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MS Xα calculations on the valence auger spectrum of CO
Volume 88, number4
14 hfay 1982
CHEMCAL PHYSICS LETTERS
MS Xu CALCULATORS OPI THE VALENCE AUGER SPECTRUM OF CO Pranawa C. DESHMUKH * and R.G. HAYES Department
of Chemistry,
Umversity of Norre Dame, Notre Dame. Indrana 46556. USA
Recmved19 February 1982
We have examtned the utdrtyOCthe MS Xo method of cakulatton of moieeulareleetroruestructure.in tbe transL(tonstale model, as a tool tn the analysis of valence Augerspectra,ustngCO as a test case. The method is not especiaiIyreliable tn preduztlonof ftnalstate energies,but servesreasonablywell in predictionof the manyekctron ~ntn~utaon to the fmalstate energies and tn predlciron of lntensuies
1. Introduction
IC rates, as c~~u~at~ by ~CGUI~ [7]. This assumes that the
Analysisof the Augerspectraof moleculesinvokmg finalstateswhichhaveholesin the valencelevels m attracting increasmg attentron.
Some time ago ~rtenburger and Bagus f I] calculated the Auger energies of methane in a very complete way, doing sepa-
rate multiconfiguratlon Hartree-Fock calculations on the ground state and on the final states. Somewhat later. Hater and Kendrtck f2] calculated the Auger spectra of several small molecules, &en et al. [3] discussed H20 and Shaw and Thomas j4] dealt with HF. Much of the recent work can be traced to work by Stegbahn et ti_ [S] and by Agren et al. [3]. These workers performed direct c~~uIations of the Auger energies of Hz0 at the SCF level and also studied
the
effectof limitedconfigurationinteracttonoperat. mgsolelyIIIthe filledsubspace.Theyalsoprovided an anaiys8 of molecular Auger transition intensttles which assumed that, because the initial hole was strongly localized on one atom, oniy valence orbltal amphtude on that atom wasslgruficant in determintng the Auger transItton rate. This approximation has been made previously by Matthews and Komnmos [6] _The rate was thus reduced to a sum of atomichke contributions. The latter were replaced by atom* Presentaddress:Departmentof Physcs and Astronomy, GeorgiaState Uni~r~ty, Atlanta. Georgta,USA.
384
continuum
functions in the atomic and motec-
ular situation are the same,at leastnear the atom having a corehole. Jennison [S] has used an approach similar to S~egb~n et al. except that he has made hi anafysis semiempiacal. He uses the known core ionization potentlals to reduce the Auger energies to fiial.;tate energies with respect to the molecular ground state. The latter are then set equal to the sum of the ionization potentials for the valence orbitals involved in the transition, plus the hole-hole interaction, calculated on groundastate orbltals. This approach includes some electronic rearrangement empirically, through the ionization potentials. Jennison [9] calculates ~ten~ties according to the general program of Siegbuhn et al. except that he in-
cludesnonsrthogonalityby projectingthe valence orbit& calculated with a core hole on the ground state orbitais and uses core-hole-state orbitah to calculate matrix elements, thus ~~lud~g rearr~gement. Agren [IO] has also calculated fmal-state energies but his method is entirely theoretical, based on a hmited configuration interactlon. In considering moIecuies based on second-row atoms, &gren does three SCF calculations on three particular fiiai states chosen to be representative of fmal states in which both holes are in Zp-based orbitals, both holes are in 2s-based orbltals or one hole is in each, respectively. These three sets of orbit& are used then to anaIyze
14 Mr1y1982
CHEMICAL PHYSICS LETTERS
Volume 88. number 4
all final states, choosing the orbital set appropriate lo the foal state under study. For each state, a CI calcu-
the mter-sphere region. Transition state calculatrons were performed on each potential Auger transiicion.
lation is done based on the appropriate orbitals and Intensities are calculated on the Cl wavefunction.
