- Email: [email protected]
X-ray Emission Spectroscopy, Applications
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2455
X-Ray Emission Spectroscopy, Applications George N Dolenko, Lermontova 35A/16, 664033 Irkutsk, Russia Oleg Kh Poleshchuk, Tomsk Pedagogical University, Tomsk, Russia Jolanta N Lato i ska, Adam Mickiewicz University, Pozna , Poland
HIGH ENERGY SPECTROSCOPY Applications
Copyright © 1999 Academic Press
MO structure investigation Any variations in the composition, structure, stereochemistry or coordination character of a molecule change its chemical properties and MO (molecular orbital) structure. MO changes are clearly observed by the fine structure of XFS (X-ray fluorescence spectroscopy). This makes it possible to relate some features of the chemical behaviour of compounds to their electronic structure and opens a way to various chemical propertyelectronic structure parameter correlations which are frequently of help for explaining and predicting the chemical properties of compounds. The transitions from valence atomic levels to vacancies in inner shells form X-ray valence emission lines, reflecting the structure of the valence levels or zones. Electron transitions between different inner levels form inner X-ray emission lines. The study of the fine structure of different valence emission lines of all the atoms in a compound allows detailed
investigation of the structure of valence levels or zones. Research into the shifts of inner X-ray emission lines allows one to investigate effective charges on the corresponding atoms. For example, consider the X-ray emission spectra of sulfur. The initial state of a sulfur atom for X-ray emission is that with a vacancy in the K or L2,3 level. This vacancy is rapidly filled (within 1016 1014 s) as a result of transitions obeying the dipole selection rules, i.e. 2p → 1s (Kα lines), 3p → 1s (Kβ lines) or 3s → 2p, 3d → 2p (L 2,3 lines) transitions. The energy released in this case is emitted from the atom as either an Auger electron or an X-ray quantum (Figure 1). Whereas SKα are inner lines, SKβ and SL2,3 are valence lines. The energies of atomic np → 1s transitions can be represented by the equations
Figure 1 Scheme showing the change of one-electron energies of 1s, 2p levels and the energy of the A Kαline in the ions A+ and A– with respect to the neutral atom A0.
2456 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
Then, with account taken of the dipole selection rules, Equation [5] is transformed into
where hQ is the energy of the emission quantum, Efin is the final energy of the system, Einit is the initial energy of the system, Enl is the energy of the system with an nl electron removed and Hnp is the oneelectron energy of the np level. Thus, in a one-electron approximation the distance between individual maxima in a spectral series is equal to the difference in one-electron energies of the corresponding atomic levels. In molecules the 3s, 3p and 3d electrons of the sulfur atom are involved in chemical bonding to form an MO system. In this case, the SKβ spectrum (S3p → S1s interatomic transitions), for example, corresponds to MO i → S 1s transitions, and the distances between spectral maxima correspond to energy differences of the appropriate occupied molecular levels:
The intensity of X-ray emission lines is determined by the relation (for the SK series as an example):
where NSnp is the np level population of the sulfur atom, E1 is the energy of Snp → S1s transitions, )Snp is the wavefunction of sulfur np orbitals and )S1s is the wavefunction of the sulfur 1s orbital. For molecules this expression is transformed to the equation
where
where )j is the wavefunction of jth AO and c ij are the coefficients.
where c i is the coefficient of
The above is also true for other X-ray emission series. Important features of X-ray emission spectra are the comparative ease of interpretation and the possibility of investigating the electronic structure from the viewpoint of any atom of the molecule investigated. Example: electronic structure of the sulfate ion
Information concerning the electronic structure of molecules provided by XFS can be well illustrated with the sulfate ion as an example. The wavefunction of any ith valent MO of the sulfate ion can be described by the equation
All possible X-ray fluorescence spectra of the sulfate ion are presented in Figure 2 whereas Figure 3 shows an MO diagram constructed from a full set of these spectra. Adjustment to the scale of the ionization potentials [IP] of valence electrons is effected by subtracting the X-ray transition energies from the IPs of the corresponding inner levels (S1s, S2p, O1s) determined by the use of data of X-ray photoelectron spectroscopy:
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2457
strong S3p O2p V bond. The 2a1 level (maxima E and V), consisting of the S3s AO and, possibly, the O2s with a small admixture of O2p AO, lies even deeper. Deep 1t2 and 1a1 MOs consisting mainly of the O2s AO are seen as low intensity long-wavelength maxima G and M respectively. Consequently, much information on the MO structure of a chemical species under investigation can be derived from X-ray emission spectra.
Determination of the effective atomic charges
Figure 2 Full set of X-ray fluorescence spectra of the sulfate ion on an energy scale corresponding to the ionization potentials of valence electrons.
From these, the following equations are derived
All MOs with c5 ≠ are displayed in the O Kα spectrum (O2p → O1s transitions), those with c2 ≠ 0 in the SKβ spectrum (S3p → S1s transitions) and those with c1 ≠ 0 and c3 ≠ 0 in the SL2,3 spectrum (S3s → S2p and S3d → S2p transitions). From the spectra shown in Figure 3 it follows that the highest occupied MO 1t1 (maximum A in the OKα spectrum) consists of only O2p electrons; next, the 3t2 and 1e levels (maxima B, C and W) significantly correspond to the S bond S3d O2p; the 2t2 level then follows (maxima D and F), which corresponds to the
The concept of the effective charge on atoms in molecules is known to be fundamental in the field of theoretical chemistry. It assumes that the entire electron distribution of an investigated atom can be considered as a point charge that coincides with the coordinates of the nucleus. This simple and obvious form of the electron density distribution in the examined species is rather approximate: in real molecules the outer electron shells of atoms substantially lose their individuality because of the delocalization of valence electrons of atoms. The approximation procedure (the replacement of the real distribution of the outer electron density of an atom by the point charge on its nucleus) is not simple in general and depends largely on the actual definition of effective charge. A number of calculations and experimental methods used for the determination of the latter are known. The effective charges on atoms (qA, where A is an element) do not belong to the class of directly observed physical characteristics, and therefore the so-called experimental determination of qA values usually means the result of the interpretation of various experimental data in terms of the corresponding model with qA as a parameter. Shifts of the energy of inner nl levels of the A atom ('Anl), defined by X-ray photoelectron spectroscopy, are sensitive to qA and the effective charges of all other atoms, and in terms of the so-called potential model can be written as
where K(Anl) is the coefficient that is characteristic of the A nl level, ∑i ≠$ qi riA) is the Madelung potential and Er is the relaxation energy. Shifts of inner AKα line (2p3/2 → 1s electron transitions are more intense than for 2p1/2 → 1s) are determined by the difference between the shifts of one-electron energies
2458 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
Figure 3
Scheme of the sulfate ion MOs obtained from the full set of X-ray fluorescence spectra.
