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SKβ emission spectra of K2SO5 and KHSO4
Spectrochlmica Acta, Vol. 29A, pp. 1293to 1300.Pergamon Press 1975.Printed inNorthern Ireland
SKp emission spectra of K&O, and KHSO, EEVA-KAARINA
KORTELA
Institute of Materials Research, University of Turku, Turku, Finland
and Department of Electrical Engineering, University of Oulu, Oulu, Finland (Received 30 October 1972) Al&m&High resolution SK/? emission spectra of S,O,‘-- and HSO,- ions were measured with a two crystal X-ray spectrometer with an instrumental FWHM resolution of 0.25 eV for SKj3 X-rays. The observed spectra are interpreted with the aid of semiempiricalmolecular orbital calculations based on the Extended Hiickel and CNDO approximations. The relative energies can in both cases be attributed to the observed featuresin the oorrespondingexperimental spectrum, but the relative intensities come out differently from the two approximations used. The influence of the two sulfur atoms in two different oxidation states is discussed in the owe of S20r.,2-. The spectra of HSO,- and SOda- are compared on the basis of the isoelectronic structure of these two ions. I. INTRODUCTION serves one possibility for the study of the ionized states in atoms, molecules and solids. The experimentally observed fine structure in the valence electron X-ray emission spectra can be assigned to the molecular orbital structure of the valence shells of the emitting atom. Approximate molecular orbital calculations have shown their capability in the interpretation of the X-ray spectra [l, 21. The molecular orbital approximation can be used not only for free molecules but also for solids where a natural division to molecular subunits, molecules [3] or complex ions [4, 61 is possible. The X-ray emission of such solids can be interpreted by a calculation on just one isolated molecule or ion. When the effects of the crystalline surroundings become appreciable, so that the energy bands can not any more be associated to the separate units, a band description is more appropriate HIGH resolution X-ray
emission spectroscopy
[f31.
The SK/? emission spectrum of different sulfur compounds has been the subject of several studies in recent years [3, 7-121. In this work we present the experimental [l] R. MANNE,J. Chem. Phye. 52, 5733 (1970). [2] M. KIASSON and R. MANNE, in Electron Spectroecopy (Edited by D. A. SHIRLEY), NorthHolland, Amsterdam (1972). [3] E-K. KORTELA,E. SUONLNEN, M. Karmas and R. D68;NNE, J. Phys. B. 5, 2032 (1972). [4] R. MANNE,J. Chem. Phye. 46, 4645 (1967). [5] I. NEFEDOV, Z.Strmkt.Khim.8,1037 (1967)[J.Stmcct.Chem.8,919 (1967)]. [6] E-K. KORTELA and R. MANNE, Proc, conf. “X-ray Spectra and Electro-nic Structure of Matter,” Mtichen (1972). [7] A. FAESSLER and E. D. SCECMID, 2. Physik 128,71 (1954). [S] G. ANDERMANN and H. CL WHITE-AD, AcZwcm.X-Ray Anal. 14, 453 (1969). [9] R. SZARUAN, H. J. K~HLZR and A. MEISEL, Spectiochim.A& 2’7B, 43 (1972). [lo] G. ?!hF&SSON and R. MANITE, Phyeica Seti@ 4, 119 (1971). [ll] Y. GOSHI,A&on. X-Ray And. 12, 518 (1969). [12] E. SCHNELL, Monatsh. Chem. 94, 703 (1963). 1293
1294
EEVA-~INA
KORTJZLAmd MA!ITI KARRAS
SK/3 emission spectra of both the pyrosulfite ion S,0,2- and of the hydrogen sulfate ion HSO, as well as the molecular orbital interpretation of these two spectra. 2. EXPERIMENTAL A double-crystal spectrometer with calcite crystals was used in the measurements. The FWHM resolution was O-25eV [13] and a typical counting rate of 100 opm was obtained at the peak position with an Ag X-ray tube (Philips PW 2169112) for secondary excitation. The energies were calibrated against the vanadium K, line of V,O, in second order with proper corrections. The prolonged X-ray exposure on the sample was not observed to cause any changes in the shape of the spectra. 3. THEORY The X-ray transition energies are calculated with the aid of the one-electron orbital energies obtained from molecular orbital calculations. The approximations used were the Extended Hiickel approximation of Hoffman [14] and the ONDO/ method of POPLEet al. [15]. We used in our calculations a CND0/2 version QCPE 141.* In the EHT calculation a minimal valence basis set of sulfur 3e and 32, and oxygen 2s and 2~ was used while in the CNDO/Z calculation also the sulfur 3d orbitals were included into the basis set. The transition probability for a photon emission between states vtiand vj can be written under molecular orbital approximation I-
