Ab-initio CI calculations of the C1s and Cl1s and 2p core excitation spectra of the freon molecules: CCl4, CFCl3, CF2Cl2 and CF3Cl

Chemical Physics 237 Ž1998. 21–42

Ab-initio CI calculations of the C1s and Cl1s and 2p core excitation spectra of the freon molecules: CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl G. Fronzoni ) , P. Decleva Dipartimento di Scienze Chimiche, UniÕersita’ di Trieste, Via L. Giorgieri 1, I-34127 Trieste, Italy Received 5 January 1998; in final form 8 June 1998

Abstract Ab-initio calculations of the discrete C1s and Cl1s and 2p core excitation spectra of the freon molecules CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl are performed in the relaxed 1h–1p CI scheme. Satisfactory agreement with the experimental patterns is obtained for all the spectra analysed, indicating the reliability of the present computational approach to assign the spectral features. The interpretation of the final states in terms of orbital composition, which is fuzzy in large molecules, is discussed in detail for the C1s spectrum of CF3 Cl, as well as the variation of the spectrum induced by a change in the C–Cl bond length. The C1s calculated spectra show significant variations with the progressive substitution of the chloride atom with the more electronegative fluorine atom and are therefore a significant probe of the electronic structure changes along the molecular series. The Cl1s and 2p results show a much less dependent behaviour of the spectra on the nature of the ligand Cl or F attached to the C-atom, as expected since the Cl is in each case attached only to a C-atom, although variations are distinctly apparent especially in the case of 2p spectra. q 1998 Elsevier Science B.V. All rights reserved.

1. Introduction The X-ray absorption spectroscopy ŽXAS. is one important technique from which information on the symmetry and electronic structure of molecules can be obtained. In the core excitation spectra, the observed structures around the ionization threshold can be interpreted as transitions of the core electron from a specific atomic level to a valence or Rydberg unoccupied orbital of the molecule. The use of XAS to probe the unoccupied energy levels of molecules has received much improvement in recent years with the advances of electron energy loss ŽEELS. and )

Corresponding author.

synchrotron photoabsorption techniques which have provided a vast amount of well-resolved experimental data w1,2x. The advantage of the XAS as a means of investigating the unoccupied molecular orbitals lies in the simplicity of the interpretation of the spectral data, compared to UV spectroscopy, due to the highly localised nature of the core levels and the relative transitions. The inner-shell spectra of molecules below edge are essentially characterised by resonances associated with the first empty molecular orbitals, which often appear as broad bands in the experiment, as well as more sharp structures involving transitions to Rydberg orbitals. The relative importance of the resonances and the Rydberg lines in the spectra varies from molecule to molecule

0301-0104r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 2 2 0 - 1

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G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

and also depends on the symmetry of the molecule as well as on the symmetry of the core level of the excited atom. These structures close to the ionization threshold ŽNEXAFS region. contain the most significant information on the low-lying unoccupied states of the molecules. Their interpretation can be strongly supported by theoretical calculations which relate each excitation energy to a virtual state whose nature Žvalence or Rydberg. and composition can be defined. Moreover, the calculations yield the oscillator strength which is also connected with the composition of the unoccupied orbitals mapping in particular the different content of the atomic orbital which carries most of the transition moment. It represents, therefore, a very important source of chemical information still not much exploited for the quite large uncertainties often affecting the spectral intensities in the experimental spectra. The more natural and simplest framework for the description of the low-lying excitations is the LCAO molecular orbital ŽMO. approach, whose limit is the inability to properly treat the continuum absorption above edge. Actually the continuum absorption can be obtained, if it is sufficiently smooth, by the Stieltjes imaging technique w3x. However, for the present, the discrete transitions calculated above edge, although partially dependent on the basis set, can be qualitatively associated with the most prominent structures of the spectrum at least in the low energy range. Good MO calculations affording accurate results for the discrete excitations have to be performed in the framework of accurate ab-initio method, such as the CI approach, capable to include explicitly the strong relaxation effects which dominate the core processes and derive from the rearrangement of the valence orbitals around the core hole. In this respect the CI approach is particularly convenient because of the possibility of employing different orbital bases for the ground and core ionized states including at the outset a large part of the relaxation contribution while the correlation effects can be described at various level of approximation. For the description of core excitations the simple 1h–1p CI relaxed scheme, which includes the single excitations from the specific core level of the probed atom and the important coupling between different excitation channels in the case of degenerate core holes Ž2p for example., has proven to be adequate to

describe the XAS spectra of several molecules and has the important advantage to require a relatively small computational cost therefore also being applicable to rather complex systems w4–8x. In the case of non-degenerate core holes, like 1s, the 1h–1p CI scheme is the same as the relaxed core HF, or static exchange ŽSTEX. approaches, widely employed w9,10x. The essential soundness of this scheme confirms that the interaction between the low-lying core hole state produced by the X-ray excitation with the excited electron is relatively small. Improved descriptions, in particular as concerns the oscillator strengths and energy separation between the valence and Rydberg transitions, may be obtained employing highly correlated ab-initio CI schemes, as shown in Refs. w7,8x, but with the limit of being applicable only to rather small molecules, due to the very fast increase of the computational effort required with the dimension of the system. In the present work the 1h–1p CI relaxed scheme is applied to the calculation of the core excited spectra of the chlorofluorocarbon molecules ŽCF3 Cl, CF2 Cl 2 , CFCl 3 , CCl 4 . both at the C1s and Cl1s and 2p edges. One reason for studying these systems is the quite large amount of experimental spectroscopic data available in the literature also including several XAS investigations w11–15x useful for comparison with the theoretical results. Interest in freon molecules derives from the recognition that they are responsible for the depletion of the Earth’s ozone layer through photochemical processes in the upper levels of the atmosphere. Therefore the spectroscopic studies are fundamental to obtain quantitative information on the interaction between these molecules and the UV and X-ray radiation. However, no theoretical calculations of the inner-shell excitation spectra of the chlorofluorocarbon molecules have been previously performed. Thus discussion of the relative experimental results is essentially based on the qualitative potential barrier model, and observed transitions are only tentatively assigned on the basis of semi-empirical MO calculations at the SCF–GS level w12,15x. The primary objective of the present study is to provide a description at the same level of accuracy of the spectral features below the C1s and Cl1s and 2p edges and their relationship with the composition of the low-lying virtual orbitals for the series of the chlorofluorocarbon molecules. Because of the locali-

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

sation of the C and Cl core excitations, it is expected that the two types of spectra will provide selective probes of the unoccupied orbitals in the region of the C- and Cl-atoms, respectively. Furthermore this series, sharing common C–Cl and C–F bonds, offers the opportunity to study the influence of the progressive substitution of the Cl-atom with the more electronegative F-atom on both the s ) valence transitions and the higher energy Rydberg transitions in the carbon and chlorine core excited spectra, and also to analyse the dependence on the core hole localisation on the central C-atom or on the peripheral Cl-atom. Actually, already in molecules of this complexity, detailed analysis of the individual levels proves difficult. Experimentally only in few small molecules, mostly hydrides, several Rydberg series have been resolved. More often this is not feasible because of the density of states and the intrinsic width associated with lifetime, vibrational and molecular field broadening. Also interpretation of the calculated spectra is not unambiguous. Even when transitions are well described as single electron excitations, the nature of the excited orbitals is often difficult to characterise, being a mixture of many atomic components, strongly non-orthogonal. Also mixing between the valence and Rydberg components may be substantial, preventing a simple classification based on quantum defect analysis. The latter is also hampered by even small errors in the basis set or in the treatment of the many electron effects. Thus to validate a qualitative interpretation based on the AO composition of the excited orbitals, we have more thoroughly investigated the C1s spectrum in CF3 Cl. Calculations have been performed employing a fully orthogonal AO basis obtained by preliminary atomic calculations with the GTO bases employed. This eliminates interatomic non-orthonormality rendering the AO composition of the MOs more transparent. As a measure of valence character of each MO we have employed the projection onto the orbitals spanned by the minimal basis set ŽMBS.. Also separate MBS calculations have been performed in order to have a qualitative picture of the ‘ valence only’ spectrum. Finally, it is interesting to examine the variation of the spectrum induced by a change in the C–Cl bond length. It is expected that strong changes are obtained for the features associated with the

23

antibonding C–Cl orbital, leaving C–F and Rydberg excitations unaffected. Such changes have been actually observed in the case of s ) shape resonances above edge, and employed as a means of estimating the bond length, for instance in molecules absorbed on surfaces w2x. The same could be profitably done with the sharp valence excitations below edge.