of A1s and A2p3/2 levels:
where E0nl is the total energy of the neutral A atom (A0) containing a vacancy in the nl level. The difference in the energy changes for different Anl levels is rather small and therefore the 'AKα values are determined by subtraction of two large and very similar quantities, 'A1s and 'A2p3/2 (the energy shift of the A1s level always prevails over that of A2p3/2). As a result, the 'AKα1 values are normally about ten times smaller than X-ray photoelectron Anl shifts. However, AKα1 shifts have an obvious advantage. The corresponding electron transitions are localized in the same potential well as that created by the Coulomb field of other atoms of the system investigated. Hence, the potential model for AKα shifts, analogous to Equation [16], can be written as
or, in a more universal form
Many authors have investigated the dependencies of Equation [19] for different inner X-ray emission lines and atoms by different methods. Table 1 gives the AKα1 shifts for some phosphorus-, sulfur- and chlorine-containing compounds and qA values obtained by the correlation of Mulliken charges calculated by the SCF ab initio method using a 4-31G** basis set for a sufficiently large series of A-containing molecules with the experimental AKα1 shifts.
Participation of the 3d atomic orbitals in L-emission spectra From the X-ray L-emission spectra of S, Cl, P, within the framework of a MO method, one can estimate the 3d-population. The basic problem is the need to calculate the matrix elements of the transitions 2p → 3s and 2p → 3d. For K β spectra of elements in period 3 in the dipole approximation, transitions are permitted from levels involving 3pAO, from which
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2459
Table 1
Experimental AKα1 shift and qA values
A
Class of compounds
'AKα1 (eV) relative to Pred, S8, Cl2
qA(e) in 4-31G** charge scale
P
R3P
–0.01 – 0.25
–0.03 – 0.25
R4P+
0.16 – 0.38
0.32 – 0.76
P(OR)3
0.48 – 0.52
0.97 – 1.05
R3PO
0.27 – 0.57
0.54 – 1.15
R3PS
0.17 – 0.24
0.34 – 0.48
(RO)3PO
0.69 – 0.76
1.39 – 1.53
S
PO43–
0.76 – 0.80
S
–0.14 – –0.02
–0.22 – 0.09
RSH
–0.08 – 0.00
–0.11 – 0.05
R2S
–0.09 – 0.14
–0.18 – –0.32
R3S+
0.00 – 0.12
0.05 – 0.28
RNSNRc
0.18 – 0.25
0.40 – 0.54
R2SO
0.36 – 0.42
0.75 – 0.87
R2SO2
0.78 – 0.85
1.57 – 1.61
SO42 – Cl
1.54 – 1.61
RCl
1.00 – 1.20
2.00 – 2.40
–0.19 – 0.01
–0.28 – 0.02
the MO are constructed. The relative intensity of separate emission lines is proportional to the squares of the factors ci2. In L-emission spectra of atoms in period 3 the MO coefficients owing to dipole rules of selection ('l = ±1), will be simultaneously displayed MO, which are constructed with participation of 3s AO and 3d AO. If the symmetry of a molecule is such that the MO of the systems can be constructed with simultaneous participation of 3s- and 3d AOs of a period 3 atom the intensity of the emission line will depend on the contributions of both the 3d and the 3s AOs to the appropriate MO. Thus estimations of ci2 values with 3d AO and 3s AO from X-ray spectra need a knowledge of matrix elements of transitions | 〈2p | r | 3d 〉 |, | 〈 2d | r | 3s 〉 |. The determination of such matrix elements becomes complicated by the problem of choosing a good 3d wavefunction. It is known that the atomic 3d functions are too diffuse and their electronic density, appropriate to them, is located far from the nuclei of atoms and to be unsuitable for participation in chemical bonds. In the case of X-ray transitions the important behaviour of 3d wavefunctions is not in the area of valence electrons but in the field of core electrons of atoms, in particular in the area of 2p AO. The 2p AO wavefunctions are located near the nucleus of an atom and have atomic character. It is possible to consider that 3d AO in this area also has atomic character. On this basis the estimation of matrix elements | 〈 2p | r | 3d 〉 | and | 〈 2p | r | 3s 〉 | is carried out to account for the intensity of X-ray atomic transitions.
The analysis of spectra of molecules and ions shows that the short-wave maximum W in L-spectra of S and Cl (Figure 2) is basically connected with an MO, in which there is a significant contribution from the 3d AO, while the contributions of the 3s AO to these MOs are insignificant. The maxima V and M are connected with an MO in which the 3s AO participates. Hence, from L-spectra it is possible to obtain experimental values of the relative intensity of various lines and to determine the contribution of AO and MO. Estimations for the ion SO42 and the molecule SF6 give I3d/I3s values that correspond to theoretical results. The consideration of results from sulfur- and chlorine-containing compounds indicate that the participation of 3d AO in various MO becomes appreciable. The study of shifts to Kα lines over a range of molecules shows that the experimental relation I 3d/I 3s increases as the Kα shift grows, physically this is connected to the growth of a positive charge on an atom of sulfur. Table 2 gives the relative experimental 3d occupations for sulfur in some compounds.