That is to say,each possiblechoiceof core orbitals and pairs of valence orbltals was considered, rransi-
Chong [ 1 l] haj recently published some rather similar work, except that he uses a senuemprrical
hon-state occupation numbers were assigned, and the problem was iterated to convergence_ The calculations were spin-restncted. Auger intensities were calculated according to the afore-mentroned analysrs of Sregbahn et al. Since the MS XQ method givesorbitals IIInumerical form, molecular orbital coefficients are not at hand. We obtained similar quantities by fittmg the appropriate angular momentum component of the orbrtd of Interest to a Herman-Skdlman [ZOJ atomic function near the nucleus. Since the molecular orbItal components have very nearly the shape of the correspondmg HermanSkdlman function near the nucleus, the fit could be made by comparing values at the ongin. The appropriate transition-state orbitals were used in the fit.
valence-only computational
method, HAM/3, and is,
thus, able to base his CI on a separate transition-state calculation for each final state. Recently, Ramaker and co-workers [ 121 have been exarninmg the use of Xa DVM calculations in the analysis of molecular Auger spectra. They obtam the final-state energy directly from calculations on the
ground state and the double-hole states, and calculate intensities usmg the Siegbahn analysis and transitionstate orbltals. Earlier, members of the same group analyzed Auger data by a method reminiscent of that of Jennison et al., except that they approxunated the hole-hole mteraction in the manner that CNDO methods approximate
interelectronic
repulsion [ 131.
Atomic Auger rates were taken from h1cCuire.s work.
Curiously, very little work has appeared in which the famdlar MSX&method has beenused to analyze
No attempt was made to adjust the values for ioniclty of the atom in the moleculeor for vanatlon in the
molecular Auger spectra. Only CF4 appears to have been studied [ 141. Our attention was drawn to the potentiahtles of the method by the work of Sen [ 151, who calculated several atomic Auger energies well usmg a single tramltion-state calculation for each tranution, involving partial occupancy of the mitial core orbital and the two final valence orbirals. Weset out to apply Sen’s technique to the valence Auger spectrum of CO, as a way of testmg the worth of the method in the context of a molecular calculation. CO seemed to be a good choice because experunental data of good quality are at !rand [ 16,171 and seieral
energy of the outgomg electron,
The absolute Auger energies calculated as descnbed are not especially good. For instance, we calculate the carbon Auger transition leaving the molecule with two holes m the 50 orbital to he at 275.9 I eV, whereas Carlson and co-workers observe the transItron which has been assigned to the above [2 I ] to fall at 250.4 eV. Part of this error may be assrgned to the
calculations
ovcrcstimauon
have been perf~xmed.
3. Results
of the carbon 1s bindmg energy by
12.8eV in our calculation.(That ISto say, IIIa tranw 2.
Computational details
Uon-. tate calculation of the carbon 1s binding energy using the parameters we use.) An earlier calculatron by Connolly [22] has ylelded simdar results for the
A conventional MS Xa code, traceable to the MIT [ 181 code was used, implemented on the Umverslty of Notre Dame IBM 3701155. Calculations were performed P* Y ti!c;;,uclear drstance of 2.132 au, tk groundstate internuclear dlstance. The carLn, oxygen and outer spheres had r-add 0.984 au, 1.148 au and 2.132 au, respectively.
exchange pararneteqcu,waschosen usingSchwartz’ method [ 191 for carbon and oxygen, and averaged in
The
zirbon 1s binding energy. Wedecided, since the absolute energies were pocr, to examine hole-hole interaction energies as others have done [ 12,211. We obtamed them indirectly from comparison of the Auger energy calculated as desctrbed above and the appropriate combination of ronizatlon potentials obtained from tranSItion-state calculations. We have thus two estimates of these quantities, from the two transltion-state calculations. These differ 385
Volume 88. number 4 Table
CHEMICAL PHYSICS LETTERS
1
Fmat-stote enegms of
State a)
various
doublehole
This workb) 41 X(39.2) .WSi40 8) 38.9(325) 45.9(47.4) 49 S(49 1) 52.4(50.9) 63 O(53 6) 67.4f61.7) 70.4(63.4) 88 6(76 3)
states
14 hfay 1982
of CO, from our ~culations, from the work ofothersand from ex~~ents
Ref. (211
Ref. [231
43.4
36.8
42.8 47.0 45.2
41.2 43.3
50.5(A)
45.7 (A)
54.4
51.4 59.7 60 4 72.2 76.0 95.6
S9.S 675 78.6 79 8 102.7
first tomration pofentids and the hole-hoie descibedtn the test. AR ener& III eV. C) The assignment of ref. [211 appbed to the data of ref. [ 161.
