Effective atomic charges and charge transfer after photoionization in sulfur compounds and phosphorus compounds

JOURNAL OF ELECTRON SPECTROSCOPY and RelatedPhenomena

ELSEVIER

Journal of Electron Spectroscopyand Related Phenomena69 (1994) 149-157

Effective atomic charges and charge transfer after photoionization in sulfur compounds and phosphorus compounds V.I. Nefedov*, V.G. Yarzhemsky Institute of Generaland Inorganic Chemistry,Russian Academyof Sciences,Moscow,RussianFederation First received28 July 1993;in final form 4 January 1994

Abstract

The effective charges, extra-atomic relaxation energy and Madelung potentials are determined in some sulphur and phosphorus compounds using experimental values and calculations. The charge transfers after photoionization are calculated using a transition state model. The charge transfer is proportional to the polarizability of the neighbor atom for the atom under investigation. The extra-atomic relaxation energy for the ls level is about 0.5-1.0 eV larger than that for 2p level. The effective atomic charges and Madelung potentials are in good agreement with existing theoretical calculations. The obtained data are checked by the independent determination of the effective atomic charges from Madelung potentials for AXn-type molecules. Keywords." Charge transfer; EARE; Effective atomic charge; Model; Phosphorus compound; Sulphur compound

1. Introduction In a previous paper [1] the effective atomic charges q, extra-atomic relaxation Re and Madelung potentials M were determined using the following set of three equations for the core level binding energy E2p (Eq. (1)), Auger transition energy EKLL (Eq. (2)) and K a line shift AEK~ (Eq. (3)) in chemical compounds. E2p = E2p(q ) + M - R2pe

(1)

EKLL = EKLL(q) -- 2 M + 3Rzpe

(2)

AEKa = Els(q ) -- E2p(q ) -- E~a

(3)

Here Ei(q) is the photoionization energy of the ith * Corresponding author.

level in the ion with the effective charge q and E ~ is the value in the element from which the shift is measured. Equation (3) is obtained from Eq. (1) and a similar equation for the ls level setting M2p = Mls

(4)

R2pe -- Rise = Re

(5)

Equations (4) and (5) are exact when the point charge approximation is used for the wavefunctions of the core levels. For example, in the case of the ith core level for the Coulomb integral in SF 6 with F2p wavefunctions one obtains

I ¢2riFl~b2F2pdT-~- I rs-Fl¢2F2pdT ~- r~-~

0368-2048/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0368-2048(94)02188-6

(6)

150

V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157

where rSF is the distance between S and F atoms in SF 6. Similarly for the Coulomb integral between the ith core in the S atom and the S3p wavefunction one obtains

values q, Aq, M, Rls e and R2pe using experimental values E 2 p , E/eLL and AEK~ as in Ref. 1, but without the use of the approximate Eq. (5).

2. Theory I

2 -1 2 ~i ri3p~bS3pd~- -= (rfflp)

(7)

where (rff~p) is the average reciprocal radius of the S3p electron. Using Eq. (6) the relation (4) can be proved. Using Eq. (7) and the expression (8) for the Re value in the transition state model the relation (5) can also be proved. The transition state model can take the relaxation energy into account for the photoionization of core electrons without calculation of the total energies for initial and final states. The electrostatic potential for the core electron changes from the initial to the final state when the mean potential value corresponding to the photoionization of the half of the core electron (which is called the transition state) is used for the calculation of the binding energy. This energy is very close to the value obtained by the difference of total energies in the initial and the final states. The relaxation energy is connected with the potential change between the initial and the transition states [2,3]. For the sake of simplicity Eq. (8) (see Appendix for derivation of Eq. (8)) is written for the SF 6 molecule assuming charge transfer Aq from the F2p to the S3p level after photoionization of the ith core level to be given by the formula

Rie=(I/2)Aq[I~b~r~s~p~3pdT--I~b2iriF~p~bF2pdT" ] - 0.5Aq[(r~-31p) - Rff~]

(8)