Application of SKα spectra to characteristic compounds It is known that the energy of valence electrons of heteroatoms in periods 2 and 3 varies linearly with changes in the energy of their core electrons. The concept of an energy level of a hypothetical electron lone pair of a sulfur atom (hnS), whose energy depends only on the charge on the sulfur atom (qS), has been suggested. The position of this level in the SKβ spectrum was related to the values of the SKα shift, which are proportional to the net charge on the sulfur atom. The following relationship was
Table 2
Relative 3d sulfur population from X-ray spectral
data
'E Kα1,2 (eV)
~¢2p~r~3d²~/ ~¢2p~r~3s²~
Molecule
I3d / I3s
(CH3)2SO
0.2
0.25
1.0
0.1
qs
Cl2SO
0.3
0.27
1.2
0.3
(C6H5)2SO
0.4
0.31
1.2
0.3
SO2
0.7
0.45
1.5
0.6
(CH3)2SO2
0.8
0.75
1.9
0.9
SF4
1.0
0.75
1.9
0.9
SO32–
1.0
0.65
1.6
0.7
(C6H5)2SO2
1.2
0.82
2.1
1.1
SF6
1.0
1.45
2.6
1.4
SO42–
1.8
1.10
2.3
1.2
2460 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
obtained by comparing the short-wave maximum in the SK spectra of saturated sulfides with the corresponding values of '(SKα): hnS(Kβ)(eV) = E(nS → 1SS) = 0.0056 × 103'SKα (eV) + 2468.37, with r = 0.973, s = 0.06, n = 26. Using the equation it is possible, knowing 'SKα values to predict the location of a hnS level in the SKβ spectra of any saturated sulfide compound. In fact, this level can be treated as a reference level in the analysis of the changes in the spectral structure caused only by orbital interactions devoid of the effect of charge changes on the sulfur atom. As an example one can consider the application for complex compounds with dimethyl sulfide. It follows from Figure 4 that the intensity of the short-wave maximum A, which in the SKβ spectra of sulfides corresponds to the transition from the nS level to the vacancy K of the sulfur atom, significantly decreases and is considerably shifted towards longer wavelength with respect to the hnS level (Kβ). This shift, ('nS = EA(SKβ) hnS(SKβ) (Table 3), characterizes quantitatively the bonding nature of the highest occupied molecular orbital. The observed shift towards longer wavelength indicates that the nS level interacts with the vacant levels of the acceptor, being mainly of the d type. The differences in shapes of the SKβ spectra of the complexes studied (Figure 4) can be explained by the presence of partly populated valence d orbitals, apart from the vacant ones, in Ti, in contrast to Sn and Sb.
Application of SK β and SK α spectra for rodano-group It is known that the NCS-group in compounds can be coordinated with a metal in three ways: MNCS (a), MSCN (b) and MNCSM (c). Inorganic thiocyanates with coordination of type (a) have a characteristically large (negative) total electronic density on the sulfur atom, lower intensity of long-wave maxima and lower energy of a short-wave maximum (Figure 5). In organic isothiocyanates the 'SKα values vary in an interval 74005800 eV with the intense short-wave maximum A in the SKβ spectra Table 3
Compound
'(SKα)a 10 –3(eV)
qs (e) in 4–31G** charge scale
hns(Kβ) (eV)
EA(Kβ) (eV)
'ns (eV)
(CH3)2S
63(6)b
0.07(2)
8.02(4)
8.1(1)
0.1(1)
2(14)
0.05(2)
8.38(8)
8.2(1)
0.2(1)
17(7)
0.08(2)
8.47(5)
8.3(1)
0.2(1)
3(10)
0.04(2)
8.35(6)
8.11(5)
0.24(8)
SbCl5S(CH3)2
TiCl42S(CH3)2 b
(EA) in the range 2467.1 2467.8 eV. In organic thiocyanates these parameters become 'SKα = 4.7 13.3 eV 10 2, EA = 2468.1 2469.1 eV (Table 4).
Parameters determined from X-ray spectra of the sulfur atoms for some of the complexes studied
SnCl42S(CH3)2
a
Figure 4 SKE spectra of some Me2S complexes. (—) centre of gravity; (---) hnS(KE). 1 = TiCl4 · 2SMe2; 2 = SbCl5 · SMe2; 3 = SnCl4 · 2SMe2; 4 = SMe2.
Relative to S8. The mean-square errors in the last significant digit, taken for 95% confidence interval by Student’s criterion, are given in parentheses.
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2461
Table 4
X-ray spectral character of some thiocyanates and isothiocyanates
EA(Kβ) (eV)
hns (Kβ) (eV) relative to 2467.0 eV
ns (eV)
Coordination type
–0.04(3)
0.2
1.1
–0.9
a
–0.13(2)
0.3
0.9
–0.6
a
Compound
∆(SKα)* 10–2 (eV)
qs (e) in 4–31G** charge scale
(I)
KNCS
–4.5(12)
(II)
NH4NCS
–9.2(6)
No.
