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Theoretical Auger energies using a frozen orbital approximation: The S(2p → mm′) and O(1s → mm′) Auger spectrum of SO2
Volume57, mlmber3
1 August 1978
TEIEORETICAL AUGER ENERGIES USING A FROZEN ORBJTAL APPROXiMATiON: THE S(2p + mm’) AND O(ls + mm’) AUGER SPECTRUM OF SO, M.A. ROBB Department of Chemistry Queen Elizabeth College, University London, UK
of London,
and G. THEODORA?X~POUJ_-OS and LG. CSIZMADIA Department of Chombrtty, Rziversity of Toronto. Toronto, Ontario, Canada Received 18 April 1978
A frozen orbital approximation (the parent orbital configuration interaction method) for calculations cn double hole states of moIecuIes gives similar assignments of ffie Auger spectra of Ha0 and H2S as SCF calculations. The POCI method is used to calculate the double valence holes of SO, and assign the S(2p -, mm’) and O(ls + mm’) Auger spectra of SO2. While for Hz0 and H2S the relaxation energy is much larger than tie contribution due to double hole confiition interaction, for SO, the two contributions are of similar magnitude_
1. Iutroduction The recent interest in the application of gas phase Auger electron spectroscopy in investigatingthe nature of molecular ions has stimulated a number of theoretical calculations of the energy of Auger transitions and their intensitiesfor a number of small molecules. In an Auger transition a core or inner hole ion decays to a lower energy double hole ion and the emitted eiectron has kinetic energy equal to the energy difference between the initial, hole and final, double hole states. The assignmentof the observed Auger lines is complicated by the fact that the number of double hole statescan be very large and by the absence of simple selection rules. Clearly, accurate calculations are necessary in order to ass@ the observed peaks [l]. In a previous c~rnmunication [2] a three configuration SCF method was used to calculate the singlet double hole statesof molecules_In this MC SCF method the wavefunction for the singSetstateshas the form:
‘I$ = {Cl@if + cyl47+ c$Jjj3 ,
(1)
where @ii, @ii are the determinantalwavetiction of +Jletwo closed shell double hole states and Gti is that of the corresponding open shell double hole state. The MC SCF methcd [2] gave virtually identical results with the results of large CI calculations [3] on the Auger energiesO(ls -+ ZZ’)* of the H,O molecule, and it was used to calculate the double hole states and assign the S(2p + mm’) Auger spectrum of H2S [2] _ Thus for relatively small systems SCF methods may be used for calculationson double hole statesleading to assignmentof Auger spectra of molecules in the gas phase_However, for larger systemsit becomes extremely cumbersome to do SCF calculationson all the possible double hole states of a molecule. For the SO2 molecule, there are 81 possible dcuble hole statesarisingby removing two electrons from the va* In thiscommunication mokculardoublehole statesare represented by lower case letters Iy and mm’ to diffkxtiatethem from atomic LL’ and= doublehole states 423
-CAL
Volume 57, number 3
PIiXWX LETTJZKS
I August 1978
od, used in this paper, wih be higher than the SCF energies of the double hole states. The difference between the SCF and the FOCI energies, for states which do not interact strongly with other states is a measure of the relaxation energy, i-e_ the energy lowering corresponding to the reorganization of the remaining electrons when 2 electrons are removed_
Ience sbeIl MO of the molecule- Obviously c simpler computational approach is required to treat such systems. Among the various methods of calculating ionization potentials, the frozen orbital approximation (or Koop,mans theorem) is the simplest method- Only one SCF calculation is required on the ground state of the parent molecule and the ionization potentials are given as the negative of the calculated orbital energies. This approach corresponds to a configuraticn interaction calculation over all possible hole states where the hoIe state wavefunctions are constructed using the ground state parent molecular orb&Is [4]. T&is approximation may aJ.sobe used for double hole states- ah double hole configurations may be constructed using the ground state parent molecule MO and the hamiltonian matrix of the double positive ion over these confi~rations is diagonalized to give orthogonal double hole states_ In this way, with one configuration interaction calculation, the approximate energies and wavefimctions are calculated for all the double hole states of a molecule_ It is expected that the energies cakulated with the parent orbital configuration interaction (POCI) meth-
2. Computational details FOCI calculations were carried out on the double hole states of Ei20, Hz S and SO,. The geometries were taken from refs. [5-T] ; rH_O = 09572 A, LHOH = l@k52”, ‘H-S = 1.335 A, LHSH = 92.5”, ‘s-O = 1.4321 & LOS0 = 110.536”. Basis sets: for H20 the basis set used is the same as that of ref. [S], for H2S the basis set used is the same as in ref. [2] _ For SO2 Huzinaga’s [9sSp] + [4s2p] oxygen [8] and Veillard’s [12&p] + [6s3p] sulphur [9] bases were augmented with d functions (cr8 = 0.846 and a0 = 0.800). AU the calculations were carried out on the CM= 7600 computer of the university of London.