much as 0.9 eV and we have averaged them. We also calculated the hole-hole interactron drrectly for the &~%afinal state as a difference in transitionstate energies[(312)~(4o)~*~ versus(30)*(40)~*~ and (30)’ 5(4u)2 versus (30)~~(40>~ 1. The two estrmates agreed to 0.15 eV and yielded an interactton of 12.9 eV. We compare our results to those of others in table 1. As noted in table I, the exper~ent~ alignment IS that of Jennison et at., with whose assignments others do not always agree. It should be noted that the quantity we tabulate is essentially that calculated by Jennison and co-workers. That is, we obtain an effectrve hole-hole interaction (whmh includes rearrangement in our case) from our data and add this to expertmental ionizatton potent&. Our direct fmal-state energies (the equiv~ent of &en’s or Huriey’s results) fare less well. For compbteness, we give our fmafstate energies u-tparentheses. They come from the calculated Auger energtes by subtraction of calculated mitral hole b~dmg energies (308.7 eV for carbon Is, 545.4 eV for oxygen Is). The relative mtensitres we caiculate,compared with relative intensities from other calculations, ap pear m table 2. Both carbon Auger and oxygen Auger intenuttes from our work and from the work of Jennison and co-workers have been scaled separately to the correspondmg (3o)* transition. It is more difficult to scale Sregbahn and Agren’s results, which comefrom CI calculationsand d~~IayconsIderable
386
422
43.7
46.6 43.9 48.6(a) 52.0 56.6 65.0 76.7 77 6 1005
a) States arc Melted by placement of holes. b) Encrgres gwen are the sum of expenmentd
by tts
ExperimentC)
Ref. 1241
45.8
48.1
51.1 57.5 65.9 73.2 75.3 95.4
~teraction/~l~at~o~
term colcutated as
Table 2 Intensitms of Auger transitions relatwe to (30)~ Ikai
state
This
from various calculations,
Jennrson
work
Sr~bahn and aPen
et al_
C SU1U 4050 fSu)*
959 202 32.41
OC
OC
0
054 5.45 0.15 3 62 004 3.72
0 81 2.76 0.48 (3 00) 0.05 7 9 4.19
(ldZ 4aln
2.38
6.65
I.61
3.46 1.72
2 25 0.4
2.0
(4oP 3050 3aln 3040 (30)2
154
138
057
0.8
1.70 1.25 1.23 (i.00)
0.44 0.96
0.7
0.4 (0 30) 004
03
1.1
0.43 4 34 026 2.01 2.37 190 0.46 2.15 1.17 (1.00) (1.00) (1.00)
configurational mixtng as well as multiplet splittmg. We have scaled the calculated intensities for the sing let transtrions of the upper levels, which are less heavtiy mixed, to the 4050 in the manner mdicated in table 3,.
