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On the application of a modified Sanderson formalism to atomic charge–C 1s binding energy correlation in some aromatic molecules
Journal of Electron Spectroscopy and Related Phenomena 85 (1997) 249–256
On the application of a modified Sanderson formalism to atomic charge–C 1s binding energy correlation in some aromatic molecules Vijaya Patil, Sujit Oke, Murali Sastry* Materials Chemistry Division National Chemical Laboratory, Pune, 411 008 India Received 15 December 1996; accepted 20 January 1997
Abstract The modified Sanderson formalism for calculation of atomic charge in organic molecules has been shown to yield good correlation with core level binding energy (BE) shifts in organic molecules where final state relaxation effects can be neglected. Based on the concept of stability ratios, which is similar to electronegativity, this approach has the advantage of being intuitive in addition to being computationally non-intensive. However, in aromatic molecules where delocalized p electrons can contribute significantly to final-state relaxation energies, no attempt has been made to study whether such a correlation is feasible. In this communication, we seek to study the correlation between the C 1s binding energy (BE) in some aromatic organic molecules and the atomic charge on the carbons determined using the modified Sanderson method. A linear regression curve is found to fit the data satisfactorily with the degree of fit being better than for charges calculated by the MNDO quantum chemical method. There is, however, a difference in the regression curves for aromatic molecules and molecules with carbon in the sp 3-hybridized state (Sastry, J. Electron Spectrosc., in press). If the discrepancy is attributed to final-state core hole relaxation effects, calculated relaxation energies are found to be unphysical. This aspect notwithstanding, the quality of the regression found for aromatic molecules suggests that the modified Sanderson formalism can be applied to aromatic molecules with some care. q 1997 Elsevier Science B.V.
1. Introduction Many important chemical properties of molecules are determined by the charges on the atoms in the molecule, its electronegativity, oxidation state, and the ionicity of its bonds [1]. The concept of effective charge on an atom is of considerable importance in chemistry and consequently many different routes, both experimental [2–4] and theoretical [5–10], have been developed for determination of the atomic charge in molecules. Estimates of the atomic charge may be obtained by experimental methods such as that using the Born–Haber thermochemical cycle [2], from the Racah B and C parameters (restricted to * Corresponding author.
compounds of transition metals) [3], and from studies on IR intensities [4]. Theoretical methods rely mainly on quantum chemical (QC) population analysis, which depend strongly on the wave functions used in the analysis [5–9]. Another quantum mechanical route yields an estimation of the charge from the electrostatic potential in the molecule [10]. As mentioned above, quantum chemical packages depend on the basis set used in the calculation in addition to being computationally intensive. These two aspects make atomic charge determination by the QC route unattractive for the experimental chemist. In the late 1960s, it was realized that core electron ionization energies are directly related to the charge on the atoms and thus contained information regarding the chemical properties of molecules. This led to
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the rapid development and increased interest in X-ray Photoemission Spectroscopy (XPS) which is an ideal tool for measurement of core level ionization energies or binding energies (BE), as they are more popularly known. Thus arose the widely used acronym, ESCA, or Electron Spectroscopy for Chemical Analysis as one major application of XPS. Further understanding of the chemistry responsible for the so-called chemical shifts of core levels with respect to that of a standard showed clearly that there were also direct relationships between core level BEs and the chemical properties of molecules, such as acidity and basicity [11–14]. Many other chemical properties and processes depend on the ability of the molecule to accept charge at specific sites, an aspect which can be studied by ESCA. This chemical specificity of ESCA has led to its widespread use in chemical [1] and biological [15] fields. But before ESCA can be used as a routine tool for determination of atomic charges from core level chemical shifts, an understanding of the physical process responsible for the chemical shifts is important. Determination of a correlation between atomic charge as determined by as simple a methodology as possible and core level BEs for different elements would then follow. The BE of a particular core level in an atom is determined by the nuclear potential experienced by the core electron and the coulomb potential energy due to all other atoms in the molecule or solid (also known as the Madelung energy), if the condensed phase is considered [1,16]. Since BEs measured by XPS are correctly defined as the difference in energies between the final state (N − 1)-electron and initial state N-electron systems [17], relaxation effects arising from screening of the core hole created during photoemission must also be included in the measured BE through a relaxation energy term. This leads to the electrostatic potential model [18] which is written as Ej = kQj + V + Ej0 + ER
(1)
where E j is the measured BE of a given core level in atom j in a molecule, E j 0 is the BE of the core level when the charge Q j is zero (the intercept of the linear regression curve between atomic charge Q j and BE), E R is the relaxation energy arising from screening of the core hole and V is the coulomb potential energy term contributed by all other atoms in the molecule
due to their charge Q l at distances R jl from the atom under consideration, i.e. V = ∑ Ql e2 =R jl
(2)
jÞl
Thus, chemical shifts reveal not only differences in the charge density at a particular site but also on the charges in neighboring atoms. The above equation is based on the assumption that the charges created due to electron transfer during bond formation (and due to extra-atomic screening electron density, where applicable) within molecules can be approximated by point charges centred on the corresponding nuclei, the so-called point-charge model [19]. It has been shown that the point-charge model does not accurately describe the potential due to charges on other atoms due to the oversimplified assumptions on which the model is based [11,19–21]. During the course of this communication, we shall address the contribution of the individual terms in Eq. (1) to the measured core level BEs. Eq. (1) implies that the charge–BE relationship is linear, which is not always the case. This will be addressed below. As mentioned earlier, a simple, mathematically uncomplicated method for calculation of atomic charges in molecules would be of immense use to the experimental chemist. It is in this respect that an alternative approach based on the concept of electronegativity is more appealing. Electronegativity, a concept first introduced by Pauling [22,23], has been used by chemists for many decades now to explain various properties of molecules, with different electronegativity scales currently being in use [24]. Many empirical rules based on the principle of electronegativity equalization [25] have been proposed and have received considerable attention from chemists. Among the empirical approaches for determination of partial charges on atoms based on the above principle, the Jolly and Perry procedure [16], the Partial Equalization of Orbital Electronegativity (PEOE) procedure introduced by Gasteiger and Marsili [26], the method of Full Equalization of Orbital Electronegativity (FEOE) of Mortier et al. [27], and the Sanderson formalism [25] have been used with differing levels of success. Carver et al. [28] proposed a modified Sanderson (MS) approach which could overcome the limitations of the original Sanderson approach, viz., atomic charges for the same element
