Shifts of the 3p213 ene;.·gy levels of germanium in different
chemical moieties were studied by using the semiempirical SCC-MO
method. The calculations were performed within the framework of
the electrostatic potential method in the point-charge approximation.
Relaxation energies were explicitly taken into account by
employing the equivalent core and transition potential methods. It
was found out that the relaxation energy plays a decisive role in
determining shifts along the series GeH4--+ Ge(CHak The results
obtained by the equivalent core and transition potential methods
are similar being in the same time in good agreement with experiment.
Performance of various semiempirical schemes in evaluating
ESCA shifts is briefly discussed

K. Rupnik

Z. B. Maksić

English

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CROATICA CHEMICA ACTA CCACAA 53 (3) 413-418 (1980) CCA-1218 YU ISSN 0011-1643 UDC 541 :539.19 Original Scientific Paper Semiempirical Studies of Inner-Core Energy Levels. Part 7. ESCA Shifts of Germanium in Molecular Systems z. B. Maksic* Organisch- Chemisches Institut der Universitiit, Im Neuenheimer Feld 270, D-69 Heidelberg 1, BR Deutschland and K. Rupnik Theoretical Chemistry Group, »Ruder Boskovic« Institute, 41001 Zagreb, Yugoslavia Rece ived April 28, 1980 Shifts of the 3p213 ene;.·gy levels of germanium in different chemical moieties were studied by using the semiempirical SCC-MO method. The calculations were performed within the framework of the electrostatic potential method in the point-charge approxi-mation. Relaxation energies were explicitly taken into account by employing the equivalent core and transition potential methods. It was found out that the relaxation energy plays a decisive role in determining shifts along the series GeH4--+ Ge(CHak The results obtained by the equivalent core and transition potential methods are similar being in the same time in good agreement with experi-ment. Performance of various semiempirical schemes in evaluating ESCA shifts is briefly discussed. X-ray photoelectron spectroscopy proved to be a useful tool in studying molecular properties in gas1, liquid2 and solid phase3. It is also a convenient technique for discussing bonding features in polymers4 chemisorption and physisorphon phenomena5,6, homogenous catalysis7 etc. An a priori treatment of the photoionization process is rather complicated because it includes l'1. SCF calculation for each ionized atom in a molecule with explicit consideration of the relativistic and cor relation effects. Consequently, it is feasible for small molecules. We have shown in a series of papers8 that the self-consistent charge molecular orbital (SCC-MO) method in conjunction with simple electro-static potential successfully accounts for the changes in core energy levels for the first and second row atoms. Additional advantage of this approach is its ease and wide applicability to large compounds of biochemical interest9 . It is the aim of this work to show that the method can be extended to heavy atoms possessing large number of electrons. In particular, we discuss here ESCA shifts of germanium 3pa12 levels in different chemical environments. All studied molecules are in vapour state. * On leave of absence from Theoretical Chemistry Group, »Ruder Boskovic« Institute, 41001 Zagreb, Yugoslavia and the Faculty of Natural Sciences, The Univer-sity of Zagreb, Marulicev trg 19, 41000 Zagreb, Yugoslavia 414 Z. B. MAKSIC AND K. RUPNIK Our approach is well documented by now10• Briefly, ESCA chemical shifts are related to ground state gross valence electrons atomic charges via the equation /).BEA= kl QA+ ks};' (ZB - 2- QB)/RAB + k4 B (1) where the ionized atom is deliberately denoted by A and the sum goes over all other atoms B rf A. The adjustable empirical parameters are found by fitting the experimental innner-shell energy shifts employing the least-squares method. The second term in eq(l) is called Madelung energy and it will be abbreviated hereafter as M. By switching on and off the weighting factor k3 we can examine the importance of M which, in turn, explicitly involves the structural characteristics of the studied molecule. The corresponding models using the sets of parameters (k1 , k3 = 0, k4) and (k1 , k3 rf 0, k4 ) are denoted by Q and Q + M, respectively. Since in eq(l) is taken into account only the initial