(III)
Ba(NCS)2
–3.6(10)
–0.02(2)
0.2
1.2
–1.0
a
(IV)
Sn(NCS)2
–7.2(8)
–0.09(2)
0.3
1.0
–0.7
a
(V)
CuSCN
4.1(8)
0.13(2)
2.0
1.6
0.4
b
(VI)
CH3SCN
4.7(8)
0.14(2)
1.8
1.7
0.1
b
(VII)
C6H5CH2SCN
5.4(11)
0.16(3)
1.6
1.7
–0.1
b
(VIII)
C6F5SCN
(IX)
C8H4OPhSCN
9.4(8)
0.23(2)
1.9
1.9
0.0
b
13.3(9)
0.31(3)
2.1
2.1
0.0
b
(X)
C6H5SCN
5.0(8)
0.15(2)
1.7
1.7
0.0
b
(XI)
CH3NCS
–4.7(8)
–0.04(2)
0.5
1.1
–0.6
a
(XII)
P(NCS)3
(XIII)
C6F5(NCS)2
(XIV)
C8H4OPhNCS
(XV)
C6H5NCS
0(2)
0.05(2)
0.2
1.4
–1.2
a
–7.4(6)
–0.09(2)
0.1
1.0
–0.9
a
5.8(9)
0.16(2)
0.8
1.7
–0.9
a
–5.3(7)
–0.05(2)
0.3
1.1
–0.8
a
The mean-square errors in the last significant digit, taken for 95% confidence interval by Student’s criterion, are given in parentheses. a Relative to S . 8
From the presence in the SKβ spectra of thiocyanates (VI), (VII) of a single short-wave maxima A that is coincident with the level hnS, it follows that the level nS does not practically couple with the SC≡1 orbitals. The existence of the advanced short-wave structure in SKβ spectra thiocyanates (VIII)(X), beyond the hnS level, must relate to nSSAr interactions. Thus, the spectra of thiocyanates (VIII)(X) indicates two orthogonal conformations of the molecules, one in which nSSAr interactions are absent giving rise to a peak coincident with the hnS level, and another in which the nS and SAr couple to give two maxima, A′ and A″, corresponding to levels nS ± SAr.
Applications of Kαshifts for electronic density redistribution Figure 5 SKβ spectra of some inorganic and organic thiocyanates and isothiocyanates. The compound numbers are defined in Table 4. The energy levels of the hypothetical lone electron pair are marked by the vertical lines.
However, the 'nS values of thiocyanates and isothiocyanates are divided almost unequivocally: 'nS ≥ 0 for thiocyanates, 'nS < 0 for isothiocyanates (in thiocyanates 3pS electronic density of atom of sulfur enters into a strongly bonding MO).
It was of interest to use the data obtained for the investigation of the electron density redistribution on complexation between a donor molecule PCl 3 or of SPCl 3 (where one can define the effective charges on all atoms by their Kα shifts) and an acceptor molecule AlBr3 containing no interfering atoms. The data presented in Table 5 show that, in spite of a positive qP growth on complexation, the total ligand electron density does not decrease (in the range of accuracy achieved) due to a strong dampening effect of the Cl atoms. This leads to a sufficient growth of
2462 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
Table 5
Change of atomic charges and bond ionicities of free ligands on their complexation
Ionicities of bonds (%)
∆A Kα a (eV)
a b c
Compound
A=P
A=S
A = Cl
P–S
P–Cl
PCl3
0.373(7)
–
–0.09(1)
–
44(5)
AlBr3PCl3
0.599(8)
–
–0.156(15)
–
72(7)
SPCl3
0.430(8)
–0.10(2)
–0.11(2)
50(6)
51(6)
AlBr3SPCl3
0.616(8)
–0.080(9)
–0.171(14)
68(7)
74(8)
b
Change of effective atomic charge (δ qA) c of ligands on their complexation in 4-31G** charge scale A=P
A=S
A = Cl
Σ δqi
0.5(1)
–
–0.10(7)
0.2(2)
0.4(1)
0.04(6)
–0.1(1)
0.1(2)
The mean-square errors in the last significant digit, taken for 95% confidence interval by Student’s criterion, are given in parentheses. The ionicity of the AB bond is equal to (|qA–qB|/2)100%. The positive sign of GqA corresponds to a decrease of the A atom electron density on complex formation.
the ionicity of all bonds of the ligands and acceptor. From Table 5 it also follows that the positive charge on the central acceptor atom grows sufficiently on complexation while the electron density on acceptor geminal of atoms does not decrease.
List of symbols ci = coefficient of
Further reading Dolenko GN (1993) X-ray determination of effective charges on sulphur, phosphorus and chlorine atoms. Journal of Molecular Structure 291: 2357.
Dolenko GN, Litvin AL, Elin VP and Poleshchuk OKh, (1991) X-ray investigation of electron density redistribution on complexation. Journal of Molecular Structure 251: 1127. Dolenko GN, Latajka Z and Ratajczak H (1995) X-ray spectral determination of the effective charges on P, S, and Cl atoms in chemical compounds with a nonempirical charge scale. Heteroatom Chemistry 6: 553557. Dolenko GN, Poleshchuk OKh and Koput J (1998) Antimonium pentachloride electron density redistribution on complexation. Heteroatom Chemistry 9: 543548. Mazalov LN and Yumatov VD (1984) Electronnoe stroenie ekstragentov. Novosobirsk: Nauka, 199 p. Nogaj B, Poleshchuk OKh, Kasprzak J, Koput J, ElinVP, Dolenko GN (1997)Changes in electron density distribution resulting from formation of antimony pentachloride complexes studied by X-ray fluorescence spectroscopy. Journal of Molecular Structure 406: 145 151. Poleshchuk OKh, Nogaj B, Dolenko GN and Elin VP (1993) Electron density redistribution on complexation in non-transition element complexes. Journal of Molecular Structure 297: 295312. Poleshchuk OKh, Nogaj B, Kasprzak J, Koput J, Dolenko GN, Elin VP, Ivanovskii AL (1994) Investigation of the electronic structure of SnCl4L2, TiCl4L2 and SbCl5L complexes by X-ray fluorescence spectroscopy. Journal of Molecular Structure 324: 215222.