ES1I~
(I)
When the molecular orbitals y’i are expanded in terms of the atomic orbitals of the basis set (2) Yi = ~cilcX16 k
the well known expression for the X-ray emission intensity is obtained [4] :
In the derivation of equation (3) only the one center dipole elements are considered to be of importance. The slowly varying energy dependent term is also omitted. The effects of these approximations have been discussed by KARLSSON and MANNEin [lo], where they have found to be of minor importance. 3. CALCULATIONS The geometries and symmetries of the two ions considered here are given in Fig. 1 [ 16, 171. In the case of pyrosulfite the geometry ww idealized to give the ion the C, symmetry. * Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington, Indiana 47401. [13] E. SUONINEN,M. KARRASand J. LEVOS~A, Acta Polytech.&and. 71 (1970). [Ia] R. HOFFMAN,J. Chem. Phya. 89, 1397 (1963). [15] J. A. POPLE, D. P. SANTRY and G. A. SEPAL, J. Chem. Phys. 48, S-129 (1965). [lS] I. LINDQUIST and M. M~RTSELL,Acta Cry&. 10, 406 (1967). [17] L. H. LOOPSTRAand C. MACGILLAVRY,Acta Cryat. 11,349 (1968).
SK/I emission spectra of K&O,
2.209 A
sI-slx
%-O1 1.499i-t %-OlJI 1*472x
1296
and KHSO,
9-Or
2.456it 2.4268 2.418& 3.1968 IH I
slt-"lu I.431It (HSO.+)-
0 0
S
0
&f
0 0 %% I
,”
109.470
0
0
0
I
I i
H
S
%c& ti
0
0
0
Ii
0 ,;ip
S
I
0
0
0 S
0
s-o b52a O-H-O 2.608
0
0
I
H Fig. 1. The geometries of and structural parameters of K&&O& and KHSO, employed in the calculations.
The basis functions needed here were the Slater orbitals. The following ionization energies were chosen in the parametrization of the EHT method Sss: -21.13 eV, s 39'* -11.05 eV, 0Z8: -32.30 eV, OBp: -14.61 eV and H: -13.60 eV [18]. The conventional value 1.75 wa,s given to the Wolfsberg-Helmholz parameter. The parametrization in the CNDO/B method was that [19]. The experimental and calculated spectra are shown in Figs. 2 and 3. The calculated spectra are obtained by convoluting Lorenzian line shapes function of FWHM 2-OeV which gives widths comparable with the experimental spectrum. The same FWHM is used for all calculated components for the simplicity although the lower energy components seem somewhat wider. [la] J.
and H. H. JAFFE,J. Phys. Chewa.67, 1101-6(1963). Molecular Orbital Theory, MoGraw-Hill, New York (1970). FfINZE
[lS]J. A. POPLE and D. L. BEVERIDUE,Approzimzte
EEVA-KAARINAKORTELAand MATTI KARRAS
1296
EHT
CNDO
E,
eV
Fig. 2. The experimental and calculated spectra of K&3,0,. The cdcnlated tmnsition-intensitiesare marked as bar heightsctndconvolutedusing the Lorenzian line shape with FWHM of 2.0 eV to obtain & comparable spectrum.
The energy scales are shifted to give maximum coincidence to the line which in our opinion corresponds to the principal maximum in the experimental spectrum. 5. RESULTS
E&0,2The pyrosulfite ion S,0,2- can formally be described as built up of a thionate group SO,- and a thionite group SO,-. The experimental spectrum measured from K&&O5 is composed of a principal maximum with some asymmetry, of a low energy peak and of two weak but rather sharp peaks on the high energy side of the main peak. These high energy components are not resolved in the spectrum recorded by SCHNELL [12]. The calculated orbital energies and relative intensities are given in Table 1. The EHT method gives the greatest intensity to the line with the highest energy. However, the relative energies of the calculated lines indicate that the assignment
1297
SKB emission spectra of K&&O, and KHSO,
EHT
CNDO
01
’
2445
I 2450
1
I
1
2455
2460
2465
E,
I
2470
I
2475
I 2400
)
ev
Fig. 3. The experimental and calcul&ed spectra of KHSO,.
