E E E

c5 E Ec5 E

0

.~'~

c~

8= i

~ o o o o

% d o o d

~

q3

,d

E~ o

~q

.,~ c~

~ b

~

~00-~ ~ i

b

~ ~

~

~.

~ - ~

~ 0 ~ -'0~ ~

-\ "~ rn

P~

5

,,,

=

.=>~

8

o

cq r,..) ~

~

178

G. Fronzoni et al. / Chemical Physics 195 (1995) 171- 193

1-BUTENE 3

exp

2

1

3[ ,~n)+2h-lp

2h-lp

10

20

E ( ev )

Fig. 2. Calculated shake-up spectra of 1-butene; experimental spectrum from Ref. [5]. of the intensities distribution with an increase of the shake-up intensity at higher energy and a narrowing of the first peak, since the two main transitions which originate it are calculated closer, giving a better representation of the experimental spectrum. The first intense line at 9.24 eV is due to two degenerate 3'rr --* 4rr transitions, relative to C1 (with intensity 0.83%) and C2 (with intensity 1.51%) ionizations. These are CT transitions, similar to that found in propene, since the 3'rr orbital is localized on the C H 3 (C4) moiety and the 4w is the "rr* relative to the C1C2 double bond. The second line at 10.11 eV with intensity 1.21% arises from the 2'rr ~ 4'n( W c - c ~ "rr~_ c) transition relative to the C1 ionization, while much lower intensity is found for the same transition relative to the C2 ionization. This can be explained on the basis of the different relaxation upon the C1 and C2 ionizations. In fact after C1 ionization the modification of the 2w orbital is

stronger than that in the case of the 3"rr one and therefore the relevant shake-up transition is more favoured. Upon C2 ionization the situation is reversed and consequently the contribution to the relevant shake-up line mainly derives from the 3'rr ---, 4'rr transition. As can be seen in Table 2, the excited states relevant to these transitions are characterized by strong mixing between the 3w ~ 4w and 2w-1 4w configurations. In this energy region there is only one weak line relative to the C3 ionization (at 10.91 eV) due to the "rrc c ~ "rrc = c shake-up transition, while no contribution derives from the ionization of C4. On going towards higher energy (in the region of bands 2 and 3) the calculation does not provide any transition with significant intensity, but instead a very large number of shake-up lines with low intensity. In particular, the band 2 is mainly contributed by transitions from the "rr occupied orbitals to n'rr* orbitals relative to the C2 and C1 ionizations, while the structure at higher energy (band 3), for which the present calculation is only indicative since it is above the shake-off limit, derives its intensity essentially from the shake-up relative to the C3 and C4 ionizations and is dominated by cr ~ cr * transitions, the relevant excited states showing the contribution of doubly excited configurations (see Table 2). Summarizing, we can say that the stronger contribution to the shake-up structures of 1-butene derives from the ionization of the carbons involved in the double bond, as in the case of propene, while the contribution of the other two carbon atoms (C3 and C4) progressively decreases with the distance from the double bond. Let us consider now the 1-pentene molecule, for which the atom numbering starts from the double bond carbon atoms as in the preceding molecules. Both 2 h - l p CI and 3 h - 2 v ( ' r r ) + 2 h - l p CI calculations give a qualitative reproduction of the broad structures of the experimental spectrum (Fig. 3) and as in the case of 1-butene, the major differences between the two calculations are seen in the low energy part of the spectrum where the 3h-2v('rr) + 2 h - l p CI calculation provides a narrower structure. It is essentially contributed by two more intense lines close in energy (at 10.24 and 10.44 eV) (see Table 2), recalling the situation already met in the preceding molecules, which are due to the 'rrc_ c ~ " n c - c transition relative to the C1 and C2 core holes