X-Ray Emission Spectroscopy, Applications George N Dolenko, Lermontova 35A/16, 664033 Irkutsk, Russia Oleg Kh Poleshchuk, Tomsk Pedagogical University, Tomsk, Russia Jolanta N Lato i ska, Adam Mickiewicz University, Pozna , Poland
HIGH ENERGY SPECTROSCOPY Applications
Copyright © 1999 Academic Press
MO structure investigation Any variations in the composition, structure, stereochemistry or coordination character of a molecule change its chemical properties and MO (molecular orbital) structure. MO changes are clearly observed by the fine structure of XFS (X-ray fluorescence spectroscopy). This makes it possible to relate some features of the chemical behaviour of compounds to their electronic structure and opens a way to various chemical propertyelectronic structure parameter correlations which are frequently of help for explaining and predicting the chemical properties of compounds. The transitions from valence atomic levels to vacancies in inner shells form X-ray valence emission lines, reflecting the structure of the valence levels or zones. Electron transitions between different inner levels form inner X-ray emission lines. The study of the fine structure of different valence emission lines of all the atoms in a compound allows detailed
investigation of the structure of valence levels or zones. Research into the shifts of inner X-ray emission lines allows one to investigate effective charges on the corresponding atoms. For example, consider the X-ray emission spectra of sulfur. The initial state of a sulfur atom for X-ray emission is that with a vacancy in the K or L2,3 level. This vacancy is rapidly filled (within 1016 1014 s) as a result of transitions obeying the dipole selection rules, i.e. 2p → 1s (Kα lines), 3p → 1s (Kβ lines) or 3s → 2p, 3d → 2p (L 2,3 lines) transitions. The energy released in this case is emitted from the atom as either an Auger electron or an X-ray quantum (Figure 1). Whereas SKα are inner lines, SKβ and SL2,3 are valence lines. The energies of atomic np → 1s transitions can be represented by the equations
Figure 1 Scheme showing the change of one-electron energies of 1s, 2p levels and the energy of the A Kαline in the ions A+ and A– with respect to the neutral atom A0.
2456 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
Then, with account taken of the dipole selection rules, Equation [5] is transformed into
where hQ is the energy of the emission quantum, Efin is the final energy of the system, Einit is the initial energy of the system, Enl is the energy of the system with an nl electron removed and Hnp is the oneelectron energy of the np level. Thus, in a one-electron approximation the distance between individual maxima in a spectral series is equal to the difference in one-electron energies of the corresponding atomic levels. In molecules the 3s, 3p and 3d electrons of the sulfur atom are involved in chemical bonding to form an MO system. In this case, the SKβ spectrum (S3p → S1s interatomic transitions), for example, corresponds to MO i → S 1s transitions, and the distances between spectral maxima correspond to energy differences of the appropriate occupied molecular levels:
The intensity of X-ray emission lines is determined by the relation (for the SK series as an example):
where NSnp is the np level population of the sulfur atom, E1 is the energy of Snp → S1s transitions, )Snp is the wavefunction of sulfur np orbitals and )S1s is the wavefunction of the sulfur 1s orbital. For molecules this expression is transformed to the equation
where
where )j is the wavefunction of jth AO and c ij are the coefficients.
where c i is the coefficient of
The above is also true for other X-ray emission series. Important features of X-ray emission spectra are the comparative ease of interpretation and the possibility of investigating the electronic structure from the viewpoint of any atom of the molecule investigated. Example: electronic structure of the sulfate ion
Information concerning the electronic structure of molecules provided by XFS can be well illustrated with the sulfate ion as an example. The wavefunction of any ith valent MO of the sulfate ion can be described by the equation
All possible X-ray fluorescence spectra of the sulfate ion are presented in Figure 2 whereas Figure 3 shows an MO diagram constructed from a full set of these spectra. Adjustment to the scale of the ionization potentials [IP] of valence electrons is effected by subtracting the X-ray transition energies from the IPs of the corresponding inner levels (S1s, S2p, O1s) determined by the use of data of X-ray photoelectron spectroscopy:
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2457
strong S3p O2p V bond. The 2a1 level (maxima E and V), consisting of the S3s AO and, possibly, the O2s with a small admixture of O2p AO, lies even deeper. Deep 1t2 and 1a1 MOs consisting mainly of the O2s AO are seen as low intensity long-wavelength maxima G and M respectively. Consequently, much information on the MO structure of a chemical species under investigation can be derived from X-ray emission spectra.
Determination of the effective atomic charges
Figure 2 Full set of X-ray fluorescence spectra of the sulfate ion on an energy scale corresponding to the ionization potentials of valence electrons.
From these, the following equations are derived
All MOs with c5 ≠ are displayed in the O Kα spectrum (O2p → O1s transitions), those with c2 ≠ 0 in the SKβ spectrum (S3p → S1s transitions) and those with c1 ≠ 0 and c3 ≠ 0 in the SL2,3 spectrum (S3s → S2p and S3d → S2p transitions). From the spectra shown in Figure 3 it follows that the highest occupied MO 1t1 (maximum A in the OKα spectrum) consists of only O2p electrons; next, the 3t2 and 1e levels (maxima B, C and W) significantly correspond to the S bond S3d O2p; the 2t2 level then follows (maxima D and F), which corresponds to the
The concept of the effective charge on atoms in molecules is known to be fundamental in the field of theoretical chemistry. It assumes that the entire electron distribution of an investigated atom can be considered as a point charge that coincides with the coordinates of the nucleus. This simple and obvious form of the electron density distribution in the examined species is rather approximate: in real molecules the outer electron shells of atoms substantially lose their individuality because of the delocalization of valence electrons of atoms. The approximation procedure (the replacement of the real distribution of the outer electron density of an atom by the point charge on its nucleus) is not simple in general and depends largely on the actual definition of effective charge. A number of calculations and experimental methods used for the determination of the latter are known. The effective charges on atoms (qA, where A is an element) do not belong to the class of directly observed physical characteristics, and therefore the so-called experimental determination of qA values usually means the result of the interpretation of various experimental data in terms of the corresponding model with qA as a parameter. Shifts of the energy of inner nl levels of the A atom ('Anl), defined by X-ray photoelectron spectroscopy, are sensitive to qA and the effective charges of all other atoms, and in terms of the so-called potential model can be written as
where K(Anl) is the coefficient that is characteristic of the A nl level, ∑i ≠$ qi riA) is the Madelung potential and Er is the relaxation energy. Shifts of inner AKα line (2p3/2 → 1s electron transitions are more intense than for 2p1/2 → 1s) are determined by the difference between the shifts of one-electron energies
2458 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
Figure 3
Scheme of the sulfate ion MOs obtained from the full set of X-ray fluorescence spectra.