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in different chemical environments in a molecule were calculated to be the same and the calculation did not differentiate between structural isomers. Carver et al. [28] introduced a group stability ratio to account for such effects and showed that very good correlation with C 1s and O 1s BEs and atomic charge calculated by the MS approach could be obtained for a series of four butanols. They also showed that a better correlation was obtained when the molecular coulomb potential term was not included in the BE calculations, indicating that the modified Sanderson method intrinsically includes the molecular potential. The MS approach was then successfully extended by Gray and Hercules [29] to other elements and it was established that molecular potential correction is automatically achieved in this method. Using the modified Sanderson approach, the Jolly and Perry procedure and ab initio quantumchemical calculations, Linert et al. [30] made a comparative study of the charge distribution in alkylboranes and alkylamines and their adducts with NH 3 and BH 3. They found that only the modified Sanderson approach could successfully predict the expected spillover and pile-up effects at the acceptor and donor atoms, respectively. As far as the atomic charge–BE correlation is concerned, most of the work has centred on carbon, perhaps due to its preeminence in organic systems. As briefly mentioned above, the MS approach applied by Carver et al. yielded a linear charge–BE relationship for carbon [28,29]. Meier and Pijpers found a nonlinear relationship between the Mulliken charge and the C 1s BE in fluorinated methanes [31]. A linear relationship was established by Folkesson and Larsson in other carbon-containing molecules [32,33]. However, in their study of some aromatic molecules, Sundberg et al. found a non-linear relationship to exist between Mulliken charges and C 1s BEs [34]. In an earlier study, one of us applied the MS formalism to linear and branched organic molecules, both in the solid and gaseous phase [35]. It was found that while a linear regression satisfactorily represented the charge–BE relationship, molecules in which carbon was either in the sp 2- or sp-hybridized state deviated significantly from the regression curve. This deviation was tentatively explained as arising due to the extra-atomic screening contribution to the measured BE which would not
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arise for sp 3-hybridized systems. It is this aspect of final state screening which this communication seeks to address through a similar study of some aromatic molecules. Aromatic molecules contain delocalized p electrons which are expected to be efficient in screening the core hole and, hence, relaxation energies must be taken into account before charges can be determined from the measured BEs [11]. We present below details of the study on C 1s BE shifts in some benzene derivatives through the use of the MS formalism for charge calculation. The BE data have been taken from the literature for all the compounds studied.
2. The concept of stability ratio Before proceeding to the MS methodology used in charge calculations, it would not be out of place to briefly review the concept of stability ratio as defined by Sanderson [36]. Arguing that the average electron density (ED), which would be a function of the atomic radius and atomic number, correlates well with many chemical properties of the atom, Sanderson proceeded to develop an "electronegativity" scale based on the compactness of atoms (which the ED reflects) which he termed the "stability ratio" (SR) [36–39]. The SR of an atom/ion was defined as the ratio of the electron density of the atom/ion to the electron density of an isoelectronic inert atom/ion (ED i), real or hypothetical. It was further postulated that an SR of unity represented maximum stability since the inert gas elements would indeed have SRs of unity in this scheme. The carbon SR of 3.79 used in the earlier study [35] is ˚, calculated using a carbon covalent radius of 0.77 A which would be the case when carbon is in the sp 3hybridized form. However, carbon in graphite (sp 2˚ and hybridized state) has a covalent radius of 0.71 A leads to an SR of 4.83. This SR is close to that of chlorine (4.93) which is counterintuitive. Hence, we have calculated a new stability ratio for carbon, 4.31, ˚ , the mean of the two using a covalent radius of 0.74 A radii mentioned above. While this appears to be a rather arbitrary way of determining the SR for carbon in the sp 2 form, it is not wholly unjustified. This new SR, when applied to the charge determination in sp 2and sp-hybridized carbon compounds of the earlier study [35], results in an improvement in the standard
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deviation of the BE energy values from 0.77 to 0.70 eV. In their study of some methyl-substituted derivatives, Gray and Hercules [29] found that correlation of the silicon and germanium charges with BE could be improved by altering the methyl group SR. This led to a modified SR for hydrogen (3.55 to 3.62) but these values resulted in a degradation of the carbon charge– BE correlation [29]. Our approach of using a new stability ratio for sp 2 carbon is, in the spirit of the Sanderson definition, based on covalent radii and is not based solely on improvement in charge–BE correlations. In the calculations on the aromatic compounds presented in this communication, the carbon SR has thus been taken to be 4.31. We mention here that the use of an SR of 3.79 for carbon in the analysis presented below does not lead to a significant deterioration in the quality of the correlation, and all the conclusions with SR = 4.31 are applicable in the former case as well. In the light of the improved correlation for linear molecules using SR = 4.31 (as discussed above), the same SR has been used for aromatic molecules. In spite of the obvious advantages of the Sanderson formalism mentioned above, this analytical route is yet to gain wide acceptance. The method of calculation of atomic charge using the MS approach has been dealt with in detail in an earlier work [35] and will not be repeated here. The determination of partial charges is slightly more complicated where cyclic molecules are concerned. Hence, by way of illustration, we show below how the charges on chlorobenzene can be determined by the MS formalism.