of Fig. 2 is the most probable. The orbital energies from the CNDO calculation differ more from the experimental ones than those obtained with the EHT calculation, but the agreement in the relative intensities is better in CNDO. The components contributing to the lowest energy peak are obviously broader than the FWHM used in our smearing procedure. In order to study the influence of the different oxidation numbers of the two sulfur atoms on their X-ray emission we calculated the emission intensity separately from each sulfur atom. The formal oxidation numbers are +6 and +4 for the thionite and the thionate group respectively. The results of this calculation are given in Table 1. Both EHT and CNDO methods give a strong localization of the outermost orbital on the thionate sulfur. The emission intensity of the thionite sulfur is lower than that of the thionate sulfur. (HSOJMercallite (KHSO,) is built up from (SO,)2- tetrahedm which are linked to each other with hydrogen bridges. There are two configurations of hydrogen bridges
EEVA-KAARINA
1298
KORTJSA and MA=
Table 1. Calculated orbital energh
KABBAS
and relative intensities
Extended Hiiokel (EHT) Rel. int.
cNDo/4 Rel.
ElltWgi~ Compound
8,00r=-
(eV)
SX
&I
Total
-3.62
68.13 37.59 0.01
10.47 8.07 2.27
78.60 46.66 2.27
0.03 0.27 0.87 0.49 1.65 0.48 2.92 3.51 4.25 1.81 4.17 1.79 3.17 1.23 0.02 0.01
0.16 0.29 1.02 0.59 6.85 5.71 7.17 3.81 3.51 8&i 4.16 12.41 3.19 3.17 2.69 0.10 0.07
-10.98
- 13.47 -13.51 - 13.67 - 13.63 -14.36 - 14.52 - 14.54 - IS.21 - IS.31 -1sm - 15.14 - 15.81 - 16.37 -17.14 - 18.71 -31.51 -31.67 -31.83 -35.80 - 37.48
WO,-1,
ElWgilZll3
-14.31 - 14.33 - 14.39 - 14.39 -1440 - 14.40 - 14.41 - 14.42 - 1442 - 14.42 - 14.56 - 14.66 - 14.66 -1410 - 14.12 - 15.33 - 15.37 - 15.45 - 16.45 - 15.41 - 15.55 - 16.74 -17.11 -18.12 -32.22 -32.28 - 32.36 -32.36 -32.62 -32.86 -35.69 -35.83
0.46 0.13 0.02 0.15 0.10 4.20 5.71 6.69 0.89 4.30 2.36 1.64 1.40 1.46 0.08 0.06
2.38 -
2.39 0.45
1.41 0.14 1.48 I.66 1.48 0.07 1.37 0.09 0.17 0.62 1.11 0.09 1.68 1.29 25.11 26.09 26.05 25.89 29.58 41.33 5.04 7.59 7.46 7.26 7.25 4.89 4.03 0.01
(eV)
- 0.43 1.21 -1.27 - 1.65 -2.19 -2.67 -3.41 -4.02 -4.40 -4.97 - 6.22 -6.35 - 6.58 -6.66 -8.51 -12.22 -23.00 -23.27 - 23.37 -26.41 -26.94 -2.36 -3.49
-3*60 -3.74 -3.18 -3.84 -4.56 -4.68 -5.38 -5.62 -6.91 -6.92
-7.75 -8.21 -8.70 -8.77 -8.83 -8.88 -9.26 -9.37 -10.83 -11.62 -11.78 -13.82 -25.41 -25.41 -25.47 -25.71 -26.75 -28.40 -29.34 -31.45
&I
Total
21.34
8.88
30.22
21.05 oQ51 0.27 4.38 1.16 4.89 9.33 2.38 16.49 20.92 0.32 0.33 12.68 4.26 2.72 1.50 9.83 0.03 3.62 0.43
0.36 0*06 0.41 1.66 7.66 7.55 1.08 5.38 2.31 1.40 14.15 15.48 18.41 0.46 8.42 8.78 2.73 12.00 1.20 0.64
21.40 0.57 0.68 6.04 8.82 12.i IO.41 7.76 18.80 22.32 14.47 15.81 30.99 4.72 11.14 IO.28 12.66 12.03 1.82 0.97
61
1.25
b,, bng b,, a,, bIo bI, b,, b,, b,, b*, b,, a,, bl, bsu a,, aI, big bIu Ozg bsu a,, bI, bzu aI, bsu b,, blu bss aI0 b,, b,, aI,
id.
