A theoretical and experimental study of the carbon 1s shake-up structure of benzene

Volume 54. number 3

15 March 1978

CHEMICAL PHYSICS LETTERS

A THEORETICAL

AND EXPERIMENTAL

STUDY

OF THE CARBON

Is SHAKE-UP STRUCTURE OF BENZENE

S LUNELL Department of Quantum Chemists. S-752 20 Uppsala. Sweden

Uppsala Unnerstty,

and

S. SVENSSON, P-A- MALMQVIST, U. CELIUS, hstitute

E. BASILIER and K. SIECBAHN

of Physics. Uppsala Unir ersity. S-751 21 Uppsaala,Sweden

Received 5 December 1977

The shake-up structure of the carbon Is electron hnc in the spectrum of benzene has been studied by ESCA in high resolution and also theoretically, by means of the Pariser-Parr-Pople (PPP) method, Including configuration interaction (CI). The calculated positions of the different shake-up lines relative to the main peak are Found to be in surprisingly good agreement with eupenment, the errors in excitation energies being a few per cent in all cases. On the basis of the calculations all observed imes in the spectrum can be assigned to excitations in the x system of the ionized molecule. 1

l_ Introduction in high resolution ESCA experiments, the lines arising from inner shell ionization are observed to have a satellite structure, usually of considerably smaller intensity than the main line [l] _Such satellite lines are considered to arise from combined ionization-excitation processes, so-called “shake-up” processes, where the inner shell ionization is dccompanied by a simultaneous excitation in the valence shell. Recent ab initio calculations on small molecules containing Ir-electrons [2,3] as well as experimental experience [4] have shown that the shake-up spectrum is dominated by excitations of the type z + II*, even when the ?r system is very small, such as in formaldehyde or formamide. One can assume that this will be true to a still larger extent in the shake-up spectrum for molecules with a larger number of n-electrons, for example benzene and other aromatic mde-

cules. For such molecules, ab initio calculations of the same quality as e.g. those in refs. [2,3], would require significant amounts of computer capacity, and must at present be considered as rather large undertakings. A fast but reliable semi-empirical method for the calcula420

tion of shake-up energies and, if possible, intensities

would therefore be desirable, and, for larger molecules, even necessary. The currently available all-valence-electron semiempirical methods have in general not yet reached such an accuracy that they can be used with confidence to calculate energies of excited states of arbitrary molecules. On the other hand, if one is interested in a more limited class of compounds, higher accuracy may be achieved. This is the case of planar, aromatic molecules, where the well-known Pariser-Parr-Pople (PPP) method [S] has been developed specifically to describe

excitations within the R system. If configuration interaction between all singly excited configurations is included, experience shows that good accuracy is obtained in the prediction of UV spectra of these classes of molecules. In view of what was said in the previous paragraph, the PPP method would therefore seem well suited to calculate shake-up states in aromatic systems_

This hypothesis has been tested in the present paper.

CHEMICAL PHYSKS

Volume 54. number 3 2. Computational

2.1. Wavefunctions

method

and energies

The calculations were done using the variant of the PPP method developed at the University of Stockholm by Fischer-Hjalmars, Roos, and co-workers [6] _ For details about the method as well as a large number of applications the reader is referred to the original papers [6] - The calculations were done on the neutral molecule and on the equivalent core species, i.e., C,H,NH’. This implies that in the final state only those doublets which can he derived from a singlet coupled valence shell are calculated to have non-zero probability. Inherent in the equivalent core approximation is thus the assumption that no significant mixing occurs between doublets of singlet and triplet “parentage”_ This assumption was found to be true for most, but not all, shake-up states in refs. [2,3] , and should become more accurate for larger s systems. This is also confirmed by the present results. Configuration interaction (CI) between all singly excited configurations was used in the calculations on the excited states. For comparison, also single configuration results are included, although these are well

known to be less accurate than the CI results.

15 March 1978

LE-lTERS

is used in the PPP method. As pointed out by FischerHjaimars 181, the ZDO approximation should be interpreted as rf the basis orbitals are orthogonalized atomic orbitals (OAO’s), obtained from the ordinary atomic orbitals by a symmetric orthonormalizatron [9] M x,=~~~~(S-“*)~~,

-

p=

l,___, M.