4. Discussion
Tables 1 and 2 suggest that the MS Xormethod can serve reasonably welJ as a tool for the mterpretatron of valence Auger spectra. It is not as successful as
Agren’s method (for instance) in producing final-state energies. In fact, it is sufficiently far off to be quite useless. Used as a method for estimating the two-hole contribution to final-state energies, however, in the framework of the analysis of Jennison
et al. or of
et al., it is quite successful. The internties predictedby the methodare not in
Ramaker
discord with those predicted by other analyses or by experiment. They can thus, serve in the assIgn-
violent
ment of spectra. It ISdifficult to compare experimental and theoretical intensities quanlitatively because of great disparities in mtensity, width and vlbratlonal structure of various features and because of the in‘trusion of features usually asslgned to satellites of various kinds. There are a few observations to be made
however. The large discrepancy between our mtensity for (In)2 and the intensity obtained by Jenmson et al. presumably can be attributed, at least in part, to the fact that configuratlonal mixing between In and 2n IS important III the initial carbon Is hole state but not in the corresponding oxygen Is hole state [25]. There is also a large discrepancy in the (So)2 state in the carbon Auger spectrum. We have, as we described earher, calculated intensities using transition-state orbrtals rather than core-hole-state orbitals. We did this because we wished to evaluate the use of a single tranntion.state calculation to descnbe an Auger transitlon both in energy and In intenstty. Our use of transltionstate orbitals is not important m determinmg the calculated intensity of the (5~)~ transition, though. Rather, It would appear that the MS Xo!calculations gve this orbital more carbon 2s character than do the LCAO calculations. Conversion of our results and the results of the analysis by Jennison et rd. to twoelectron contnbutlons, by subtracting the sum of ionization potentials (for the two electrons removed) from the final-state energies, leaves a roughly constant contribution of lo-13 eV from our results. Ramaker and co-workers found similar results for 02. The roughly corresponding result from Jennison’s analysis increases with fiialstate energy from = 10 eV to ~26 eV. The difference, about the calculated Intensities,
in general, is not surpnsing
14 hlry 1982
CHEMICAL PHYSICSLETTERS
Volume 88. number 4
because
Jenmson et al.
calculate hole-hole repulsion on ground-state orbitals whereas our result includes rearrangement, which becomes increasingly important in the higher states. Jennson’s calculations, however, yield greater hole-
hole repulsion for states with two holes m the same
orbital than for other states at comparable energy. This effect IS not noted in our calculations nor, on the whole, m the calculations of Ramaker and coworkers. It has the result, m CO, of suggesting a stnking misassignment of the (50)~ fiial state. Our crlculations would make (la)’ rhe most stable find state, the assignment of table I is almost surely
whereas
correct.
5. Conclusions
MS Xa calculations in the transition-state model appear to produce an adequate descnptlon of the valence Auger spectra of molecules,Judgmg from our expenence with CO, if they are used as part of a semiempirical description of the spectra. They fare less well in predicting final-state energies or Auger energies directly. They also appear to overestmlate the stabdization of states with two holes in the same orbital
Acknowledgement The authors wish to thank Dr. I. Tse for useful help with the MS Xa code and to thank Dr. D. Jennison, who has made several useful comments on the work. The support of NIH under Grant GM25453 is acknowledged gratefully.
References [I] 1.B Ortenburger and P.S. Bays, Phys Rev. Al I (1975) 1501. [2] I.H. Hdber and J. Kendrtck, Mol. Phys. 31 (1976) 849. [3j H. &en, S. Svensson and V.I. Wahlgren,Chem. Phys. Letters 35 (197.5) 336. [4] RN. Shaw Jr. sod TD Thomas, Phys. Rev. Al t (1975) 1491. [S] H. Slrgbahn. L Asplund and P. Kelfve.Chcm. Phys. Letters 35 (1975) 330. [6] I A.D. Matthew and Y. Komnioos. Surface SCI.53 (1975) 716. [7J EJ.hlffiue,Phys.Rev.
I85 (1969)
1.
181 D.R. Jennison,Chem. Phys. Letters 69 (1980)435. [9] D.R. Jennaon,Phys. [IO]
H
Agren.
Rev. A23 (1981)
121.5.
J. Chem. Phys. 75 (1981) 1267.
[ 111 D.P.Chong.Chcm.Phys.