4.00 1.51 6.62 6.78 3.23 1.63 0.04 3.65 0.36 10.92 8,77 11.57 9.38 9.24 1.66 0.23 9.90 3.01 7.70 5.14 5.62 4.21 3.84 0.01 0.73
1299
SK@ emission spectra of KJ120, and KHS04
with equal probability [17]. The (SOJa- tetrahedra may be linked by a hydrogen bridge on both sides of the symmetry centre, thus forming a sort of a double molecule. The point group of this double molecule is D,,. In the other configuration the (SO,)z- tetrahedra are linked by bridges repeating through a glide plane thus forming inGnite chains Fig. 1. The bond lengths in the tetrahedra and the lengths of the hydrogen bridges have been found to be the same for both configurations [17]. The results presented here are calculated for the double molecule. A calculation for a chain of three tetrahedra was also made, but the results obtained were essentially the same as those for the (HSO,),. The experimental spectrum consists of a main peak with some structure both on the high and the low energy sides and of a further peak at about 146 eV lower energy than the main peak. The calculated orbital energies with the symmetry assignments of the orbitals and relative intensities are given in Table 1. The experimental and calculated spectra are shown in Fig. 3. The structure of the high energy side has too high intensity according to the CNDO calculation. There are components with non-zero intensity also in the results of the EHT calculation which can be assigned to the extra struotures of the main peak but they are too weak to show up clearly in the smearing procedure. Sulfate ion SO,2- which is isoelectronic with the HSO,- ion studied here has full tetrahedral symmetry (TJ. The occupied orbitals with increasing energy are la, It, 2a, 2t, le 3t, It, [20]. In the SK/? X-ray emission only transitions from the t, orbitals are allowed and thus the experimental spectrum consists of the main peak (St,) with a very weak component on the high energy side (3t,) and one other peak of lower energies (I&). The irreducible representations of Td can be obtained as sums of the irreducible representations of the point group D2,, of (HSO,-),. However, the totally symmetric A, representation does no split when going from l’& to D,. There are transitions from orbitals a, of (HSO,-), at the energies comparable to that of the orbital 2a, of SOd2-which have non-zero intensity (Table 1) and the low energy shoulder in the experimental spectrum of HSO,- originates from these, in this case allowed, transitions from those a, levels. 6. DISCUSSION The SK/? emission of the two molecules studied here can be interpreted by molecular orbital calculations. E’rom the two methods used in the calculations the EHT gives a better overall agreement in relative energies of the observed lines. The CNDO method seems to give the relative intensities more correctly in the case of s2052-. This is probably due to the well-known fact that Extended Hiickel method gives highly exaggerated polarities to polar bonds like S-O. This is due to the lack of the explicit electron interaction and a self-consistent procedure in the EHT method. The result obtained here is in agreement with the results obtained for the SO,- ion only, S~ARCJAN et al. [9] report of a very satisfactory agreement of their calculations with experiments in the case of the sulfite ion when also the sulfur 3d orbitals are included in the basis set of the CNDO calculation. This better agreement [20] R.
MANNE,
M. KARRAS
and
E.
SUONINEN, Chem. Phys. Letters 15, 34
(1972).
1300
EEVA-KAARINAKORTELAmd MATTI WS
in comparison to the calculation of K~RLSSON and ~MBNNE[lo] without sulfur 3d orbitals was explained by Szargan et al. to be due to the enlarged basis set. It should, however, be noticed that Karlsson and Manne obtained very good X-ray emission intensities with VALENCE, an approximate MO-LCAO-SC%’ method with only sulfur 39 and 3~ orbitals in the basis set. Though the sulfur 3d orbitals have some influence to the bonding, the discrepancies between the results obtained here with EHT and CNDO in calculating wavefunctions and X-ray emission intensities from (S20rJ2- ion can in our opinion not be explained with the aid of the sulfur 3d orbtials only. The spectrum of HSO,- shows that the hydrogen bridges linking the SOa2tetrahedra to each other have only a minor influence on the K@ emission spectrum of the central sulfur atoms. The new features in the spectrum arise from the change in symmetry when sulfate ions form double molecules and infinite chains with hydrogen bridges as links. A similar effect is found in the spectrum of MgSO, + 4H,O where the hydrogen bridges arise probably from the crystal water. AcImowledgemente-Theauthors wish to thank Prof. ROLFMAm at the University of Bergen, Norway for several very useful discussions. The work wm supportedby the N&ion&l Research Councilfor Technical Sciencesof Finland.