3. Modified Sanderson formalism for cyclic molecules The main problem in cyclic molecules is that there is no way of attaching the tail of a chain to the head to form a ring, as required by the MS formalism. For this purpose, a slightly modified procedure was proposed by Carver and Hercules [29] without changing the basic concept of electronegativity equalization. For chlorobenzene, Scheme 1 illustrates this. The SR of the first carbon atom, i.e. the carbon attached to chlorine is given by SRC1 = (SRC SRCl SRring a SRring b )1=4
(3)
Scheme 1.
where ring a is yCH–CHyCH–CHyCH–and ring b is –CHyCH–CHyCHyCH–CHy. In this procedure for calculating the SR of the ring, one can terminate the procedure after three or four bond lengths since induction effects rarely extend beyond three bond lengths [29]. The partial charge on the carbon is then given as [28,29,35] ]C1 = (SRC1 − SRC )=DSRC
(4)
where DSR C is defined as the change in stability ratio for a complete one-electron transfer for the element under consideration and has been shown to be 2.08 times the square root of the element stability ratio [25]. Using Eq. (3) and Eq. (4) together with the SR values given in Table 1, we have determined the partial charge on carbons in a series of benzene derivatives in the solid condensed phase for which reliable BE data is available in the literature. Table 2 gives a listing of the molecules studied together with the Sanderson partial charge on the carbons and the corresponding BE values taken from the literature [40–43]. We have also performed QC MNDO charge calculations for comparison with the Sanderson charges. These values are also shown in Table 2. We present below the results of the carbon charge– BE correlation analysis. Table 1 Sanderson stability ratios used in atomic charge calculations for this study Element H C N O F Cl
DSR
SR 3.55 4.31 4.49 5.21 5.75 4.93
3.92 4.32 4.41 4.75 4.99 4.62
Stability ratios and normalization factors were taken from [36].
V. Patil et al./Journal of Electron Spectroscopy and Related Phenomena 85 (1997) 249–256
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Table 2 Atomic charges on carbon calculated for aromatic molecules using the modified Sanderson formalism and QC MNDO calculations together with the corresponding BEs taken from the literature
1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Molecule
Sanderson charge
MNDO charge
Binding energy/eV
C 6H 6 C 6Cl 6 C 6F 6 C 6H 12 C 6H 12O 6 C 6O 6 C 6H 5Cl(1) C 6H 5Cl(2) C 6H 5Cl(3) C 6H 5Cl(4) C 6H 5F(1) C 6H 5F(2) C 6H 5F(3) C 6H 5F(4) C 6H 5CH 3(1) C 6H 5CH 3(2) C 6H 5CH 3(3) C 6H 5CH 3(4) C 6H 5CCl 3 (1) C 6H 5CCl 3(2) C 6H 5CCl 3(3) C 6H 5CCl 3(4) C 6H 5CF 3(1) C 6H 5CF 3(2) C 6H 5CF 3(3) C 6H 5CF 3(4) C 6H 5CHCl 2(1) C 6H 5CHCl 2(2) C 6H 5CHCl 2(3) C 6H 5CHCl 2(4)
−0.0924 0.0693 0.1546 −0.1212 −0.0012 0.0990 −0.0149 −0.0668 −0.0830 −0.0868 0.0237 −0.0545 −0.0788 −0.0842 −0.0886 −0.0911 −0.0919 −0.0921 −0.0231 −0.0841 −0.0841 −0.0874 −0.0055 −0.0805 −0.0808 −0.0739 −0.0429 −0.0759 −0.0864 −0.0888
0.0280 −0.0590 0.1350 – – – 0.0007 −0.0396 −0.0562 −0.0504 0.1466 −0.0880 −0.0350 −0.0709 −0.1000 −0.0407 −0.0642 −0.0531 −0.1770 −0.0091 −0.0749 −0.0153 −0.1670 −0.0082 −0.0730 −0.0165 −0.1418 −0.0054 −0.0720 −0.0258
284.9 287.6 289.5 288.4 286.9 288.5 287.1 286.0 285.5 285.3 287.8 285.4 285.9 285.2 286.4 285.1 285.2 284.5 286.6 285.8 285.7 285.2 286.9 286.5 286.0 285.5 286.2 285.5 285.1 284.7
Numbers in parenthesis refer to the position of carbons as per Scheme 1 in the text. Data were taken from the following references: for compounds 1, 7, 11, 15, 19 and 23, from Ref. [40], for compounds 2 and 3, from Ref.[41], data for compounds 5 and 6, Ref.[42], and data for compound 27 were taken from Ref.[43].
4. Results and discussion Fig. 1 shows a plot of the C 1s BEs as a function of the Sanderson partial charge for the data of Table 2. It is seen that a linear regression curve fits the data extremely well, with a small standard deviation of 0.44 eV. The parameters obtained from the fit are shown in the figure. This standard deviation is better than that obtained in the earlier study (0.77 eV) [35]. An interesting clustering of data is observed in Fig. 1 and is indicated by an arrow. By way of comparison, the regression curve (dashed line) obtained from the earlier study of linear and branched organic molecules [35] is also shown for the charges calculated. There is
considerable deviation from this regression curve for many of the data points of Table 2 and thus cannot be considered to be a fair representation of the Sanderson charge–BE relationship in the aromatic molecules of this study. One regression curve for each element would be the ideal situation but it is clear that for carbon, which can exist in different hybridized states, the problem is more complex. Charges on the atoms of the molecules studied were also determined using a QC MNDO package for the PC. Fig. 2 shows the MNDO charge–C 1s BE data given in Table 2. The correlation is much worse than that obtained by charges calculated using the MS method (0.68 versus 0.93) and consequently, the
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Fig. 1. Plot of Sanderson atomic charge versus C 1s BE. Solid line is the fit to the data, while the dashed line is the regression curve using parameters from Ref. [35]. The parameters obtained from the fit are also shown in the figure.
standard deviation in the BE is also poorer (1.35 eV versus 0.44 eV). As for MS charges (Fig. 1), the parameters from the fit are given in Fig. 2. It is clear that the MS approach gives better charge–BE correlations for aromatic molecules. This finding is similar to
those observed by others for many other molecules [28–30]. This finding is particularly surprising for aromatic molecules since the MNDO scheme does take into account electron correlation whereas the MS formalism does not. One would, therefore, expect a better correlation with MNDO charges in molecules where screening would be efficient. The discrepancy between the charge–BE curve obtained and that expected based on the earlier study (Fig. 1) may arise due to different factors, as indicated by Eq. (1). The coulomb potential term, which was not taken into account in the earlier work [35], is known to worsen the correlation as observed by Carver et al. [28] and Gray et al. [29]. The discrepancy mentioned above is not accounted for, nor is the correlation improved if the coulomb potential energy term is included for the benzene derivatives of this study as well, providing further evidence that the MS formalism intrinsically takes this term into account. The calculated charge on the carbons for the benzene derivatives could also be different if the SR for carbon is not correct. But this aspect has been taken into account through a new SR based on the appropriate covalent radius for carbon in such compounds. The most logical reason for the discrepancy is
Fig. 2. Plot of MNDO atomic charge versus C 1s BE. The solid line is a fit to the data. The parameters obtained from the fit are shown in the figure.