Letters82
(1981) 511. 387
Volume 88. number 4
CHEMICAL PHYSICS LBlTERS
[ 121 BJ. Dunlap, P.A. Mti and D.E. Rademaker. J. Chem. Phys. 75 (1981) 300. [ 131 DE. Ranraker, JS. Murday , NH. Turner, G. Moore, M. Lagally and J. Hou.ston,Phys. Rev. Bl9 (1979) 5375. [ 141 M. Barber, JD. Clark and A. Hinchbffe.Chem. Phys. Letters 48 (1977) 593. [IS] K.D. Sen. J.Chem. Phys. 73 (1980) 4104. [ 161 WE ModdemaqTA. Carlson.M.0. Krause, BP. Pullen, WE. Bull and CX. Schweitzer. J. Chem. Phys. 55 (1971) 2317. [ 171 K. Sregbahn, C. Nordling,G. Johansscn, I. Hedman, P.F. Hedh. K. Rimin. V. Celius.T. Bercmark. L 0. Weme. R. Manne and Y. Baer, ESCA applied to free molecules (North-Holland, Amsterdam, 1969).
388
14 May 1982
[ 181 KH. Johnson, J. Chem. Phys. 45 (1966) 3085. [ 191 K. Schwartz, Phys. Rev. B5 (1972) 2466. [20] F. Herman and S. Skillman. Atomic structure calculations (P:enticeHaS, Englewood Chffs, 1963). 1211 J.A. Kelber, D.R. Jemuson and R.R. Rye, J.Chem. Phys. 75 (1981) 652. 1221 J.W.D. Connolly, H. Siegbatm. V. Celius and C. Nordbng, J. Chem. Phys. 58 (1973) 4265. [23] H. Agren and H. Siegbahn, Chem. Phys. Letters 72 (1980) 498. [24] A.C. Hurly, J. Mol. Spectry.9 (1962) 18. [Xl D.R. Jennison. J.A. Kelber and R.R. Rye.Chem. Phys.
Letters 77 (1981) 604.
14 hfay 1982
CHEMCAL PHYSICS LETTERS
MS Xu CALCULATORS OPI THE VALENCE AUGER SPECTRUM OF CO Pranawa C. DESHMUKH * and R.G. HAYES Department
of Chemistry,
Umversity of Norre Dame, Notre Dame. Indrana 46556. USA
Recmved19 February 1982
We have examtned the utdrtyOCthe MS Xo method of cakulatton of moieeulareleetroruestructure.in tbe transL(tonstale model, as a tool tn the analysis of valence Augerspectra,ustngCO as a test case. The method is not especiaiIyreliable tn preduztlonof ftnalstate energies,but servesreasonablywell in predictionof the manyekctron ~ntn~utaon to the fmalstate energies and tn predlciron of lntensuies
1. Introduction
IC rates, as c~~u~at~ by ~CGUI~ [7]. This assumes that the
Analysisof the Augerspectraof moleculesinvokmg finalstateswhichhaveholesin the valencelevels m attracting increasmg attentron.
Some time ago ~rtenburger and Bagus f I] calculated the Auger energies of methane in a very complete way, doing sepa-
rate multiconfiguratlon Hartree-Fock calculations on the ground state and on the final states. Somewhat later. Hater and Kendrtck f2] calculated the Auger spectra of several small molecules, &en et al. [3] discussed H20 and Shaw and Thomas j4] dealt with HF. Much of the recent work can be traced to work by Stegbahn et ti_ [S] and by Agren et al. [3]. These workers performed direct c~~uIations of the Auger energies of Hz0 at the SCF level and also studied
the
effectof limitedconfigurationinteracttonoperat. mgsolelyIIIthe filledsubspace.Theyalsoprovided an anaiys8 of molecular Auger transition intensttles which assumed that, because the initial hole was strongly localized on one atom, oniy valence orbltal amphtude on that atom wasslgruficant in determintng the Auger transItton rate. This approximation has been made previously by Matthews and Komnmos [6] _The rate was thus reduced to a sum of atomichke contributions. The latter were replaced by atom* Presentaddress:Departmentof Physcs and Astronomy, GeorgiaState Uni~r~ty, Atlanta. Georgta,USA.