state this approach is termed ground state potential model (GPM). The energy of the relaxation process accompanying photoionization is to some extent absorbed in the weighting factors ki (i = 1, 3, 4). The GPM method is sufficient for first row atoms with very few exceptions8• However, the effect of the final (ionic) state can be explicitly taken into account by using the transition potential10 or equivalent core11 methods. The transition potential formalism is based on the idea that both initial and final states could be incorporated in the transition operator. This procedure retains an appealing feature of the Koopman's theorem that only one calculation per atom is needed because the reorganization energy is implicitly included in transition operator's eigenvalues. The ESCA shifts are then given in the point-charge electrostatic potential approximation by L\ BE A (t) = kl (t) QA* (t) + k3 (t) };' (ZB - 2 - QB (t))/RAB + k4 (t) (2) B where the gross valence electrons charges refer to a molecule possessing a pseudoatom A*. Its atomic parameters are arithmetic means of the values corresponding to atoms with nuclear charges ZA and ZA + 1. According to the equivalent core concept valence electrons adjust upon the ejection of a core electron as if the nuclear charge of the ionized atom would be increased by a unit and the inner-shell is completed by an additional electron. The resulting electrostatic potential formula is of the form L\ BEA (e.c.) = k1 (e.c.) [;A QA + ;A+i QA (e.c.)] + + k3 (e.c.) [MA+ MA+i (e.c.)] + k 4 (e.c.) (3) where /;A is Slater effective nuclear charge ZA - SA and SA is a screening constant. It arises due to the one-center integrals of the llr operator. The entities QA (e. c.) and MA+1 (e. c.) are obtained for the equivalent core calculation which is executed for the ground state molecular geometry. It is tacitly assumed here that nuclei are too inert to follow the relaxation of the electronic cloud. This is in most cases justified. The experimental ESCA shifts for germanium are not very abundant12• The calculated values for seven different molecules obtained by using eqs(l-3) INNER-CORE ENERGY LEVELS 415 TABLE I Comparison Between the Calculated ESCA Shifts of Germanium 3p312 Levels as Obtained by the SCC-MO Ground State Potential, Transition Potential and Equivalent Cores Approaches and the Corresponding Experimental Data• Molecule QGP (Q+M)GP QTP (Q+M)TP (Q+M)Ec Exp. GeH4 -1.0 -1.0 -1.1 -1.8 -1.8 -1.29 GeHsCHs -1.4 -1.4 -1.1 -1.0 -1.1 -0.88 Ge(CHa)4 -2.3 - .-2.4 -1.1 0.1 0.0 0 GeF4 -5.6 -5.6 -5.9 -5.9 -5.9 -5.71 GeH3Cl -1.6 -1.6 -1.5 -2.5' -2.5 -2.19 GeCl4 -2.8 -2.8 -4.0 -3.4 -3.3 -4.08 GeHsBr -1.3 -1.3 -1.2 -1.7 -1.7 -2.0 standard deviations present results 1.2 1.2 0.6 0.4 0.4 EHT" 1.2 1.0 CND0/2• 0.5 0.5 • Experimental data are taken from ref. 12. and SCC-MO semiempirical wavefunctions* are displayed in Table I. One observes that the relaxation energy plays a dominant role in determining the Ge 3p312 level shifts. This is apparent in the series Ge(CH3) 4 , GeH3CH, and GeH4 where the GPM approach fails to reproduce the experimental trend. The explicit inclusion of the relaxation puts the calculated values on line with the measured data. An analysis in terms of the germanium effective charges and Madelung contribution to the 3p3; 2 level shifts is illuminating. They are compared with the corresponding entities appearing in equivalent core and transition potential methods in Table II. It is apparent that the Ge ground state effective charges increase along the series GeH4 , GeH3CH3 and Ge(CH3) 4 because the methyl group is in this case a better electron acceptor than hydrogen. By using the simple concept that a larger effective TABLE II Comparison Between the Ground State Effective Charges of Ge and Madelung Term and the Corresponding Entities Appearing in Equivalent Core and Transi tion Potential Methods" Molecule q(SCC) q(e.c.) q(t.p.) M M(e.c.) M(t.p.) GeH4 0.16 0.35 0.35 -0.10 0.10 0.10 GeHsCHs 0.24 0.37 0.34 --0.14 0.08 0.08 Ge(CHs)4 0.46 0.43 0.36 - 0.23 0.01 0.05 GeF, 1.20 1.27 1.27 -0,72 -0.47 -0.46 GeHsCl 0.28 0.43 0.43 -0.14 0.06 0.06 GeCl4 0.56 0.63 0.62 -0.26 -0.06 -0.06 GeHsBr 0.22 0.38 0.38 -0.12 0.08 0.08 • Effective atomic charge is defined as qA = ZA - n - QA where n is a number inner-core electrons and QA is gross valence electrons atomic charge. The average effective atomic charge in equivalent core method is given by qA (e.c.) = (qA (e.c.) + q (SCC))/2. Effective charges and Madelung terms are measured in ! e I and eV, respectively. * Simple sp basis set was employed. 