SKp emission spectra of K&O, and KHSO, EEVA-KAARINA
KORTELA
Institute of Materials Research, University of Turku, Turku, Finland
and Department of Electrical Engineering, University of Oulu, Oulu, Finland (Received 30 October 1972) Al&m&High resolution SK/? emission spectra of S,O,‘-- and HSO,- ions were measured with a two crystal X-ray spectrometer with an instrumental FWHM resolution of 0.25 eV for SKj3 X-rays. The observed spectra are interpreted with the aid of semiempiricalmolecular orbital calculations based on the Extended Hiickel and CNDO approximations. The relative energies can in both cases be attributed to the observed featuresin the oorrespondingexperimental spectrum, but the relative intensities come out differently from the two approximations used. The influence of the two sulfur atoms in two different oxidation states is discussed in the owe of S20r.,2-. The spectra of HSO,- and SOda- are compared on the basis of the isoelectronic structure of these two ions. I. INTRODUCTION serves one possibility for the study of the ionized states in atoms, molecules and solids. The experimentally observed fine structure in the valence electron X-ray emission spectra can be assigned to the molecular orbital structure of the valence shells of the emitting atom. Approximate molecular orbital calculations have shown their capability in the interpretation of the X-ray spectra [l, 21. The molecular orbital approximation can be used not only for free molecules but also for solids where a natural division to molecular subunits, molecules [3] or complex ions [4, 61 is possible. The X-ray emission of such solids can be interpreted by a calculation on just one isolated molecule or ion. When the effects of the crystalline surroundings become appreciable, so that the energy bands can not any more be associated to the separate units, a band description is more appropriate HIGH resolution X-ray
emission spectroscopy
[f31.
The SK/? emission spectrum of different sulfur compounds has been the subject of several studies in recent years [3, 7-121. In this work we present the experimental [l] R. MANNE,J. Chem. Phye. 52, 5733 (1970). [2] M. KIASSON and R. MANNE, in Electron Spectroecopy (Edited by D. A. SHIRLEY), NorthHolland, Amsterdam (1972). [3] E-K. KORTELA,E. SUONLNEN, M. Karmas and R. D68;NNE, J. Phys. B. 5, 2032 (1972). [4] R. MANNE,J. Chem. Phye. 46, 4645 (1967). [5] I. NEFEDOV, Z.Strmkt.Khim.8,1037 (1967)[J.Stmcct.Chem.8,919 (1967)]. [6] E-K. KORTELA and R. MANNE, Proc, conf. “X-ray Spectra and Electro-nic Structure of Matter,” Mtichen (1972). [7] A. FAESSLER and E. D. SCECMID, 2. Physik 128,71 (1954). [S] G. ANDERMANN and H. CL WHITE-AD, AcZwcm.X-Ray Anal. 14, 453 (1969). [9] R. SZARUAN, H. J. K~HLZR and A. MEISEL, Spectiochim.A& 2’7B, 43 (1972). [lo] G. ?!hF&SSON and R. MANITE, Phyeica Seti@ 4, 119 (1971). [ll] Y. GOSHI,A&on. X-Ray And. 12, 518 (1969). [12] E. SCHNELL, Monatsh. Chem. 94, 703 (1963). 1293
1294
EEVA-~INA
KORTJZLAmd MA!ITI KARRAS
SK/3 emission spectra of both the pyrosulfite ion S,0,2- and of the hydrogen sulfate ion HSO, as well as the molecular orbital interpretation of these two spectra. 2. EXPERIMENTAL A double-crystal spectrometer with calcite crystals was used in the measurements. The FWHM resolution was O-25eV [13] and a typical counting rate of 100 opm was obtained at the peak position with an Ag X-ray tube (Philips PW 2169112) for secondary excitation. The energies were calibrated against the vanadium K, line of V,O, in second order with proper corrections. The prolonged X-ray exposure on the sample was not observed to cause any changes in the shape of the spectra. 3. THEORY The X-ray transition energies are calculated with the aid of the one-electron orbital energies obtained from molecular orbital calculations. The approximations used were the Extended Hiickel approximation of Hoffman [14] and the ONDO/ method of POPLEet al. [15]. We used in our calculations a CND0/2 version QCPE 141.* In the EHT calculation a minimal valence basis set of sulfur 3e and 32, and oxygen 2s and 2~ was used while in the CNDO/Z calculation also the sulfur 3d orbitals were included into the basis set. The transition probability for a photon emission between states vtiand vj can be written under molecular orbital approximation I-