384
continuum
functions in the atomic and motec-
ular situation are the same,at leastnear the atom having a corehole. Jennison [S] has used an approach similar to S~egb~n et al. except that he has made hi anafysis semiempiacal. He uses the known core ionization potentlals to reduce the Auger energies to fiial.;tate energies with respect to the molecular ground state. The latter are then set equal to the sum of the ionization potentials for the valence orbitals involved in the transition, plus the hole-hole interaction, calculated on groundastate orbltals. This approach includes some electronic rearrangement empirically, through the ionization potentials. Jennison [9] calculates ~ten~ties according to the general program of Siegbuhn et al. except that he in-
cludesnonsrthogonalityby projectingthe valence orbit& calculated with a core hole on the ground state orbitais and uses core-hole-state orbitah to calculate matrix elements, thus ~~lud~g rearr~gement. Agren [IO] has also calculated fmal-state energies but his method is entirely theoretical, based on a hmited configuration interactlon. In considering moIecuies based on second-row atoms, &gren does three SCF calculations on three particular fiiai states chosen to be representative of fmal states in which both holes are in Zp-based orbitals, both holes are in 2s-based orbltals or one hole is in each, respectively. These three sets of orbit& are used then to anaIyze
14 Mr1y1982
CHEMICAL PHYSICS LETTERS
Volume 88. number 4
all final states, choosing the orbital set appropriate lo the foal state under study. For each state, a CI calcu-
the mter-sphere region. Transition state calculatrons were performed on each potential Auger transiicion.
lation is done based on the appropriate orbitals and Intensities are calculated on the Cl wavefunction.
That is to say,each possiblechoiceof core orbitals and pairs of valence orbltals was considered, rransi-
Chong [ 1 l] haj recently published some rather similar work, except that he uses a senuemprrical
hon-state occupation numbers were assigned, and the problem was iterated to convergence_ The calculations were spin-restncted. Auger intensities were calculated according to the afore-mentroned analysrs of Sregbahn et al. Since the MS XQ method givesorbitals IIInumerical form, molecular orbital coefficients are not at hand. We obtained similar quantities by fittmg the appropriate angular momentum component of the orbrtd of Interest to a Herman-Skdlman [ZOJ atomic function near the nucleus. Since the molecular orbItal components have very nearly the shape of the correspondmg HermanSkdlman function near the nucleus, the fit could be made by comparing values at the ongin. The appropriate transition-state orbitals were used in the fit.
valence-only computational
method, HAM/3, and is,
thus, able to base his CI on a separate transition-state calculation for each final state. Recently, Ramaker and co-workers [ 121 have been exarninmg the use of Xa DVM calculations in the analysis of molecular Auger spectra. They obtam the final-state energy directly from calculations on the
ground state and the double-hole states, and calculate intensities usmg the Siegbahn analysis and transitionstate orbltals. Earlier, members of the same group analyzed Auger data by a method reminiscent of that of Jennison et al., except that they approxunated the hole-hole mteraction in the manner that CNDO methods approximate
interelectronic
repulsion [ 131.
Atomic Auger rates were taken from h1cCuire.s work.
Curiously, very little work has appeared in which the famdlar MSX&method has beenused to analyze
No attempt was made to adjust the values for ioniclty of the atom in the moleculeor for vanatlon in the
molecular Auger spectra. Only CF4 appears to have been studied [ 141. Our attention was drawn to the potentiahtles of the method by the work of Sen [ 151, who calculated several atomic Auger energies well usmg a single tramltion-state calculation for each tranution, involving partial occupancy of the mitial core orbital and the two final valence orbirals. Weset out to apply Sen’s technique to the valence Auger spectrum of CO, as a way of testmg the worth of the method in the context of a molecular calculation. CO seemed to be a good choice because experunental data of good quality are at !rand [ 16,171 and seieral
energy of the outgomg electron,
The absolute Auger energies calculated as descnbed are not especially good. For instance, we calculate the carbon Auger transition leaving the molecule with two holes m the 50 orbital to he at 275.9 I eV, whereas Carlson and co-workers observe the transItron which has been assigned to the above [2 I ] to fall at 250.4 eV. Part of this error may be assrgned to the
calculations
ovcrcstimauon
have been perf~xmed.