2. Computational details Calculations of the core excitation spectra have been performed in the ab-initio CI scheme following the procedure outlined in previous papers w5,6x. Here we report only the main points of the procedure: Ž1. Relaxation of the valence orbitals in the response to the core hole formation has been taken into account by the use of the SCF orbitals optimized for the core hole state corresponding to the core excitation considered ŽC1s and Cl1s and 2p.. In the case of equivalent atoms, the core hole has been always localised on a single centre and the molecular symmetry accordingly reduced. Ž2. The core excited spectra are described in the 1h–1p CI Žor single excitation. scheme, which comprises all the single excitations from the fixed core hole. Coupling between the different excitation channels, which are present in the case of degenerate core holes Ž2p in the present case., is included in the scheme and proves important in determining oscillator strength values. Ž3. To make evaluation of the transition moments easier, the set of relaxed orthogonal orbitals are also employed for the CI description of the ground state. The relaxation has been described by the mixing of single excitations Ž1h–1p CI. obtaining a wavefunction of comparable quality as the single determinant SCF ground state. Ž4. The transition moments are computed in the dipole velocity form, f s 23 vy1 M 2

M s ² c f ,=c i :

because of the slight non-orthogonality between initial and core excited states of the same symmetry Žsee before. which may give additional error in the dipole length transition moments while the dipole velocity form is less affected by this problem.

24

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

While maintaining the simplicity in the present computational scheme, it is important to provide an adequate basis set capable of giving a good description of one or more shells of Rydberg orbitals. The basis set adopted is the correlated basis set cc-pVDZ Žcorrelation consistent polarised valence double zeta., p ro p o s e d b y D u n n in g w 1 6 x , i.e . th e Ž12s,8p,1d.rŽ5s,5p,1d. set for the Cl-atom and the Ž9s,4p,1d.rŽ3s,2p,1d. set for the first-row C- and F-atoms. For the Cl core excited spectra calculations, the chlorine set has been enlarged by adding additional diffuse functions needed to describe the transition towards the Rydberg orbitals. In particular we add four diffuse s,p functions with exponents obtained with the even-tempered criterion Ž b s 3. and five d-functions, the first one with exponent a d s 0.1800, and the last four with the same exponents as the last four p-functions. Furthermore, we have also included a more compact d-function Ž a d s 1.5510., in order to obtain a well-balanced basis set of d-functions capable of correctly describing the oscillator strength associated with the 2p ™ 3d transition in the Cl2p spectra. The final DZ basis set for chlorine is therefore the Ž10s,9p,7d.. It should be noted that this basis set has been tested in our recent work on the Cl1s and 2p core excited spectra of the HCl molecule w8x and has proven to be adequate to describe correctly the distribution of the oscillator strength among valence and Rydberg final states. This set is employed to describe the Cl-atom on which the core hole is localised; for the other Cl-atoms of the molecule the original set Ž5s,5p,1d. is adopted. For calculation of the C1s core excited spectra, the carbon DZ basis set Ž9s4p1d.rŽ3s,2p,1d. has been supplemented with three s,p diffuse functions with exponents obtained with the even-tempered criterion Ž b s 3. and four d-functions, the first one with exponent a d s 0.1668 and the last three with the same exponents as the last three p-functions. The final DZ basis set for the C-atom is therefore the Ž6s,5p,5d. set. Orthonormal AO bases have been obtained from the above bases by performing separate SCF atomic

calculations. These have been employed in the C1s core spectra calculations. The occupied orbitals of the free atoms define the minimal basis set. MBS orbitals have been employed for further analysis on the CF3 Cl molecule, by performing a separate MBS calculation, and by projecting the MOs obtained with the extended basis onto the MBS, to have a precise characterization of the valence content. SCF, CI and transition moment calculations have been performed with the MELDF set of programs w17x. Experimental geometries are employed for all molecules w18–21x.

3. Results and discussion Before starting the discussion, a remark is in order. For all the calculated core excitation spectra we report the term values ŽTV. referred to the energy of the hole state single configuration which correctly represents the ionization limit corresponding to the 1h–1p CI excitation energies of the final states. In this way we can separate the pre-edge discrete transitions, for which an accurate description is expected from the present CI approach, and the discrete transitions above the ionization limit for which only a qualitative estimate of the resonant structures eventually present can be given in the lower-energy region. 3.1. C1s core excitation spectra Let us analyse first the CF3 Cl molecule which has been choosen to discuss in detail the interpretation of the calculated excited states in terms of the orbital composition also considering possible pattern variations as a function of the C–Cl bond length. The results of this analysis are collected in Table 1 and Fig. 1. The three different C–Cl bond lengths used for the calculation of the CF3 Cl C1s spectrum are: the equilibrium RŽC–Cl. distance Ž R eq ., a shorter distance Ž R 1 s R eq y 0.25 au. and a longer distance Ž R 2 s R eq q 0.25 au.. Fig. 1 shows the 1h–1p re-

Fig. 1. MBS and EBS calculations of the C1s core excitation spectrum of CF3 Cl for three C–Cl bond length: R1 s R eq y 0.25 au, R s R eq and R 2 s R eq q 0.25 au. Lines are convoluted with Gaussians of 0.6 eV FWHM.

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

25

a

3.13 2.84 2.09 2.05 1.56 1.40 1.33 1.29 1.06 1.01 0.96 0.69 0.58 0.38

3.954 0.002 0.145 0.150 3.054 0.008 0.206 0.002 1.630 0.008 2.844 0.001 0.169 4.532

f = 10 y 2

R ŽC – Cl. s R 1 TV 0.73 0.06 0.26 0.02 0.42 0.0001 0.03 0.02 0.13 0.01 0.001 0.001 0.02 0.07

Valence character 4.55 2.82 2.09 2.10 1.48 1.39 1.39 1.29 1.05 1.01 0.84 0.68 0.63 0.27

s ) ŽC – Cl. s) C p ) C q s ) ŽC – F . p) C s ) ŽC – F . q Žp,d . ) C d) C d ) C q s ) ŽC – Cl. Žs,d . ) C s ) ŽC – F . q d ) C p) C s ) ŽC – F . q d ) C d) C d ) C q s ) ŽC – Cl. s ) ŽC – F . q Žp,d . ) C 4.363 0.058 0.227 0.011 1.515 0.076 0.042 0.022 0.823 0.000 2.686 0.000 0.047 6.354

f = 10 y 2

R ŽC – Cl. s R eq TV

Final state

R ŽC – Cl. considered: R 1 s R eq y 0.25 au, R s R eq and R 2 s R eq q 0.25 au.