179

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193 I-PENTENE

exp

! 2

;,

~

J

i

f

i

i% 3h-2v (n) +2h-lp

3-

2h-lp

3-

5

15

25

The results of the present calculations for cisbutene are reported in Table 3 and in Fig. 4 together with the experimental data. We indicate as C1 the carbon atom on the double bond and C3 that of the methyl group. The experimental spectrum shows an intense shake-up peak at low energy (band 1) followed by a less intense structure separated by about 3 eV (band 2) and by two other structures (bands 3 and 4) on going to higher energy. Both calculated spectra reproduce the lowest energy intense structure (band 1) while very low intensity is calculated at the 2 h - l p CI level at higher energy below the shake-off limit. The 3 h - 2 v ( ' n ) + 2 h - l p CI gives a general improvement of the spectral description in better accordance with the experiment. As we can see in Table 3, band 1 is contributed by two lines, the first one at 9.53 eV is attributed to the 3'rr ~ 4"rr ('rrc_ c 'nc c) transition, associated with the ionization of C1, and the second less intense one at 10.49 eV is

E(eV)

Fig. 3. Calculated shake-up spectra of 1-pentcne; experimental spectrum from Ref. [5].

c is - 2 - B U T E N E

1

l e×p 1 4

respectively. Very low intensity is calculated for the CT transitions which are provided in this energy range and are associated with the C1 and C2 ionizations and it is also remarkable that in general the shake-up states are characterized by strong mixing of configurations. The higher energy part of the calculated spectrum is quite flat and is contributed by numerous lines of very low intensity, as observed also for the other molecules of the series, mainly relative to the core ionized alkyl carbons C3 and C4, the relevant states being characterized by strong mixing of configurations. Instead the ionization of C5 does not provide any shake-up structure with significant intensity. Therefore also in the case of 1-pentene the most considerable contribution to the shake-up derives from the ionizations of the carbons involved in the double bond while that associated with the carbons of the alkyl group is modest. Consider now the series of 2-butene isomers, i.e. cis-, trans-and iso-butene, which allows to analyze the effects of this kind of substitutions on the C = C double bond on the shake-up structure.

k,_/

i:1

3h-2v(n) +2h-lp

2h-lp

9

15

21 F~(eV}

Fig. 4. Calculated shake-up spectra of cis-2-butene; experimental spectrum from Ref. [5].

180

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

.2-~ c4 {q

{q

~4 {-i

i . ¢

T T T T T T 7 T T T T T ' T T T T T ~u'uT

~

Z

~

~

g

-

~

-

-

....

~

-

~

u :

~

~7 ~+

0

=

ssssss ~4

=

ee

~oee

~e

e

o {}

{-i -~

r

.

o

T T T T T ¥ T T ~ ~ ~ ' ~

b

b

b

b

~

b

b

b

'

.

.

.

.

.

.

.

.

I I - -

.

T T T T T T T T T T T ~

b

b

b

b

b

~

b

b

'u~u Ju,u

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

~

i

i

i

~

i

i ~

2

m .x ~ .~

1.~ m

m

.=

~==

~o~

181

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

182

m

*fi

Ii ~

~

~

~

~.

eq

ttq

e6

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

183

.=_

E

z

184

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

due to the same transition relative to the C3 ionization. In the energy region of the experimental band 2 the intensity of the calculated lines is very low; the C1 ionization provides a shake-up line at 12.36 eV associated with a 3'rr ~ n'rr* transition, while the two weak lines at 11.24 and 11.46 eV derive from the C3 ionization and are associated with transitions of CT character. The calculated intensity slightly increases in the region of band 3 where the main contribution to the shake-up derives from the C3 ionization, while above the shake-off limit (band 4) several lines, mainly due to the o" ~ cr * transitions, contribute to generate an intense feature. For this molecule the spectral situation appears overall more complicated than in the case of 1-butene and there are some differences between the 2 h - l p CI and the 3h-2v('rr) + 2 h - l p CI results, in particular as concerns the loss of intensity of the C1 shake-up in the simpler scheme. Stronger correlation effects can be therefore anticipated and increased importance of

I-PENTENE

I I-BUTENE

PROPENE

iso-BUTENE

exp 3 1

:'-

,..

2

. :L ,.

'" :

:"~'"" ~L":

15

-

25

35 E(eV)

k 3 h - 2 v (n) + 2 h - l p

/ 2h-lp

lO

20

E{eV)

Fig. 5. Calculated shake-up spectra of iso- propene; experimental spectrum from Ref. [5].