ES1
(I)
When the molecular orbitals y’i are expanded in terms of the atomic orbitals of the basis set (2) Yi = ~cilcX16 k
the well known expression for the X-ray emission intensity is obtained [4] :
In the derivation of equation (3) only the one center dipole elements are considered to be of importance. The slowly varying energy dependent term is also omitted. The effects of these approximations have been discussed by KARLSSON and MANNEin [lo], where they have found to be of minor importance. 3. CALCULATIONS The geometries and symmetries of the two ions considered here are given in Fig. 1 [ 16, 171. In the case of pyrosulfite the geometry ww idealized to give the ion the C, symmetry. * Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington, Indiana 47401. [13] E. SUONINEN,M. KARRASand J. LEVOS~A, Acta Polytech.&and. 71 (1970). [Ia] R. HOFFMAN,J. Chem. Phya. 89, 1397 (1963). [15] J. A. POPLE, D. P. SANTRY and G. A. SEPAL, J. Chem. Phys. 48, S-129 (1965). [lS] I. LINDQUIST and M. M~RTSELL,Acta Cry&. 10, 406 (1967). [17] L. H. LOOPSTRAand C. MACGILLAVRY,Acta Cryat. 11,349 (1968).
SK/I emission spectra of K&O,
2.209 A
sI-slx
%-O1 1.499i-t %-OlJI 1*472x
1296
and KHSO,
9-Or
2.456it 2.4268 2.418& 3.1968 IH I
slt-"lu I.431It (HSO.+)-
0 0
S
0
&f
0 0 %% I
,”
109.470
0
0
0
I
I i
H
S
%c& ti
0
0
0
Ii
0 ,;ip
S
I
0
0
0 S
0
s-o b52a O-H-O 2.608
0
0
I
H Fig. 1. The geometries of and structural parameters of K&&O& and KHSO, employed in the calculations.
The basis functions needed here were the Slater orbitals. The following ionization energies were chosen in the parametrization of the EHT method Sss: -21.13 eV, s 39'* -11.05 eV, 0Z8: -32.30 eV, OBp: -14.61 eV and H: -13.60 eV [18]. The conventional value 1.75 wa,s given to the Wolfsberg-Helmholz parameter. The parametrization in the CNDO/B method was that [19]. The experimental and calculated spectra are shown in Figs. 2 and 3. The calculated spectra are obtained by convoluting Lorenzian line shapes function of FWHM 2-OeV which gives widths comparable with the experimental spectrum. The same FWHM is used for all calculated components for the simplicity although the lower energy components seem somewhat wider. [la] J.
and H. H. JAFFE,J. Phys. Chewa.67, 1101-6(1963). Molecular Orbital Theory, MoGraw-Hill, New York (1970). FfINZE
[lS]J. A. POPLE and D. L. BEVERIDUE,Approzimzte
EEVA-KAARINAKORTELAand MATTI KARRAS
1296
EHT
CNDO
E,
eV
Fig. 2. The experimental and calculated spectra of K&3,0,. The cdcnlated tmnsition-intensitiesare marked as bar heightsctndconvolutedusing the Lorenzian line shape with FWHM of 2.0 eV to obtain & comparable spectrum.
The energy scales are shifted to give maximum coincidence to the line which in our opinion corresponds to the principal maximum in the experimental spectrum. 5. RESULTS
E&0,2The pyrosulfite ion S,0,2- can formally be described as built up of a thionate group SO,- and a thionite group SO,-. The experimental spectrum measured from K&&O5 is composed of a principal maximum with some asymmetry, of a low energy peak and of two weak but rather sharp peaks on the high energy side of the main peak. These high energy components are not resolved in the spectrum recorded by SCHNELL [12]. The calculated orbital energies and relative intensities are given in Table 1. The EHT method gives the greatest intensity to the line with the highest energy. However, the relative energies of the calculated lines indicate that the assignment
1297
SKB emission spectra of K&&O, and KHSO,
EHT
CNDO
01
’
2445
I 2450
1
I
1
2455
2460
2465
E,
I
2470
I
2475
I 2400
)
ev
Fig. 3. The experimental and calcul&ed spectra of KHSO,.