11a 1 12a 1 8e 13a 1 9e 10e 14a 1 15a 1 11e 16a 1 12e 13e 17a 1 14e

MO

Table 1 Calculated C1s core excitation spectra of CF3 Cl for different R ŽC – Cl. bond length a

0.84 0.05 0.15 0.02 0.42 0.02 0.0002 0.02 0.19 0.01 0.03 0.0001 0.008 0.10

Valence character s ) ŽC – Cl. s) C p ) C q s ) ŽC – F . p) C s ) ŽC – F . q Žp,d . ) C d) C d) C Žs,d . ) C d ) C q s ) ŽC – F . Žp,d. ) C s ) ŽC – F . q d ) C d) C d) C s ) ŽC – F . q d ) C

Final state 5.99 2.80 2.09 2.09 1.43 1.38 1.41 1.28 1.05 1.01 0.76 0.67 0.64 0.11

4.721 0.077 0.239 0.0002 0.783 0.009 0.010 0.027 0.549 0.002 1.600 0.007 0.018 7.458

f = 10 y 2

R ŽC – Cl. s R 2 TV

0.87 0.05 0.12 0.02 0.29 0.01 0.0002 0.02 0.22 0.01 0.10 0.0002 0.005 0.18

Valence character

s ) ŽC – Cl. s) C p ) C q s ) ŽC – F . p) C s ) ŽC – F . q d ) C d) C d) C Žs,d . ) C Žp,d . ) C q s ) ŽC – F . p) C Žp,d . ) C q s ) ŽC – F . d) C d) C s ) ŽC – F . q d ) C

Final state

26 G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

laxed CI results obtained with the minimal basis set ŽMBS. and with the extended basis set ŽEBS.. The very modest MBS description is, however, useful to get a first representation of the spectral pattern in terms of the valence only virtual orbitals, which in the C3v molecular symmetry are the 11a 1 MO, with dominant s ) ŽC–Cl. character, and the 8e and 12a 1 MOs, with s ) ŽC–F. dominant character. Considering the spectrum relative to the equilibrium geometry Ž R s R eq ., we can see that the oscillator strength distributes essentially between the first transition towards the 11a 1 s ) ŽC–Cl. antibonding orbital and the second one relative to the couple of degenerate 8e s ) ŽC–F. antibonding orbitals; the transition to the last s ) ŽC–F. orbital Ž12a 1 . instead shows a drop of the intensity due to a decrease of the C2p atomic component in the orbital composition. The same spectral pattern is also present in the other two MBS calculated spectra, with the only significant variation associated with the energy position of the s ) ŽC–Cl. transition, as expected; at this level of description the s ) ŽC–F. transitions appears almost unaffected by the change of the C–Cl bond length. Going to the results obtained in the extended basis set, reported in Table 1 and Fig. 1, it is well apparent that the increased complexity of the spectra is associated with the greater number of possible final states on which the oscillator strength redistributes. In particular, we note that in all spectra several lines with different intensity contribute to the second broad band, while the first low-lying peak is again descripted by only one transition towards the 11a 1 molecular orbital. This suggests that the 11a 1 final state mantains its prevalent s ) ŽC–Cl. valence character while the higher energy valence s ) ŽC–F. orbitals tend to mix with Rydberg orbitals originating several final states of mixed valence–Rydberg character, in line with the assignment proposed on the basis of the MO composition of the SCF–C1sy1 core hole state. In order to estimate more quantitatively the valence contribution to the excited states, we analysed the projection of the virtual MOs in the extended basis ŽC1sy1 SCF MOs. onto the space spanned by the minimal SCF virtual MOs. We define the ‘ valence character’ of each MO as the square norm of its projection. These data are reported in Table 1 together with the calculated oscillator strengths which essentially map the C2p atomic

27

component of the final states and are, therefore, a measure of the valence character of the state, can be used to provide a definite characterization of the excited states. Focusing our attention on the results relative to the equilibrium geometry, we can see that the valence character for the 11a 1 virtual orbital is quite high Ž0.84., definitely confirming the valence nature of the corresponding final state. The series of lines with negligible oscillator strength values present in the calculated spectrum of Table 1 Ž12–17 a 1 , 10 and 13e. are attributed to transitions towards final states of essentially Rydberg nature, on the basis of the composition of the relative C1sy1 core hole MO. The very low overlap squared values found for the corresponding virtual MOs confirm these attributions. The remaining spectral lines present below edge are relevant to transitions involving final states contributed to a different extent by s ) ŽC–F. antibonding orbitals, responsible for the quite high calculated oscillator strength values, and C p ) , d ) Rydberg components. The valence character obtained for these states Žsee Table 1. confirms their mixed valence–Rydberg nature. However, the oscillator strengths calculated for these states do not always match the overlap squared values relative to the corresponding virtual MO. In fact, the composition of the final states in the present approach also depends on the extent of the mixing of the 1h–1p configurations, which is quite consistent in the case of the excited states of e-symmetry and responsible for the calculated oscillator strengths. As an example, we can see that the 12e transition Žat 0.84 eV. shows a quite large oscillator strength Ž2.686. although its valence s ) ŽC–F. contribution appears very modest Ž0.03.. In fact the C1s ™ 11e and C1s ™ 12e 1h–1p configurations are strongly mixed in the resulting final states labelled 11e and 12e, and therefore the quite large s ) ŽC–F. valence contribution found for the 11e virtual orbital is redistributed over two final excited states influencing their intensities in the final spectrum. It is interesting to follow the variation of the spectra with the C–Cl bond length. As the C–Cl distance increases, the interaction between orbitals of adjacent atoms decreases, therefore reducing the splitting between bonding and antibonding states. This decrease is significant for the orbital directed along the bond, so we expect that it affects the

28

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

s ) ŽC–Cl. valence orbitals, as already observed in the minimal basis set description, leaving almost unaffected the orbitals with predominant Rydberg character. Table 1 and Fig. 1 show that this trend is correctly followed by the 11a 1 final state whose energy position is shifted towards higher TV as the C–Cl distance increases while the energies of the other lines stay almost unaffected. In the spectra, however, it is well apparent that it is a different intensity distribution among the transitions contributing to the second intense spectral structure which is essentially contributed by final states with mixed valence–Rydberg character. The comparative analysis of the data reported in Table 1 indicates that the Rydberg character of the 9e, 11e and 12e transitions increases with the C–Cl bond length and this is reflected by the decrease of their intensity in the spectra. An opposite trend, however, is followed by the valence s ) ŽC–F. contribution to the 14e transition with a consequent slight increase of the oscillator strength with the C–Cl bond length. Therefore, the change in the C–Cl distance quite significantly affects the composition of the virtual states which present a mixed valence–Rydberg character. The quantitative information inferred from both the valence character and spectral variations associated with the C–Cl bond length is completely consistent with the description of the calculated excited states based on analysis of the composition of the C1sy1 core ionized molecular orbital and the 1h–1p configurations contributing to the final states, which will be applied to assign the spectral features of all the calculated core excitation spectra discussed below. Let us examine now the C1s calculated spectra of the series of chlorofluorocarbon molecules, reported in Table 2 and Fig. 2, together with the experimental data. The features calculated above the ionization threshold Žup to f 4 eV. are reported only in Fig. 2. The CCl 4 spectrum is the simplest of the series being dominated by one intense band at low energy followed by weaker structures leading to the C1s ionization threshold, as seen in Fig. 2. The main peak Žat 2.97 eV. is attributed to the s ) ŽC–Cl. valence transition into the 8t 2 unoccupied virtual orbital, which is contributed by 2p carbon and 3p chlorine atomic components responsible for the high oscillator strength calculated for this transition Žsee

Table 2.. The following calculated lines below threshold are relative to transitions to the next t 2 virtual levels of Rydberg nature and are very weak. The calculated spectral pattern is consistent with the potential barrier model w22,23x according to which, when a core excitation occurs in the central C-atom, the Cl-atoms produce a sort of cage effect forming a potential well in which the 1s excited electron of the C-atom is trapped. This squeezes the Rydberg orbitals outside the well and strongly decreases the relative transition probabilities. We have considered analysis of the Rydberg series in terms of quantum defects, but the series appear significantly perturbed Žalso basis set inadequacy is possible. so that effective quantum numbers n ) s Ž Ry . r Ž TVn . do not fit into a regular pattern. Considering in more detail the comparison between the calculated and available experimental results reported in Table 2, we see that the 1h–1p CI TVs are strongly underestimated and in particular the TV of the first line Ž8t 2 . is too low by about 2.5 eV so that the energy separation between this line and the following Rydberg transitions also appears too small. The underestimate of the TV is a general defect of the present 1h–1p CI relaxed scheme which can be attributed to an incomplete treatment of relaxation in the core excited states due to use of the SCF orbitals of the core hole configuration. This may lead to an excessive relaxation for the neutral system with respect to the ionized one which destabilizes the excited states giving term values that are too low. Moreover, neglect of additional correlation between the ionic core and excited electron also increases the energy of the excited states relative to the threshold and, in fact, our recent work on the Cl1s and 2p core excitation spectra of HCl shows that inclusion of higher excitations in the CI computational scheme Žup to 3h–3p. improves the 1h–1p CI results, bringing them in accord quantitatively with the experiment w8x. The substitution of a Cl-atom with the first F-atom appears in the calculated spectrum of CFCl 3 as a small perturbation which apparently influences the spectral pattern only for the lowering of molecular symmetry from the Td point group of CCl 4 to the C 3v point group which splits the t 2 orbital into a 1 q e orbitals; we can therefore expect a redistribution of the 8t 2 intensity observed for the CCl 4 molecule between these two states Ž12a 1 and 11e,

