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Configuration interaction in the L2,3—MM Auger spectrum of HCl and Ar
CHEMWAL
Volume 98, number 5
~ONFiGU~~ON
INTERACTION
8 July 1983
PHYSICS LETTERS
IN THE Lz, ,-MM AIJGER SPECTRUM
OF HCI AND As
Olav M. KVALHEIM Department of Chemistry. University of Bergen, N-5000 Bergeq Norway Received 25 hfarch 1983
The L 2,3-MM Auger spectra of HCI and Ar have been calculated. Strong interaction between the Auger diagram state 40~~ and correlation states explains the absence of the L ~,s-LM: peak in the HCl spectrum. For argon semi-internal CI reproduces the high-kinetic-energy redon, while 3.fairly large expansion of contkgntions is necessary to reproduce the low-kinetic-energy
part of the spectrum_
2. Introduction
2. Computationaf.
Calculations of the Auger spectra for several molecules show the necessity of correlated wavefunctions for the interpretation of these spectra. So far, the K-LL spectra of HF fl-31, I+0 [4], CH4 [5,6], CO [7],N2 [S,YJ,NO jSj,CO2 [Sj and the L7,3-MM spectrum of Cl, [9] have been calculated with correlated wavefun&ons. Most calculations [4-91 were perfomled in the semi-internal CXscheme. More extensive CI calculations were performed for HF ii] and N2 IS] _ 1~ addition a semiempirical method with correlated functions f2 J and the Green’s function method have been used [3] _ Recently, Aksela et al. [lo] published the experimental L,,,-MM spectrum of HCI together with an interpretation of the high-klmeticener,T region based upon energies obtained with the direct CI approach_ In this note we present a calculation of intensities as well as energies over the whole range of the I+, 3 MM Auger spectrum of HCI. Dyall and Larkis have shown the importance of interaction between diagram states and correlation states with the configuration 3p-33dl in the L 2,,-MM Auger spectrum of argon [l I] _ Since this kind of interaction might be expected to be important also for HCl, we calculated the L,,,-MM spectrum of argon to make sure that our basis sets can reproduce such correlation states.
All calculations were perfomled with the Bergen ab initio CI program package on a Univac 11 lo/S2 computer f 12,131. The program uses integrals over a GTO basis generated by the MCXECULE program [ 14]_ The moiecular-orbital basis is obtained by the UIBMOL program (15-l 7]_ The integral transformation is from Roos’ direct Ci package [ 181. Eigenvalues and eigenvectors are extracted using Lanczos’ method in a program written by Manne [ 19 J. Since the integral program only permits twofold symmetry operations, the calculations for Ar and HCI were done in the point groups Da and C,,, respectively, rather than in the full symmetries, R3 and Cmv_ For hydrogen a (4s, lp) basis was contracted to (2s, lp) with the s exponents of Huzinaga f20j scaled by a factor of 1.25 and with the (2s) contraction of Dunning [21]. The p exponent was O-8, as recommended by Roos and Siegbahn [23] _ For Ar and Cl a (12s, lOp,4d) basis set contracted to (7s,5p,3d) was used. The (12s,9p) basis of Veillard [23] with the (7s,4p) contraction prescribed by Dunning [24], was augmented with four d functions and one p function in the following way: First, one d exponent was optimized in the RHF approximation with coupling coefficients representing an average of configurations with five electrons in the valence orbitals and one electron occupying the 3d level, i.e. 3sz3p33d3 I 3sl3p33dl and 3@3p53dl_ The splitting factors given by Dunning
0 009-26 14/83/0000-0000/$03.00
0 1983 North-Holland
de&&
457
Volume
98. number
5
CHEhlICAL
PHYSICS
and Hay [X] _0.75 and 1.9. converted the single d exponent 0.4 and 0.35 of Ar and Cl. respectively, into two exponents. 0.76 and 0.30 for Ar and 0.665 and O-1625 for Cl. This splitting reduced the energy of the 3$3p33d1 terms of Ar by ~3 eV. Two further d functions were added, with esponent 0.1 and 0.035 for Ar and 0.09 and 0.03 for Cl. Finally. a 4p function with exponent 0.025 for Ar and 0.02 for Cl was added. No s functions were added, since each set of Cartesian d functions [ 141 also introduces an additional function of 5 type. The two d functions with largest exponents were contracted after a RHF calculation for the average of tile configurations representing the Auger diagram states. giving finally the contracted basis sets (7s. Sp, 3d). Calculations for A$+ verified that this basis set generated a satisfactory description of the lowest unoccupied orbitals. i.e. 3d. 4s 4p. -Id. Following the s;lme procedure as earlier [6]. only one RHF calculation was performed for each of Ar and HCI (internuclear distdnce 2.4087 au) using couphg coefficients representing an average of the Auger didgram states. The molecular orbitals obtained from these calculations were used in all the following calculations. The Cl expansions were constructed with the following restrictions: (1) Excitations from core orbitals (i.e. 1s. 2s, 2p) were excluded. (2) the MOs wit11 the highest orbital energies were deleted. i.e. for Ar 1 orbitals of s symmetry and 1 of p symmetry. for HCl 8 orbitals of u symmetry and 2 of 71symmetry. The Cl calculatrons for Ar were performed at two levels of accuracy. giving expansions of 66 to 73 configuration state functions (CSFs) in the semi-internal scheme. and ranging from 13 18 to 1 S97 CSFs in a calculJtion including single and double excitations with respect to all Auger diagram states fulfilling the symmetry restrictions (SDCI). For HC1 calculations were performed only on the SDCI level, giving 2747 CSFs for 1 Z+ and rn, 3679 CSFs for sC+, 3811 CSFs for ‘C-. 2636 CSFs for 1Il. and 3764 CSFs for 3fI_
45s
LETTERS
8 July 1983
3. Auger spectrum of argon The experimental Lz.3-MM Auger spectrum of argon was first obtained by Melhorn and Stalherm [26] _Later a highly resolved spectrum was recorded by Werme et al. [27]. The diagram states were first calculated by Rubenstein and Snyder [28] in the extreme LS coupling scheme. Assad and Mehlhorn [29] recalculated the spectrum in the intermediate coupling scheme using Rubenstein’s radial integrals [30] _ McGuire [3 1] and Walters and Bhalla [32] calculated absolute rates for the L ?,,-MM transitions of argon. Both calculations gave too high relative L3 3-Ml M7 3 and too low k, 3-Mf rate compared wit
vcJume
98, number
CHEMICAL
5
PHYSICS
LETTERS
8 July 1983
Table 1 Relative energies and rates of the diagram states and the most intense correlation states in the L2, a-MM Auger spectrum of AI State a)
Relative rate d)
Relative cneqzy this work semi-
DY~U[Ill
Werme 1271
semi-
SDCI C)
CI b)
SDCI
0
0
0
0
40.8
40.9
51.0
40.3
2.0
2.2
1.6
48.2
48.2
40.0
44.4
5.0
4.2
5.1
4.0
11.0
10.9
9.0
15.2
14.8
14.6
14.0
14.2
10.2
10.5
11.7
12.2
19.7
19.8
18.4
17.7
S-4
8.5
5.7
s-3
27.4
27.2
27.6
26.1
0.25
0.60
0.19
3.0
29.6
28.6
28.7
26.4
1.50
1.29
3.2
2.2
30.1
29.0
29.8
27.2
4.1
3.9
4.9
4.7
33.7
33.2
32.4
30.9
1.00
1.07
0.67
1.7
34.5
34.2
32.9
31.5
0.32
0.30
O-3?
0.88
0.18
0.15
0.39
0.60
0.45
0.73
35.7
34.9
41.2
40.3
0.55
0.36
50.8
45.8
0.21
0.23
35.2
the correlation states in the same energy region. Our calculated relative rates for the diagram states and the most intense correlation states compare well with experiment. However, two major discrepancies are obvious: First, our calculations overestimate the relative rate of (3~~~)’ D at the cost of (3~-~)tS. Second, the relative rate of the correlation state (3~-~4s’)‘P calculated with SDCI is only 20% compared to experiment. As shown earlier for neon [34] and methane [6], the inclusion of the cross term corresponding to es)~s1i+l(1s-I)2S)
<([(2p-2)1S]
Werme [ 271
2.1
33.4
a) Labelled by the dominant contiguration. b) Relative to -525.2568 c) Relative to -525.3102 au ‘D. d) Relative to L2,3-h1& = 100.
x
Dyall [ll]
internal CI
internal
(([G -qS]
this work
es)%lHl(ls-‘)%>
in the calculation of the transition rates increases the rate of the diagram state corresponding to (2p-2)‘s
1.1s
au ‘D.
and decreases the rate corresponding to (2s-‘)l S. Contrary to the suggestion of Werme et al_ [27], we expect this effect to increase the rate of (3p-9’s at the expense of (~s-~)~S. Our calculation on argon reproduces the intense peaks in the spectrum fairly well. Since SDCI gives somewhat better results than semi-internal CI, and our calculation was performed without prior experimental information, we used SDCI for the calculation of the HCl spectrum_
4. Auger spectrum
of HCI
Table 2 shows relative energies and relative rates of the L_, 3 -M? 3 transition of HCI. The rates were computed us&McGuire’s rates for argon [31,33] 459
Volume 96, number 5 Table 2 Relative energies
CHEMICAL
and rates of the L 2,3-X1&
Auger
PHYSICS
transitions
Relative
energy
this \\ ork a)
8 July
LETTERS
of HCI Relative
(eV)
exp.