Here, {x,] are the OAO’s, (0,) the original atomic orbitals, S the overlap matrix of the atomic orbitals, and M the number of atoms. From (2) it can be seen that a replacement of one of the atomic orbitals ~111 affect not only the OAO which is centered on the same atom, but also all the other OAO’s. This has to be accounted for when calculating the overlap between initial and final state wavefunctions. The equivalent core approximation means that the nuclear charge of the ionized atom is increased by one, whereas the others are unchanged. As discussed above, however, this will change the entire OAO basis in the ionized molecule rather than just one basis function. Before calculating the overlap integrals entering expression (l), it is therefore convenient to make a reverse transformation back to the original atomic orbital basis. That is, if the orbit& obtained from the PPP calculations have the form

2.2. Intensities In the sudden approximation [7] the intensity a given shake-up line is proportional to

(3)

of

(1) where 90 is the wavefunction of the N - 1 remaining electrons in the neutral molecule, and &nh is the (IV 1)electron wavefunction of the n,th state of the ionized system (cf. also ref. [2]). In the present case a “frozen orbital” approximation is used, in the sense that the u-skeleton of the ionized molecule is assumed to be the same for the ground and all shake-up states of the ionized molecule. The relative intensities of the different lines are then obtained from (1) with ip,-, and Fx equal to the n-electron wavefunctions for the initial and final states, respectively. The overlap integral in (1) is then easily calculated as a determinant of overlap integrals or a sum of such determinants. There is one comp!ication, however, arising from the zero differential overlap (ZDO) approximation, which

one can write

where the coefficients basis is given by

in the original

atomic

orbital

M

(5) The atomic orbitals in (4) can be approximated by ordinary Slater-type orbit&, giving well defined overlap integrals that can be calculated with standard programs. These can then be used to calcuiate the probability (I).

421

CHEMICAL PHYSICS LETTERS

Volume 54, number 3

The C 1s shake-up spectrum from benzene in the gas phase was recorded on the high-resolution ESCA instrument using monochromatized X-ray radiation [lo]. The samples were commercially obtained and of 99.9% purity grade. The pressure in the sample compartment was held at 13 Pa which was sufficiently low to make contributions to the spectrum from melastically scattered electrons negligible. This was checked by making a separate recording dt a higher pressure. No important changes occurred in the spectrum.

4. Results and discussion PPP orbita& and Cl coefficients for the ionized system are given in tables 1 and 2, using the symmetry labeling appropriate to the equivalent core species

orbitals for a benzene molecule with a Is-hole, obtained by the PPP methoda)

Symmetry desknation

Ibt

2bt

la2

orbital energy (eV) Cit Ct2

-19 054

-16.2299

-15.5162

Cl3 Ck

Cl5 Cifi

0 6608 0.4015 0.2959 0.2567 0.2959 0.4015

-0.5634 -0.0278 0.4152 0 5800 0.4152 -0.0278

a) The atomic orbit& arc numbered consecutively

Table 2 CI coefficients

0 -0.5161 -0.4834 0 0.4834 0.5161

2a2

4’a

-5.6991

-4.2717

-1.6347

-0.4595 0.4754 0.1105 -0.5590 0.1105 0.4754

0 -0.4834 0.5161 0 -0.5161 0.4834

-0.1867 0.3347 -0.4773 0.5342 -0.4773 0.3347

around the ring, startins with the ionized atom.

for the t At cvcited states of the ionized benzene molecule

Configuration a)

2bl 4 3bl la2 -f 2a2 lb1 + 3bt 2bl+ 4bl lb1 -4bt

State 1

2

3

4

0.8983 -0.3772 0.2216 0 0379 0.0161

0.3915 0.9196 -0.0247 0.0192 -0.0047

-0.1969 0.1034 0.9384 0.2489 -0.0898

0.0066

-0.0309

-0.0293 -0.2462 09670 0.0587

0.0215 0.0956 -0.0352 0.9941

a) The designation 2bl - 3bt means that one of the 2bt orbitals in the (Ibl)2(2br)Z(laz)Z by a 3bl orbital, and the unpaired spins are ccupled to a singlet.

422

March 1978

(C2,,). The ground state orb&Is for the neutral benzene molecule, which are used in calculating the intensities, are entirely determined by symmetry in this case. In table 2 only final states of A, symmetry are included, since these are the only ones which can be observed, according to the monopole selection rule given by eq. (1). Table 3 gives the energies and intensities of the different shake-up lines obtained with and without CI, as well as the experimental values. A comparison between the theoretical (CI) and experimental excitation energies shows a very satisfactory agreement for all the strong bands (see table 3 and fig. I)- The largest errors arise for the excitations of highest energy, which is entirely to be expected in any !imited CI calculation involving a minimal basis set. Apart from the highest transition, which is off by about 12%, the position of the remaining peaks relative to the main peak is correctly predicted within 25%.