(

2.97 12.97 1.81 0.20 1.24 0.66 0.83 0.01 0.45 0.80

TV

2.67

3.92 3.24 2.49 1.87 1.34 1.28 0.88 0.63 0.50

f = 10 y 2 TV

8t 2 s CCl. 6.12 3.3 9t 2 p ) C 5.30 9.7 10t 2 p ) , d ) C ) ) 11t 2 p , d C 12t 2 p ) , d ) C 3.32

)Ž

f = 10 y 2 Final state c 1.37 9.77 0.05 0.20 0.02 0.42 0.02 0.12 0.53

12a 1 s CCl. 11e s ) ŽCCl. 13a 1 s ) C 12e p ) C 15a 1 d ) C 14e d ) C q s ) ŽC,Cl. 15e p ) C 18a 1 s ) ŽCF . 17e d ) C q s ) ŽC,Cl.

)Ž

f = 10 y 2 Final state c

1h – 1p

Ref. w23 x. Ref. w15 x. s , p ) and d ) are referred to orbitals with predominant Rydberg character.

c )

b

a

1.8

5.4 9.9

TV f = 10 y2 TV

CFCl 3 EXP b

EXP a 1h y 1p

CCl 4

3.88 3.33

4.15 3.48 2.64 1.97 1.96 1.50 1.31 1.05 0.92 0.54 0.44

2.69 5.57 0.06 0.06 1.73 1.50 0.20 1.60 0.51 0.25 1.13

13a 1 s CCl. 9b 1 s ) ŽCCl. 14a 1 s ) C 7b 2 p ) C q s ) ŽCF . 10b 1 p ) C q s ) ŽCCl. 8b 2 p ) ,d ) C q s ) ŽCF . 11b 1 p ) ,d ) C 9b 2 s ) ŽCF . q p ) C 10b 2 p ) C 13b 1 d ) C q s ) ŽCCl. 11b 2 s ) ŽCF . q p ) C

)Ž

f = 10 y 2 Final state c

1h – 1p f = 10 y 2 TV

6.22 3.7 5.31 6.2

TV

EXP b

CF2 Cl 2

Table 2 Experimental and theoretical term values TV ŽeV . and oscillator strengths f for C1s core excitation spectra of CCl 4 , CFCl 3 , CF 2 Cl 2 and CF 3 Cl

4.8

2.24

3.0

3.65 16.4

6.15

TV

4.55 2.82 2.09 1.48 1.39 1.05 0.84 0.63 0.27

4.36 0.06 0.23 1.52 0.04 0.82 2.69 0.05 6.35

11a 1 s ) ŽCCl. 12a 1 s ) C 8e p ) C q s ) ŽCF . 9e s ) ŽCF . q d ) C 14a 1 d ) C 11e d ) C q s ) ŽCF . 12e s ) ŽCF . q d ) C 17a 1 d ) C 14e s ) ŽCF . q d ) C

f = 10 y 2 Final state c

1h y 1p f = 10 y 2 TV

CF3 Cl EXP b

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42 29

30

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

Fig. 2. Calculated C1s core excitation spectra of CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl. Lines are convoluted with Gaussians of 0.5 eV FWHM for the first three molecules and of 0.8 eV FWHM for CF3 Cl molecule. Experimental spectra from Ref. w15x are reported in inserted boxes.

respectively.. However, the s ) ŽC–Cl. valence contribution is distributed quite differently between these two MOs, as is apparent from the orbital composition which indicates for the 12a 1 virtual orbital a

smaller contribution from the C2p and Cl3p atomic components and the presence of quite important C2s component. The consequence is that the calculated 12a 1 oscillator strength is much lower than that

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

relative to the next excitation towards the 11e final state. This first calculated structure correctly reproduces the experimental one, as concerns both the energy separation and intensity distribution between the 12a 1 and 11e lines Žsee Fig. 2.; there is, however, an underestimate of the calculated TVs, as is well apparent in Table 2 and already commented on in the case of the CCl 4 C1s spectrum. There is no evidence of the shoulder at the higher energy side of the main peak observed in the experiment, and this confirms the attribution proposed for this shoulder as being due to Jahn–Teller splitting of the 11e transition w15x. The following calculated lines below threshold show very low intensity with respect to the main peak, being mostly associated with transitions towards orbitals with mixed valence ŽC–Cl. ) –Rydberg character; this mixing tends to distribute the oscillator strengths among many excitations reducing their intensity. This pattern below edge resembles that calculated for the CCl 4 molecule while the experimental spectrum of CFCl 3 Žsee Fig. 2. shows in this region an increase of the intensity with respect to the case of CCl 4 , in particular for the presence of feature 4 which is assigned to the transition towards the s ) ŽC–F. antibonding orbital. In the case of the theoretical spectrum, a transition involving a final state with a predominant s ) ŽC–F. character Ž19a 1 . is calculated just above threshold ŽTV s y0.24 eV, f s 2.10 = 10y2 .. Apart from the too large intensity found for this transition, which is an artefact of the discretization of the continuum due to the use of a finite basis set, this calculated value reflects a bonding situation in which the larger C–F bond strength with respect to the C–Cl bond is responsible for the lower energy of the s ŽC–F. bonding orbitals with respect to s ŽC–Cl. bonding orbitals: the consequence is a destabilization of the s ) ŽC–F. antibonding orbitals, with respect to the s ) ŽC–Cl. ones, which can push them above the ionization threshold. It is to be expected that a more accurate treatment of correlation effects, lowering the energies of the excited states, could shift all the calculated spectral pattern away from the threshold and redistribute more correctly the anomalous intensity collected in the 19a 1 final state over the lower intensity lines present below edge. The calculated spectral pattern of the CF2 Cl 2 molecule appears more complex than the preceding

31

ones Žsee Fig. 2., and this is in part due to the lowering of the molecular symmetry Žfrom C 3v to C 2v point group. which redistributes the intensity over a larger number of final states but also depends on the introduction of a second F-atom which makes the C–Cl and C–F bonds quite distinct producing a spectral pattern which differs from the preceding ones Žsee Fig. 2.. The lower energy structure calculated around 4eV is contributed by two transitions towards the 13a 1 and 9b 1 unoccupied virtual orbitals, as expected on the basis of the symmetry descent Ža 1 q e in C 3v split in a 1 q b 1 q b 2 in C 2v . while the transition to the b 2 orbital Ž7b 2 at 1.97 eV. shows a negligible intensity. The first b 2 transition with appreciable intensity is towards the 8b 2 virtual orbital Žat 2.65 eV. therefore shifted by about 2.6 eV from the first 13a 1 line. The 13a 1 and 9b1 lines are associated with final state with a predominant s ) ŽC–Cl. valence character and both their energy separation and intensity distribution correctly reproduce the experimental feature Žsee Fig. 2.. The 8b 2 transition involves a level of predominant s ) ŽC–F. character with stronger participation of C and F 2p atomic components and contributes to the quite broad band calculated near the ionization threshold together with several other lines of similar intensity. Among these lines only the first one Ž10b1 at 1.96 eV. is relative to a transition involving a final state with s ) ŽC–Cl. character, while the other three most intense transitions are towards b 2 levels which have a predominant s ) ŽC–F. valence character. The other less intense lines falling in this energy range are relative to final states with predominant p Rydberg contributions from the C-atom. A general satisfactory agreement between the calculated and experimental spectra is reached, as is well apparent in Fig. 2; the effect of the usual underestimate of the TVs is the shift of the spectral structures towards the ionization threshold so that the higher energy calculated transitions which involve levels of predominant carbon p Rydberg character, are pushed above the threshold. Consider finally the results obtained for the most fluorinated molecule of the series CF3 Cl. The spectrum differs quite consistently from the preceding ones, as seen in Fig. 2, also if the intensity distribution over the calculated spectral lines follows the trend expected from the previous considerations. In