of Fig. 2 is the most probable. The orbital energies from the CNDO calculation differ more from the experimental ones than those obtained with the EHT calculation, but the agreement in the relative intensities is better in CNDO. The components contributing to the lowest energy peak are obviously broader than the FWHM used in our smearing procedure. In order to study the influence of the different oxidation numbers of the two sulfur atoms on their X-ray emission we calculated the emission intensity separately from each sulfur atom. The formal oxidation numbers are +6 and +4 for the thionite and the thionate group respectively. The results of this calculation are given in Table 1. Both EHT and CNDO methods give a strong localization of the outermost orbital on the thionate sulfur. The emission intensity of the thionite sulfur is lower than that of the thionate sulfur. (HSOJMercallite (KHSO,) is built up from (SO,)2- tetrahedm which are linked to each other with hydrogen bridges. There are two configurations of hydrogen bridges
EEVA-KAARINA
1298
KORTJSA and MA=
Table 1. Calculated orbital energh
KABBAS
and relative intensities
Extended Hiiokel (EHT) Rel. int.
cNDo/4 Rel.
ElltWgi~ Compound
8,00r=-
(eV)
SX
&I
Total
-3.62
68.13 37.59 0.01
10.47 8.07 2.27
78.60 46.66 2.27
0.03 0.27 0.87 0.49 1.65 0.48 2.92 3.51 4.25 1.81 4.17 1.79 3.17 1.23 0.02 0.01
0.16 0.29 1.02 0.59 6.85 5.71 7.17 3.81 3.51 8&i 4.16 12.41 3.19 3.17 2.69 0.10 0.07
-10.98
- 13.47 -13.51 - 13.67 - 13.63 -14.36 - 14.52 - 14.54 - IS.21 - IS.31 -1sm - 15.14 - 15.81 - 16.37 -17.14 - 18.71 -31.51 -31.67 -31.83 -35.80 - 37.48
WO,-1,
ElWgilZll3
-14.31 - 14.33 - 14.39 - 14.39 -1440 - 14.40 - 14.41 - 14.42 - 1442 - 14.42 - 14.56 - 14.66 - 14.66 -1410 - 14.12 - 15.33 - 15.37 - 15.45 - 16.45 - 15.41 - 15.55 - 16.74 -17.11 -18.12 -32.22 -32.28 - 32.36 -32.36 -32.62 -32.86 -35.69 -35.83
0.46 0.13 0.02 0.15 0.10 4.20 5.71 6.69 0.89 4.30 2.36 1.64 1.40 1.46 0.08 0.06
2.38 -
2.39 0.45
1.41 0.14 1.48 I.66 1.48 0.07 1.37 0.09 0.17 0.62 1.11 0.09 1.68 1.29 25.11 26.09 26.05 25.89 29.58 41.33 5.04 7.59 7.46 7.26 7.25 4.89 4.03 0.01
(eV)
- 0.43 1.21 -1.27 - 1.65 -2.19 -2.67 -3.41 -4.02 -4.40 -4.97 - 6.22 -6.35 - 6.58 -6.66 -8.51 -12.22 -23.00 -23.27 - 23.37 -26.41 -26.94 -2.36 -3.49
-3*60 -3.74 -3.18 -3.84 -4.56 -4.68 -5.38 -5.62 -6.91 -6.92
-7.75 -8.21 -8.70 -8.77 -8.83 -8.88 -9.26 -9.37 -10.83 -11.62 -11.78 -13.82 -25.41 -25.41 -25.47 -25.71 -26.75 -28.40 -29.34 -31.45
&I
Total
21.34
8.88
30.22
21.05 oQ51 0.27 4.38 1.16 4.89 9.33 2.38 16.49 20.92 0.32 0.33 12.68 4.26 2.72 1.50 9.83 0.03 3.62 0.43
0.36 0*06 0.41 1.66 7.66 7.55 1.08 5.38 2.31 1.40 14.15 15.48 18.41 0.46 8.42 8.78 2.73 12.00 1.20 0.64
21.40 0.57 0.68 6.04 8.82 12.i IO.41 7.76 18.80 22.32 14.47 15.81 30.99 4.72 11.14 IO.28 12.66 12.03 1.82 0.97
61
1.25
b,, bng b,, a,, bIo bI, b,, b,, b,, b*, b,, a,, bl, bsu a,, aI, big bIu Ozg bsu a,, bI, bzu aI, bsu b,, blu bss aI0 b,, b,, aI,
id.