TabIel Theoretialand~perImentaIk-rZrAugere~ergiesofH2@a) Doubleholestate
fluaerc) POE
uRek=f)
&e)
E$p
3B1 <3a;llbi1)
493.20
'At (lbr2) 'RI (3ai'Ibi') 3Az (ibi'Ib$) 3B2 (32i'lb;') 'Al(3ai2) 'A2 (Ibi'lb-1) s '% <2i’lG ) ‘4 (lG*) 'RI (2ai11bi1) 'AI C2ai13ait) 3~ <2ai'lb$) 'RI Caitlbi') tAl <2ai13ai1) lB2 (2ai'l~') 'At (2ai2)
491.96 491.04 490-19 488.99 488.94 48859 486-76 482.92 473.07 471.93 468.92 46592 464.92 460.64 444.30
9.20 8.81 8.53 7-76 7.33 7.46 7.32 7.08 6.07 8.92 8.68 8.88 7-47 9.36
0.00 -0.52 -0.13 -0.00 o-00 -0.55 -0.01 -0.01 -0.32 0.00 -0.01 0.00 0.12 0.38 O-01 1.00
502.40 500.77 499.57 497.95 496.32 496.40 495-91 493.84 488.99 480.85 474.64 473.80 468-11 453.66
b,
Eg;ger
Expt b,
50262d) 500.77 499.57 497.74d) 496.35d) 496.40 495.72 493.79 488.32 482.14d) 48iI66d) 475.83d) 474.02 473-46 467.26 451.45
500.8 498.6
493.8
486.7 482.1 475.3 472.4 467.7 450.8
All quantities 2re in eV_ b)Fromref.[3frrcferenceholestatecmrgyE
2)
424
_
Volume 57,number3
CHBMICALPHYSICSLBTlBBS
lAu9ust1978
Doublehotestate
E&yr
E$gg
EBBLAXb)
ECJ c)
Coefficient d)
rAr(2bi2) 3& (52ix2bi') 'B1 <5ai12bi1) 3A2(2b$12bi1) rA2(2Gr2bi1) 3B2(2b~15ni1) *Al(5ai2) 1Bq(2b$Sai') 'A1
139.22 138.79 136.88 136.03 135.05 133.48 133.48 131.71 128.23 i26.17 123.11 122.81 121.26 118.42 115.00 105.10
136.13 135.48 133.83 133.53 132.60 131.17 131.02 129.16 122.25 122.25 119.95 117.58 117.95 114.79 111.57 101.35
3.09 3.24 3.05 2.50 2.45 2.31 2.46 2.55 1.85 3.92 3.16 5.23 3.31 3.63 3.43 3.75
-0.30 -0.00 -l.15 0.00 0.00 0.00 -0.53 -0.20 -0.30 0.00 0.00 0.15 0.00 0.32 0.17 0.81
0.9904 1.0 0.9954 1.0 1.0 1.0 0.9615 0.9943 0.9637 1.0 1.0 0.9954 1-G 0.9878 0.9943 0.9843
2)Withres~ecttoSCFS~Pholestate E~=-392_40222h&~e~ b) EEL= = Ep - Et=. d) Coe~~c~entofthe~ea~co~iguration~en~the~stco~umn~~the~ expantion.