32

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

fact, we observe a further drop of the intensity of the first low-lying transition Ž11a 1 at 4.55 eV. with a parallel increase of the second structure below the threshold, which becomes the most intense feature of the calculated spectrum. This spectral pattern is in agreement with the experimental one, as seen in Fig. 2, apart from some details discussed below. The first calculated band Žat 4.55 eV. is relative to the transition towards the s ) ŽC–Cl. antibonding orbital, as already stressed, and is separated by about 3.5 eV from the next intense structure. This energy separation is overestimated with respect to the experimental one by about 1 eV while the calculated intensity distribution between these two bands appears consistent with the experimental estimate Žthe oscillator strength value obtained summing over all calculated transitions contributing to the second structure is 11.8, which is about 3 times larger than the oscillator strength of the 11a 1 transition.. The most intense transitions of the strong band close to the threshold are relative to final states of predominant ŽC–F. ) antibonding character Žsee Table 2. which tend to be destabilized with respect to the corresponding ŽC– Cl. ) ones, as previously discussed, generating the too large energy separation observed between this band and the first s ) ŽC–Cl. transition Ž11a 1 .. Furthermore, the overestimated TVs typical of the present 1h–1p CI scheme produces a shift of all the spectral feature towards the edge so that we find a series of quite intense lines also above threshold. These are relevant to transitions involving final states which again show important contribution from ŽC– F. ) antibonding orbitals. Also considering this last calculated structure, in the limit already indicated for our computed discretized transitions above edge, the theoretical spectrum correctly reproduces all the experimental structures observed below the ionization threshold Žsee Fig. 2.. Some general comments on the trends along the series can be made on the basis of the previous considerations. The theoretical results indicate that the s ) ŽC–Cl. antibonding orbitals are located below the s ) ŽC–F. orbitals and this is consistent with the more electronegative character of the F-atom with respect to the Cl-atom. In fact, the first calculated line in all spectra is associated to the transition towards a s ) ŽC–Cl. final state whose energy appears quite sensitive to the addition of the F-atom, as

is well apparent in Fig. 2, being shifted to lower TV from CCl 4 to CF3 Cl Žby f 1.6 eV.. Also the intensity distribution over the spectral features varies along the series depending on the number of Cl- and F-atoms in the molecule. For the more chlorinated CCl 4 and CFCl 3 molecules, the intensity is concentrated in the lower energy structure associated with unoccupied orbitals with strong s ) ŽC–Cl. character. The mixing between these low-lying virtual orbitals and the Rydberg orbitals at higher energy is quite small and the Rydberg transitions below threshold show negligible intensity. As the number of F-atoms increases, a competition in the distribution of the oscillator strengths between the s ) ŽC–Cl. and s ) ŽC–F. antibonding orbitals is apparent. Furthermore, as the s ) ŽC–F. orbitals are quite high in energy, they can mix with the Rydberg orbitals with a consequent distribution of the intensity among more final states which appear quite near the threshold in the calculated spectrum of CF2 Cl 2 . This situation is even more evident in the spectrum of the most fluorinated CF3 Cl molecule where most of the intensity is collected in a structure at higher energy contributed by several transitions close to the threshold. 3.2. Cl 1s and 2p core excitation spectra The calculated Cl1s and 2p spectra of the freon molecules are reported in Figs. 3 and 4 which show the spectral trends along the series with the progressive replacement of the Cl-atom with the F-atom. In the figures the total oscillator strengths relative to all the Cl-atoms present in the molecule are reported. In Tables 3 and 4 we collect the excitation data relative to the two different Cl core holes Ž1s and 2p. for each molecule in order to have direct and clearer insight into the different contributions of the Cl 3s and 3p components in the final states. In fact, due to the strong localisation of the core transitions the relevant oscillator strengths can be a sort of measure of the Cl s, p and d content in the MO empty orbitals. Tables 3 and 4 report for each molecule the oscillator strengths normalized to a single Cl-atom in order to facilitate comparison along the series. Consider first the results relative to the Cl1s excitations in the discrete region. It is well apparent from Fig. 3 that all the spectra are dominated by a

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

33

Fig. 3. Calculated Cl1s core excitation spectra of CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl. Lines are convoluted with Gaussians of 0.6 eV FWHM. Experimental spectra from Ref. w12x are reported in inserted boxes.

single low-lying feature which has a very similar energy along the series Ž4.45, 4.44, 4.51 and 4.62 eV on going from CCl 4 to CF3 Cl. and also a similar

oscillator strength value per Cl-atom Ž f s 0.355, 0.351, 0.364 and 0.392 from CCl 4 to CF3 Cl.. This peak is assigned to the Cl1s transition towards the

34

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

Fig. 4. Calculated Cl2p core excitation spectra of CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl. Lines are convoluted with Gaussians of 0.6 eV FWHM. Experimental spectra from Ref. w15x are reported in inserted boxes.

first s ) antibonding molecular orbital. In the CCl 4 molecule this virtual orbital has a s ) ŽC–Cl. character and acquires a quite mixed s ) ŽC–Cl. and

s ) ŽC–F. character in the fluorinated molecules. As seen in Tables 3 and 4, the labels of the virtual molecular orbitals do not match those expected from

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

the symmetry point group of the molecule, due to the reduced symmetry used in the calculations when the core hole is localised on one peripheral atom, as in the present case for chlorine Žfor all molecules we use the C s point group.. Of course the virtual orbitals also relax in the field of the core hole, and both their ordering and composition change according to the localisation of the hole. This lowering of the symmetry is responsible for a different mixing of the atomic orbitals with respect to that obtained in the full symmetry so that the first valence molecular orbital of the chlorofluorocarbon molecules Žof AX symmetry. now also contains fluorine atomic components at variance with the case of the C1s hole state where this first virtual orbital has only a s ) ŽC–Cl. character. In any case, the calculated Cl1s oscillator strengths do not appear influenced by the different fluorine atomic components in the final MO, being quite constant along the series, as already commented. Weaker lines are present in the calculated spectra between the first dominant peak and the ionization threshold: summing up their oscillator strengths we obtain a quite broad feature whose intensity remains similar along the series with respect to the intensity of the main line Žthe percentage is 58%, 66% 54% and 50% for CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl, respectively., as well as its energy position and separation from the first structure. These patterns are in good agreement with the experimental observations w12x. In particular for the CCl 4 molecule we can observe in this energy region Žsee Table 3. first a very weak transition Ž2.60 eV. toward a Rydberg final state with predominant s ) character followed by two other transitions Žat 1.91 and 1.65 eV. little more intense towards orbitals with contribution from Cl p ) Rydberg orbitals. The next lines leading to the Cl1s ionization threshold are very close in energy: among these only the transitions towards Rydberg final states with predominant Cl p component or mixed valence–Rydberg character contribute with appreciable intensity to the structure before edge. The substitution of a Cl-atom with a F-atom in the CFCl 3 molecule does not produce significant variation in the spectral pattern, as is well apparent in Fig. 3. As previously discussed, the first strong absorption peak is relative to the s ) valence transition into the first unoccupied orbital Ž22aX .. The following

