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Electronic properties of sulphur hexafluoride. Optical absorption and x-ray emission from SCF MO LCAO computations
Volume 17, number 1
1 Novemkr
CHEMICAL PHYSICS LETTERS
1972
ELECTRONIC PROPERTIES OF SULPHUR HEXAFLUORIDE. OPTICAL ABSORPTION AND X-RAY EMISSION FROM SCF MO LCAO COMPUTATIONS F.A. GIANTURCO .!kborarorio di Chimica Quantistica ed Energetica Mokcoiare de1 C.N.R., Piso, Ital)
Rcccived
31 Jzly 1972
The enhanced lines and frequent lack of evidence for Rydtxxg structures, already discussed in a past paper on !hc X-ray absorption spectra of this molccuk, are here again interpreted for optical absorption as originating from “shake-up” and skke-off’ processes among computed SCF 510 LCAO levels. Similar mcchxkms, 9s well as oneelectron jumps are invoked for S and F tluorcsccncc spectra (Iin and I$) where they also a!!ow for 3 qualitative one-to-one correspondence between tile excited multiple ions involved and the computed “many-hole” confi_eurations. The electron-scavenger properties of SFc are suggested to be mainly responsible for the moderate success of the rather crude model eipto&d here for coGputnti;k.
1.
Introduction
An increasingly large amount of experimental and theoretical evidence has recently been gathered on the effects of inner- and outer-electron excitations in simple molecular systems [l] . Thus, it has been generally accepted that, when photoionization occurs in an inner shell, an electron in an outer, bound, orbital can be excited by the sudden change of the initial po-
tential due to the loss of a shielding electron [2]. The transitions
are therefore
governed
by “monopole”
sc-
lection rules and good agreement is found with cxperimcnts when Hnrtree-Fock (HF) single-electron wavefunctions are employed [3] , Moreover, when photoionization occurs in the outer shell, another electron in a bound orbital with similar “atomic” features can also undergo excitation, a fact which is explained theoretically only when intra- and inter-shell correlations arc explicitly included in the initial-state wavefunctions [4]. For more complex molecular systems it has also been demonstrated that extensive excitation occurs simultaneously with phot.oionization, but a complete understanding of its nature is still awaited for, even though several theoretical attempts have appeared recently [S-7].
In t’le present note we focus our attention on one of the most popular model-systems for the above processes, i.e., the sulphur hexatluoridc octahedral molecule. The interest in such a compound was prompted, among other reasons, by its unusual behaviour in electron-attachment experiments using monoenergetic electrons [8,9] . In fact, it was found there that the electron-attachment process !eading to the formation of SF; occurs over an extremely narrow energy range and with an exceptionally large cross section. This largely precludes the possibility that these ions result from radiative capture, for which the cross section would be about 1O-5 times smaller [ 10) and, in any case, would not be confined to such a narrow energy range. The process occurring must be one in which the electron is captured to a nearly “stationary” SF6,
the surplus
energy
will be distributed
over a great
number of modes of motion and break-up can only occur when this energy is concentrated in a suitable mode, before which considerable time may elapse [91. In a qualitative way, one may say that the effective potential generated outside the molecule by the outer e!ectrons charge distribution (chiefly fluorine lone-pairs, in chemical jargon) is here capable of supporting a few, closely spaced, bound states which, in 127
Volume
17, number
CHEMICAL
I
PHYSICS
2. Emission
turn, ORE hopes to describe convincingly via the Iowest-lying virtual orbit& generated by an SCF MO LCAO description of the ground state wavefunction
This has provided us with a satisfactory picture for the N; scattering resonance at = 2.0 eV, mainly assigned to a shape resonance of an incident d-wave electron [IZ], and it is in the process of being extended to more general, non-linear, molecular systems [ 131 for which a fairly adequate description of the groundstate wavefunction is availabie in the HF scheme. Moreover, the feasibility of our compured w.f. of the SF6 ground-state configuration for describing several of its experimenta properties has already been tested in some previous papers [G, 141, where ESCA ionization energies, K- and L-absorption spectra from both sulphur and fluorine atoms have been reported and discussed. We extend here the study to the computed assignments for some recently measured fluorescence lines [!5], with the aim of both continuing to test our wavefunction and of pointing out, at the same time, the multi-electron nature of the rearrangement processes following an inner-ionization or excitation in molecular systems of such complexity. All compu‘tations were performed within the sudden approximatioh described elsewhere [6,2 l] .
peaks
-----_I_-_~-Espcrimcntal
bands
a
Assigned
spectra
The above main line has already been assigned to a dipole-allowed process of filling in the 1s-electron vacancy (from now on designated as a [Is] state) on the central atom by one of t!!e tlu valence orbit& with iarge sulphur $-function contributions [G] . \hat appears to be possible from these additional experiments is the suggestion that the principal part of the whole spectrum is associated to “diagrammatic” transitions to final states with single vacancies in the three tlil binding orbit& [ 171. Thus, the calculated transitions from our SCF wavefunction, in the sudden approximation, are reported in the upper part of table 1. They also seem in qualitative agreement with experiments when the re-
Table 1 transitions --
and computed
for sulph~~r K:p lines in SF6 [eV) Transition (arbitrary
transitions
broad
2448.5
[lqgl
-
very strong, sharp
2467.1
IlQ!
weak
2472.5
[lqgl
2444
2463
shoulder
very weak vcly
wea!c
aFromrcf. MO’S.
128
[lSJ;b
c k=2p
cl,
J
nsgiveninref.
moments units)
c
b medium,
November 1972
When both photons and electrons were employed as exciting sources [ 151 , the experimental spectra for the moiecule in the gas phase exhibited one sharp, intense, peak (2467.1 cV> flanked by two other small ones (at 2448.5 eV and 2472.5 eV respectively). OnIy the electronzxcited spectra presented what were termed “resonance radiation” phenomena, i.e., a low broad peak at 2444 eV and a low shoulder at abol;t 2463 eV j15].