V. Patil et al./Journal of Electron Spectroscopy and Related Phenomena 85 (1997) 249–256
that final-state screening effects, which are negligible for sp 3-hybridized carbon systems, are important and must be taken into account. The charge calculated by the MS method for the benzene derivatives does not consider multiple bonding and is based solely on differences in the electronegativities of the constituent atoms. The charge thus calculated should yield a BE corresponding to that predicted for systems with negligible relaxation energies, and any discrepancy between observed and calculated BEs may be attributed to final-state relaxation effects. We proceed tentatively, based on this reasoning, and estimate the relaxation energies for the carbons in the molecules studied. These relaxation energies are determined by taking differences between measured BEs and calculated BEs using a no-relaxation regression curve (dashed line, Fig. 1). But one glance at Fig. 1 shows that this would lead to unphysical negative relaxation energies. The role of screening of the core hole is to reduce the measured BE. This should lead, therefore, to measured BEs for aromatic molecules which are less than those calculated assuming no relaxation effects are operative (using the regression curve of Ref. [35]). This is not the case for 28 of the 30 charges calculated using the MS method (Table 2, Fig. 1). While there will be major differences in the BEs of aromatic molecules due to extra-atomic screening, it is clear that the MS method cannot be used to make an estimation of relaxation energies. Attempts to seek a single regression curve between carbon atomic charge and C 1s BEs using any method are expected to encounter problems due to the different hybridized states in which carbon can exist. Differences do exist in the regression curves for sp 3hybridized carbon and carbon in other hybridizations and, hence, different regression curves need to be applied depending on the situation. It is therefore important to obtain these regression curves for routine use. It is heartening that the MS method, with its inherent simplicity, gives extremely good charge– BE correlation for aromatic molecules as well, albeit with different fitting parameters than those observed for sp 3-hybridized carbon [35]. Hence, the modified Sanderson formalism can be applied to aromatic molecules with some caution. The clustering of data points is an observation which will be dealt with in a later communication where the number of delocalized
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electrons in the molecule is systematically altered, e.g. by intoducing nitrogens into the benzene ring. Another question which one needs to ask is why the MS method leads to unphysical relaxation energies. The use of the MS formalism, which considers charge separation due to electronegativity differences, in situations where final state effects are non-negligible, may not be correct. This also needs further consideration.
References [1] K. Siegbahn, C. Nordling, A. Fahlman, R. Norbert, J. Hedman, G. Johnsson, T. Bergmark, S.E. Karlsson, I. Lindgren, B. Lindberg, ESCA- Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy, Nova Acta Regiae Soc. Sci. Upsaliensis, Ser. IV, Vol. 20. [2] L.A. Maij, Latv. PSR Zinat. Akad. Vestis. Kim. Ser. 3 (1978) 7. [3] K. Jorgensen, Oxidation Numbers and Oxidation States, Springer Verlag, Berlin, 1969, Chapt. 5. [4] M. Gussoni, C. Castiglioni, G. Zerbi, J. Mol. Struct. (Theochem). 138 (1986) 203. [5] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [6] A.E. Reed, R.B. Weinstock, F. Weinhold, J. Chem. Phys. 83 (1985) 735. [7] M.E. Schwartz, J. Am. Chem. Soc. 94 (1972) 6899. [8] R.F.W. Bader, Acc. Chem. Res. 18 (1985) 9. [9] R.J. Meier, A.P. Pijpers, J. Electron Spectrosc. 50 (1990) 129. [10] F.A. Momany, J. Phys. Chem. 52 (1978) 592. [11] T.D. Thomas, M.R.F. Siggel, L.J. Saethre, J. Electron. Spectrosc. 51 (1990) 417. [12] R.S. Brown, A. Tse, J. Am. Chem. Soc. 102 (1980) 5222. [13] S.R. Smith, T.D. Thomas, J. Am. Chem. Soc. 100 (1978) 5459. [14] R.L. Martin, D.A. Shirley, J. Am. Chem. Soc. 96 (1974) 5299. [15] M.M. Millard, in: M. Friedman (Ed.), Advances in Experimental Medicine and Biology, Plenum Press, New York, 1974, Vol. 48, p. 589. [16] W.L. Jolly, W.B. Perry, J. Am. Chem. Soc. 95 (1973) 5442. [17] G. Ertl, J. Kuppers, Low Energy Electrons and Surface Chemistry, VCH Verlagsgesellschaft, Weinheim, Germany, 1985, p. 69. [18] D.T. Clark, in : W. Dekeyser (Ed.), Chemical Aspects of ESCA in Electron Emission Spectroscopy, D. Reidel Publishing Co., Dordrecht, Holland, 1973, p. 373. [19] T.D. Thomas, J. Am. Chem. Soc. 92 (1970) 4184. [20] L.J. Saethre, M.R.F. Siggel, T.D. Thomas, J. Electron. Spectrosc. 49 (1989) 119. [21] L.J. Saethre, M.R.F. Siggel, T.D. Thomas, J. Am. Chem. Soc. 113 (1991) 5224. [22] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, New York, 1960.