3. Experimental

Table 1 Occupiedand unoccupiedmoleculx

15

5

ground state of the ion is substituted

Volume 54, number 3

15 March 1978

CHEMICAL PHYSICS LETTERS

TabIe 3 Comparison of theoreticA and experlmental results for K-shell hole states and satellites in benzene State

Without Cl

Assignment (cf. table 2)

energy

b)

intensity

a)’

(eV)

1

‘(2bI --) 3bl)

2 3 4 5

*(la;?-+2aa) I(lb I-L%) ‘(2bl -+4br) ‘(lb, A4bl)

6.18 6.76 8.68 9.18 12.09

a) In % of the main peak area. b) Relative to main lime at Eg = 290

14 0.2 7 0.7 0.1

energy b)

intensity”)

5.92 6 87 8.76 9.2i 12.13

intensitya)

(eW 7 4 11 0.03 0.4

5.9 7.0 8.3

2 6 3

10.7

1

42 eV.

GH, 13s

Experiment energyb)

(eV)

Shake-up intensities are-well-known to be extremely sensitive to the details of the wavefunctions Ill] , and can hence not be expected to be very accurately determined in a calculation of the present type. This expectation is confirmed by the results of table 3, which shows that the intensities in most cases are wrong by a factor 3-4 and in a non-systematic manner. Even though the calculated intensities hence must be looked at rather sceptically, they do single out three lines as being dominant in the shake-up spectrum. namely those arising from the 2b 1 + 3b 1, 1a2 + 2a2, and 1bl + 3bl excitations, and place these at energies where strong shake-up lines indeed are observed_ The lb 1 + 4b 1 satellite is predicted to be weaker, but

I

With CI

shake-up spectrum

la,-20,

Fig. 1. Experimental C 1s shake-up spectrum of benzene. Calculated positions of the different shake-up hnes are indicated by arrows.

is also found in an energy region where other excitation processes

may be expected

to become

significant.

The 2b, * 4b, satellite predicted at 9.21 eV is calculated to have very small intensity, and would not be easy to detect in the experimental spectrum, where it would be covered by the tail of the lb1 --f 3bl peak at 8.3 eV. A slight asymmetry of the latter peak may, however, confirm its presence. it can be noticed that the intensities are much more affected by the CI than the energies are. Tne single configuration calculation thus incorrectly predicts the la2 + 2a2 sate!lite to have virtually no intensity, in marked contrast to the CI result. This phenomenon has been noticed also in ab initio calculations [ Ill_

5. Conclusion The application of the PPP Cl method for calculating the carbon 1s shake-up structure in the ESCA spectrum of benzene has given surprisingly good results, especially for the positions of the different shake-up peaks. The method thus seems to be suited for such calculations on aromatic molecules which are too large for ab iniiio calculations. As more experimental high resolution ESCA spectra become available, the usefulness of the method can be tested on a larger number of systems. If a similar accuracy is obtained also in these cases, the PPP CI method will prove to be a valuable, yet relatively simple and very inexpensive, tool for interpreting and predicting shake-up structures in aromatic molecules_

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Volume 54. number 3

CHEMICAL

PHYSICS

References [ 1] K. Siegbahn, C. Nortiling, G. Johansson. J_ Hedman. P.F. Hed&, K. Hamrm, U. Gelius, T. Bergmark, L-0. Wcrme, R. Manne and Y. Baer. ESCA ,rpphed to free molecules (North-Holland, Amsterdam, 1969). [2] H. Basch, Chem. Phys. 10 (197.5) 157. [3] H. Basch, Chem. Phys. Letters 37 (1976) 447. [4] D.T. Clark, A. Dilks, J. Peeling and -H-R. Thom,rs, Faraday Discussions Chem. Sot. 60 (1975) 183; S. Lunell, S. Svensson. P-A hlAmqvisr, E. Basdier and K. Siegbahn, unpublished results. [S] R. Pariser and R-G. Parr, J. Chem. Phys. 21 (1953) 466, 767; J.A. Pople, Trans. fxaday Sot. 49 (1953) 1375.

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LETTERS

15 March 1978

(61 B. Roos and P.N. Skancke, Acta Chem. Stand. 21 (1967) 233; B. Roos. ActaChem. Stand. 21 (1967) 2318; I. Fischer-Hjalmars and hl. Sundbom, Acta Chem._Scand. 22 (1968) 607. [7J T. Aberg, Ann. Acad. Sci. Fenn. A6 (1967) 308. [8] I. Fischer-Hjaimars. J. Chem. Phys. 42 (1965) 1962. (91 P--O. Ldwdm, J. Chem. Phys. 18 (1950) 365. [lo] U. Gelius, E. Basilier. S. Svensson. T. Bergmark and K. Siegbahn, J. Electron Spectry. 2 (1974) 405. [ 1 I] S. Svensson, H. Xgren and U-1. Wahlgren. Chem. Phys. Letters 38 (1976) 1.