The point charge approximation is expected to be a good approximation for the wavefunction of the core level. However the direct calculation of the Coulomb integrals in Eqs. (6) and (7) had shown this approximation to be really good in the case of Eq. (6) but some differences are found in the case of Eq. (7) for i = ls and 2p levels in the atoms from Na to CI. The aim of this paper is to determine the

Equations (1) and (2) are used as in Ref. 1, but Eq. (3) is no longer valid because Eq. (5) is not used. The K a transition takes place between two states with a hole in an inner level, i.e. the charge transfer Aq due to the extra-atomic relaxation is already completed. Instead of Eq. (3) one obtains

AEI~ = Els(q-

Aq) - g2p(q - Aq) - E ~

(9)

The extra-atomic relaxation should also be taken into account for the K a value EKe(0) in the free element. Some arguments which will be presented below are in favor of Aq ~ 0.9 in $8 and P4, which are taken as initial points for the determination of K a line shifts in chemical compounds. Now the connection between R2pe and Aq will be derived. Using Eqs. (1) and (2) one obtains R2pe = 0.5[E~p(q) - 2E2p(q) - all

(10)

where al = EI~ - g 2 p - EK/~Lis the experimental value of the Auger parameter, which is taken from Ref. 1. Equation (10) coincides with Eq. (13) in Ref. I, but is valid for R2pe and not for Rise. The extra-atomic relaxation is connected with the charge transfer Aq to the ionized atom from the others. In the case of the free AX n molecule (for example SF6) , the charge transfer goes from the F2p orbitals mainly to S3p and to a lesser extent to S3s orbitals. When the latter contribution is omitted, the simple Eq. (11) can be written for the connection between Aq and R2pe in the framework of the transition state model (see Eqs. (8) and (10)) Aq = [g2p(q) - 2g2p(q ) -- oQ]/(E2pp, - RA1) (ll) where RAX is the interatomic distance between atoms A and X in molecule AXn; E2pp, represents the interaction of the valence p' electron of the

V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157 atom A with the X2p electron for an average of states configuration E2pp'

=

F°(2pp ') - (1/6)G°(2pp ') - (1/15)G2(2pp ')

(12)

where F °, G ° and G 2 correspond to the Coulomb and exchange integrals. Note that according to the transition state model these integrals are calculated for the ions with valence charge ( q - Aq/2) and with the potential corresponding to the presence of the half hole of the 2p electron, i.e. these integrals are found by the interpolation of the calculated values for the ions of atom A with different valence charges q with one and no hole present in the 2p shell. Equation (9) was used to find ( q - Aq) in the compound under consideration. E(q) values are calculated in Ref. 1. Using this ( q - Aq) value together with Eq. (l 1), q and Aq values are found. The g E p e values can be calculated from Eq. (10) or from the equation similar to that for the Else value in the transition state model (Eq. (13)) (compare with Eq. (8)) Rise = 0.5Aq[Els p, - RA1]

(13)

where Elsp, = F ° ( l s p ') - (1/6)G 1(lsp'). It is also possible to calculate Rlse without the transition state model, when R2pe is known. For this purpose the binding energy of the core electron is represented in the form

Ei = Ei(q - Aq) + M'

(14)

where M t = M in Eq. (1), but M~ = Mj, i = ls and j = 2p (see Eq. (4)). Combining Eqs. (1) and (14) for i = ls and 2p one obtains Rise = R2pe + [Els(q) - E2p(q)] - [Els(q - Aq) - E2p(q - Aq)]

(15)

The experimental values are taken to be the same as in Ref. 1. The integrals are calculated with the Hartree-Fock functions. The values obtained are given in Tables 1 and 2. The values q and Aq are given for two values of charge transitions A q 0 = 0 . 6 and Aq0 = 0.9 in $8 and P4. The values q and Aq do

151

not depend critically on the Aq0 values. The value Aq0 ----0.9 is preferred both for $8 and for P4. Some additional arguments for Aq0----0.9 are given below. The charge transfer Aq after photoionization can also be calculated in the point charge approximation using Eq. (8). The charge transfer to 3s orbitals can be taken into account, when the average (rv l) between r31 and r3s1 is considered Aq = 2Rea/[(rv 1) - R ~ ]

(16)