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[23] An excellent review of electronegativity and its use in the calculation of atomic charges is given in: K.D. Sen, C.K. Jorgensen, Electronegativity, Springer-Verlag series on Structure and Bonding, Vol. 66, 1987. [24] E. Sacher, J.F. Currie, J. Electron Spectrosc. 46 (1988) 173, and references therein. [25] R.T. Sanderson, Chemical Bonds and Bond Energy, Academic Press, New York, 1976. [26] J. Gasteiger, M. Marsili, Tetrahedron 36 (1980) 3219. [27] W.J. Mortier, K.V. Genechten, J. Gasteiger, J. Am. Chem. Soc. 107 (1985) 829. [28] J.C. Carver, R.C. Gray, D.M. Hercules, J. Am. Chem. Soc. 96 (1974) 6851. [29] R.C. Gray, D.M. Hercules, J. Electron Spectrosc. 12 (1977) 37. [30] W. Linert, V. Gutmann, P.G. Perkins, Inorg. Chim. Acta 69 (1983) 61. [31] R.J. Meier, A.P. Pijpers, J. Electron Spectrosc. 50 (1990) 129.
[32] B. Folkesson, R. Larsson, J. Electron Spectrosc. 50 (1990) 251. [33] B. Folkesson, R. Larsson, J. Electron Spectrosc. 50 (1990) 267. [34] P. Sundberg, R. Larsson, B. Folkesson, J. Electron Spectrosc. 46 (1988) 19. [35] M. Sastry, J. Electron. Spectrosc., in press. [36] R.T. Sanderson, J. Chem. Edu. 29 (1952) 539. [37] R.T. Sanderson, J. Chem. Edu. 31 (1954) 2. [38] R.T. Sanderson, J. Am. Chem. Soc. 105 (1983) 2259. [39] R.T. Sanderson, Inorg. Chem. 25 (1986) 3518. [40] D.T. Clark, D. Kilcast, W.K.R. Musgrave, Chem. Commun. (J. Chem. Soc. Section D) (1971) 516. [41] D.T. Clark, R.D. Chambers, D. Kilcast, W.K.R. Musgrave, J. Chem. Soc. Faraday Trans. II 68 (1972) 309. [42] U. Gelius, P.F. Heden, J. Hedman, B.J. Lindberg, R. Manne, R. Nordberg, C. Nordling, K. Siegbahn, Phys. Scr. 2 (1970) 70. [43] D.T. Clark, D. Kilcast, J. Chem. Soc. A (1971) 3286.
On the application of a modified Sanderson formalism to atomic charge–C 1s binding energy correlation in some aromatic molecules Vijaya Patil, Sujit Oke, Murali Sastry* Materials Chemistry Division National Chemical Laboratory, Pune, 411 008 India Received 15 December 1996; accepted 20 January 1997
Abstract The modified Sanderson formalism for calculation of atomic charge in organic molecules has been shown to yield good correlation with core level binding energy (BE) shifts in organic molecules where final state relaxation effects can be neglected. Based on the concept of stability ratios, which is similar to electronegativity, this approach has the advantage of being intuitive in addition to being computationally non-intensive. However, in aromatic molecules where delocalized p electrons can contribute significantly to final-state relaxation energies, no attempt has been made to study whether such a correlation is feasible. In this communication, we seek to study the correlation between the C 1s binding energy (BE) in some aromatic organic molecules and the atomic charge on the carbons determined using the modified Sanderson method. A linear regression curve is found to fit the data satisfactorily with the degree of fit being better than for charges calculated by the MNDO quantum chemical method. There is, however, a difference in the regression curves for aromatic molecules and molecules with carbon in the sp 3-hybridized state (Sastry, J. Electron Spectrosc., in press). If the discrepancy is attributed to final-state core hole relaxation effects, calculated relaxation energies are found to be unphysical. This aspect notwithstanding, the quality of the regression found for aromatic molecules suggests that the modified Sanderson formalism can be applied to aromatic molecules with some care. q 1997 Elsevier Science B.V.
1. Introduction Many important chemical properties of molecules are determined by the charges on the atoms in the molecule, its electronegativity, oxidation state, and the ionicity of its bonds [1]. The concept of effective charge on an atom is of considerable importance in chemistry and consequently many different routes, both experimental [2–4] and theoretical [5–10], have been developed for determination of the atomic charge in molecules. Estimates of the atomic charge may be obtained by experimental methods such as that using the Born–Haber thermochemical cycle [2], from the Racah B and C parameters (restricted to * Corresponding author.