of A1s and A2p3/2 levels:
where E0nl is the total energy of the neutral A atom (A0) containing a vacancy in the nl level. The difference in the energy changes for different Anl levels is rather small and therefore the 'AKα values are determined by subtraction of two large and very similar quantities, 'A1s and 'A2p3/2 (the energy shift of the A1s level always prevails over that of A2p3/2). As a result, the 'AKα1 values are normally about ten times smaller than X-ray photoelectron Anl shifts. However, AKα1 shifts have an obvious advantage. The corresponding electron transitions are localized in the same potential well as that created by the Coulomb field of other atoms of the system investigated. Hence, the potential model for AKα shifts, analogous to Equation [16], can be written as
or, in a more universal form
Many authors have investigated the dependencies of Equation [19] for different inner X-ray emission lines and atoms by different methods. Table 1 gives the AKα1 shifts for some phosphorus-, sulfur- and chlorine-containing compounds and qA values obtained by the correlation of Mulliken charges calculated by the SCF ab initio method using a 4-31G** basis set for a sufficiently large series of A-containing molecules with the experimental AKα1 shifts.
Participation of the 3d atomic orbitals in L-emission spectra From the X-ray L-emission spectra of S, Cl, P, within the framework of a MO method, one can estimate the 3d-population. The basic problem is the need to calculate the matrix elements of the transitions 2p → 3s and 2p → 3d. For K β spectra of elements in period 3 in the dipole approximation, transitions are permitted from levels involving 3pAO, from which
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2459
Table 1
Experimental AKα1 shift and qA values
A
Class of compounds
'AKα1 (eV) relative to Pred, S8, Cl2
qA(e) in 4-31G** charge scale
P
R3P
–0.01 – 0.25
–0.03 – 0.25
R4P+
0.16 – 0.38
0.32 – 0.76
P(OR)3
0.48 – 0.52
0.97 – 1.05
R3PO
0.27 – 0.57
0.54 – 1.15
R3PS
0.17 – 0.24
0.34 – 0.48
(RO)3PO
0.69 – 0.76
1.39 – 1.53
S
PO43–
0.76 – 0.80
S
–0.14 – –0.02
–0.22 – 0.09
RSH
–0.08 – 0.00
–0.11 – 0.05
R2S
–0.09 – 0.14
–0.18 – –0.32
R3S+
0.00 – 0.12
0.05 – 0.28
RNSNRc
0.18 – 0.25
0.40 – 0.54
R2SO
0.36 – 0.42
0.75 – 0.87
R2SO2
0.78 – 0.85
1.57 – 1.61
SO42 – Cl
1.54 – 1.61
RCl
1.00 – 1.20
2.00 – 2.40
–0.19 – 0.01
–0.28 – 0.02
the MO are constructed. The relative intensity of separate emission lines is proportional to the squares of the factors ci2. In L-emission spectra of atoms in period 3 the MO coefficients owing to dipole rules of selection ('l = ±1), will be simultaneously displayed MO, which are constructed with participation of 3s AO and 3d AO. If the symmetry of a molecule is such that the MO of the systems can be constructed with simultaneous participation of 3s- and 3d AOs of a period 3 atom the intensity of the emission line will depend on the contributions of both the 3d and the 3s AOs to the appropriate MO. Thus estimations of ci2 values with 3d AO and 3s AO from X-ray spectra need a knowledge of matrix elements of transitions | 〈2p | r | 3d 〉 |, | 〈 2d | r | 3s 〉 |. The determination of such matrix elements becomes complicated by the problem of choosing a good 3d wavefunction. It is known that the atomic 3d functions are too diffuse and their electronic density, appropriate to them, is located far from the nuclei of atoms and to be unsuitable for participation in chemical bonds. In the case of X-ray transitions the important behaviour of 3d wavefunctions is not in the area of valence electrons but in the field of core electrons of atoms, in particular in the area of 2p AO. The 2p AO wavefunctions are located near the nucleus of an atom and have atomic character. It is possible to consider that 3d AO in this area also has atomic character. On this basis the estimation of matrix elements | 〈 2p | r | 3d 〉 | and | 〈 2p | r | 3s 〉 | is carried out to account for the intensity of X-ray atomic transitions.
The analysis of spectra of molecules and ions shows that the short-wave maximum W in L-spectra of S and Cl (Figure 2) is basically connected with an MO, in which there is a significant contribution from the 3d AO, while the contributions of the 3s AO to these MOs are insignificant. The maxima V and M are connected with an MO in which the 3s AO participates. Hence, from L-spectra it is possible to obtain experimental values of the relative intensity of various lines and to determine the contribution of AO and MO. Estimations for the ion SO42 and the molecule SF6 give I3d/I3s values that correspond to theoretical results. The consideration of results from sulfur- and chlorine-containing compounds indicate that the participation of 3d AO in various MO becomes appreciable. The study of shifts to Kα lines over a range of molecules shows that the experimental relation I 3d/I 3s increases as the Kα shift grows, physically this is connected to the growth of a positive charge on an atom of sulfur. Table 2 gives the relative experimental 3d occupations for sulfur in some compounds.