C?ECI = Ep
- rrii_
3. Results and discus&on The calculated 0( 1s + Li’) Auger energies of Hz0 are given in table 1. The difference between the POCI and the SCF values (“relaxation energy”) and the difference between the POCI eigenvalue and the diagonalelement ofthe hamiltonian matrix before diagonalization are also given. This latter difference gives a measure of the interaction between the double hole configurations. As shown, in table 1 the configuration interaction is negligible compared to the relaxation energy which is large with small variation (6.07-9.36 eV) for all states. These results show that the POCI calculation would lead to the same assignment of the Auger spectrum of Hz0 as the MC SCF calculations. A similar situation is encountered when the S(2p -+ mm’) Auger energies of H2S are calculated (cf. table 2). The configuration interaction is much smaller than the relaxation energy which is again fairly constant and both methods lead to the same assignments of the Auger spectrum of H2S. The relaxation energies for the double valence hole states of H2S are smaller than those for H30. The calculated molecular orbital energies of SO2 are given in table 3. The near degeneracy of several of
Table3 lhes)-mmetriesandener@esofthegroundstatemolecular orbitalsofS02 Shell symmetry
MO svmmetry
Orbitaleneqy
KS
1%
92.202767
Ko
lb2
20.619941
Ko
2%
20.619910
Ls
?G
-9.171178 -6.860733 -6.860132 -6.858003
1% 4al valence
5ar 3ba :< 7ar 2 Ia2
8al
-1.520922 -l.413?15 -0.879647 -G-705642 -G.7026441 -0.673461 -0.548606 -0.521593 -0.502413
E3.(S02)=-547.2G8388hartnz 425
Volume
(1) (2) (3) (4) (5) (6) U) (8) (9) (10) (ii) (12) (13) (14) (1%
57,
number
3
i August1978
cFE?dICALPHYSICSLETTERs
-2.04
-1.15 -124 -155 -3.1 -2-s -4-06 -231 -O_Ol 4.08 -449 0.73 -204 -0.75 -131
(Z) (17)
-1.72 0.14
(18)
-235 fl9) (20) (21) (22) (23) C-J) (25) (26)
(28) (2% 00,
(31) (32) (33) (34) (35) (Ml (37-l 08) (39)
-x60 -:33 -3.09 -6.46 0.41 058 -3.21
0.63 092 4.17 1.12 OM) 1.73 080 1.92 -0.16 227 365 1.08 224
118(1_78)d 460 2.19 1.98 5.87 1.15W
-l.lSC)
Volume 57, number 3
CHEMICAL
PHYSICS
the valence shell MO’s is expected to cause strong interaction between the double hole configurations which are numerous. The calculated Auger energies for SO2 range from 140.81 to 75.24 eV for the S(2p + mm’) and from 503.62 to 438.05 eV for the O(ls + mm’) transitioIls. In table 4 the configuration interaction contribution of the 39 lowest total energy double hole states * is given and compared with the SCF results for a few of the states_ As shown in table 4 the double hole states of SO2 are linear combinations of the many double hole configuration. The numbers listed under k$-kYji show that some of the states interact strongly- The magnitude of the configuration interaction contribution (Erc relaxation energy (i%f Z$$EEloEtEtE (double hole state n&nber 10) the PO& total ene& is lower than the SCF total energy by 1.18 eV. Clearly the FOCI results indicate that there is an extensive interaction between the original valence shell double hole configurations. This effect is out of the range of a three configuration SCF calculation and it could be investigated only with extensive and expensive MC SCF calculations_ The oxygen *S + llun’ and the sulphur ?P3i2 + mm’ Auger energies were calculated using the computed total energies of the double hole states and total energies for the initial hole states of 0 1s and S 2p hole states respectively, corresponding to the experimental IP for Y, 0 1s and S 2~3,~ electrons in the SO2 molecule -c_In this way, errors due to the inaccuracy of the computed initial hole state energy are not present. The results of these calculations are given along with the available experimental Auger energies in table 5. The theoretical values correspond to Auger transitions from a ‘tveighted average” hole state between the 2P,,2 and the *P,,, hole states. However, the Auger energy corresponding to the 2P3j2 initial state is only 0.433 eV larger than that corresponding to the average initial state [2] and since the peaks arising from transitiors from the 2P,,, state are
9 Only the Iowest 39 from the total of 81 double hole sfates are listed because their energies lie within the range which co~esponds to the experimentally observed Auger energies. Ip = 174.8 eV, 0 2S Ip = 539.6 eV_ Reference total energy: S ‘Ps/2 = -540.78428,O 2S = -527.37744.