compounds of transition metals) [3], and from studies on IR intensities [4]. Theoretical methods rely mainly on quantum chemical (QC) population analysis, which depend strongly on the wave functions used in the analysis [5–9]. Another quantum mechanical route yields an estimation of the charge from the electrostatic potential in the molecule [10]. As mentioned above, quantum chemical packages depend on the basis set used in the calculation in addition to being computationally intensive. These two aspects make atomic charge determination by the QC route unattractive for the experimental chemist. In the late 1960s, it was realized that core electron ionization energies are directly related to the charge on the atoms and thus contained information regarding the chemical properties of molecules. This led to
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the rapid development and increased interest in X-ray Photoemission Spectroscopy (XPS) which is an ideal tool for measurement of core level ionization energies or binding energies (BE), as they are more popularly known. Thus arose the widely used acronym, ESCA, or Electron Spectroscopy for Chemical Analysis as one major application of XPS. Further understanding of the chemistry responsible for the so-called chemical shifts of core levels with respect to that of a standard showed clearly that there were also direct relationships between core level BEs and the chemical properties of molecules, such as acidity and basicity [11–14]. Many other chemical properties and processes depend on the ability of the molecule to accept charge at specific sites, an aspect which can be studied by ESCA. This chemical specificity of ESCA has led to its widespread use in chemical [1] and biological [15] fields. But before ESCA can be used as a routine tool for determination of atomic charges from core level chemical shifts, an understanding of the physical process responsible for the chemical shifts is important. Determination of a correlation between atomic charge as determined by as simple a methodology as possible and core level BEs for different elements would then follow. The BE of a particular core level in an atom is determined by the nuclear potential experienced by the core electron and the coulomb potential energy due to all other atoms in the molecule or solid (also known as the Madelung energy), if the condensed phase is considered [1,16]. Since BEs measured by XPS are correctly defined as the difference in energies between the final state (N − 1)-electron and initial state N-electron systems [17], relaxation effects arising from screening of the core hole created during photoemission must also be included in the measured BE through a relaxation energy term. This leads to the electrostatic potential model [18] which is written as Ej = kQj + V + Ej0 + ER
(1)
where E j is the measured BE of a given core level in atom j in a molecule, E j 0 is the BE of the core level when the charge Q j is zero (the intercept of the linear regression curve between atomic charge Q j and BE), E R is the relaxation energy arising from screening of the core hole and V is the coulomb potential energy term contributed by all other atoms in the molecule
due to their charge Q l at distances R jl from the atom under consideration, i.e. V = ∑ Ql e2 =R jl
(2)
jÞl
Thus, chemical shifts reveal not only differences in the charge density at a particular site but also on the charges in neighboring atoms. The above equation is based on the assumption that the charges created due to electron transfer during bond formation (and due to extra-atomic screening electron density, where applicable) within molecules can be approximated by point charges centred on the corresponding nuclei, the so-called point-charge model [19]. It has been shown that the point-charge model does not accurately describe the potential due to charges on other atoms due to the oversimplified assumptions on which the model is based [11,19–21]. During the course of this communication, we shall address the contribution of the individual terms in Eq. (1) to the measured core level BEs. Eq. (1) implies that the charge–BE relationship is linear, which is not always the case. This will be addressed below. As mentioned earlier, a simple, mathematically uncomplicated method for calculation of atomic charges in molecules would be of immense use to the experimental chemist. It is in this respect that an alternative approach based on the concept of electronegativity is more appealing. Electronegativity, a concept first introduced by Pauling [22,23], has been used by chemists for many decades now to explain various properties of molecules, with different electronegativity scales currently being in use [24]. Many empirical rules based on the principle of electronegativity equalization [25] have been proposed and have received considerable attention from chemists. Among the empirical approaches for determination of partial charges on atoms based on the above principle, the Jolly and Perry procedure [16], the Partial Equalization of Orbital Electronegativity (PEOE) procedure introduced by Gasteiger and Marsili [26], the method of Full Equalization of Orbital Electronegativity (FEOE) of Mortier et al. [27], and the Sanderson formalism [25] have been used with differing levels of success. Carver et al. [28] proposed a modified Sanderson (MS) approach which could overcome the limitations of the original Sanderson approach, viz., atomic charges for the same element
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in different chemical environments in a molecule were calculated to be the same and the calculation did not differentiate between structural isomers. Carver et al. [28] introduced a group stability ratio to account for such effects and showed that very good correlation with C 1s and O 1s BEs and atomic charge calculated by the MS approach could be obtained for a series of four butanols. They also showed that a better correlation was obtained when the molecular coulomb potential term was not included in the BE calculations, indicating that the modified Sanderson method intrinsically includes the molecular potential. The MS approach was then successfully extended by Gray and Hercules [29] to other elements and it was established that molecular potential correction is automatically achieved in this method. Using the modified Sanderson approach, the Jolly and Perry procedure and ab initio quantumchemical calculations, Linert et al. [30] made a comparative study of the charge distribution in alkylboranes and alkylamines and their adducts with NH 3 and BH 3. They found that only the modified Sanderson approach could successfully predict the expected spillover and pile-up effects at the acceptor and donor atoms, respectively. As far as the atomic charge–BE correlation is concerned, most of the work has centred on carbon, perhaps due to its preeminence in organic systems. As briefly mentioned above, the MS approach applied by Carver et al. yielded a linear charge–BE relationship for carbon [28,29]. Meier and Pijpers found a nonlinear relationship between the Mulliken charge and the C 1s BE in fluorinated methanes [31]. A linear relationship was established by Folkesson and Larsson in other carbon-containing molecules [32,33]. However, in their study of some aromatic molecules, Sundberg et al. found a non-linear relationship to exist between Mulliken charges and C 1s BEs [34]. In an earlier study, one of us applied the MS formalism to linear and branched organic molecules, both in the solid and gaseous phase [35]. It was found that while a linear regression satisfactorily represented the charge–BE relationship, molecules in which carbon was either in the sp 2- or sp-hybridized state deviated significantly from the regression curve. This deviation was tentatively explained as arising due to the extra-atomic screening contribution to the measured BE which would not
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arise for sp 3-hybridized systems. It is this aspect of final state screening which this communication seeks to address through a similar study of some aromatic molecules. Aromatic molecules contain delocalized p electrons which are expected to be efficient in screening the core hole and, hence, relaxation energies must be taken into account before charges can be determined from the measured BEs [11]. We present below details of the study on C 1s BE shifts in some benzene derivatives through the use of the MS formalism for charge calculation. The BE data have been taken from the literature for all the compounds studied.