Application of SKα spectra to characteristic compounds It is known that the energy of valence electrons of heteroatoms in periods 2 and 3 varies linearly with changes in the energy of their core electrons. The concept of an energy level of a hypothetical electron lone pair of a sulfur atom (hnS), whose energy depends only on the charge on the sulfur atom (qS), has been suggested. The position of this level in the SKβ spectrum was related to the values of the SKα shift, which are proportional to the net charge on the sulfur atom. The following relationship was
Table 2
Relative 3d sulfur population from X-ray spectral
data
'E Kα1,2 (eV)
~¢2p~r~3d²~/ ~¢2p~r~3s²~
Molecule
I3d / I3s
(CH3)2SO
0.2
0.25
1.0
0.1
qs
Cl2SO
0.3
0.27
1.2
0.3
(C6H5)2SO
0.4
0.31
1.2
0.3
SO2
0.7
0.45
1.5
0.6
(CH3)2SO2
0.8
0.75
1.9
0.9
SF4
1.0
0.75
1.9
0.9
SO32–
1.0
0.65
1.6
0.7
(C6H5)2SO2
1.2
0.82
2.1
1.1
SF6
1.0
1.45
2.6
1.4
SO42–
1.8
1.10
2.3
1.2
2460 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
obtained by comparing the short-wave maximum in the SK spectra of saturated sulfides with the corresponding values of '(SKα): hnS(Kβ)(eV) = E(nS → 1SS) = 0.0056 × 103'SKα (eV) + 2468.37, with r = 0.973, s = 0.06, n = 26. Using the equation it is possible, knowing 'SKα values to predict the location of a hnS level in the SKβ spectra of any saturated sulfide compound. In fact, this level can be treated as a reference level in the analysis of the changes in the spectral structure caused only by orbital interactions devoid of the effect of charge changes on the sulfur atom. As an example one can consider the application for complex compounds with dimethyl sulfide. It follows from Figure 4 that the intensity of the short-wave maximum A, which in the SKβ spectra of sulfides corresponds to the transition from the nS level to the vacancy K of the sulfur atom, significantly decreases and is considerably shifted towards longer wavelength with respect to the hnS level (Kβ). This shift, ('nS = EA(SKβ) hnS(SKβ) (Table 3), characterizes quantitatively the bonding nature of the highest occupied molecular orbital. The observed shift towards longer wavelength indicates that the nS level interacts with the vacant levels of the acceptor, being mainly of the d type. The differences in shapes of the SKβ spectra of the complexes studied (Figure 4) can be explained by the presence of partly populated valence d orbitals, apart from the vacant ones, in Ti, in contrast to Sn and Sb.
Application of SK β and SK α spectra for rodano-group It is known that the NCS-group in compounds can be coordinated with a metal in three ways: MNCS (a), MSCN (b) and MNCSM (c). Inorganic thiocyanates with coordination of type (a) have a characteristically large (negative) total electronic density on the sulfur atom, lower intensity of long-wave maxima and lower energy of a short-wave maximum (Figure 5). In organic isothiocyanates the 'SKα values vary in an interval 74005800 eV with the intense short-wave maximum A in the SKβ spectra Table 3
Compound
'(SKα)a 10 –3(eV)
qs (e) in 4–31G** charge scale
hns(Kβ) (eV)
EA(Kβ) (eV)
'ns (eV)
(CH3)2S
63(6)b
0.07(2)
8.02(4)
8.1(1)
0.1(1)
2(14)
0.05(2)
8.38(8)
8.2(1)
0.2(1)
17(7)
0.08(2)
8.47(5)
8.3(1)
0.2(1)
3(10)
0.04(2)
8.35(6)
8.11(5)
0.24(8)
SbCl5S(CH3)2
TiCl42S(CH3)2 b
(EA) in the range 2467.1 2467.8 eV. In organic thiocyanates these parameters become 'SKα = 4.7 13.3 eV 10 2, EA = 2468.1 2469.1 eV (Table 4).
Parameters determined from X-ray spectra of the sulfur atoms for some of the complexes studied
SnCl42S(CH3)2
a
Figure 4 SKE spectra of some Me2S complexes. (—) centre of gravity; (---) hnS(KE). 1 = TiCl4 · 2SMe2; 2 = SbCl5 · SMe2; 3 = SnCl4 · 2SMe2; 4 = SMe2.
Relative to S8. The mean-square errors in the last significant digit, taken for 95% confidence interval by Student’s criterion, are given in parentheses.
X-RAY EMISSION SPECTROSCOPY, APPLICATIONS 2461
Table 4
X-ray spectral character of some thiocyanates and isothiocyanates
EA(Kβ) (eV)
hns (Kβ) (eV) relative to 2467.0 eV
ns (eV)
Coordination type
–0.04(3)
0.2
1.1
–0.9
a
–0.13(2)
0.3
0.9
–0.6
a
Compound
∆(SKα)* 10–2 (eV)
qs (e) in 4–31G** charge scale
(I)
KNCS
–4.5(12)
(II)
NH4NCS
–9.2(6)
No.