*Experimental
S 2pqz
LETTJZRS
1 August 1973
twice as intense as those arising from the 21?1,2state, it is possible to assign the Auger spectrum using the theoretical values which are very close to the *P3/2 values. As shown in table 5, the agreement of the theoretical Auger energies with the experimental is good for Table 5 Sulphur ‘psfz -, mm’ and oxygen 2S -, mm’ Auger energies (eV) of SO2 Double hole state
Oxygen 2S+mm’
number
POCI
symmetry
IAl
:f:
3B2
(3) (4) 0) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39)
3A2 ‘A2 3B1 % %
l Al 3B2 IAl IA2 3A2 3-% 3B2 3B1 % 352 )?I B2 3A1 3A2 lfh lA2 3B1 3B2 52 % 3A1 3.42 lA1 532 3B1 ‘A2 ‘Al 3B2 lB1 3A2 ‘R2
1Al
502.9 502.81 502.78 502.40 501.48 501.42 501.21 500.80 500.80 500.47 499.58 499.55 499.44 499.28 499.03 498.65 498.62 497.19 495.44 495.43 494.92 494.90 494.66 494.48 494.22 493.89 493.23 492.37 491.73 491.68 491.61 490.28 490.23 489.78 489.60 488.99 487.87 487.80 487.04
Sulphur 2P3n + mm -
exper. a)
POCI
e~pa_ a)
505.1
138.09 138.00 137.97 137.65 137.28 136.61 136.40 136.00 135.48 135.66 134.77 134.74 134.63 134.47 134.22 133.84 133.81 132.38 130.65 130.62 130.11 13o_I)9 129.85 129.68 129.41 129.08 128.42 127.56 126.92 126.87 126.52 125.47 125.43 124.97 124.79 124.18 123.06 123.00 122.23
139.3
504.4 503.0
501.5
498.1
496.3
493.5
491.0
138.4
137.01
136.0
133.1
131.8
130.7
129.2
126.7
a) From reE [ 101.
427
Vohune 57. number 3
CHEMICAL
PHYSICS
both energy regions. The assignment shown in table S may be made by aliowing for a relaxation energy contriiution of about 1 to 2 eV. There are many transitions assigned to each experimental value because the double hole states are very close in energy, While a vary large MC SCF calculation may alter the position of certain of the states, it is expected that the assignment obtained with the EQCI calculation is valid. on the basis of the agreement between the POCI and ‘&e experimental v&es. A calculation of the transition probabilities might lead to a more definite assignment of the Auger energies.
428
LETTERS
1 August 1978
References [ 11 LH, Haier and J. Kendrick, MOL Pllys. 31(19x) 849. f21 fLEtk Eade, EEA. Robb, G. Theodorakopoulos and LG. Chismadia. Chem, Phys. Letters 52 (1977) 526. amI U.L Wahlgren, Chem. Phys [3] H,Agren,S.SLetters 3.5 (1975) 336.
[41 M-D_ Newton, J. Chem. Phyr 48 (1968) 2825. [S] S. prime azd M.A. Robb, Tkeoret. Chim. Acta 42 (1976) 181.
[6] G. Theodorakopoulos, LG. Csizmadia, MA Robb, k Kucsman and L Kapovits, 1. Chem. Sot_ Faraday Trans. II 73 (1977) 293. [7] S. Rothenkrg and lLF_ Schaefer III, J. Chem, Phyr 53 (1970) 3014. [8] S.Huziaga, J. Chem. Phys 42 (1965) 1293. [9] A. VeiiIard, Theoret. Chim_ Acta 12 (1968) 405. [ ZOJ M. Thompsoa, PA. Hewitt and D.S. WoEscroft, Anal_ Chem. 48 (1976) i336.