In the transition state, which corresponds to the photoionization of one half of the core electron, using the equivalent core approximation one should replace atom A(Z) by A'(Z + 0.5). In the compounds of the 3rd Period the rv 1 values for v = 3s differ slightly from that for v = 3p. Although this difference is not important and one can take (rAlv)= (rA13p) or (rAlv)= 1/2[(rA]3p ) + (rAlas)] , we believe that the following expressions for AX, compounds with maximal oxidation number of the atom A to be more realistic: (rAlv) = 0.65(rA13p) + 0.35(rAjas )

(17)

and for the other compounds of AXn-type (rA,lv) = 0.75(rAlap) + 0.25(rAlas)

(18)

The expressions (15) and (16) take into account the contribution of partial charges q3s and q3p to the total charge qA as follows from general considerations and analysis of MO LCAO contributions. In many cases there is no averaging problem for rAlv values. For example, for neutral or negatively charged atoms such as CI in C12 or in NaCI, S in $8 or H2S the charge transfer takes place to A3p orbitals only, because 3s orbitals are completely filled. On the contrary in Na metal the charge transfer is to the A3s orbitals. Expression (16) is valid for the free molecules AX n with equivalent X ligands, i.e. SF6, SiF4, PC13. We can extend the validity of this equation to the molecules with slightly different X ligands such as SF4 or PF 5 averaging over different interatomic distances RA-X and charges qx and q~. The further extension of Eqs. (11), (13) and (16) can be achieved for molecules of the type AXnYt, where X

V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157

152

Table 1 Effective atomic charges q/a.u., charge transfers Aq/a.u., extra-atomic relaxation energy Rie/eV and Madelung potential M eV in phosphorus compounds Molecule

PC13 SPC13 OPC13 PF 3 SPF 3 OPF3 PF 5

qa

0.78 1.01 1.08 1.18 1.55 1.55 1.75

Aq0 = 0.6

Aq0 = 0.9

q

Aqb

qmad

q

Aqb

Aqe

R2pe

R~de

Rise d

Rise e

M

1.42 1.82 1.89 1.79 2.37 2.30 2.51

0.95 1.08 1.08 0.87 1.03 0.96 0.96

1.24 1.80 1.79 1.48 2.37 2.09 2.35

1.28 1.70 1.78 1.68 2.30 2.23 2.44

0.92 1.07 1.07 0.85 1.04 0.97 0.85

0.77 0.86 0.84 0.67 0.81 0.84

5.23 6.13 5.82 4.08 5.38 4.66 4.90

5.16 6.26 5.75 4.14 5.24 4.73 4.90

5.80 6.90 6.61 4.71 6.32 5.53 5.84

6.20 7.31 7.00 5.02 6.59 5.79 6.06

-8.78 -13.10 -14.15 -13.69 -21.21 -20.07 -21.84

aFrom Ref. 1. bEq. (11). CEq. (16). dEq. (15). *Eq. (13).

and Y are atoms. In these cases averaging over A - X and A - Y interatomic distances is necessary. For more complicated molecules such as P(OCH3) 3 or crystals such as SiO2 and NaCI, Eqs. (8) or (16) cannot be directly applied, because in these cases we have several unknown values AqL corresponding to the different L atoms outside the first coordination sphere. The general expression for Re has the form Re = 0.5Aq(rAlv) --

~-~(L)(AqL/RA_L)

Re = 0.5Aqmin(rA,lv)

(20)

The simplification corresponds to the situation in metals. For example, the Na atoms (or Na + ions) are equivalent in the metal lattice relative to the free electron gas. Each Na atom participates with the same AqL value in the charge transfer Aq to the photoionized A atom from free electron gas. The average R~,IL value is large and the second number in the right hand part of Eq. (19) can be neglected. Equation (20) is similar to that proposed in Ref. 4 for the calculation of R e values in metals when Aq = 1. The Aqmax value can be calculated when we set

(19)

~--~(L)AqL = 1/2AqL Equation (19) can be used for the calculation of two limiting values Aqmin and Aqmax. Aqmin can be calculated when we set

Re = 0.5Aqmax[(rAlv) -- R1-1]

(21)