[ 101
theory
1
L2-(1”-2)3s-
0
0
0
2
L3-(2s-‘)35
1.6
1.5
1.7 18.8
L,-(&T-~)‘A
1.8
1.8
1.7
Lt-(2n-2)‘x+
3-O
2.7
2.9
Z]
65
L~-(50-‘2s-‘)311 L3-(21r-~)‘A
3.4 3.9
3.5 3.1
4-0 3.4
‘::;I
7
L3 -(Zn-‘)’
\‘+
4.6
4.3
4.7
8
L3-_(50-‘2n-l)ln
s-5
s-5
6.4
9
L3-(50-‘2=-‘)3rr
5.5
5.7
18.2
10
L2-(50-‘2a-‘)‘II
7.2
12.8
11
Lz-(5a-‘)‘x+
12
L,-(sa2)’
11.1
[lo)
C)
5.6
19.0
‘:::) 1.8
28.4
‘$:;I
37.4
29.4
36.3
3.6
9.7 d)
12.1
x+
exp.
4.6
3
7.1
rate b)
this \\ ork
[ lo]
4
10.6
1983
7.2
d)
J)
Rrl.nirc IO -458.9521 au 3\--. b) R&rive to L2_3-Ms_3 = 100. d) Rc~,ugnrd. WC tf\t C) Nurmdurd to the theoretiwl r&x
accounting
for the splitting
of P and D states
into
S
.ind II and S. I1 and A. respectively.
-62 _ rate.
Energies
are given
relative
to hne
1
-,’ 1+ ground state)_ Fig. 1 shows the bar specand 2 (IiCltlum of HCI using the measured L2,3 spin-orbit splitting 1.6 eV [35] _The experiment of Akseia et al. [lo] is included for comparison. Several conclusions can be drawn from this calculation. First. relative energies for the lowest L2,3-M$ 3 rransition in each synmetry compare well with the hirect Cl calculation of the smle states [lo]. Secondly, rhe experimental spectrum contains four main peaks in the L 1,3-h1~V3 region (see fig. 1). indicating that 360
3
Rchtive energies and mtea of the Lz,3-M:. .md correlation
The ram so obtained were divided in rhe statistical ratio 2: 1 for trmsitions from Lj and L,. respectively. and used together with the squared CI coefficients of the diagram states in each symmetry. The rates were nornlalircd to 100% intensity for the L7-. 3-R1s,3 rrmsitions. T,tble 3 shows the relative energies and rates for the - 41 1hl,,, and L,,,- Mf transitions and the most L,M.2 intense correlation states. Sums of transition rates from L, and L, are given in percent of the total L3.3
Table
states
state 3)
(Jo-’
in the Auger
Line
ln-=)311
spectrum
Lz,3-hlIMZ.3 of HCI
number
Relative energy b) (eV)
Relative rate c,
13.15
13.3
1.55
(Z71-~6o’)‘n
14,18
14.7
0.76
(Z~r-~6o’)‘11
15,lP
15.1
2.25
(50- *2,7-Z6,9)3r+
17.20
16.3
1.54
(40-“n-~)~I1
21.23
18.7
4.37
(4o-‘50-‘)3x+
7, ‘5 __,_
19.1
1.88
(50-‘2a-‘60’)1‘+
24.26
20.6
0.91
(4,-*50-l)‘,+
27,28
22.5
1.38
(50-‘Zrr-‘3dn1)‘n
29,30
25.5
2.64
(5o-‘?a-‘3d6
31.33
782
1.41
32.34
29.4
0.43
(40-y
z+
*)‘s+
a) Lzxbelled by the d ominnnt contiguIation. b) Relative to the HCI** ground state. C) Relative to L 2,3-hI;,3 = 100.
8 July 1983
CHEMICAL PHYSICS LElTERS
730
140
150 Kinetic
160 Energy
(eV)
170
180
Fie. 1. Augerspectrumof HCI. Bar spectrumfrom present CI calculation usingcalculated rates of argon [31.33]. Experimental c&e fro& Al&a et al. [ IO] _ _ several diagram states interfere. Aksela et al. [IO] assigned all the L,,,-M$,, transitions to these peaks. Our calculation shows, however, that the (50~*)1X+ doublet (1 I and 12 in fig. 1) lies outside the region covered by these four peaks. By adding the calculated rate of the individual transitions under each peak, we find excellent agreement with experiment in this region. Thirdly, as far as it is possible to tell, our calculation reproduces the spectrum also in the low-kineticenergy region. Table 3 shows that interaction between diagram states and correlation states is more pronounced for HCl than for Ar. Correlation almost completely wipes out the transition to the diagram state (4~r-~)l I?. Only 12% of the RHF wavefunction is retained for that state_ The increased importance of correlation for the Auger spectrum of HCl compared to argon is not only due
to the lower symmetry of the molecule which allows further mixing. More important is the presence of the low-lying antibonding (I orbital which is mainly hydrogen 1s. Interaction between the triplet Ml M2 3 diagram states and correlation states with three el&trons in the 3p orbital and one in 60 is much more important than the interaction with correlation states with the 3p-33dl configuration. However, for the singlet Ml M2 3 diagram states the 3pm33d1 interaction is of equal importance.