1 August 1978
TEIEORETICAL AUGER ENERGIES USING A FROZEN ORBJTAL APPROXiMATiON: THE S(2p + mm’) AND O(ls + mm’) AUGER SPECTRUM OF SO, M.A. ROBB Department of Chemistry Queen Elizabeth College, University London, UK
of London,
and G. THEODORA?X~POUJ_-OS and LG. CSIZMADIA Department of Chombrtty, Rziversity of Toronto. Toronto, Ontario, Canada Received 18 April 1978
A frozen orbital approximation (the parent orbital configuration interaction method) for calculations cn double hole states of moIecuIes gives similar assignments of ffie Auger spectra of Ha0 and H2S as SCF calculations. The POCI method is used to calculate the double valence holes of SO, and assign the S(2p -, mm’) and O(ls + mm’) Auger spectra of SO2. While for Hz0 and H2S the relaxation energy is much larger than tie contribution due to double hole confiition interaction, for SO, the two contributions are of similar magnitude_
1. Iutroduction The recent interest in the application of gas phase Auger electron spectroscopy in investigatingthe nature of molecular ions has stimulated a number of theoretical calculations of the energy of Auger transitions and their intensitiesfor a number of small molecules. In an Auger transition a core or inner hole ion decays to a lower energy double hole ion and the emitted eiectron has kinetic energy equal to the energy difference between the initial, hole and final, double hole states. The assignmentof the observed Auger lines is complicated by the fact that the number of double hole statescan be very large and by the absence of simple selection rules. Clearly, accurate calculations are necessary in order to ass@ the observed peaks [l]. In a previous c~rnmunication [2] a three configuration SCF method was used to calculate the singlet double hole statesof molecules_In this MC SCF method the wavefunction for the singSetstateshas the form:
‘I$ = {Cl@if + cyl47+ c$Jjj3 ,
(1)
where @ii, @ii are the determinantalwavetiction of +Jletwo closed shell double hole states and Gti is that of the corresponding open shell double hole state. The MC SCF methcd [2] gave virtually identical results with the results of large CI calculations [3] on the Auger energiesO(ls -+ ZZ’)* of the H,O molecule, and it was used to calculate the double hole states and assign the S(2p + mm’) Auger spectrum of H2S [2] _ Thus for relatively small systems SCF methods may be used for calculationson double hole statesleading to assignmentof Auger spectra of molecules in the gas phase_However, for larger systemsit becomes extremely cumbersome to do SCF calculationson all the possible double hole states of a molecule. For the SO2 molecule, there are 81 possible dcuble hole statesarisingby removing two electrons from the va* In thiscommunication mokculardoublehole statesare represented by lower case letters Iy and mm’ to diffkxtiatethem from atomic LL’ and= doublehole states 423
-CAL
Volume 57, number 3
PIiXWX LETTJZKS
I August 1978
od, used in this paper, wih be higher than the SCF energies of the double hole states. The difference between the SCF and the FOCI energies, for states which do not interact strongly with other states is a measure of the relaxation energy, i-e_ the energy lowering corresponding to the reorganization of the remaining electrons when 2 electrons are removed_
Ience sbeIl MO of the molecule- Obviously c simpler computational approach is required to treat such systems. Among the various methods of calculating ionization potentials, the frozen orbital approximation (or Koop,mans theorem) is the simplest method- Only one SCF calculation is required on the ground state of the parent molecule and the ionization potentials are given as the negative of the calculated orbital energies. This approach corresponds to a configuraticn interaction calculation over all possible hole states where the hoIe state wavefunctions are constructed using the ground state parent molecular orb&Is [4]. T&is approximation may aJ.sobe used for double hole states- ah double hole configurations may be constructed using the ground state parent molecule MO and the hamiltonian matrix of the double positive ion over these confi~rations is diagonalized to give orthogonal double hole states_ In this way, with one configuration interaction calculation, the approximate energies and wavefimctions are calculated for all the double hole states of a molecule_ It is expected that the energies cakulated with the parent orbital configuration interaction (POCI) meth-
2. Computational details FOCI calculations were carried out on the double hole states of Ei20, Hz S and SO,. The geometries were taken from refs. [5-T] ; rH_O = 09572 A, LHOH = l@k52”, ‘H-S = 1.335 A, LHSH = 92.5”, ‘s-O = 1.4321 & LOS0 = 110.536”. Basis sets: for H20 the basis set used is the same as that of ref. [S], for H2S the basis set used is the same as in ref. [2] _ For SO2 Huzinaga’s [9sSp] + [4s2p] oxygen [8] and Veillard’s [12&p] + [6s3p] sulphur [9] bases were augmented with d functions (cr8 = 0.846 and a0 = 0.800). AU the calculations were carried out on the CM= 7600 computer of the university of London.