Table 2 Effective atomic charges q/a.u., charge transfers Aq/a.u., extra-atomic relaxation energy Rie/eV and Madelung potential M eV in sulfur compounds Molecule

SOC12 SO2 SOF 2 SO2C1: SF4 SO2C1F SO2F2 SFsC1 SF6

qa

0.93 1.21 1.43 1.59 1.73 1.85 1.86 1.95 2.18

Aqo = 0.6

Aqo = 0.9

q

Aq b

qmad

q

Aq b

Aqc

R2pe

R~pde

Rise d

Rlse e

M

1.35 1.58 1.91 2.23 2.27 2.47 2.47 2.61 2.77

0.79 0.71 0.78 0.92 0.80 0.86 0.85 0.90 0.81

1.05 1.30 1.72 2.35 2.26 2.64 2.40 2.74 2.88

1.21 1.46 1.81 2.15 2.19 2.40 2.40 2.55 2.72

0.77 0.68 0.77 0.93 0.80 0.87 0.86 0.91 0.83

0.66 0.60 0.63 0.75 0.68 0.75 0.74 0.82 0.80

4.74 3.59 4.37 5.72 4.86 5.28 4.95 5.79 5.13

4.93 3.91 4.21 5.56 4.51 5.20 4.85 5.80 5.45

5.64 4.41 5.33 6.90 5.90 6.42 6.08 7.00 6.25

5.24 4.10 5.02 6.58 5.63 6.16 5.83 6.76 6.07

-8.34 -13.04 -16.21 -20.51 -20.49 -24.35 -23.63 -24.00 -26.59

a From Ref. 1. b Eq. (11). c Eq. (16). d Eq. (15). e Eq. (13).

V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157

153

Table 3 Aqmiu, Aqmax and Aqz+l valuesa; the atom under investigation is underlined Compound

Aqmin/a.u.

Aqmax/a.u.

Compound

Aqmin/a.u.

Aqz+l/a.u.

Aqmax/a.u.

Na Mg a

1.01 1.1(p) 0.75(s)

(1.0) (1.0)

NaSiF6 CsPF6

0.55 0.56

0.64 0.65

0.96 0.95

A1 Si S NaC1 KC1

1.01 0.78 0.61 0.20 0.20

(1.0) (1.0) 0.93 0.25 0.26

Li3AIF6 Li4SiO4 Na3PO4 Na2SO4 Na2SO3

0.58 0.60 0.63 0.56 0.56

0.58 0.64 0.66 0.84 0.97

(1.0) (1.0) (1.0) (1.0) 0.98

a See text.

where R1 is the interatomic distance between atom A and the atoms in its first coordination sphere. In this case all the charge transfers AqL from distant atoms have been attributed to the atoms with minimal value R, which lead to the maximal Aq values. This boundary case with some exceptions is not of much use, because the calculated Aqmax values are too large, i.e. larger than unity, which is a natural limit for Aqmax based on the physical meaning of Aq values. The calculated Aq, Aqmin and Aqmax values (Eqs. (16), (20), (21)) are given in Tables 1-3. The Aq values have also been calculated for some other atoms in chemical compounds. These values are equal to 0.83 and 0.69 for the Si atom in SiC14 and SiF4, 0.30 and 0.14 for the CI atom in C12 and HC1. When the calculated Aqmax value was larger than unity, the value 1.0 is given in parentheses. The Re values for these calculations are taken from Ref. 1. The values (rA,lv) are found by interpolation using Hartree-Fock values for free atoms and ions [5]. The experimental interatomic distances R are used.

qp corresponding to the 3s and 3p electrons in the compounds under investigation in this paper. As has been already mentioned in Ref. 1 the qs and qp values have approximately the same influence on the energy characteristics as AEK~ and AE2p of the inner electrons. That is why within the present approach only the determination of the total charge q = qs + qp is possible. This charge is of interest for the quantitative description of the core level properties, for the evaluation of the Madelung potential as well for the determination of the accepter properties of the ligands around the atom under investigation. The effective charges of sulfur and phosphorus atoms in free molecules determined in this paper

qth

16

20

24

au

PF5 o

o SPF3

3. Discussion

3.1. The effective charges q We begin with some remarks concerning the physical nature of the effective charges q. The detailed description of the chemical bonding implies knowledge of the effective charges qs and

16

20

24 au

q

Fig. 1. The correlation between experimental atomic effective charges q (this work) and theoretical values qth [6].