5. Conchlsion The test calculations of the Auger spectrum of Ar show the importance of well-fitted basis functions for the lower excited orbitals, especially 3d. DyaU and 461
CHEhffCAt
Vofume 98. number 5
Larkins’ calculation mined
by numerical
PHYSICS LEl’TERS
on argon [ 1 X] with orbitals deterintegration gives results of a similar
quality for the most intense
transitions. Excitations to the lowest HCl sigma antibonding orbital gives a new
source of correfation compared to the atomic case. These molecular correlation states interact strongly with the diagram states in the L, ,--Ml M2,3 region of the spectrum_ However. excitat&s to 3d and to Rydberg-like orbitals. i.e. 4~. 4d. are still important in the region with lowest kinetic energy. The combination of low resolution and small relative rate in this region makes any assigmnent of limited vafue, indicating that high computational precision is not necessary. This might generally be true for molecular L,,,--MM spectra. In analogy with argon, we expect the energies of this part to be 2-3 eV too low relative to the highkinetic-energy part of the spectrum_ The present quali-
tative approach for the calculation for transition rates. neglecting effects such as correlation in the initial. states, relaxation. final-state interchannel rniGng and using the rates of the isoelectronic argon atom, seems to be good enough for a clear interpretation of the spectrum.
Acknowledgement I want to thank Rolf Manne for many useful suggestions and discussions during this work.
References [ 11 0.M. liitalhcim .md K;. Fxpi
121 ]3] [4] [S] [6] [7]
462
Jr.. Chem. Phys. Letters 67 (1979) 127. D-P. Chong, Chem. Phys. Lctrers 81 (1981) 51 IC. Liegener, Chem. Phls. Letters 90 (1982) 188. Ii. Agen and H. Sic&ahn, Chem. Phys. Letters 69 (1980) 421. 1-H. Hilher and J. Kendrisk. hfol. Phys. 31 (1976) 649. 0.M. Kv.dhcim, Chem. Phys. Letters 86 (1982) 159. H. Agrrtn and H. Siqbahn. Chem. Phys. Letters 72 t19sll) 498.
8 July 1983
[8] H. A8ren. J. Chem. Phys. 75 (1981) 1267. [9] 0. Sunde. Thesis, University of Bergen (1981). unpublished (in Non% egian). [IO] H. Aksrla, S. Aksela. M. Hotokka and M. Jawtti. private communication_ [ ll] K.G. DyaB and F-P. Larkms, J_ Phys. B15 (1982) 2793. [ lZ] 0.X Kvalheim.Thesis, University of Bergen (1978), unpublished (in Norwegian)_ [ 131 R. hlJnne and O-hi. Kvalheim, Proceedings of the 4th Seminar on Computational Methods in Quantum Chemistry, Max-Planck-Institut fiir Physik und Astrophysik. Munich (1979) p. 269. 1141 J. AImi&f. USIP Report 721109, University of Stockholm (1972). [IS] K. Fzegri Jr. and R. Manne, Mol. Phys. 31 (1976) 1037. 1161 MT. $WIand, Ii. Fazgri Jr. and R. Manne, Chem. Phys. Letters 40 (1976) 185. [ 171 R. Xlanne and K. F.zE_eriJr.. Mol. Phys. 33 (1977) 5% 1181 B+ Roes. in: Compurarional techniques in quantum chemisuy and molecular physics, eds. G.H.F. Diercksen, B.T. Sutcliffe and A. Veillard fReide1, Dordrecht, 1975). 1191 R. Arneber:. J. hfiiller and R. hianne, Chem. Phys. 65 (1982) 249. [ 201 S. Huzinaea. J. Chem. Phys. 42 (1965) 1293. [ 2 1 j T.H. Dunning Jr.. J. Chem. Phys. 53 (1970) 2823. IX!] B. Roos and P. Siegbahn,Theoret. Chim. Acta 17 (1970) 199. 123) A. Veil&d. Theoret. Chim. Acta 11 (1968) 44~ ]24] T-H. Dunning Jr., Chem. Phys. Letters 7 (1970) 423. [X] T.H. Dunning Jr. and P.J. Hay, in: hfodern theoretical chemistry, Vol. A, ed. H.F. Schaefer III (Plenum Press, Neu York, 1977). [26] 1%‘.hfehlhorn and D. Stalherm. Z. Physik 217 (1968) 291, 1271 LO. Werme. T. Bergmark and I;. Siegbahn, Physica Scripta 8 (1973) 149_ [ZSj R.A. Rubenstein and J-N. Snyder, Phys. Rev_ 97 (1955) _1653. (291 W-N. Asaad and W. hlehlhorn. 2. Physik 217 (1968) 304. [30] R.A. Rubenstein, Ph.D. Thesis, University of Illinois (1955). 1311 E-J. hfcGuire, Phys. Rev. A3 (1971) 1801. 1321 D.L. Walters and C-P. Bhalla, Phys. Rev. A4 (1971) 2164. 1331 E.J. hlc(;uire, Phys. Rev. Al 1 (1975) 1880. [34] C-P. BhaIfa. Phys. Letters 44A (1973) 103. [35] E.J. Aitken. h1.K. Bahl. K.D. Bomben. J. Gimzenski. G.S. Nolan and T.D. Thomas, J. Am. Chem. Sot. 102 (1980) 4879.