416 Z. B. MAKSIC AND K. RUPNIK positive charge means lesser electron repulsion on the host atom one can deduce that the 3p312 level in Ge(CH3 ) ., is lower than in GeH, and GeH3 CH0 • Contradiction with the experiment indicates that relaxation energy changes are responsible for the ESCA shifts. This is obvious from the results of the equivalent core and transition potential calculations (Table II). The charges q(e.c.) and q(t.p.) again change in the wrong direction but the differences are considerably less pronounced. On the other hand, the relaxation due to the flow of charge involved in the Madelung term overcompensates the one-center contributions of the Ge atoms and ste>.bilizes GeH3CH3 and GeH, levels r elative to that in Ge(CH3) ., establishing a semiquantitative agreement with experi-mental measurements: The rest o:[ the data for GeF4 , GeH3Cl, GeCl, and GeH3Br are compatible with the simple rule of thumb that a larger effective positive charge qGe causes lower 3p,,12 levels, the most stable one being that in GeF,. It is of some interest to compare our results with earlier findings of Perry and Jolly12. Their EHT calculations exhibit the same standard devi-ation of 1.2 eV for the the GPJ.\II approach but the relaxation process is much better described by the SCC-MO method (Table I) . The CND0/2 results are not improved by the inclusion of the relaxation energy but the GPM results were already quite good (a - 0.5 eV) what is comparable with the standard deviation of our SCC-MO RP approach (a - 0.4 eV). Good performance of the CND0/2 method is probably a consequence of the special parametrization adopted by Perry and Jolly in their attempt to encompass the atoms of the second and third rows12 • Namely, CND0/2 results are generally inferior to the SCC-MO ones for the first row atoms8 . The possible reasons are briefly discussed at the end of this section. It is worth to mention that the equivalent core and transition potential methods yield similar results (Tables I and II) as could be anticipated on the basis of a general analysis of Goscinski and Siegbahn13 . The trend observed in this family of compounds parallels that found in a series of alkanes11 • Pireaux et al.14 established experimentally that binding energies decrease with an increase in number of carbon atoms in linear n-alkanes CnHcn+ 2 - The whole range of the shifts is, however, small (0.6 eV). Ab initio calculations employing ST0-4.31 G basis set have shown that the net charges of the central carbon atoms slightly increase along the series14. Since the binding energies decrease it m eans that the simple rule of thumb does not work here exactly as in the case of methylated germanes. The changes in BE are apparently governed here by the relaxation energies. Indeed, CND0/2 calculations using transition potential formalism as well as 11 SCF ab initio equivalent core treatment have shown that changes in Ma-delung potentials, caused by the creation of a positive hole, are responsible for the observed trend14• It should pointed out, however, that in both calcu-lations the relaxation energies had to be scaled by using a factor of 0.5 in order to restore the agreement between the theory and experiment. This is not surprising because the ab initio /1 SCF calculations were executed emplo-ying poor minimum ST0-3G basis set while it is known that the basis sets close to the double zeta quality ar e a necessary prerequisite for obtaining reasonable estimates of relaxation energy15. Our search through the literature revealed also that CND0/2 gives good ESCA shifts for a particular series of molecules if the adjustable parameters in the electrostatic formula are specially fitted for this purpose. However, these p arameters widely differ from one series to another. Hence the general performance of the CND0/2 INNER- CORE ENERGY LEVELS 417 method is not satisfactory. This can be ascribed to some inherent inconsistencies of this semiempir:cal scheme which in fact has not the proper theoretical structure while for example SCC-MO method does have it16. To conclude, the rule of thumb, according to which the higher net charge of the host atom corresponds to the