35

very small line Žat 2.74 eV. is relative to the transition to a Rydberg orbital with predominant Cl s ) component as already observed also in the calculated CCl 4 spectrum, while the next two lines Žat 2.01 and 1.99 eV. are associated to transitions towards orbitals with strong Cl p participation, again in line with the previous analysis on the CCl 4 molecule. The calculation provides several other transitions below threshold towards orbitals with quite mixed valence–Rydberg character so the oscillator strengths are distributed among many excitations with low intensity. The calculated spectrum reproduces well the experimental one as seen in Fig. 3, in particular if we consider the decomposition of the discrete experimental features in the spectral components w12x; it is to be noted that the calculated energy separation between the first structure and the following lower lines is underestimate by about an eV with respect to the experiment, as seen in more detail in Table 3. This depends on the limit of the present computational model to reproduce quantitatively the experimental data, as already stressed in the discussion relative to the C1s spectra. The spectrum of CF2 Cl 2 can be interpreted on the basis of the same considerations made for the preceding molecules, both as concerns the assignment of the spectral lines and comparison with the experimental data, as seen in Table 4 and Fig. 3. The most fluorinated molecule CF3 Cl again shows a spectral pattern completely in line with the preceding ones, as also observed in the experiments, although the detail of the spectral structure before threshold is slightly changed, as is apparent in Fig. 3. In particular, there is a slight increment of the intensity of the feature contributing by Cl p Rydberg states Žcalculated at 2.01 and 1.99 eV. which could depend on a stronger Cl p Rydberg character of the final states at variance with the preceding more chlorinated molecule where the corresponding states also showed a ŽC–Cl. valence contribution. The increased sharpness of this feature in the experiment is well reproduced in the calculated spectrum. From the present analysis on the Cl1s spectra, apart from the unequivocal s ) antibonding character of the first strong absorption peak, we propose to attribute the small peak indicated as feature ‘E’ in the experimental spectra of the CFCl 3 , CF2 Cl 2 and CF3 Cl w12x to the formally forbidden transition to the

3.4

4.5

0.48 0.48 0.03 0.07 0.07 0.13 0.05 0.05 0.01 0.003 0.01 0.08 0.04 0.16 0.10 0.001 0.005 0.04 0.03 0.03 0.01 0.01 0.003 0.04 0.08 0.01 0.04

0.03 0.004

0.02

0.02

1.65 1.27

1.15

1.11

0.03

; 0

0.01

0.35

1.69

1.91

1.98

2.60

4.45

f = 10

X

Y 17a d ) Cl q s ) ŽCCl. X 34a d ) Cl q s ) ŽCCl. X Y 34a q 17a

33a s ) ŽCCl. q d ) Cl

X

32a s ) q d ) q p ) Cl

X

28a p ) Cl Y 14a p ) Cl X 29a d ) Cl q s ) ŽCCl. Y 15a d ) Cl q s ) ŽCCl. X Y 29a q 15a X Y 29a q 15a X 30a s ) ŽCCl. q p ) Cl

X

27a s ) Cl q s ) ŽCCl.

3.24

4.05

26a s ) Cl

X

6.55

2p

25a s ) ŽCCl.

X

Final state

4.62 4.49 4.28 2.74 2.63 2.61 2.09 1.98 1.97 2.03 1.91 1.83 1.82 1.72 1.71 1.62 1.60 1.39 1.27 1.26 1.26 1.15 1.13 1.23 1.12 1.11

TV

6.4

f = 10

TV

y2

2p

y2

CFCl 3 EXP b

EXP a 1s

2p

CCl 4

4.63 4.50 4.29 2.88 2.76 2.75 2.12 2.01 2.00 1.99 2.08 1.97 1.96 1.78 1.68 1.67 1.73 1.61 1.60 1.47 1.35 1.36 1.45 1.32 1.41 1.29 1.28

TV

2p

0.52 0.53 0.03 0.08 0.07 0.15 0.01 0.004 0.002 0.01 0.03 0.01 0.01 0.002 0.08 0.09 0.11 0.05 0.02 0.01 0.01 0.02 0.01 0.01 0.04 0.01 0.03

f = 10

y2

2.2

3.6

6.5

1s

EXP c

Table 3 Experimental and theoretical term values TV ŽeV . and oscillator strengths f for Cl1s and 2p excitation spectra of CCl 4 and CFCl 3

1.29

1.35 1.33

1.35

1.62

1.66

1.99 1.96

2.01

2.74

4.44

TV

1s

;0

;0 0.004

0.001

0.02

;0

0.02 0.01

0.01

0.01

0.35

f = 10 y2

X

29a d ) q s ) Cl

Y

15a d ) Cl X 28a d ) q s ) Cl

X

27a d ) q p ) q s ) Cl

X

26a s ) Cl q s ) ŽCCl.

Y

14a d ) Cl q s ) ŽCCl.

Y

13a p ) Cl 25a p ) Cl q s ) ŽCCl.

X

24a p ) Cl q s ) ŽCCl.

X

23a s ) Cl

X

22a s ) ŽCCl. q s ) ŽCF .

Final state

36 G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

b

Ref. Ref. c Ref.

a

w23 x. w15 x. w12 x.

1.09 0.83 0.73 0.71 0.82 0.71 0.70 0.75 0.63 0.55 0.43 0.41 0.52 0.40 0.26 0.14

0.004 0.01 0.01 0.01 0.01 0.004 0.13 0.01 0.01 0.01 0.01 0.01 0.03 0.03 0.01 0.01

0.01 0.005

0.01

0.01 0.01

0.002

0.98 0.72

0.70

0.63 0.43

0.14

X

Y

43a d ) Cl Y 22 d ) Cl X Y 44a q 23a d ) Cl

X

42a p ) q s ) Cl

X

40a s ) q p ) Cl

X

39a q 20a s ) ŽCCl. q d ) Cl

X

35a p ) Cl X 38a d ) q s ) Cl 1.24 1.12 1.11 1.17 1.05 1.13 1.00 1.07 0.93 0.85 0.75 0.72 0.65 0.71 0.60 0.49 0.47 0.55 0.44 0.39 0.27 0.15 0.14 0.09

0.06 0.01 0.01 0.01 0.12 0.005 0.01 0.004 0.005 0.03 0.01 0.01 0.05 0.005 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.01 0.01 0.02 0.04 0.02 0.01

0.001 0.001 0.002

0.42 0.28 0.15

0.003

0.01 0.01 0.01

0.003

0.02

0.66 0.60 0.49

0.73

1.01 1.01 0.96

1.04

1.12

42a s ) ŽCF . q s ) ŽCCl.

X

22a d ) Cl

Y

40a d ) Cl

X

39a d ) Cl

X

X

36a s ) q p ) Cl X 37a p ) Cl X 38a p ) q d ) Cl

X

35a s ) Cl

X

31a p ) Cl Y 17a p ) Cl X 32a p ) Cl

16a d )

Y

X

30a p ) q s ) q d ) Cl

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42 37

2.3

3.43

0.62 0.60 0.04 0.08 0.07 0.18 0.001 0.01 0.004 0.01 0.01 0.01 0.01 0.03 0.003 0.01 0.02 0.04 0.03 0.02 0.01 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.01 0.01 2.4

3.2

6.6

0.02 0.01

0.01 ;0

0.001

;0 0.01 0.01 0.003

0.01

1.60 1.41

1.39

1.37 1.31 1.05 1.04

1.06

0.02

2.11 2.09 2.00

0.01

0.36

2.91

4.51

CCl. q s ) ŽCF .

)Ž

)

CCl.

)Ž

13a p ) q d ) Cl

Y

30a s Cl q s

X

29a s ) ŽCCl. q d ) q s ) Cl

X

28a d ) q p ) Cl

X

12a d ) Cl

Y

27a d ) q s ) Cl

X

X 25a s ) ŽCCl. q d ) Cl X 26a d ) q s ) Cl

Y

10a p ) Cl X 24a p ) q s ) Cl

23a p ) Cl

X

22a s ) Cl q s ) ŽCCl.