Volume 98, number 5
~ONFiGU~~ON
INTERACTION
8 July 1983
PHYSICS LETTERS
IN THE Lz, ,-MM AIJGER SPECTRUM
OF HCI AND As
Olav M. KVALHEIM Department of Chemistry. University of Bergen, N-5000 Bergeq Norway Received 25 hfarch 1983
The L 2,3-MM Auger spectra of HCI and Ar have been calculated. Strong interaction between the Auger diagram state 40~~ and correlation states explains the absence of the L ~,s-LM: peak in the HCl spectrum. For argon semi-internal CI reproduces the high-kinetic-energy redon, while 3.fairly large expansion of contkgntions is necessary to reproduce the low-kinetic-energy
part of the spectrum_
2. Introduction
2. Computationaf.
Calculations of the Auger spectra for several molecules show the necessity of correlated wavefunctions for the interpretation of these spectra. So far, the K-LL spectra of HF fl-31, I+0 [4], CH4 [5,6], CO [7],N2 [S,YJ,NO jSj,CO2 [Sj and the L7,3-MM spectrum of Cl, [9] have been calculated with correlated wavefun&ons. Most calculations [4-91 were perfomled in the semi-internal CXscheme. More extensive CI calculations were performed for HF ii] and N2 IS] _ 1~ addition a semiempirical method with correlated functions f2 J and the Green’s function method have been used [3] _ Recently, Aksela et al. [lo] published the experimental L,,,-MM spectrum of HCI together with an interpretation of the high-klmeticener,T region based upon energies obtained with the direct CI approach_ In this note we present a calculation of intensities as well as energies over the whole range of the I+, 3 MM Auger spectrum of HCI. Dyall and Larkis have shown the importance of interaction between diagram states and correlation states with the configuration 3p-33dl in the L 2,,-MM Auger spectrum of argon [l I] _ Since this kind of interaction might be expected to be important also for HCl, we calculated the L,,,-MM spectrum of argon to make sure that our basis sets can reproduce such correlation states.
All calculations were perfomled with the Bergen ab initio CI program package on a Univac 11 lo/S2 computer f 12,131. The program uses integrals over a GTO basis generated by the MCXECULE program [ 14]_ The moiecular-orbital basis is obtained by the UIBMOL program (15-l 7]_ The integral transformation is from Roos’ direct Ci package [ 181. Eigenvalues and eigenvectors are extracted using Lanczos’ method in a program written by Manne [ 19 J. Since the integral program only permits twofold symmetry operations, the calculations for Ar and HCI were done in the point groups Da and C,,, respectively, rather than in the full symmetries, R3 and Cmv_ For hydrogen a (4s, lp) basis was contracted to (2s, lp) with the s exponents of Huzinaga f20j scaled by a factor of 1.25 and with the (2s) contraction of Dunning [21]. The p exponent was O-8, as recommended by Roos and Siegbahn [23] _ For Ar and Cl a (12s, lOp,4d) basis set contracted to (7s,5p,3d) was used. The (12s,9p) basis of Veillard [23] with the (7s,4p) contraction prescribed by Dunning [24], was augmented with four d functions and one p function in the following way: First, one d exponent was optimized in the RHF approximation with coupling coefficients representing an average of configurations with five electrons in the valence orbitals and one electron occupying the 3d level, i.e. 3sz3p33d3 I 3sl3p33dl and 3@3p53dl_ The splitting factors given by Dunning
0 009-26 14/83/0000-0000/$03.00
0 1983 North-Holland
de&&
457
Volume
98. number
5
CHEhlICAL
PHYSICS
and Hay [X] _0.75 and 1.9. converted the single d exponent 0.4 and 0.35 of Ar and Cl. respectively, into two exponents. 0.76 and 0.30 for Ar and 0.665 and O-1625 for Cl. This splitting reduced the energy of the 3$3p33d1 terms of Ar by ~3 eV. Two further d functions were added, with esponent 0.1 and 0.035 for Ar and 0.09 and 0.03 for Cl. Finally. a 4p function with exponent 0.025 for Ar and 0.02 for Cl was added. No s functions were added, since each set of Cartesian d functions [ 141 also introduces an additional function of 5 type. The two d functions with largest exponents were contracted after a RHF calculation for the average of tile configurations representing the Auger diagram states. giving finally the contracted basis sets (7s. Sp, 3d). Calculations for A$+ verified that this basis set generated a satisfactory description of