increased inner-shell binding energy, is a good qualitative criterion if relatively large differences in charge along the series of compounds are expected. It fails, however, if the net charges of the atom suffering the ionization differ ·only slightly while in the same time more and more atoms participate in the relaxation process. Finally, it should be stressed that the procedure adopted in this paper is only a model which mimics the more rigorous SCF treatment. It is ba:sed on the fictitious concept of point charge and its success lies in a fact that the 1/r operator is insensitive to the finer details of the electronic charge distribution17•18 . Similar insensitivity of the one one-electron operator, which are otherwise extremely delicate probes of the electron charge density in various regions of molecules, was observed for second moments and the related diamagnetic part of the magnetic susceptibility19•20 . The latter can be also satisfactorily accounted for by the point charge approximation. Acknowl edgment. - One of us (Z. B. lVI.) w ould like to thank Alexander von Humboldt Foundation for research felloship and Professor R. Gleiter for his hospitality and encouragement. We are grateful to the referee for calling to our attention ref. (14). REFERENCES 1. K. Siegbahn, C. Nordling, G. Johansson, J. Hedman, P. F. He d en, K. H a m r in, U. G e 1 i us, T. B erg mark, L. 0 . W er me, R. Manne, and Y. Baer. ESCA AppLied to Free Molecules, North H olland, Amsterdam, 1969. 2. H . S i e g b a h n, L. Asp 1 u n d, P . Ke 1 f v e, and K. S i e g bah n, J . El. Spectry. Rel. Phenom., 7 (1975) 411 and the references cited therein. 3. U . Ge 1 i us, P . F . He den, J. He cl man, B. J. Lin dberg, R. Manne, R. Nord b erg, C. No rd 1 i n g, and K. S i e g b ah n, Phys. Ser. 2 (1970) 70. 4. J. De 1ha 11 e, J. M. Andre, S. De 1ha11 e, J . J. Pi re aux, R. Ca u-d an o, and J. J. Ver b is t, J. Chem. Phys. 60 (1974) 595. 5. A. F. Car 1 e y, R. W. J o y n er, and M. W. R o b er t s, Chem. Phys. Lett. 27 (1974) 580. 6. B. Gu m ha 1 t er, J. Phys. C: Solid State Phys. 10 (1977) L 219; B. Gum ha 1-t er, Surface Sci . 80 (19'79) 459. 7. C. And e rsson and R. Larsson, Chem. Ser. 11 (1977) 140 and the refe-rences cited therein. 8. Z . B. M a ks i c and K. Ru p n i k, Croat. Chem. Acta 50 (1977) 307; Z. B. Maks i c, K. Ru p n i k, and M. Eck ert - Ma ks i c, J. El. Spectry. Rel. P henom. 16 (1979) 371; Z. B . 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Ca u d an o, and K. Sieg b ah n, Phys. Rev. A 14 (1976) 2133. 15. D. T. Clark, B. J. Crom arty, and A. Sgamellotti, J. EL Spectry. Rel. Phenom. 13 (1978) 85; ibid. 17 (1979) 149 and the references cited therein. 16. D. B. Cook, P. C. Hollis, and R. McWeeny, MoZ. Phys. 13 (1967) 553; F. Dries s 1 er and W. Kutz e 1 n i g g, Theor. Chim. Acta 43 (1977) 307. 17. B. J. Rosenberg and I. Shavitt, J . Chem. Phys. 63 (1975) 2162; c. F. Jack e 1 s and E. R. Davidson, J. Chem. Phys. 63 (1975) 4672. 18. H. F. Schaefer, III, The Electronic Structure of Atoms and Molecules, Reading, Mass., Addison-Wesley, 1972. 19. Z. B. Maks i c and N. Mika c, Chem. Phys. Lett. 56 (1978) 363; J. Mol. Struct. 44 (1978) 255. 20. Z. B. Maks i c and N. Mika c, MoZ. Phys. 40 (1980) 455. SAZETAK Semiempirijski studij energijskih razina elektrona unutrasnjih ljuski. Dio 7. ESCA pomaci 3p3/2 razina germanija u molekularnim sustavima z. B . Maksic i K. Rupnik Pomaci energijskih 3p312 razina germanija u molekularnim sustavima razmatrani su primjenom semiempirijske metode samousaglasenog naboja (SCC-MO). Raeuni su izvrseni u okviru modela elektrostatskog potencijala u priblizenju tockastog naboja. Relaksacijske energije uzete su eksplicite u obzir koristenjem metoda ekvi-valentnih jezgri i prelaznog potencijala. Ustanovljeno je da relaksacijske energije imaju odlucujucu ulogu u odredivanju ESCA pomaka u nizu GeH4 -+ Ge(CH3) 4• Rezultati dobiveni metodama ekvivalentnih jezgri i prelaznog potencijala su u dobrom slaganju s eksperimentalnim podacima. ORGANISCH-CHEMISCHES INSTITUT DER UNIVERSITXT IM NEUENHEIMER FELD 270 D-69 HEIDELBERG 1 BR DEUTSCHLAND I GRUPA ZA TEORIJSKU KEMIJU INSTITUT •RUDER BOSKOVICc, 41001 ZAGREB JUGOSLAVIJA Prispjelo 28. travnja 1980. 

Semiempirical Studies of Inner-Core Energy Levels. Part 7. ESCA Shifts of Germanium in Molecular Systems

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