Fig. 6. 2h-lp CI valence spectra of propene, 1-butene and 1pentene. The experimental value of the first IE is added to the calculated relative energies. Calculated lines are convoluted with Gaussians of 0.6 eV fwhm.

highly excited configurations in the shake-up states is expected. The experimental spectrum of trans-butene is very similar to that of cis-butene, as pointed out in the experimental work [5]. The present calculations confirm this spectroscopical equivalence between the two forms in the lower energy part (see Table 3). Minor differences, notably a gain of intensity, are seen in the spectral region of band 2 and increased importance of the CT transitions is pointed out. Let us examine finally the results for isobutene reported in Table 3 and in Fig. 5. For this molecule

G. Fronzoni et a L / Chemical Physics 195 (1995) 171-193

C1 is the terminal carbon atom on the double bond, C2 the inner carbon atom and C3 is the carbon atom of the methyl group. As for the other molecules the experimental spectrum (see Fig. 5) shows a prominent shake-up peak in the lower energy region (band 1), followed by two broad structures of comparable intensity at higher energy (bands 2 and 3). In this case the two CI schemes afford similar spectra although a better reproduction of the experiment is given at the 3h-2v('rr)+ 2 h - l p CI level. The first shake-up structure (band 1 in the experiment) is contributed essentially by two lines very close in energy (at 9.16 and 9.26 eV in 3 h - 2 v ( ' n ) + 2 h - l p

Ii I-PENTENE

I-BUTENE

[

,

~

PROPENE

15

:

~

-

"

..

~

25

35

Fig. 7. 2h-lp CI inner valence spectra of propene, |-butene and l-pentene. The experimental value of the first IE is added to the calculated relative energies. Calculated lines are convoluted with Gaussians of 1.00 eV fwhm. Experimental spectra from Ref. [36] are shown in the inserted boxes (note that the energy scale is different).

185

CI) and of similar intensity, associated with the 3'rr ~ 4,n ('rrc_ c ~ 7re_ c) transitions relative to the C2 and C1 ionizations respectively [5]. At lower energy (7.79 eV) a weak line associated with the C1 ionization is provided, relatively to the 3~ ~ 4 ' r r transition with the other valence coupling, which could correspond to the shoulder of the experimental band 1 at 5.9 eV. The C3 ionization is instead accompanied by a modest shake-up in this energy region and its contribution is comparable to that deriving from the ionizations of the double bond carbons in the higher energy region (see Table 3), where the cr ~ o~* transitions are mixed with the ~ ,n * ones. As already observed for the preceding molecules, also in this case the shake-up features in the higher energy region, below and above the shake-off limit, are contributed by a large number of lines of very low intensity. As a general comment we can say that the 3h2v('rr) + 2 h - l p CI scheme gives a satisfactory reproduction of the experimental data, giving further details in the higher energy part with respect to the previous calculations. The shake-up peak at low energy can be a sort of fingerprint of the strength of relaxation effects following the creation of a core hole on the carbon atoms on the double bond. This relaxation is strongly inhibited by the presence of methyl substituents on the double bond, as can be inferred by the drop of intensity found on going from ethylene [5], to propene, cis-butene and iso-butene. Also the presence of an aliphatic chain inhibits relaxation, in fact if we sum up the calculated intensity at the 3 h - 2 v ( ' n ) + 2 h - l p CI level of all lines which contribute to the low energy peak in ethylene [15], propene, 1-butene and 1-pentene, we see that this intensity decreases by one third on going along the series, in agreement with the experimental results. So we can anticipate that in the compounds with aliphatic chain substituents with 6 or 7 carbon atoms this peak can be hardly experimentally detectable and the shake-up spectra would show therefore the characteristics of those of the alkanes [41]. On the other hand this behaviour is already apparent in the experimental spectrum of 1-pentene [5]. 3.2. Valence spectra As already pointed out, the CI calculations of the valence spectra present additional computational