3. Results
of the carbon 1s bindmg energy by
12.8eV in our calculation.(That ISto say, IIIa tranw 2.
Computational details
Uon-. tate calculation of the carbon 1s binding energy using the parameters we use.) An earlier calculatron by Connolly [22] has ylelded simdar results for the
A conventional MS Xa code, traceable to the MIT [ 181 code was used, implemented on the Umverslty of Notre Dame IBM 3701155. Calculations were performed P* Y ti!c;;,uclear drstance of 2.132 au, tk groundstate internuclear dlstance. The carLn, oxygen and outer spheres had r-add 0.984 au, 1.148 au and 2.132 au, respectively.
exchange pararneteqcu,waschosen usingSchwartz’ method [ 191 for carbon and oxygen, and averaged in
The
zirbon 1s binding energy. Wedecided, since the absolute energies were pocr, to examine hole-hole interaction energies as others have done [ 12,211. We obtamed them indirectly from comparison of the Auger energy calculated as desctrbed above and the appropriate combination of ronizatlon potentials obtained from tranSItion-state calculations. We have thus two estimates of these quantities, from the two transltion-state calculations. These differ 385
Volume 88. number 4 Table
CHEMICAL PHYSICS LETTERS
1
Fmat-stote enegms of
State a)
various
doublehole
This workb) 41 X(39.2) .WSi40 8) 38.9(325) 45.9(47.4) 49 S(49 1) 52.4(50.9) 63 O(53 6) 67.4f61.7) 70.4(63.4) 88 6(76 3)
states
14 hfay 1982
of CO, from our ~culations, from the work ofothersand from ex~~ents
Ref. (211
Ref. [231
43.4
36.8
42.8 47.0 45.2
41.2 43.3
50.5(A)
45.7 (A)
54.4
51.4 59.7 60 4 72.2 76.0 95.6
S9.S 675 78.6 79 8 102.7
first tomration pofentids and the hole-hoie descibedtn the test. AR ener& III eV. C) The assignment of ref. [211 appbed to the data of ref. [ 161.
much as 0.9 eV and we have averaged them. We also calculated the hole-hole interactron drrectly for the &~%afinal state as a difference in transitionstate energies[(312)~(4o)~*~ versus(30)*(40)~*~ and (30)’ 5(4u)2 versus (30)~~(40>~ 1. The two estrmates agreed to 0.15 eV and yielded an interactton of 12.9 eV. We compare our results to those of others in table 1. As noted in table I, the exper~ent~ alignment IS that of Jennison et at., with whose assignments others do not always agree. It should be noted that the quantity we tabulate is essentially that calculated by Jennison and co-workers. That is, we obtain an effectrve hole-hole interaction (whmh includes rearrangement in our case) from our data and add this to expertmental ionizatton potent&. Our direct fmal-state energies (the equiv~ent of &en’s or Huriey’s results) fare less well. For compbteness, we give our fmafstate energies u-tparentheses. They come from the calculated Auger energtes by subtraction of calculated mitral hole b~dmg energies (308.7 eV for carbon Is, 545.4 eV for oxygen Is). The relative mtensitres we caiculate,compared with relative intensities from other calculations, ap pear m table 2. Both carbon Auger and oxygen Auger intenuttes from our work and from the work of Jennison and co-workers have been scaled separately to the correspondmg (3o)* transition. It is more difficult to scale Sregbahn and Agren’s results, which comefrom CI calculationsand d~~IayconsIderable
386
422
43.7
46.6 43.9 48.6(a) 52.0 56.6 65.0 76.7 77 6 1005
a) States arc Melted by placement of holes. b) Encrgres gwen are the sum of expenmentd
by tts
ExperimentC)
Ref. 1241
45.8
48.1
51.1 57.5 65.9 73.2 75.3 95.4
~teraction/~l~at~o~
term colcutated as
Table 2 Intensitms of Auger transitions relatwe to (30)~ Ikai
state
This
from various calculations,
Jennrson
work
Sr~bahn and aPen
et al_
C SU1U 4050 fSu)*
959 202 32.41
OC
OC
0
054 5.45 0.15 3 62 004 3.72
0 81 2.76 0.48 (3 00) 0.05 7 9 4.19
(ldZ 4aln
2.38
6.65
I.61
3.46 1.72
2 25 0.4
2.0
(4oP 3050 3aln 3040 (30)2
154
138
057
0.8
1.70 1.25 1.23 (i.00)
0.44 0.96
0.7
0.4 (0 30) 004
03
1.1
0.43 4 34 026 2.01 2.37 190 0.46 2.15 1.17 (1.00) (1.00) (1.00)
configurational mixtng as well as multiplet splittmg. We have scaled the calculated intensities for the sing let transtrions of the upper levels, which are less heavtiy mixed, to the 4050 in the manner mdicated in table 3,.