(III)
Ba(NCS)2
–3.6(10)
–0.02(2)
0.2
1.2
–1.0
a
(IV)
Sn(NCS)2
–7.2(8)
–0.09(2)
0.3
1.0
–0.7
a
(V)
CuSCN
4.1(8)
0.13(2)
2.0
1.6
0.4
b
(VI)
CH3SCN
4.7(8)
0.14(2)
1.8
1.7
0.1
b
(VII)
C6H5CH2SCN
5.4(11)
0.16(3)
1.6
1.7
–0.1
b
(VIII)
C6F5SCN
(IX)
C8H4OPhSCN
9.4(8)
0.23(2)
1.9
1.9
0.0
b
13.3(9)
0.31(3)
2.1
2.1
0.0
b
(X)
C6H5SCN
5.0(8)
0.15(2)
1.7
1.7
0.0
b
(XI)
CH3NCS
–4.7(8)
–0.04(2)
0.5
1.1
–0.6
a
(XII)
P(NCS)3
(XIII)
C6F5(NCS)2
(XIV)
C8H4OPhNCS
(XV)
C6H5NCS
0(2)
0.05(2)
0.2
1.4
–1.2
a
–7.4(6)
–0.09(2)
0.1
1.0
–0.9
a
5.8(9)
0.16(2)
0.8
1.7
–0.9
a
–5.3(7)
–0.05(2)
0.3
1.1
–0.8
a
The mean-square errors in the last significant digit, taken for 95% confidence interval by Student’s criterion, are given in parentheses. a Relative to S . 8
From the presence in the SKβ spectra of thiocyanates (VI), (VII) of a single short-wave maxima A that is coincident with the level hnS, it follows that the level nS does not practically couple with the SC≡1 orbitals. The existence of the advanced short-wave structure in SKβ spectra thiocyanates (VIII)(X), beyond the hnS level, must relate to nSSAr interactions. Thus, the spectra of thiocyanates (VIII)(X) indicates two orthogonal conformations of the molecules, one in which nSSAr interactions are absent giving rise to a peak coincident with the hnS level, and another in which the nS and SAr couple to give two maxima, A′ and A″, corresponding to levels nS ± SAr.
Applications of Kαshifts for electronic density redistribution Figure 5 SKβ spectra of some inorganic and organic thiocyanates and isothiocyanates. The compound numbers are defined in Table 4. The energy levels of the hypothetical lone electron pair are marked by the vertical lines.
However, the 'nS values of thiocyanates and isothiocyanates are divided almost unequivocally: 'nS ≥ 0 for thiocyanates, 'nS < 0 for isothiocyanates (in thiocyanates 3pS electronic density of atom of sulfur enters into a strongly bonding MO).
It was of interest to use the data obtained for the investigation of the electron density redistribution on complexation between a donor molecule PCl 3 or of SPCl 3 (where one can define the effective charges on all atoms by their Kα shifts) and an acceptor molecule AlBr3 containing no interfering atoms. The data presented in Table 5 show that, in spite of a positive qP growth on complexation, the total ligand electron density does not decrease (in the range of accuracy achieved) due to a strong dampening effect of the Cl atoms. This leads to a sufficient growth of
2462 X-RAY EMISSION SPECTROSCOPY, APPLICATIONS
Table 5
Change of atomic charges and bond ionicities of free ligands on their complexation
Ionicities of bonds (%)
∆A Kα a (eV)
a b c
Compound
A=P
A=S
A = Cl
P–S
P–Cl
PCl3
0.373(7)
–
–0.09(1)
–
44(5)
AlBr3PCl3
0.599(8)
–
–0.156(15)
–
72(7)
SPCl3
0.430(8)
–0.10(2)
–0.11(2)
50(6)
51(6)
AlBr3SPCl3
0.616(8)
–0.080(9)
–0.171(14)
68(7)
74(8)
b
Change of effective atomic charge (δ qA) c of ligands on their complexation in 4-31G** charge scale A=P
A=S
A = Cl
Σ δqi
0.5(1)
–
–0.10(7)
0.2(2)
0.4(1)
0.04(6)
–0.1(1)
0.1(2)
The mean-square errors in the last significant digit, taken for 95% confidence interval by Student’s criterion, are given in parentheses. The ionicity of the AB bond is equal to (|qA–qB|/2)100%. The positive sign of GqA corresponds to a decrease of the A atom electron density on complex formation.
the ionicity of all bonds of the ligands and acceptor. From Table 5 it also follows that the positive charge on the central acceptor atom grows sufficiently on complexation while the electron density on acceptor geminal of atoms does not decrease.
List of symbols ci = coefficient of
Further reading Dolenko GN (1993) X-ray determination of effective charges on sulphur, phosphorus and chlorine atoms. Journal of Molecular Structure 291: 2357.
Dolenko GN, Litvin AL, Elin VP and Poleshchuk OKh, (1991) X-ray investigation of electron density redistribution on complexation. Journal of Molecular Structure 251: 1127. Dolenko GN, Latajka Z and Ratajczak H (1995) X-ray spectral determination of the effective charges on P, S, and Cl atoms in chemical compounds with a nonempirical charge scale. Heteroatom Chemistry 6: 553557. Dolenko GN, Poleshchuk OKh and Koput J (1998) Antimonium pentachloride electron density redistribution on complexation. Heteroatom Chemistry 9: 543548. Mazalov LN and Yumatov VD (1984) Electronnoe stroenie ekstragentov. Novosobirsk: Nauka, 199 p. Nogaj B, Poleshchuk OKh, Kasprzak J, Koput J, ElinVP, Dolenko GN (1997)Changes in electron density distribution resulting from formation of antimony pentachloride complexes studied by X-ray fluorescence spectroscopy. Journal of Molecular Structure 406: 145 151. Poleshchuk OKh, Nogaj B, Dolenko GN and Elin VP (1993) Electron density redistribution on complexation in non-transition element complexes. Journal of Molecular Structure 297: 295312. Poleshchuk OKh, Nogaj B, Kasprzak J, Koput J, Dolenko GN, Elin VP, Ivanovskii AL (1994) Investigation of the electronic structure of SnCl4L2, TiCl4L2 and SbCl5L complexes by X-ray fluorescence spectroscopy. Journal of Molecular Structure 324: 215222.