186

G. Fronzoni et a L / Chemical Physics 195 (1995) 171-193

problems, due to the need of extracting several roots to describe the whole inner valence region and the consequent necessity of reducing both the basis set and the CI schemes. On the other hand the description of inner valence region is of particular interest because of the presence of strong many-body effects which are often responsible for the breakdown of the one-particle picture. Therefore the only CI scheme applicable to systems of a certain size is the 2 h - l p CI one, which allows in any case to analyze the most important correlation effects. For large molecules one can resort to the more restricted 2 h - l v CI, which has been successfully applied to unsaturated hydrocarbons [16]. In the present investigation we employ also this scheme in order to verify its capability to deal with the molecules under study, in view of applying it to larger systems of the same kind. Consider first propene, 1-butene and 1-pentene, the relevant results being reported in Table 4 and in Figs. 6 and 7. We will focus the discussion on the relative energies rather than on the absolute values, since we are mostly interested on the trend of the spectra along the series. As concerns the intensities, they are expressed in terms of R~k values and of course for a direct comparison with the experimental data these values should be multiplied by the experimental cross sections of the respective main ionization, which are not available for these molecules. As concerns the comparison between the CI results and the experimental data of the outer valence region for propene and 1-butene (see Table 4), we observe a substantial good accordance for the relative energies, both for the 2 h - l p CI and the 2 h - l v CI schemes, apart from an overestimate of the energies in the latter scheme. We note in passing that for propene the GF calculation [36], in which polarization functions are not included and the DZ basis set is employed, gives an inversion of the ordering of the la" and 8a' ionizations with respect to the 2 h - l p CI results. A similar situation is found for 1-butene as concerns the la" and 9a' ionizations. In the case of 1-pentene the ordering of the states provided by the CI and GF calculations is indeed the same for all the states of the outer valence region. On going along the series, both the 2 h - l v CI and 2 h - l p CI results reproduce the expected trends, with a progressive shift of the first "rr band to lower energy and a decrease of the energy separation between this peak

and the following o- ionizations (10a' at 2.68 eV in propene, 13a' at 2.10 eV in 1-butene and 16a' at 1.69 eV in 1-pentene in 2 h - l p CI). From Fig. 6, which collects the full 2 h - l p CI valence spectra of the series, the increasing complexity of the outer valence features is well apparent on going from propene to 1-pentene, essentially due to the increased number of the final states. The absence of satellite peaks in this energy region is to be noted, at variance with the situation met in the case of unsaturated hydrocarbons with conjugated double bonds, where the number of satellites in the outer valence region increases with the length of the chain [16]. For the molecules here examined correlation effects are instead less important in this region and do not appear to be associated with the increasing complexity of the systems. The Rik values are quite high for all three molecules, allowing to interpret this energy region in terms of a single-particle model. Going now to the inner valence region, we observe in the Table 4 that the energy gap with the outer valence part becomes smaller on going along the series, being the 2 h - l p CI values 2.52 eV for propene, 2.02 eV for 1-butene and 1.88 eV for 1-pentene, recalling this time the behaviour observed for the unsaturated hydrocarbons [16]. The inner valence region is more complex to describe, as is well apparent in Fig. 7, in particular on going to the higher energy side of the spectra, where we observe a progressive fragmentation of the main ionization peaks in several lines of smaller intensity. The results for propene are reported in detail in Table 4 and in Fig. 7, together with the experimental spectrum [36]. The 2 h - l p CI calculation provides a satisfactory reproduction of the experimental pattern. The first three bands are associated with the 6a', 5a' and 4a' ionizations; the lowest energy peak (at 8.97 eV relative energy), more separated by the rest of the spectral structure, still maintains a considerable intensity (Rik = 0.813) and is accompanied by low intensity satellites. The next two peaks show instead a progressive decrease of the primary intensity accompanied by a parallel increase both of the number and the intensity of the satellite states (see Table 4). The last structure of the spectrum is contributed by many peaks, mainly deriving from the 4a' ionization. As concerns the 2 h - l v CI results, the overestimate of the energies with respect to the 2 h - l p CI values,