TabIel Theoretialand~perImentaIk-rZrAugere~ergiesofH2@a) Doubleholestate
fluaerc) POE
uRek=f)
&e)
E$p
3B1 <3a;llbi1)
493.20
'At (lbr2) 'RI (3ai'Ibi') 3Az (ibi'Ib$) 3B2 (32i'lb;') 'Al(3ai2) 'A2 (Ibi'lb-1) s '% <2i’lG ) ‘4 (lG*) 'RI (2ai11bi1) 'AI C2ai13ait) 3~ <2ai'lb$) 'RI Caitlbi') tAl <2ai13ai1) lB2 (2ai'l~') 'At (2ai2)
491.96 491.04 490-19 488.99 488.94 48859 486-76 482.92 473.07 471.93 468.92 46592 464.92 460.64 444.30
9.20 8.81 8.53 7-76 7.33 7.46 7.32 7.08 6.07 8.92 8.68 8.88 7-47 9.36
0.00 -0.52 -0.13 -0.00 o-00 -0.55 -0.01 -0.01 -0.32 0.00 -0.01 0.00 0.12 0.38 O-01 1.00
502.40 500.77 499.57 497.95 496.32 496.40 495-91 493.84 488.99 480.85 474.64 473.80 468-11 453.66
b,
Eg;ger
Expt b,
50262d) 500.77 499.57 497.74d) 496.35d) 496.40 495.72 493.79 488.32 482.14d) 48iI66d) 475.83d) 474.02 473-46 467.26 451.45
500.8 498.6
493.8
486.7 482.1 475.3 472.4 467.7 450.8
All quantities 2re in eV_ b)Fromref.[3frrcferenceholestatecmrgyE
2)
424
_
Volume 57,number3
CHBMICALPHYSICSLBTlBBS
lAu9ust1978
Doublehotestate
E&yr
E$gg
EBBLAXb)
ECJ c)
Coefficient d)
rAr(2bi2) 3& (52ix2bi') 'B1 <5ai12bi1) 3A2(2b$12bi1) rA2(2Gr2bi1) 3B2(2b~15ni1) *Al(5ai2) 1Bq(2b$Sai') 'A1
139.22 138.79 136.88 136.03 135.05 133.48 133.48 131.71 128.23 i26.17 123.11 122.81 121.26 118.42 115.00 105.10
136.13 135.48 133.83 133.53 132.60 131.17 131.02 129.16 122.25 122.25 119.95 117.58 117.95 114.79 111.57 101.35
3.09 3.24 3.05 2.50 2.45 2.31 2.46 2.55 1.85 3.92 3.16 5.23 3.31 3.63 3.43 3.75
-0.30 -0.00 -l.15 0.00 0.00 0.00 -0.53 -0.20 -0.30 0.00 0.00 0.15 0.00 0.32 0.17 0.81
0.9904 1.0 0.9954 1.0 1.0 1.0 0.9615 0.9943 0.9637 1.0 1.0 0.9954 1-G 0.9878 0.9943 0.9843
2)Withres~ecttoSCFS~Pholestate E~=-392_40222h&~e~ b) EEL= = Ep - Et=. d) Coe~~c~entofthe~ea~co~iguration~en~the~stco~umn~~the~ expantion.