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V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157

are about 25% higher than the values found in Ref. 1 where the approximation (5) was used. There is a good linear correlation between these two sets of q values, which is why the regularities obtained for the effective charges in Ref. 1 are preserved, i.e. the experimental effective charges correlate with calculated ones, and the binding energy of the inner electron depends approximately linearly on the effective charge of the atom under investigation. As an example of such correlations, in Fig. 1 the correlation between experimental q values from this work and theoretical q values from Ref. [6] is presented for phosphorus compounds.

3.2. Charge transfer Aq after photoionization The charge transfers Aq are calculated in two different ways for the molecules and the values presented in Tables 1 and 2 show a good correlation. This can be considered as an additional proof of the reliability of the values obtained. In the case of phosphorus compounds some Aq values are larger than unity. This result could be connected both with the errors in values used and with the limitations of the theory. As was expected the Aq values increase with the increase of extraatomic relaxation Re. Due to this relationship the main properties of Aq values, i.e. dependence on the nature of atom X in AXn molecules, follow the same pattern as R e values, as discussed in Ref. 1. The additivity for Aq values can also be proved in the case of the point charge approximation for Aq values. The increments for H, F, CI and O atoms are equal to 0.170, 0.156, 0.207 and 0.236 for Si, P, S and C1 compounds of the AXn type. The correlation between Aq and qad values can be essentially improved if the different increments are considered for different elements and the oxidation numbers of the element A are also taken into account, but the known number of the Aq values is not large enough for such detail. Now we consider the cases where some independent estimation of Aq values can be obtained. In the case of the metals we expect the Aq value to be not far from unity, because a comparatively complete screening of the core hole is expected. This is really what takes place for metals Na, Mg and A1, where the Aq values are around 1.0

(Table 3). In the non-metallic elements such as Si, $8 Aq values are smaller than in metals. In the metals Na and A1 the charge is transferred to the 3s and 3p shell respectively. The situation in Mg metal needs some comment. In a formal way it is the 3p shell which is expected to be filled, but in this case Aqmin = 1.1 (Table 3). The difference from the unity is small and can be explained by the simplifications involved in Eq (20). However it is also reasonable to assume partial ionization of the Mg3s shell in Mg metal. If the Mg3s shell is filled, Aqmin is equal to 0.75. The partial filling of the Mg3s shell after photoionization of the Mg atom in the metal explains why Aqmin(P) > 1. In NaCl and KCI Aq is expected to be around 0.23 (Table 3) (the Aq value should be even smaller than 0.23, because of the extra-atomic relaxation in ionic crystals partly caused by the polarization (see Appendix); however the polarization of Na + and K + ions is small). While the effective charge of Cl ion should be equal to -0.87 [1] in these crystals, the 3p shell is completely filled after photoionization. This is also expected for the Ar atom to which the Cl ion in the Z + 1 approximation transforms after photoionization in KC1 or NaCl crystal. The 3p shell is not however completed in the C1 atom after photoionization in C12 or HC1, because this result is not expected for the initial state of ArCl + and ArH +. The Z + 1 approximation is also useful for the estimation of Aq values based on the experimental qA values in the isoelectronic series of the type AlE 3-, SiF 2- and PF6-. When the anion glF~- is considered as completely isolated in a crystal, it corresponds to the anion SiF62- after photoionization of A1. The effective charges of A1 in AIF 3- and Si in SiF 2- are equal to 1.05 and 1.47 respectively [1]. The corresponding charge transfer in Aqz+IAIF63- is equal to 0.58. The values Aqz+l in Table 3 calculated from data in Ref. 1 are between Aqmin and Aqmax. The values Aqz+l could not be considered as experimental values of Aq, because anions such as SO]- or SiF 2- are not completely isolated in crystals. After photoionization of the central atom in SO~- or SiF6zaccording to the Z + 1 approximation one should consider anions CIO4 or PF 6 in Na2SO 4 or Na2SiF 6 crystals. This is not equivalent to the