2. The concept of stability ratio Before proceeding to the MS methodology used in charge calculations, it would not be out of place to briefly review the concept of stability ratio as defined by Sanderson [36]. Arguing that the average electron density (ED), which would be a function of the atomic radius and atomic number, correlates well with many chemical properties of the atom, Sanderson proceeded to develop an "electronegativity" scale based on the compactness of atoms (which the ED reflects) which he termed the "stability ratio" (SR) [36–39]. The SR of an atom/ion was defined as the ratio of the electron density of the atom/ion to the electron density of an isoelectronic inert atom/ion (ED i), real or hypothetical. It was further postulated that an SR of unity represented maximum stability since the inert gas elements would indeed have SRs of unity in this scheme. The carbon SR of 3.79 used in the earlier study [35] is ˚, calculated using a carbon covalent radius of 0.77 A which would be the case when carbon is in the sp 3hybridized form. However, carbon in graphite (sp 2˚ and hybridized state) has a covalent radius of 0.71 A leads to an SR of 4.83. This SR is close to that of chlorine (4.93) which is counterintuitive. Hence, we have calculated a new stability ratio for carbon, 4.31, ˚ , the mean of the two using a covalent radius of 0.74 A radii mentioned above. While this appears to be a rather arbitrary way of determining the SR for carbon in the sp 2 form, it is not wholly unjustified. This new SR, when applied to the charge determination in sp 2and sp-hybridized carbon compounds of the earlier study [35], results in an improvement in the standard
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deviation of the BE energy values from 0.77 to 0.70 eV. In their study of some methyl-substituted derivatives, Gray and Hercules [29] found that correlation of the silicon and germanium charges with BE could be improved by altering the methyl group SR. This led to a modified SR for hydrogen (3.55 to 3.62) but these values resulted in a degradation of the carbon charge– BE correlation [29]. Our approach of using a new stability ratio for sp 2 carbon is, in the spirit of the Sanderson definition, based on covalent radii and is not based solely on improvement in charge–BE correlations. In the calculations on the aromatic compounds presented in this communication, the carbon SR has thus been taken to be 4.31. We mention here that the use of an SR of 3.79 for carbon in the analysis presented below does not lead to a significant deterioration in the quality of the correlation, and all the conclusions with SR = 4.31 are applicable in the former case as well. In the light of the improved correlation for linear molecules using SR = 4.31 (as discussed above), the same SR has been used for aromatic molecules. In spite of the obvious advantages of the Sanderson formalism mentioned above, this analytical route is yet to gain wide acceptance. The method of calculation of atomic charge using the MS approach has been dealt with in detail in an earlier work [35] and will not be repeated here. The determination of partial charges is slightly more complicated where cyclic molecules are concerned. Hence, by way of illustration, we show below how the charges on chlorobenzene can be determined by the MS formalism.
3. Modified Sanderson formalism for cyclic molecules The main problem in cyclic molecules is that there is no way of attaching the tail of a chain to the head to form a ring, as required by the MS formalism. For this purpose, a slightly modified procedure was proposed by Carver and Hercules [29] without changing the basic concept of electronegativity equalization. For chlorobenzene, Scheme 1 illustrates this. The SR of the first carbon atom, i.e. the carbon attached to chlorine is given by SRC1 = (SRC SRCl SRring a SRring b )1=4
(3)
Scheme 1.
where ring a is yCH–CHyCH–CHyCH–and ring b is –CHyCH–CHyCHyCH–CHy. In this procedure for calculating the SR of the ring, one can terminate the procedure after three or four bond lengths since induction effects rarely extend beyond three bond lengths [29]. The partial charge on the carbon is then given as [28,29,35] ]C1 = (SRC1 − SRC )=DSRC
(4)
where DSR C is defined as the change in stability ratio for a complete one-electron transfer for the element under consideration and has been shown to be 2.08 times the square root of the element stability ratio [25]. Using Eq. (3) and Eq. (4) together with the SR values given in Table 1, we have determined the partial charge on carbons in a series of benzene derivatives in the solid condensed phase for which reliable BE data is available in the literature. Table 2 gives a listing of the molecules studied together with the Sanderson partial charge on the carbons and the corresponding BE values taken from the literature [40–43]. We have also performed QC MNDO charge calculations for comparison with the Sanderson charges. These values are also shown in Table 2. We present below the results of the carbon charge– BE correlation analysis. Table 1 Sanderson stability ratios used in atomic charge calculations for this study Element H C N O F Cl
DSR
SR 3.55 4.31 4.49 5.21 5.75 4.93
3.92 4.32 4.41 4.75 4.99 4.62
Stability ratios and normalization factors were taken from [36].
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Table 2 Atomic charges on carbon calculated for aromatic molecules using the modified Sanderson formalism and QC MNDO calculations together with the corresponding BEs taken from the literature
1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Molecule
Sanderson charge
MNDO charge
Binding energy/eV
C 6H 6 C 6Cl 6 C 6F 6 C 6H 12 C 6H 12O 6 C 6O 6 C 6H 5Cl(1) C 6H 5Cl(2) C 6H 5Cl(3) C 6H 5Cl(4) C 6H 5F(1) C 6H 5F(2) C 6H 5F(3) C 6H 5F(4) C 6H 5CH 3(1) C 6H 5CH 3(2) C 6H 5CH 3(3) C 6H 5CH 3(4) C 6H 5CCl 3 (1) C 6H 5CCl 3(2) C 6H 5CCl 3(3) C 6H 5CCl 3(4) C 6H 5CF 3(1) C 6H 5CF 3(2) C 6H 5CF 3(3) C 6H 5CF 3(4) C 6H 5CHCl 2(1) C 6H 5CHCl 2(2) C 6H 5CHCl 2(3) C 6H 5CHCl 2(4)
−0.0924 0.0693 0.1546 −0.1212 −0.0012 0.0990 −0.0149 −0.0668 −0.0830 −0.0868 0.0237 −0.0545 −0.0788 −0.0842 −0.0886 −0.0911 −0.0919 −0.0921 −0.0231 −0.0841 −0.0841 −0.0874 −0.0055 −0.0805 −0.0808 −0.0739 −0.0429 −0.0759 −0.0864 −0.0888
0.0280 −0.0590 0.1350 – – – 0.0007 −0.0396 −0.0562 −0.0504 0.1466 −0.0880 −0.0350 −0.0709 −0.1000 −0.0407 −0.0642 −0.0531 −0.1770 −0.0091 −0.0749 −0.0153 −0.1670 −0.0082 −0.0730 −0.0165 −0.1418 −0.0054 −0.0720 −0.0258
284.9 287.6 289.5 288.4 286.9 288.5 287.1 286.0 285.5 285.3 287.8 285.4 285.9 285.2 286.4 285.1 285.2 284.5 286.6 285.8 285.7 285.2 286.9 286.5 286.0 285.5 286.2 285.5 285.1 284.7
Numbers in parenthesis refer to the position of carbons as per Scheme 1 in the text. Data were taken from the following references: for compounds 1, 7, 11, 15, 19 and 23, from Ref. [40], for compounds 2 and 3, from Ref.[41], data for compounds 5 and 6, Ref.[42], and data for compound 27 were taken from Ref.[43].