X

21a s

X

Final state

2.09

3.52

6.7

2p

4.71 4.58 4.35 3.05 2.93 2.91 2.11 2.09 2.08 2.12 2.00 1.99 1.73 1.54 1.42 1.40 1.51 1.39 1.37 1.38 1.37 1.31 1.29 1.17 1.06 1.16 1.04 1.03 1.06 1.04

f = 10 y2

6.74

TV

TV

2p

1s

EXP a

f = 10 y 2

CF3Cl 1s

EXP a

EXP b

2p

CF2 Cl 2

4.87 4.70 4.45 3.21 3.10 3.07 2.32 2.20 2.16 1.60 1.48 1.46 1.55 1.43 1.42 1.47 1.45 1.33 1.30 1.10 1.00 0.96 0.85 0.83 0.93 0.82 0.80 0.92 0.81 0.79

TV

2p

0.72 0.71 0.05 0.06 0.05 0.25 0.001 0.01 0.0003 0.04 0.05 0.02 0.02 0.02 0.03 0.05 0.06 0.001 0.03 0.0002 ;0 0.04 0.05 0.04 0.03 0.02 0.03 0.02 0.02 0.03

f = 10 y2

2.4

2.8

6.7

1s

EXP b

Table 4 Experimental and theoretical term values TV ŽeV . and oscillator strengths f for Cl1s and 2p excitation spectra of CF2 Cl 2 and CF3 Cl

1s

0.80

0.82

1.10 1.03 0.84

;0

0.002

0.03 0.01 ;0

0.01

0.004

1.47 1.32

0.001

0.02 ;0

0.06

0.02

0.39

f = 10 y2

1.43

2.05 1.47

2.21

3.07

4.62

TV

X

Y

30a q 14a d ) Cl

X

29a s ) q d ) Cl

Y

12a p ) Cl X 27a p ) Cl X Y 28a q 13a d ) Cl

X

25a s ) q p ) q d ) Cl

23a s ) q d ) q p ) Cl

X

X

24a d ) Cl Y 11a d ) Cl

X

Y

21a p ) Cl X Y 22a q 10a d ) Cl

X

20a q 9a p ) Cl

X

19a s ) Cl q s ) ŽCCl.

X

18a s ) ŽCCl. q s ) ŽCF .

Final state

38 G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

b

a

Ref. w15 x. Ref. w12 x.

1.07 0.96 0.94 0.93 0.92 0.81 0.79 0.79 0.78 0.89 0.77 0.76 0.78 0.66 0.64 0.63 0.62 0.65 0.53 0.50 0.63 0.52 0.51 0.60 0.48 0.44 0.43 0.14 0.13

0.02 0.02 0.01 0.02 0.01 0.03 0.03 0.02 0.02 0.02 0.01 0.02 0.02 0.01 0.02 0.003 0.003 0.01 0.01 0.01 0.02 0.10 0.08 0.01 0.01 0.04 0.02 0.02 0.03 0.01 0.02 0.02

0.002

0.63 0.62 0.54

0.49

0.003 0.01

0.44 0.14

;0

0.01

0.66

0.47

0.002

;0

0.78 0.77

;0 ;0

0.02

0.80 0.79

0.96

X

40a d ) Cl q s ) ŽCCl.

X

18a d ) Cl

Y

38a d ) Cl

X

17a d ) Cl q s ) ŽCCl.

Y

16a p ) Cl X 36a p ) Cl X 37a p ) q d ) Cl

Y

35a s ) q d ) Cl q s ) ŽCCl.

X

33a s ) q d ) Cl

X

15a d ) Cl

Y

32a d ) q s ) Cl Y 14a d ) Cl

X

31a s ) ŽCCl. q s ) Cl 0.74 0.72 0.66 0.65 0.53 0.52 0.59 0.47 0.46 0.26

0.001 0.01 0.01 0.05 0.06 0.05 0.04 0.05 0.06 0.01 0.002

0.46

0.003

0.02 0.001

0.66 0.52

0.28

0.01

0.74

X

20a d ) Cl q s ) ŽCCl.

35a d ) Cl q s ) ŽCCl.

X

32a p ) Cl X 34a d ) q Cl q s ) ŽCCl.

X

X

31a p ) q d ) q s ) Cl

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42 39

40

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

Rydberg orbital with predominant Cl s ) character; the more intense following structure, labelled ‘F’ in the experiments, can be related to transitions towards Rydberg orbitals with strong Cl p ) participation. The last feature leading to the ionization threshold Žlabel ‘G’ in the experiments. is contributed by transitions to higher states involving Cl p and d Rydberg components often mixed with residual s ) ŽC–Cl. valence contribution. As a general comment, we can observe that in contrast to the large variations observed in the C1s spectra of this series of molecules, the Cl1s spectra are remarkably similar and these trends reflect the localised character of the core excitation: the local chemical environment of the C-atom is quite different in the molecules considered but it is much more similar around the Cl-atoms since in each molecule the Cl-atom is attached only to the C-atom. The environment probed by the relatively compact Cl1s orbital does not seem to be significantly perturbed by the addition of electronegative F-atoms in the molecule and this is reflected by the very similar values of the electron binding energies and by the similar distribution of the oscillator strengths over the final states of all molecules of the series. Consider now the theoretical results relative to the Cl2p spectra which are reported in Table 3 Žfor CCl 4 and CFCl 3 . and Table 4 Žfor CF2 Cl 2 and CF3 Cl. and in Fig. 4. In the Cl2p experimental spectra reported in Fig. 4 the two series of structures related to the Cl2p 3r2 and Cl2p1r2 ionization thresholds appear strongly overlapped and not easy to disentangle. The present theoretical approach does not include the spin–orbit splitting and therefore the experimental results considered for comparison are relative to the transitions converging to a single edge. The Cl2p calculated spectra appear more complex than the corresponding Cl1s ones, as it is well apparent comparing Figs. 3 and 4; moreover, for each final orbital, there are three distinct transitions starting from the three Cl2p orbitals which have slightly different SCF energies for the reduced symmetry used in the calculations Žsee Tables 3 and 4.. All the 2p spectra are characterised by a low-energy dominant peak, which appears very broad in the experiments followed by a second less intense structure whose intensity percentage with respect to the first structure remains quite constant along the series. The

last structure in the spectra before edge shows quite a different shape on going from CCl 4 to CF3 Cl and appears to be contributed by a very large number of lines among which the intensity is spread. The first peak is attributed to the transition to the first unoccupied virtual valence orbital which is a purely s ) ŽC– Cl. antibonding level in CCl 4 and presents contributions also from the fluorine p atomic orbitals in the other molecules of the series, as already underlined in the discussion relative to the Cl1s spectra. Addition of electronegative F-atoms therefore causes a certain change in the composition of the final states relative to the first peak in the spectrum which is reflected in the spectra by the progressive small shift towards higher TV values of the first valence peak and by the parallel increase of the oscillator strength per Cl-atom of the first peak on going from CCl 4 to CF3 Cl Žsumming over the three transitions which contribute to this peak we obtain for each molecule: f Ž=10y2 . s 0.985, 1.079, 1.264 and 1.476, respectively. at variance with the case of the Cl1s spectra where the first valence peak maintains quite similar energy and intensity along the series. The second structure in the 2p calculated spectra is well recognisable being separated from the first peak by about 1.8 eV in CCl 4 , 1.67eV in CFCl 3 , 1.58eV both in CF2 Cl 2 and CF3 Cl; it is attributed to the transitions from the 2p Cl orbitals into the first Rydberg orbital with predominant Cl s ) components and shows comparable intensity percentage with respect to the first peak in all spectra Žf 28% in CCl 4 and CFCl 3 and f 26% in CF2 Cl 2 and CF3 Cl.. As seen in Tables 3 and 4 this final state collects much more intensity Ž) 10 times. in the 2p spectra than in the Cl1s spectra where the relative transition is formally forbidden by the dipole selection rules, and this supports the attribution proposed for this spectral feature. To discuss the last structure of the 2p calculated spectra, it is convenient to consider each molecule separately. In the CCl 4 2p spectrum Žsee Fig. 4. this feature is quite close to the Cl s ) band and more intense, being contributed by a large number of states leading to the ionization threshold. Most of its intensity, however, is concentrated in the energy range around 1.8 eV relative to several transitions associated to final states Ž29aX and 15aY . with a mixed character from valence ŽC–Cl. and Cl d )