the lowest unoccupied orbitals. i.e. 3d. 4s 4p. -Id. Following the s;lme procedure as earlier [6]. only one RHF calculation was performed for each of Ar and HCI (internuclear distdnce 2.4087 au) using couphg coefficients representing an average of the Auger didgram states. The molecular orbitals obtained from these calculations were used in all the following calculations. The Cl expansions were constructed with the following restrictions: (1) Excitations from core orbitals (i.e. 1s. 2s, 2p) were excluded. (2) the MOs wit11 the highest orbital energies were deleted. i.e. for Ar 1 orbitals of s symmetry and 1 of p symmetry. for HCl 8 orbitals of u symmetry and 2 of 71symmetry. The Cl calculatrons for Ar were performed at two levels of accuracy. giving expansions of 66 to 73 configuration state functions (CSFs) in the semi-internal scheme. and ranging from 13 18 to 1 S97 CSFs in a calculJtion including single and double excitations with respect to all Auger diagram states fulfilling the symmetry restrictions (SDCI). For HC1 calculations were performed only on the SDCI level, giving 2747 CSFs for 1 Z+ and rn, 3679 CSFs for sC+, 3811 CSFs for ‘C-. 2636 CSFs for 1Il. and 3764 CSFs for 3fI_
45s
LETTERS
8 July 1983
3. Auger spectrum of argon The experimental Lz.3-MM Auger spectrum of argon was first obtained by Melhorn and Stalherm [26] _Later a highly resolved spectrum was recorded by Werme et al. [27]. The diagram states were first calculated by Rubenstein and Snyder [28] in the extreme LS coupling scheme. Assad and Mehlhorn [29] recalculated the spectrum in the intermediate coupling scheme using Rubenstein’s radial integrals [30] _ McGuire [3 1] and Walters and Bhalla [32] calculated absolute rates for the L ?,,-MM transitions of argon. Both calculations gave too high relative L3 3-Ml M7 3 and too low k, 3-Mf rate compared wit
vcJume
98, number
CHEMICAL
5
PHYSICS
LETTERS
8 July 1983
Table 1 Relative energies and rates of the diagram states and the most intense correlation states in the L2, a-MM Auger spectrum of AI State a)
Relative rate d)
Relative cneqzy this work semi-
DY~U[Ill
Werme 1271
semi-
SDCI C)
CI b)
SDCI
0
0
0
0
40.8
40.9
51.0
40.3
2.0
2.2
1.6
48.2
48.2
40.0
44.4
5.0
4.2
5.1
4.0
11.0
10.9
9.0
15.2
14.8
14.6
14.0
14.2
10.2
10.5
11.7
12.2
19.7
19.8
18.4
17.7
S-4
8.5
5.7
s-3
27.4
27.2
27.6
26.1
0.25
0.60
0.19
3.0
29.6
28.6
28.7
26.4
1.50
1.29
3.2
2.2
30.1
29.0
29.8
27.2
4.1
3.9
4.9
4.7
33.7
33.2
32.4
30.9
1.00
1.07
0.67
1.7
34.5
34.2
32.9
31.5
0.32
0.30
O-3?
0.88
0.18
0.15
0.39
0.60
0.45
0.73
35.7
34.9
41.2
40.3
0.55
0.36
50.8
45.8
0.21
0.23
35.2
the correlation states in the same energy region. Our calculated relative rates for the diagram states and the most intense correlation states compare well with experiment. However, two major discrepancies are obvious: First, our calculations overestimate the relative rate of (3~~~)’ D at the cost of (3~-~)tS. Second, the relative rate of the correlation state (3~-~4s’)‘P calculated with SDCI is only 20% compared to experiment. As shown earlier for neon [34] and methane [6], the inclusion of the cross term corresponding to es)~s1i+l(1s-I)2S)
<([(2p-2)1S]
Werme [ 271
2.1
33.4
a) Labelled by the dominant contiguration. b) Relative to -525.2568 c) Relative to -525.3102 au ‘D. d) Relative to L2,3-h1& = 100.
x
Dyall [ll]
internal CI
internal
(([G -qS]
this work
es)%lHl(ls-‘)%>
in the calculation of the transition rates increases the rate of the diagram state corresponding to (2p-2)‘s
1.1s
au ‘D.
and decreases the rate corresponding to (2s-‘)l S. Contrary to the suggestion of Werme et al_ [27], we expect this effect to increase the rate of (3p-9’s at the expense of (~s-~)~S. Our calculation on argon reproduces the intense peaks in the spectrum fairly well. Since SDCI gives somewhat better results than semi-internal CI, and our calculation was performed without prior experimental information, we used SDCI for the calculation of the HCl spectrum_
4. Auger spectrum
of HCI
Table 2 shows relative energies and relative rates of the L_, 3 -M? 3 transition of HCI. The rates were computed us&McGuire’s rates for argon [31,33] 459
Volume 96, number 5 Table 2 Relative energies
CHEMICAL
and rates of the L 2,3-X1&
Auger
PHYSICS
transitions
Relative
energy
this \\ ork a)
8 July
LETTERS
of HCI Relative
(eV)
exp.