G. Fronzoni et al. /Chemical Physics 195 (1995) 171-193

already present in the outer valence region, is accompanied also by a somewhat different intensity distribution in the final part of the spectrum, essentially due to a further fragmentation of the peaks deriving from the 4a' ionization. On the whole the shape of the inner valence spectrum is however well accounted for also at this CI level. This indicates that in this kind of systems the main correlation effects may be interpreted as quasidegeneracy effects over a very small orbital space and shows the usefulness of this limited CI model for interpretative purposes and for practical calculations. The CI results for the inner valence region of l-butene are presented in Table 4 and in Fig. 7, which shows the more complex structure of the spectrum with the first peak closer in energy to the next ones than in the case of propene and a more pronounced fragmentation of the last ionization peak (5g), for which a breakdown of the one particle picture occurs. The experimental features are reproduced nicely by 2 h - l p CI (see Fig. 7) both as concerns the energy separations and the intensity distribution, with four main peaks followed by a correlation structure at higher energy. The Rik value calculated for the first ionization peak (8a' at 8.46 eV relative energy) is quite high (0.826) and comparable to the first inner valence peak in propene; also the next two ionizations (7a' at 11.58 eV and 6a' at 14.08 eV relative energy) follow the trend previously observed, showing a progressive decrease of the primary intensity and a parallel increase of the satellites intensity. The last ionization (5a') spreads its intensity over a large number of lines among which it is possible to identify two more intense components (at 15.96 and 16.04 eV relative energy) mainly responsible for the fourth peak in the calculated spectrum. The rest of the higher energy weaker lines contributes instead to the last small structure which can be associated with the shoulder of the highest energy peak in the experimental spectrum [36]. Looking at the 2 h - l v CI results, we observe only a small deterioration of the accord with the 2h-lp CI energy values on going to higher energy, the experimental spectral pattern being qualitatively reproduced. The experimental inner valence spectrum of 1pentene (Fig. 7) resembles that of the 1-butene molecule, apart from the presence of one more peak

187

and a less prominent correlation shoulder at the higher energy side. The 2 h - l p CI results reproduce correctly the experimental pattern, with the more intense peaks regularly spaced in energy, with only a slight overestimate of the separations (see Fig. 7). The first two peaks, corresponding to the 10a' and 9a' ionizations, maintain a considerable intensity (Rik = 0.820 and Rik = 0.773 respectively) while the intensity of the next 8a' ionization is lower (Rik = 0.487), the remaining part being distributed over a certain number of satellite states, as is well apparent in Table 4, resembling the spectral pattern calculated for 1-butene. A breakdown of the one-particle model is reached in the case of the last two ionizations (7a' and 6a') which are contributed by several components with maximum Rik values of 0.347 (7a' at 14.92 eV relative energy) and 0.302 (6a' at 16.45 eV relative energy), revealing the increased importance of the correlation effects. Also for this molecule the 2 h - l v CI results are in good agreement with the 2h-lp CI ones (see Table 4) apart from the expected overestimate of the energy separation. As a last observation, looking at the calculated inner valence spectra of the three systems examined, we can note that in the highest energy part we find a correlation tail quite far apart from the other peaks in propene, less separated in 1-butene and a broad band in 1-pentene. So this feature is going to disappear or to be broader and incorporated in the main bands as the chain becomes longer. We recall that a progressive broadening of the shake-up structures with the length of the chain is also apparent in the core ionizations, so as regards the satellite structures, some intensity is lost both in the valence and in the core spectra in the largest systems. Let us analyze the valence spectra of the isoelectronic series of cis-, trans- and iso-butene, which allows to study the isomeric effects on the valence shell electronic structure. Several PES measurements have been made for these three molecules [26-31] and also from a theoretical point of view some ab initio calculations are available [26,27,32,33], although a complete analysis of the inner valence spectra has not been performed yet. In all 2 h - l p CI spectra reported in Fig. 8 we note the presence of a first feature contributed by eight close-lying states followed by a more complex structure which extends up to the higher energy side of the spectra and

188

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G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

190

is o- BUTENE

stead present in the case of the fifth and sixth ionizations of the cis-butene molecule, which are assigned to the 6a~ and la, states by the present 2 h - l p CI calculation (at 4.91 and 5.27 eV relative energy), while an inverted order is provided by the previous CI calculations [32] with relative energy values of 4.86 and 4.78 eV respectively. We have performed some test calculations using the more extended 3h-2v('rr)-lp CI scheme in order to test the influence of higher excited configurations on the energies of these two outer valence states. The order-

trans-2-BUTENE

iso-BUTENE

cis-2-BUTENE

trans-2-BUTENE

15

25

35 E(eV)

Fig. 8. 2h-lp CI valence spectra of cis-2-butene, trans-2-butene and iso-butene. The experimental value of the first IE is added to the calculated relative energies. Calculated lines arc convoluted with Gaussians of 0.6 eV fwhm.