V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157

anions CIO; or PF6 in NaC104 or NaPF 6 crystals. Nevertheless the correspondence found between Aqmin, Aqz+l and Aqmaxvalues is further support for the calculated Aq values. The Aq data in Tables 1-3 suggest the value Aq = 0.9 for $8 and P4. Indeed, the Aq value for $8 must be larger than for SO2, because two S atoms attached to the ionized S atom in $8 must result in a larger charge transfer than two O atoms in SO2. According to similar arguments, Aq must be larger in P4 than in PCI 3. As was mentioned above, the Aq and q values in the compounds investigated do not depend critically on the Aq0 value (Tables 1 and 2), which is why the choice of the value Aq0 = 0.9 is justified. 3.3. Extra-atomic relaxation energy

According to Eqs. (13) and (15) Rl~ > R2pe

(22)

because Elsp, > E2pp, and Els(q)- E2p (q) > EI~ (q - Aq) - E2p(q - Aq). The results of calculations using Eqs. (13) and (15) are in good agreement for Rlse values. The data given by Eq. (13) are about 0.2-0.4eV higher than those calculated by Eq. (15) (Tables 1 and 2). The results of Eq. (15) seem to be more exact, because the transition state model is not involved directly. We do not know any experimental literature

20 Mth

pFo

eV

155

data for the relationship of the type (22) between extra-atomic relaxation energies for different core levels of chemical compounds. However, in the case of the metals the extra-atomic relaxation is known to increase with increase of the binding energy of the core electron. This is proved both theoretically [7] and experimentally [8]. The R2pe values obtained in Ref. 1 can be regarded as R2pe values in the point charge approximation because the relation (5) was used (compare Eq. (10) in this paper and Eq. (13) in Ref. 1 and see comments after Eq. (10) in this paper). The R e values from Ref. 1 are on average about 0.3 eV smaller than that of R2pe. Both R2pe and Rise values follow the same patterns as R e and discussion of Re data in Ref. 1 is also valid for R2pe and Rlse values. For example, both R2pe and Rlse values can be calculated using an additive scheme for the molecule AX,. R2pe = lo + Z

aini

(23)

i

The additivity increments a i are equal to 0.718eV for C1, 0.378eV for F, 1.102eV for S and 0.587eV for O; 10 = 3.001 eV in the case of R2pe in phosphorus compounds. The corresponding values for CI, F, O and 10are 0.824, 0.467, 0.633 and 2.646 for sulfur compounds. The increments a i are proportional to the polarizability of the corresponding elements i as > acl > ao > aF. In Tables 1 and 2 the additive values for R2pe are compared with the experimental ones. 3.4. Madelung potential

15 o~

~

o SPF3

PF3 ~ 3PCi ~/

10

o

OPCI3 SPC3l

15

M

20

eV

Fig. 2. The correlation between experimental Madelung potentials M (this work) and theoretical values Mth [6].

The values of Madelung potential in Tables 1 and 2 are considerably larger than those found in Ref. 1. This is connected with the increased effective atomic charge in the present work. However the correlation between the present values and the data in Ref. 1 is very good. The present data are also in good agreement with the theoretical values [6] (Fig. 2). The obtained M values can be used for independent calculation of the effective atomic charges qmad of atom A in molecules mXn, as described in Ref. 1. These qmad charges must coincide with the

156

V.L Nefedov, V.G. Yarzhemsky/J.ElectronSpectrosc.Relat. Phenom.69 (1994) 149-157

charges q obtained above, as is really the case (Tables 1 and 2). This result indicates the high consistency of the M and q values obtained in the present paper for the initial (normal) state of the molecules.