[ 101
theory
1
L2-(1”-2)3s-
0
0
0
2
L3-(2s-‘)35
1.6
1.5
1.7 18.8
L,-(&T-~)‘A
1.8
1.8
1.7
Lt-(2n-2)‘x+
3-O
2.7
2.9
Z]
65
L~-(50-‘2s-‘)311 L3-(21r-~)‘A
3.4 3.9
3.5 3.1
4-0 3.4
‘::;I
7
L3 -(Zn-‘)’
\‘+
4.6
4.3
4.7
8
L3-_(50-‘2n-l)ln
s-5
s-5
6.4
9
L3-(50-‘2=-‘)3rr
5.5
5.7
18.2
10
L2-(50-‘2a-‘)‘II
7.2
12.8
11
Lz-(5a-‘)‘x+
12
L,-(sa2)’
11.1
[lo)
C)
5.6
19.0
‘:::) 1.8
28.4
‘$:;I
37.4
29.4
36.3
3.6
9.7 d)
12.1
x+
exp.
4.6
3
7.1
rate b)
this \\ ork
[ lo]
4
10.6
1983
7.2
d)
J)
Rrl.nirc IO -458.9521 au 3\--. b) R&rive to L2_3-Ms_3 = 100. d) Rc~,ugnrd. WC tf\t C) Nurmdurd to the theoretiwl r&x
accounting
for the splitting
of P and D states
into
S
.ind II and S. I1 and A. respectively.
-62 _ rate.
Energies
are given
relative
to hne
1
-,’ 1+ ground state)_ Fig. 1 shows the bar specand 2 (IiCltlum of HCI using the measured L2,3 spin-orbit splitting 1.6 eV [35] _The experiment of Akseia et al. [lo] is included for comparison. Several conclusions can be drawn from this calculation. First. relative energies for the lowest L2,3-M$ 3 rransition in each synmetry compare well with the hirect Cl calculation of the smle states [lo]. Secondly, rhe experimental spectrum contains four main peaks in the L 1,3-h1~V3 region (see fig. 1). indicating that 360
3
Rchtive energies and mtea of the Lz,3-M:. .md correlation
The ram so obtained were divided in rhe statistical ratio 2: 1 for trmsitions from Lj and L,. respectively. and used together with the squared CI coefficients of the diagram states in each symmetry. The rates were nornlalircd to 100% intensity for the L7-. 3-R1s,3 rrmsitions. T,tble 3 shows the relative energies and rates for the - 41 1hl,,, and L,,,- Mf transitions and the most L,M.2 intense correlation states. Sums of transition rates from L, and L, are given in percent of the total L3.3
Table
states
state 3)
(Jo-’
in the Auger
Line
ln-=)311
spectrum
Lz,3-hlIMZ.3 of HCI
number
Relative energy b) (eV)
Relative rate c,
13.15
13.3
1.55
(Z71-~6o’)‘n
14,18
14.7
0.76
(Z~r-~6o’)‘11
15,lP
15.1
2.25
(50- *2,7-Z6,9)3r+
17.20
16.3
1.54
(40-“n-~)~I1
21.23
18.7
4.37
(4o-‘50-‘)3x+
7, ‘5 __,_
19.1
1.88
(50-‘2a-‘60’)1‘+
24.26
20.6
0.91
(4,-*50-l)‘,+
27,28
22.5
1.38
(50-‘Zrr-‘3dn1)‘n
29,30
25.5
2.64
(5o-‘?a-‘3d6
31.33
782
1.41
32.34
29.4
0.43
(40-y
z+
*)‘s+
a) Lzxbelled by the d ominnnt contiguIation. b) Relative to the HCI** ground state. C) Relative to L 2,3-hI;,3 = 100.
8 July 1983
CHEMICAL PHYSICS LElTERS
730
140
150 Kinetic
160 Energy
(eV)
170
180
Fie. 1. Augerspectrumof HCI. Bar spectrumfrom present CI calculation usingcalculated rates of argon [31.33]. Experimental c&e fro& Al&a et al. [ IO] _ _ several diagram states interfere. Aksela et al. [IO] assigned all the L,,,-M$,, transitions to these peaks. Our calculation shows, however, that the (50~*)1X+ doublet (1 I and 12 in fig. 1) lies outside the region covered by these four peaks. By adding the calculated rate of the individual transitions under each peak, we find excellent agreement with experiment in this region. Thirdly, as far as it is possible to tell, our calculation reproduces the spectrum also in the low-kineticenergy region. Table 3 shows that interaction between diagram states and correlation states is more pronounced for HCl than for Ar. Correlation almost completely wipes out the transition to the diagram state (4~r-~)l I?. Only 12% of the RHF wavefunction is retained for that state_ The increased importance of correlation for the Auger spectrum of HCl compared to argon is not only due
to the lower symmetry of the molecule which allows further mixing. More important is the presence of the low-lying antibonding (I orbital which is mainly hydrogen 1s. Interaction between the triplet Ml M2 3 diagram states and correlation states with three el&trons in the 3p orbital and one in 60 is much more important than the interaction with correlation states with the 3p-33dl configuration. However, for the singlet Ml M2 3 diagram states the 3pm33d1 interaction is of equal importance.