changes noteworthy along the series. The ionization energies of the outermost rr states of the isomers are practically identical, due to the similarity of the bonding nature of the C = C rr orbitals in the series. The next three calculated ionizations (6b z, 7a~ and 5b 2 in cis-butene, 2au, 7ag and 6b u in trans-butene and 5b 2, 8a I and 4b 2 in iso-butene) have very similar energy separation in the molecules, according to the experimental trend and the results of previous CI calculations [32,33]. Some discrepancies are in-

cis-2-BUTENE

15

25

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Fig. 9. 2h-lp CI inner valence spectra of cis-2-butene, trans-2butene and iso-butene. The experimental value of the first IE is added to the calculated relative energies. Calculated lines are convoluted with Gaussians of 1.00 eV fwhm. Experimental spectra from Ref. [36] are shown in the inserted boxes (note that the energy scale is different).

G. Fronzoni et aL/ Chemical Physics 195 (1995) 171-193

ing provided by this calculation is however the same as the 2 h - l p CI one, even with an increase of the energy separation between the two levels (from 0.36 eV at 2 h - l p CI level to 0.76 eV at 3h-2v('rr)-lp CI level). Performing instead a 2 h - l p CI calculation with the same basis set adopted in Ref. [32], we have obtained a decrease of the 2 h - l p CI energy separation between the two states to only 0.03 eV. On the basis of these tests, considering also the small energetic differences which come into play, we conclude that this discrepancy can be associated with the different basis sets used in the two calculations, rather than with a different level of correlation effects included in the two different computational schemes. On the other hand the recent experiment of Mathers et al. [26] provides two structures in this energy region which are 0.2 eV apart in fair agreement with the present calculations. It is still important to point out the absence of satellite lines in the outer valence spectra of the isomers, as observed also for the series previously analysed. The spectra become more complicated in the inner valence region and are notably different along the series, as is well apparent in Fig. 9. The calculated energy gap between the outer and the inner valence part is very small in cis-butene (1.11 eV) and noteworthy larger in trans- and iso-butene (2.66 and 2.10 eV respectively), reflecting correctly the experimental behaviour [26]. The 2 h - l p CI results for cis-butene (Fig. 9) reproduce quite correctly the experimental pattern, with the first ionization peak (4b 2 at 8.56 eV relative energy) well separated from the following spectral structures where the increase of many-body effects is clearly apparent on going to higher energies. In fact the Rik values move from 0.833 of the 4b 2 ionization to 0.676 of the 4al ionization to progressively lower values for the last two ionizations 3b 2 and 3al, with a spread of the intensity over a growing number of states (see also Table 5). A complete breakdown of the one-particle model is reached by the last ionization (3a~) responsible for the correlation tail present in the higher energy part of the calculated spectrum, which is present also in the experiment. The 2 h - l v CI results, reported in Table 5, show a substantial accordance with the 2 h - l p CI ones, with the discrepancies found for the other systems. In the 2 h - l p CI inner valence spectrum of trans-