C?ECI = Ep
- rrii_
3. Results and discus&on The calculated 0( 1s + Li’) Auger energies of Hz0 are given in table 1. The difference between the POCI and the SCF values (“relaxation energy”) and the difference between the POCI eigenvalue and the diagonalelement ofthe hamiltonian matrix before diagonalization are also given. This latter difference gives a measure of the interaction between the double hole configurations. As shown, in table 1 the configuration interaction is negligible compared to the relaxation energy which is large with small variation (6.07-9.36 eV) for all states. These results show that the POCI calculation would lead to the same assignment of the Auger spectrum of Hz0 as the MC SCF calculations. A similar situation is encountered when the S(2p -+ mm’) Auger energies of H2S are calculated (cf. table 2). The configuration interaction is much smaller than the relaxation energy which is again fairly constant and both methods lead to the same assignments of the Auger spectrum of H2S. The relaxation energies for the double valence hole states of H2S are smaller than those for H30. The calculated molecular orbital energies of SO2 are given in table 3. The near degeneracy of several of
Table3 lhes)-mmetriesandener@esofthegroundstatemolecular orbitalsofS02 Shell symmetry
MO svmmetry
Orbitaleneqy
KS
1%
92.202767
Ko
lb2
20.619941
Ko
2%
20.619910
Ls
?G
-9.171178 -6.860733 -6.860132 -6.858003
1% 4al valence
5ar 3ba :< 7ar 2 Ia2
8al
-1.520922 -l.413?15 -0.879647 -G-705642 -G.7026441 -0.673461 -0.548606 -0.521593 -0.502413
E3.(S02)=-547.2G8388hartnz 425
Volume
(1) (2) (3) (4) (5) (6) U) (8) (9) (10) (ii) (12) (13) (14) (1%
57,
number
3
i August1978
cFE?dICALPHYSICSLETTERs
-2.04
-1.15 -124 -155 -3.1 -2-s -4-06 -231 -O_Ol 4.08 -449 0.73 -204 -0.75 -131
(Z) (17)
-1.72 0.14
(18)
-235 fl9) (20) (21) (22) (23) C-J) (25) (26)
(28) (2% 00,
(31) (32) (33) (34) (35) (Ml (37-l 08) (39)
-x60 -:33 -3.09 -6.46 0.41 058 -3.21
0.63 092 4.17 1.12 OM) 1.73 080 1.92 -0.16 227 365 1.08 224
118(1_78)d 460 2.19 1.98 5.87 1.15W
-l.lSC)
Volume 57, number 3
CHEMICAL
PHYSICS
the valence shell MO’s is expected to cause strong interaction between the double hole configurations which are numerous. The calculated Auger energies for SO2 range from 140.81 to 75.24 eV for the S(2p + mm’) and from 503.62 to 438.05 eV for the O(ls + mm’) transitioIls. In table 4 the configuration interaction contribution of the 39 lowest total energy double hole states * is given and compared with the SCF results for a few of the states_ As shown in table 4 the double hole states of SO2 are linear combinations of the many double hole configuration. The numbers listed under k$-kYji show that some of the states interact strongly- The magnitude of the configuration interaction contribution (Erc relaxation energy (i%f Z$$EEloEtEtE (double hole state n&nber 10) the PO& total ene& is lower than the SCF total energy by 1.18 eV. Clearly the FOCI results indicate that there is an extensive interaction between the original valence shell double hole configurations. This effect is out of the range of a three configuration SCF calculation and it could be investigated only with extensive and expensive MC SCF calculations_ The oxygen *S + llun’ and the sulphur ?P3i2 + mm’ Auger energies were calculated using the computed total energies of the double hole states and total energies for the initial hole states of 0 1s and S 2p hole states respectively, corresponding to the experimental IP for Y, 0 1s and S 2~3,~ electrons in the SO2 molecule -c_In this way, errors due to the inaccuracy of the computed initial hole state energy are not present. The results of these calculations are given along with the available experimental Auger energies in table 5. The theoretical values correspond to Auger transitions from a ‘tveighted average” hole state between the 2P,,2 and the *P,,, hole states. However, the Auger energy corresponding to the 2P3j2 initial state is only 0.433 eV larger than that corresponding to the average initial state [2] and since the peaks arising from transitiors from the 2P,,, state are
9 Only the Iowest 39 from the total of 81 double hole sfates are listed because their energies lie within the range which co~esponds to the experimentally observed Auger energies. Ip = 174.8 eV, 0 2S Ip = 539.6 eV_ Reference total energy: S ‘Ps/2 = -540.78428,O 2S = -527.37744.