5. Conchlsion The test calculations of the Auger spectrum of Ar show the importance of well-fitted basis functions for the lower excited orbitals, especially 3d. DyaU and 461
CHEhffCAt
Vofume 98. number 5
Larkins’ calculation mined
by numerical
PHYSICS LEl’TERS
on argon [ 1 X] with orbitals deterintegration gives results of a similar
quality for the most intense
transitions. Excitations to the lowest HCl sigma antibonding orbital gives a new
source of correfation compared to the atomic case. These molecular correlation states interact strongly with the diagram states in the L, ,--Ml M2,3 region of the spectrum_ However. excitat&s to 3d and to Rydberg-like orbitals. i.e. 4~. 4d. are still important in the region with lowest kinetic energy. The combination of low resolution and small relative rate in this region makes any assigmnent of limited vafue, indicating that high computational precision is not necessary. This might generally be true for molecular L,,,--MM spectra. In analogy with argon, we expect the energies of this part to be 2-3 eV too low relative to the highkinetic-energy part of the spectrum_ The present quali-
tative approach for the calculation for transition rates. neglecting effects such as correlation in the initial. states, relaxation. final-state interchannel rniGng and using the rates of the isoelectronic argon atom, seems to be good enough for a clear interpretation of the spectrum.
Acknowledgement I want to thank Rolf Manne for many useful suggestions and discussions during this work.
References [ 11 0.M. liitalhcim .md K;. Fxpi
121 ]3] [4] [S] [6] [7]
462
Jr.. Chem. Phys. Letters 67 (1979) 127. D-P. Chong, Chem. Phys. Lctrers 81 (1981) 51 IC. Liegener, Chem. Phls. Letters 90 (1982) 188. Ii. Agen and H. Sic&ahn, Chem. Phys. Letters 69 (1980) 421. 1-H. Hilher and J. Kendrisk. hfol. Phys. 31 (1976) 649. 0.M. Kv.dhcim, Chem. Phys. Letters 86 (1982) 159. H. Agrrtn and H. Siqbahn. Chem. Phys. Letters 72 t19sll) 498.
8 July 1983
[8] H. A8ren. J. Chem. Phys. 75 (1981) 1267. [9] 0. Sunde. Thesis, University of Bergen (1981). unpublished (in Non% egian). [IO] H. Aksrla, S. Aksela. M. Hotokka and M. Jawtti. private communication_ [ ll] K.G. DyaB and F-P. Larkms, J_ Phys. B15 (1982) 2793. [ lZ] 0.X Kvalheim.Thesis, University of Bergen (1978), unpublished (in Norwegian)_ [ 131 R. hlJnne and O-hi. Kvalheim, Proceedings of the 4th Seminar on Computational Methods in Quantum Chemistry, Max-Planck-Institut fiir Physik und Astrophysik. Munich (1979) p. 269. 1141 J. AImi&f. USIP Report 721109, University of Stockholm (1972). [IS] K. Fzegri Jr. and R. Manne, Mol. Phys. 31 (1976) 1037. 1161 MT. $WIand, Ii. Fazgri Jr. and R. Manne, Chem. Phys. Letters 40 (1976) 185. [ 171 R. Xlanne and K. F.zE_eriJr.. Mol. Phys. 33 (1977) 5% 1181 B+ Roes. in: Compurarional techniques in quantum chemisuy and molecular physics, eds. G.H.F. Diercksen, B.T. Sutcliffe and A. Veillard fReide1, Dordrecht, 1975). 1191 R. Arneber:. J. hfiiller and R. hianne, Chem. Phys. 65 (1982) 249. [ 201 S. Huzinaea. J. Chem. Phys. 42 (1965) 1293. [ 2 1 j T.H. Dunning Jr.. J. Chem. Phys. 53 (1970) 2823. IX!] B. Roos and P. Siegbahn,Theoret. Chim. Acta 17 (1970) 199. 123) A. Veil&d. Theoret. Chim. Acta 11 (1968) 44~ ]24] T-H. Dunning Jr., Chem. Phys. Letters 7 (1970) 423. [X] T.H. Dunning Jr. and P.J. Hay, in: hfodern theoretical chemistry, Vol. A, ed. H.F. Schaefer III (Plenum Press, Neu York, 1977). [26] 1%‘.hfehlhorn and D. Stalherm. Z. Physik 217 (1968) 291, 1271 LO. Werme. T. Bergmark and I;. Siegbahn, Physica Scripta 8 (1973) 149_ [ZSj R.A. Rubenstein and J-N. Snyder, Phys. Rev_ 97 (1955) _1653. (291 W-N. Asaad and W. hlehlhorn. 2. Physik 217 (1968) 304. [30] R.A. Rubenstein, Ph.D. Thesis, University of Illinois (1955). 1311 E-J. hfcGuire, Phys. Rev. A3 (1971) 1801. 1321 D.L. Walters and C-P. Bhalla, Phys. Rev. A4 (1971) 2164. 1331 E.J. hlc(;uire, Phys. Rev. Al 1 (1975) 1880. [34] C-P. BhaIfa. Phys. Letters 44A (1973) 103. [35] E.J. Aitken. h1.K. Bahl. K.D. Bomben. J. Gimzenski. G.S. Nolan and T.D. Thomas, J. Am. Chem. Sot. 102 (1980) 4879.