Acknowledgement We thank the Russian Fund for Fundamental Research for financial support for this work.

transition and final states ~I/in = CAffIAv+ CXXI/Xv

(A3)

~I/T : CA~I/A, l t v + CxtI/Xv

(A4)

~in = CA~ffA" II II v "~-CxtI/xv

(A5)

where ~Av and ~Xv are valence electron wavefunctions of A and X atoms, for which CA < CA respectively. ' < 4 and Cx > c~ > The corresponding charge transfer from tPAv atomic orbitals to ~1'x are equal Aq x = 0.5Aq = Z ( A ) ( c ~ - c2)

References

Aq = Z ( a ) ( c ~ 2, - c2) [1] V.I. Nefedov, V.G. Yarzhemsky, A.V. Chuvaev and E.M. Trishkina, J. Electron Spectrosc. Relat. Phenom., 46 (1988) 381. [2] G. Howat and O. Goseinsky, Chem. Phys. Lett., 30 (1975) 87. [3] O. Goscinski, M. Hehenberger, B. Roos and P. Siegbahn, Chem. Phys. Lett., 33 (1975) 427. [4] L. Ley, S.P. Kowalczyk, F.R.Mc Feely, R.A. Pollak and D.A. Shirley, Phys. Rev. B, 8 (1973) 2392. [5] V.F. Bratzev, Tables of Atomic Wave Functions, Nauka, Moscow, 1966 (in Russian). [6] R.N. Sodhi and R.G. Cavell, J. Electron Spectrosc. Relat. Phenom., 32 (1983) 283. [7] N.J. Castellani and D.B. Leroy, J. Electron Spectrosc. Relat. Phenom., 59 (1992) 197. [8] J. Vayrynen, T.T. Rantala, E. Minni and E. Suoninen, J. Electron Spectrosc. Relat. Phenom., 31 (1983) 293. [9] V.I. Nefedov, J. Electron Spectrosc. Relat. Phenom., 63 (1993) 355.

Appendix We consider the free molecule AX n with positively charged A atom for which

qA = n]qx]

Aq = AqA = nlAqx [

(ml)

where qA and qx are effective charges of atoms A and X, Aqx and Aqh are charge transfers from atoms X to the atom A after photoionization. The core electron binding energy Ei is given by

E~ = El(q) + M - Re

(A2)

The photoionization is accompanied by change of the molecular orbital tI/in ---+ ff~ltT ---+ kOf for initial,

(a6)

In the transition state, which corresponds to the photoionization of the half of the core electron, using the equivalent core approach one should replace atom A(Z) by A ' ( Z + 1/2), and M by M x in Eq. (A2).

Ei = El(q) + M T

(AT)

g T = --O.5Aq I.f ffj2ri-vl~2A,v dT-- I ~2ri-xlk~2v dT ] (A8) where ~i is the wavefunction of the core electron of atom A. For the sake of simplicity the exchange integrals are omitted (see Eqs. (12) and (13)). For the operator r~ ~ the exchange integrals are negligibly small. The expression for M T takes into account the change in the dynamic electrostatic potential for the core electron due to the charge transfer from ~Xv to ~A'v orbitals, i.e. extra atomic relaxation. Equation (A8) implies that the extra-atomic relaxation is connected with the charge transfer Aq only. This conclusion is correct within the MO LCAO approximation for the free molecules AX,, which are considered here. The changes in the electron density distrbution and in the electrostatic potentials are completely taken into account as presented by Eqs. (A3)-(AS) and (A8). However in the ionic crystals as well as in the crystals with molecular lattices, where charge transfer between lattice units is not possible or small, the polariz-

V.L Nefedov, V.G. Yarzhemsky/J. Electron Spectrosc. Relat. Phenom. 69 (1994) 149-157

ation of the surrounding units must also be taken into account, because the core electron hole induces dipoles in these units [9]. Using the point charge approximation for ~2 one obtains M T = M - 0.5Aq[(rA,lv) -- R -1] where ( r A l v ) = ~ r - l ~ 2 , v d r interatomic distance. Note (rA)v) corresponds to the with ordinal number Z +

and that ion 1/2.

(A9) R is the A - X the mean value of the A' atom The interatomic

157

relaxation after photoionization of the core electron in A ( q ) ion is completely taken into account in the El(q) values [1]. However part of the extra-atomic relaxation R e is also connected with interatomic relaxation in atom A after charge transfer to A from X atoms. Based on Eqs. (A2), (A7) and (A9) we obtain for R e the expression R e = 0.5Aq[(rA,lv) -- R -l]

(A10)