4. Results and discussion Fig. 1 shows a plot of the C 1s BEs as a function of the Sanderson partial charge for the data of Table 2. It is seen that a linear regression curve fits the data extremely well, with a small standard deviation of 0.44 eV. The parameters obtained from the fit are shown in the figure. This standard deviation is better than that obtained in the earlier study (0.77 eV) [35]. An interesting clustering of data is observed in Fig. 1 and is indicated by an arrow. By way of comparison, the regression curve (dashed line) obtained from the earlier study of linear and branched organic molecules [35] is also shown for the charges calculated. There is
considerable deviation from this regression curve for many of the data points of Table 2 and thus cannot be considered to be a fair representation of the Sanderson charge–BE relationship in the aromatic molecules of this study. One regression curve for each element would be the ideal situation but it is clear that for carbon, which can exist in different hybridized states, the problem is more complex. Charges on the atoms of the molecules studied were also determined using a QC MNDO package for the PC. Fig. 2 shows the MNDO charge–C 1s BE data given in Table 2. The correlation is much worse than that obtained by charges calculated using the MS method (0.68 versus 0.93) and consequently, the
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Fig. 1. Plot of Sanderson atomic charge versus C 1s BE. Solid line is the fit to the data, while the dashed line is the regression curve using parameters from Ref. [35]. The parameters obtained from the fit are also shown in the figure.
standard deviation in the BE is also poorer (1.35 eV versus 0.44 eV). As for MS charges (Fig. 1), the parameters from the fit are given in Fig. 2. It is clear that the MS approach gives better charge–BE correlations for aromatic molecules. This finding is similar to
those observed by others for many other molecules [28–30]. This finding is particularly surprising for aromatic molecules since the MNDO scheme does take into account electron correlation whereas the MS formalism does not. One would, therefore, expect a better correlation with MNDO charges in molecules where screening would be efficient. The discrepancy between the charge–BE curve obtained and that expected based on the earlier study (Fig. 1) may arise due to different factors, as indicated by Eq. (1). The coulomb potential term, which was not taken into account in the earlier work [35], is known to worsen the correlation as observed by Carver et al. [28] and Gray et al. [29]. The discrepancy mentioned above is not accounted for, nor is the correlation improved if the coulomb potential energy term is included for the benzene derivatives of this study as well, providing further evidence that the MS formalism intrinsically takes this term into account. The calculated charge on the carbons for the benzene derivatives could also be different if the SR for carbon is not correct. But this aspect has been taken into account through a new SR based on the appropriate covalent radius for carbon in such compounds. The most logical reason for the discrepancy is
Fig. 2. Plot of MNDO atomic charge versus C 1s BE. The solid line is a fit to the data. The parameters obtained from the fit are shown in the figure.
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that final-state screening effects, which are negligible for sp 3-hybridized carbon systems, are important and must be taken into account. The charge calculated by the MS method for the benzene derivatives does not consider multiple bonding and is based solely on differences in the electronegativities of the constituent atoms. The charge thus calculated should yield a BE corresponding to that predicted for systems with negligible relaxation energies, and any discrepancy between observed and calculated BEs may be attributed to final-state relaxation effects. We proceed tentatively, based on this reasoning, and estimate the relaxation energies for the carbons in the molecules studied. These relaxation energies are determined by taking differences between measured BEs and calculated BEs using a no-relaxation regression curve (dashed line, Fig. 1). But one glance at Fig. 1 shows that this would lead to unphysical negative relaxation energies. The role of screening of the core hole is to reduce the measured BE. This should lead, therefore, to measured BEs for aromatic molecules which are less than those calculated assuming no relaxation effects are operative (using the regression curve of Ref. [35]). This is not the case for 28 of the 30 charges calculated using the MS method (Table 2, Fig. 1). While there will be major differences in the BEs of aromatic molecules due to extra-atomic screening, it is clear that the MS method cannot be used to make an estimation of relaxation energies. Attempts to seek a single regression curve between carbon atomic charge and C 1s BEs using any method are expected to encounter problems due to the different hybridized states in which carbon can exist. Differences do exist in the regression curves for sp 3hybridized carbon and carbon in other hybridizations and, hence, different regression curves need to be applied depending on the situation. It is therefore important to obtain these regression curves for routine use. It is heartening that the MS method, with its inherent simplicity, gives extremely good charge– BE correlation for aromatic molecules as well, albeit with different fitting parameters than those observed for sp 3-hybridized carbon [35]. Hence, the modified Sanderson formalism can be applied to aromatic molecules with some caution. The clustering of data points is an observation which will be dealt with in a later communication where the number of delocalized
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electrons in the molecule is systematically altered, e.g. by intoducing nitrogens into the benzene ring. Another question which one needs to ask is why the MS method leads to unphysical relaxation energies. The use of the MS formalism, which considers charge separation due to electronegativity differences, in situations where final state effects are non-negligible, may not be correct. This also needs further consideration.
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[23] An excellent review of electronegativity and its use in the calculation of atomic charges is given in: K.D. Sen, C.K. Jorgensen, Electronegativity, Springer-Verlag series on Structure and Bonding, Vol. 66, 1987. [24] E. Sacher, J.F. Currie, J. Electron Spectrosc. 46 (1988) 173, and references therein. [25] R.T. Sanderson, Chemical Bonds and Bond Energy, Academic Press, New York, 1976. [26] J. Gasteiger, M. Marsili, Tetrahedron 36 (1980) 3219. [27] W.J. Mortier, K.V. Genechten, J. Gasteiger, J. Am. Chem. Soc. 107 (1985) 829. [28] J.C. Carver, R.C. Gray, D.M. Hercules, J. Am. Chem. Soc. 96 (1974) 6851. [29] R.C. Gray, D.M. Hercules, J. Electron Spectrosc. 12 (1977) 37. [30] W. Linert, V. Gutmann, P.G. Perkins, Inorg. Chim. Acta 69 (1983) 61. [31] R.J. Meier, A.P. Pijpers, J. Electron Spectrosc. 50 (1990) 129.
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