4.00 1.51 6.62 6.78 3.23 1.63 0.04 3.65 0.36 10.92 8,77 11.57 9.38 9.24 1.66 0.23 9.90 3.01 7.70 5.14 5.62 4.21 3.84 0.01 0.73
1299
SK@ emission spectra of KJ120, and KHS04
with equal probability [17]. The (SOJa- tetrahedra may be linked by a hydrogen bridge on both sides of the symmetry centre, thus forming a sort of a double molecule. The point group of this double molecule is D,,. In the other configuration the (SO,)z- tetrahedra are linked by bridges repeating through a glide plane thus forming inGnite chains Fig. 1. The bond lengths in the tetrahedra and the lengths of the hydrogen bridges have been found to be the same for both configurations [17]. The results presented here are calculated for the double molecule. A calculation for a chain of three tetrahedra was also made, but the results obtained were essentially the same as those for the (HSO,),. The experimental spectrum consists of a main peak with some structure both on the high and the low energy sides and of a further peak at about 146 eV lower energy than the main peak. The calculated orbital energies with the symmetry assignments of the orbitals and relative intensities are given in Table 1. The experimental and calculated spectra are shown in Fig. 3. The structure of the high energy side has too high intensity according to the CNDO calculation. There are components with non-zero intensity also in the results of the EHT calculation which can be assigned to the extra struotures of the main peak but they are too weak to show up clearly in the smearing procedure. Sulfate ion SO,2- which is isoelectronic with the HSO,- ion studied here has full tetrahedral symmetry (TJ. The occupied orbitals with increasing energy are la, It, 2a, 2t, le 3t, It, [20]. In the SK/? X-ray emission only transitions from the t, orbitals are allowed and thus the experimental spectrum consists of the main peak (St,) with a very weak component on the high energy side (3t,) and one other peak of lower energies (I&). The irreducible representations of Td can be obtained as sums of the irreducible representations of the point group D2,, of (HSO,-),. However, the totally symmetric A, representation does no split when going from l’& to D,. There are transitions from orbitals a, of (HSO,-), at the energies comparable to that of the orbital 2a, of SOd2-which have non-zero intensity (Table 1) and the low energy shoulder in the experimental spectrum of HSO,- originates from these, in this case allowed, transitions from those a, levels. 6. DISCUSSION The SK/? emission of the two molecules studied here can be interpreted by molecular orbital calculations. E’rom the two methods used in the calculations the EHT gives a better overall agreement in relative energies of the observed lines. The CNDO method seems to give the relative intensities more correctly in the case of s2052-. This is probably due to the well-known fact that Extended Hiickel method gives highly exaggerated polarities to polar bonds like S-O. This is due to the lack of the explicit electron interaction and a self-consistent procedure in the EHT method. The result obtained here is in agreement with the results obtained for the SO,- ion only, S~ARCJAN et al. [9] report of a very satisfactory agreement of their calculations with experiments in the case of the sulfite ion when also the sulfur 3d orbitals are included in the basis set of the CNDO calculation. This better agreement [20] R.
MANNE,
M. KARRAS
and
E.
SUONINEN, Chem. Phys. Letters 15, 34
(1972).
1300
EEVA-KAARINAKORTELAmd MATTI WS
in comparison to the calculation of K~RLSSON and ~MBNNE[lo] without sulfur 3d orbitals was explained by Szargan et al. to be due to the enlarged basis set. It should, however, be noticed that Karlsson and Manne obtained very good X-ray emission intensities with VALENCE, an approximate MO-LCAO-SC%’ method with only sulfur 39 and 3~ orbitals in the basis set. Though the sulfur 3d orbitals have some influence to the bonding, the discrepancies between the results obtained here with EHT and CNDO in calculating wavefunctions and X-ray emission intensities from (S20rJ2- ion can in our opinion not be explained with the aid of the sulfur 3d orbtials only. The spectrum of HSO,- shows that the hydrogen bridges linking the SOa2tetrahedra to each other have only a minor influence on the K@ emission spectrum of the central sulfur atoms. The new features in the spectrum arise from the change in symmetry when sulfate ions form double molecules and infinite chains with hydrogen bridges as links. A similar effect is found in the spectrum of MgSO, + 4H,O where the hydrogen bridges arise probably from the crystal water. AcImowledgemente-Theauthors wish to thank Prof. ROLFMAm at the University of Bergen, Norway for several very useful discussions. The work wm supportedby the N&ion&l Research Councilfor Technical Sciencesof Finland.