191

butene, (Table 5 and Fig. 9), we observe a first peak (4b u at 8.86 eV relative energy) very similar, both as concerns the energy position and the intensity, the analogous one in cis-butene, while the second part of the spectrum is quite different. In fact the second peak (4ag at t2.29 eV relative energy) is closer in energy than in the preceding case and in the last two ionizations in trans-butene (3bo and 3ag) the intensity is distributed over a large number of lines, with a maximum Ri~ value of 0.410 for the 3b u ionization and of 0.226 for the 3ag one. In the higher energy part of the spectrum we observe instead a correlation tail, similar to that calculated in the case of cis-butene, contributed by the lower intensity satellite states of the 3b u and 3ag ionizations. The 2 h - l v CI results reported in Table 5 follow the behaviour previously observed for the other molecules, reproducing correctly at a qualitative level the experimental pattern. Finally let us consider the inner valence spectrum of iso-butene (Fig. 9 and Table 5). At the 2 h - l p CI level the first ionization peak (6a I at 8.48 eV relative energy) has similar characteristics to those of the analogous peak observed for the preceding isomers, while the rest of the spectral pattern is less structured and more separated from the first line than in the preceding cases (4.68 eV of energy separation with respect to 4.07 eV in trans-butene and 3.43 eV in cis-butene). For iso-butene the 2 h - l p CI calculation generates a large number of satellites already in correspondence of the second inner valence ionization (5a 1 at 13.16 eV relative energy) for which the maximum R~k value is 0.515, the lowest one observed in this series. The 5a 1 ionization and the following one 2b 2 are close in energy (0.8 eV) and contribute therefore to the same band which results to be the most intense of the inner valence spectrum, again at variance with the two preceding isomers. The last ionization 4al, more separated by the two lower energy ionizations, is responsible for the last structure of the calculated spectral pattern and spreads its intensity over a large number of satellite states. The 2 h - l v CI results of Table 5 compare satisfactorily with the 2 h - l p CI ones. As a final comment on these isomers we may point out the noteworthy differences found in both outer and inner valence calculated spectra, which reproduce the experimental behaviour, as can be seen

192

G. Fronzoni et al. / Chemical Physics 195 (1995) 171-193

in Fig. 8. O n l y the first peak, w h i c h d e r i v e s f r o m the i o n i z a t i o n o f the 'rr c = c orbital, has the s a m e c h a r a c teristics, w h i l e a d i f f e r e n t p a t t e r n is f o u n d in the rest o f the o u t e r v a l e n c e spectra. T h e first p e a k o f the i n n e r v a l e n c e spectra is a g a i n s i m i l a r in the three c o m p o u n d s w h i l e different p a t t e r n s are s e e n at h i g h e r energy, in a g r e e m e n t w i t h the e x p e r i m e n t . Last w e p o i n t out that the p r e s e n t c a l c u l a t i o n s p r o v i d e t w o f e a t u r e s w h i c h h a v e b e e n put f o r w a r d in the recent e x p e r i m e n t for the t h r e e i s o m e r s [26], i.e. the p r e s e n c e o f satellite s t r u c t u r e s b e t w e e n the t w o first i n n e r v a l e n c e i o n i z a t i o n p e a k s a n d the c o m p l e x structure at h i g h e n e r g y f o l l o w e d b y a c o r r e l a t i o n tail.

4. Conclusions W e h a v e s h o w n the v e r s a t i l i t y o f the CI s c h e m e s a d o p t e d and t h e i r c a p a b i l i t y o f r e p r o d u c i n g the exp e r i m e n t a l t r e n d o f b o t h the core and the v a l e n c e ionization spectra of hydrocarbons containing one d o u b l e b o n d ; so for the l i m i t e d c o m p u t a t i o n a l effort r e q u i r e d they c a n b e a p p l i e d w i t h c o n f i d e n c e to longer chain systems. A s c o n c e r n s the trend of the spectra, t w o m a i n p o i n t s are r e m a r k a b l e : - T h e core s h a k e - u p spectra are m o r e s e n s i t i v e to the v a r i a t i o n o f the l e n g t h o f the c h a i n a t t a c h e d to the d o u b l e b o n d r a t h e r t h a n to the d i f f e r e n t substitut i o n s o n the d o u b l e b o n d , in fact n o t a b l e d i f f e r e n c e s are seen in the s p e c t r a o f p r o p e n e , 1 - b u t e n e a n d 1-pentene, w h i l e s t r o n g similarity, also as regards the a s s i g n m e n t a n d the m e c h a n i s m s i n v o l v e d in the s h a k e - u p transitions, are s e e n for the 2 - b u t e n e isomers; - O n the c o n t r a r y a r e v e r s e d b e h a v i o u r is f o u n d for b o t h the o u t e r a n d i n n e r v a l e n c e spectra, w h i c h are s t r o n g l y i n f l u e n c e d b y the d i f f e r e n t p o s i t i o n s o f the substituents.

Acknowledgement This work was supported by grants from MURST ( 6 0 % a n d 4 0 % c o n t r i b u t i o n s ) o f Italy a n d C N R o f R o m e (Italy).

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