*Experimental
S 2pqz
LETTJZRS
1 August 1973
twice as intense as those arising from the 21?1,2state, it is possible to assign the Auger spectrum using the theoretical values which are very close to the *P3/2 values. As shown in table 5, the agreement of the theoretical Auger energies with the experimental is good for Table 5 Sulphur ‘psfz -, mm’ and oxygen 2S -, mm’ Auger energies (eV) of SO2 Double hole state
Oxygen 2S+mm’
number
POCI
symmetry
IAl
:f:
3B2
(3) (4) 0) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39)
3A2 ‘A2 3B1 % %
l Al 3B2 IAl IA2 3A2 3-% 3B2 3B1 % 352 )?I B2 3A1 3A2 lfh lA2 3B1 3B2 52 % 3A1 3.42 lA1 532 3B1 ‘A2 ‘Al 3B2 lB1 3A2 ‘R2
1Al
502.9 502.81 502.78 502.40 501.48 501.42 501.21 500.80 500.80 500.47 499.58 499.55 499.44 499.28 499.03 498.65 498.62 497.19 495.44 495.43 494.92 494.90 494.66 494.48 494.22 493.89 493.23 492.37 491.73 491.68 491.61 490.28 490.23 489.78 489.60 488.99 487.87 487.80 487.04
Sulphur 2P3n + mm -
exper. a)
POCI
e~pa_ a)
505.1
138.09 138.00 137.97 137.65 137.28 136.61 136.40 136.00 135.48 135.66 134.77 134.74 134.63 134.47 134.22 133.84 133.81 132.38 130.65 130.62 130.11 13o_I)9 129.85 129.68 129.41 129.08 128.42 127.56 126.92 126.87 126.52 125.47 125.43 124.97 124.79 124.18 123.06 123.00 122.23
139.3
504.4 503.0
501.5
498.1
496.3
493.5
491.0
138.4
137.01
136.0
133.1
131.8
130.7
129.2
126.7
a) From reE [ 101.
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CHEMICAL
PHYSICS
both energy regions. The assignment shown in table S may be made by aliowing for a relaxation energy contriiution of about 1 to 2 eV. There are many transitions assigned to each experimental value because the double hole states are very close in energy, While a vary large MC SCF calculation may alter the position of certain of the states, it is expected that the assignment obtained with the EQCI calculation is valid. on the basis of the agreement between the POCI and ‘&e experimental v&es. A calculation of the transition probabilities might lead to a more definite assignment of the Auger energies.
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References [ 11 LH, Haier and J. Kendrick, MOL Pllys. 31(19x) 849. f21 fLEtk Eade, EEA. Robb, G. Theodorakopoulos and LG. Chismadia. Chem, Phys. Letters 52 (1977) 526. amI U.L Wahlgren, Chem. Phys [3] H,Agren,S.SLetters 3.5 (1975) 336.
[41 M-D_ Newton, J. Chem. Phyr 48 (1968) 2825. [S] S. prime azd M.A. Robb, Tkeoret. Chim. Acta 42 (1976) 181.
[6] G. Theodorakopoulos, LG. Csizmadia, MA Robb, k Kucsman and L Kapovits, 1. Chem. Sot_ Faraday Trans. II 73 (1977) 293. [7] S. Rothenkrg and lLF_ Schaefer III, J. Chem, Phyr 53 (1970) 3014. [8] S.Huziaga, J. Chem. Phys 42 (1965) 1293. [9] A. VeiiIard, Theoret. Chim_ Acta 12 (1968) 405. [ ZOJ M. Thompsoa, PA. Hewitt and D.S. WoEscroft, Anal_ Chem. 48 (1976) i336.