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

Rydberg orbitals. In Table 3 we can observe that for the corresponding transition Žtowards 29aX and 15aY . in the Cl1s spectrum Žat 1.69 eV. the calculation provides a very low oscillator strength value reflecting therefore a much stronger participation of the Cl d component in these final states. The following calculated lines before edge show very low intensity; as seen in Table 3 the relative final states mainly have a mixed valence–Rydberg character without predominant components so that the oscillator strengths distribute over many excitations reducing their intensity. This is consistent with the low oscillator strength values calculated for these final states also in the 1s spectrum Žsee Table 3. and previously commented. As concerns the comparison with the experimental data for CCl 4 w23x reported in Table 3, apart from the expected underestimate of the TVs, a good accord is reached for the energy separation between the first two structures in the present spectrum, 1.7 eV being the experimental and 1.8 eV the calculated values; furthermore, there is also good agreement between the experimental feature observed at about 2.8 eV from the first low-energy peak and the quite intense transitions provided by the calculation at about 1.8 eV Žtowards 29aX and 15aY orbitals. and separated from the first calculated peak by about 2.7 eV. The same structure in the CFCl 3 molecule shows a reduced intensity with respect to the preceding CCl 4 molecule; again we find a group of transitions in an energy region around 1.7 eV which collects most of the intensity, as observed for the CCl 4 molecule. The relevant final states Ž14aY and 26aX . have a predominant Cl d ) and s ) Rydberg character, as is also inferred by the relatively small oscillator strength values found for the corresponding transitions Žsee Table 3. in the Cl1s spectrum. We can observe another transition towards a final state Ž16aY . with a predominant Cl d ) Rydberg character at 1.05 eV which shows appreciable intensity in the 2p spectrum while in the Cl1s spectrum Žat 1.04 eV. has a negligible intensity Žsee Table 3.. The calculated spectral pattern of the CFCl 3 molecule compares quite well with the experiment w15x Žsee Fig. 4. apart from a slight underestimate of the theoretical energy separation between the first two structure Ž1.67 against 2.5 eV of the experiment., and therefore we propose to attribute the experimental peaks 3 and 4

41

to transitions towards orbitals with predominant Cl s and d Rydberg character. In CF2 Cl 2 the last calculated structure before threshold appears less structured than in the preceding spectra deriving its intensity from many weak lines among which the oscillator strengths is quite uniformly distributed. As seen in Table 4, the nature of the final states resembles that found for the CFCl 3 molecule but the contribution to the final states from the Cl atomic components available for the transition moment tends to decrease with the number of Clatoms in the molecule with a consequent reduction of the calculated oscillator strength values. This is even more marked in the spectrum of the CF3 Cl molecule for which we also note a global reduction of the intensity of this last structure with respect to the dominant peak. For these two molecules comparison of theoretical with experimental data is more difficult. In analogy to the CFCl 3 molecule we associate the second calculated structure of the CF2 Cl 2 spectrum Žf 3 eV. to the experimental peak 3 Ž3.43 eV. and the last structure starting f 2 eV to the observed transitions between 2.3 and 1.67 eV w15x. Also following this trend for the CF3 Cl molecule, we attribute experimental peak 2 Ž3.52 eV. to the calculated transitions towards 19aX s ) Cl Rydberg orbital Ž; 3 eV. and the experimental peaks 3–5 to the last calculated structure starting f 2 eV. The present analysis of the Cl2p calculated spectra shows that, apart from the first valence state, the other final states do not show important participation of the fluorine atomic components. Instead, these are present in final states lying at higher energy and pushed above threshold by the present calculation as also observed in the case of the C1s spectra. With the exception of the first s ) valence transition, the Cl2p spectral structures essentially have a Cl Rydberg nature and the oscillator strengths therefore map the s and d chlorine Rydberg content of the final states. Comparison with the oscillator strength values of corresponding transitions in the Cl1s spectra is consistent with this attribution.

4. Conclusions Calculated C1s and Cl1s and 2p core excited spectra of CCl 4 , CFCl 3 , CF2 Cl 2 and CF3 Cl

42

G. Fronzoni, P. DecleÕar Chemical Physics 237 (1998) 21–42

molecules have been analysed by means of the 1h–1p CI relaxed scheme. The good agreement between calculated and experimental spectra proves the reliability of the present scheme for the assignment of spectral features. An improvement towards a quantitative accord with the experimental data, which is warranted by the quality of current data, can be achieved by enlarging the CI space w8x but this requires further investigation in order to reduce the computational effort involved in high excitation levels previously employed. Analysis of the spectral pattern along the series shows significant variations in the case of the C1s core hole associated with the progressive substitution of the Cl-atom with the F-atom. The observed trend can be interpreted in terms of the more electronegative character of the F-atom with respect to the Cl-atom which shifts the transitions towards final states with s ) ŽC–F. character at higher energy than those towards s ) ŽC–Cl. final states and also being responsible for the higher polarity of the C–F bond with respect to the C–Cl bond, favours the s ) ŽC–F. transitions which collect stronger intensity. Moreover, the s ) ŽC–F. excitations lie in the energy region of Rydberg excitation, giving rise to a large valence–Rydberg mixing, with intesity spread over several electronic states. On the contrary, the Cl1s and 2p spectra appear less sensitive to the nature of the ligand Cl or F attached to the central C-atom, and this is a demonstration of the localised character of the core excitation: the electronic structure of the molecules considered are quite similar around the Cl-atoms since, in each case, it is attached only to the C-atom and therefore is not significantly perturbed by the other ligand atoms.

References w1x A.P. Hitchcock, D.C. Mancini, J. Electron Spectry. 67 Ž1994. 1. w2x J. Stohr, ¨ NEXAFS Spectroscopy, Springer, Berlin, 1992. w3x I. Cacelli, V. Carravetta, R. Moccia, Mol. Phys. 59 Ž1986. 385. w4x M. Ohno, P. Decleva, J. Chem. Phys. 98 Ž1993. 8070. w5x P. Decleva, G. Fronzoni, A. Lisini, Chem. Phys. 168 Ž1992. 51. w6x G. Fronzoni, P. Decleva, A. Lisini, M. Ohno, J. Electron Spectry. 62 Ž1993. 245. w7x G. Fronzoni, M. Stener, A. Lisini, P. Decleva, Chem. Phys. 210 Ž1996. 447, and references therein. w8x G. Fronzoni, M. Stener, P. Decleva, G. De Alti, Chem. Phys. 00 Ž1998. 000. ˚ w9x H. Agren, V. Carravetta, O. Vahtras, L.G.M. Petterson, Chem. Phys. Lett. 222 Ž1994. 75. ˚ w10x V. Carravetta, H. Agren, L.G.M. Petterson, O. Vahtras, J. Chem. Phys. 102 Ž1995. 5589. w11x M.J. Hanus, E. Gilberg, J. Phys. B 9 Ž1976. 137. w12x R.C.C. Perera, P.L. Cowan, D.W. Lindle, R.E. La Villa, T. Jach, R.D. Deslattes, Phys. Rev. A 43 Ž1991. 3609. w13x G. O’Sullivan, J. Phys. B 15 Ž1982. 2385. w14x F.W. Lytle, R.B. Greegor, G.H. Via, J.M. Brown, G. Meitzner, J. Phys. C8 47 Ž1986. 149. w15x W. Zhang, T. Ibuki, C.E. Brion, Chem. Phys. 160 Ž1992. 435. w16x T.H. Dunning, J. Chem. Phys. 90 Ž1989. 1007. w17x E.R. Davidson, MELDF, QCPE Program 580, QCPE Bull. 9 Ž1989. 98. w18x R.C. Weast ŽEd.., CRC Handbook of Chemistry and Physics, 48th ed., 1968. w19x M.W. Long, Q. Williams, T.L. Weatherly, J. Chem. Phys. 33 Ž1960. 508. w20x H. Takeo, C. Matsumara, Bull. Chem. Soc. Jpn 50 Ž1977. 636. w21x V. Typke, M. Dakkouri, H. Oberhammer, J. Mol. Struct. 44 Ž1978. 85. w22x J.L. Dehmer, J. Chem. Phys. 56 Ž1972. 4496. w23x A.P. Hitchcock, C.E. Brion, J. Electron Spectry. 14 Ž1978. 417.