4. Discussion
Tables 1 and 2 suggest that the MS Xormethod can serve reasonably welJ as a tool for the mterpretatron of valence Auger spectra. It is not as successful as
Agren’s method (for instance) in producing final-state energies. In fact, it is sufficiently far off to be quite useless. Used as a method for estimating the two-hole contribution to final-state energies, however, in the framework of the analysis of Jennison
et al. or of
et al., it is quite successful. The internties predictedby the methodare not in
Ramaker
discord with those predicted by other analyses or by experiment. They can thus, serve in the assIgn-
violent
ment of spectra. It ISdifficult to compare experimental and theoretical intensities quanlitatively because of great disparities in mtensity, width and vlbratlonal structure of various features and because of the in‘trusion of features usually asslgned to satellites of various kinds. There are a few observations to be made
however. The large discrepancy between our mtensity for (In)2 and the intensity obtained by Jenmson et al. presumably can be attributed, at least in part, to the fact that configuratlonal mixing between In and 2n IS important III the initial carbon Is hole state but not in the corresponding oxygen Is hole state [25]. There is also a large discrepancy in the (So)2 state in the carbon Auger spectrum. We have, as we described earher, calculated intensities using transition-state orbrtals rather than core-hole-state orbitals. We did this because we wished to evaluate the use of a single tranntion.state calculation to descnbe an Auger transitlon both in energy and In intenstty. Our use of transltionstate orbitals is not important m determinmg the calculated intensity of the (5~)~ transition, though. Rather, It would appear that the MS Xo!calculations gve this orbital more carbon 2s character than do the LCAO calculations. Conversion of our results and the results of the analysis by Jennison et rd. to twoelectron contnbutlons, by subtracting the sum of ionization potentials (for the two electrons removed) from the final-state energies, leaves a roughly constant contribution of lo-13 eV from our results. Ramaker and co-workers found similar results for 02. The roughly corresponding result from Jennison’s analysis increases with fiialstate energy from = 10 eV to ~26 eV. The difference, about the calculated Intensities,
in general, is not surpnsing
14 hlry 1982
CHEMICAL PHYSICSLETTERS
Volume 88. number 4
because
Jenmson et al.
calculate hole-hole repulsion on ground-state orbitals whereas our result includes rearrangement, which becomes increasingly important in the higher states. Jennson’s calculations, however, yield greater hole-
hole repulsion for states with two holes m the same
orbital than for other states at comparable energy. This effect IS not noted in our calculations nor, on the whole, m the calculations of Ramaker and coworkers. It has the result, m CO, of suggesting a stnking misassignment of the (50)~ fiial state. Our crlculations would make (la)’ rhe most stable find state, the assignment of table I is almost surely
whereas
correct.
5. Conclusions
MS Xa calculations in the transition-state model appear to produce an adequate descnptlon of the valence Auger spectra of molecules,Judgmg from our expenence with CO, if they are used as part of a semiempirical description of the spectra. They fare less well in predicting final-state energies or Auger energies directly. They also appear to overestmlate the stabdization of states with two holes in the same orbital
Acknowledgement The authors wish to thank Dr. I. Tse for useful help with the MS Xa code and to thank Dr. D. Jennison, who has made several useful comments on the work. The support of NIH under Grant GM25453 is acknowledged gratefully.
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