IllI*
Experimental
1
LETTERS
d
2480
0.11
0.10
0.27
- [4tl”1
2501
0.36
0.56
0.49
-
[5tlul
2509
0.07
0.30
0.14
(la;;
t;,,)
-+(3t
(I,;;
tf”)’
[l.S];c
[3tlul
c
k=2p
(4t;;
c&
;:
-
< lo+
t;u)
2472
f?“)
2497
c 1o-3
2499
<
from
present
wavefunction;
d dipole
matrix
elements
from
1o-3
present
Volume 17, number I
1 November
CHEMICAL PHYSICS LETTERS
lative computed intensities+ are concerned [ 191. In addition to ionization caused by the one-electron processes involved in the initial photoelectron ejection, it is an established fact [4] that several additional ionizations can occur by electron “shake-off” accompanying photoionization and by multiple Auger processes. Moreover, “shake-up” phenomena are also invoked to exp!ain the presence of additional emission peaks in the ener,T region of strong absorption maxirna [3 l] _It therefore follows that the computed virtual MO’s of the present mo!ecule, already fcund reliable for explaining the observed absorption spectra, can here be called upon for assigning the broad “bumps” detected with electron sources [ 1.51. This is shown in table 1 and again reasonable agreement is found with observations. It should be mentioned, however, that the narrow spacings among the top vzilence orbit& and the lowest-!ying virtual MO’s [6] permit several symmetry-allowed transitions to fall very close to each other: this means that the assignments reported in the table should be considered as indicative of only some of the most likely rearrangemen t processes [ 16, IS] . When a Z,p-electron is removed from the central atom, another fluorescence transition involving singleparticle excitation can take place, the vacancy being filled by tile outer orbit& allowed by electric dipole selection rules. In the SF, molecule, two intense broad bands (at 153 and 162 eV respectively) have been dEtected in the enerw region of the sulphur L, 3 fluorescence line and their assi&nments invoked as &idence for d-orbital participation in sulphur bonding [ 15) . This means that the suggested transitions involve final-state configurations holding one vacancy in an MO with large sulphur 3s- and 3d-contributions. Our two most intense computed excitaticns (with transition moments N in the dipole approximation) are the following:
[2 t1,(2p)]
+ [5 alg(3s)] at 170eV (AI= 0.27),
12 t,,(Zp)]
+ [3 e,(3d)]
at 177 eV (N = 0.20)
and are in fair agreement with the observed separations between the two broad lines of La Villa’s measurements [ 151. It is obvious, however, that other i I70r the various merits of the approximations c and d of the table, set refs. [ I _ 15,191.
of columns b,
“diagrammatic”
transitions
could
be involved
1972
in the
relevant energy region, e.g., those from the 4a1,(3s), 2ep(3d) and 1tZB(3d) valence orbit& [6] , although any experiment discriminating among them is still a long way off. 2.2. 711esitlphctr K, spectiwn As early as fifty years ago, Lindh and Lundquist [20] first showed that the sulphur K-X-ray spectrum could be affected by bonding. Since then, many studies have been made showing chemical effects on both positions and intensities of K, iines in sulphur compounds, and simple theoretical models have been suggested for correlating these shifts with the localized charge on the relevant atoms [21] i. A similar series of results has been obtained for the satellite lines to the parent K, fluorescence transition [ 22, 231 and the assignments generally suggested for ihese lines are here employed
to interpret
the experimenta!
findings
on the SF, molecule.
Thus, while the main peak of the unresolved o1 ,2 doublet at 2309.3 eV [2J is attribufed to a singleparticle transition of the type [K] -+ [L2,3], the most intense of the peaks on its high-energy side is assigned to single-electron transitions from KL double vacancy states, narneIy [KL] -+ [L’] . For atomic systems with L-,C-coupling treatment of involved multiplets, such transitions should give rise to a fiveline group for all possible final states after rearrangement [2,25], although in a molecular environment the above “channel indices” are hardly behaving as “good” quantum numbers. The identification of a, cu3 and cy4 was therefore made by analogy with the relative positions and intensity of similar satellite lines of other sulphur K, spectra in the literature [24], and the results collected in table 2. Here again the square bracket notation indicates the one- or two-hole configuration and the upper indices the spin multiplicities. The general agreement with the experimental line separations, in spite of the crudeness of the “frozen orbitaI” approximation, seems to suggest that once more
f The K&,,: experimental shift provides here a net Char!$ on sulphur of+2.38 when the semi-empirical equation from ref. (21 j is used. The calculated net charge (in the hlullikcn sense [32]) with the present L141.
wavefdnction
was found to be +2.36
Volume
17, number
1
1 November
CHEMICAL PHYSICS LETTERS
1972
Trible 2
Experimental R, spectrum and computed transitions for sulphur in SF6 Observed line a)
------
Esperimcntal energy (eV) s) _...-- -----_-_-_
-___
Computed ______
a1 ,’
2309.3
a’
2317.8
l[lsLg
a3
2322.7
3[1qg
2325.4 _--_.----__----
Lllsfg -_-_---------.__-----
a4 --
transition
"1 lq&
(eV) -
~--
- ?2qul
2331
3qgl
+ LDqg2tLuI
2346
3s]cl
-+3[3qS2tlul
2353
2tLu] -L L[2t;J
2357
n) From ref. [ 15] .
the MO scheme for these “monopole” ionizations provides us with a fairly realistic physical picture what happens in SF6.
[3] of
emission spectrum in the fluorine K, energy region [ 151 exhibited again some broad, weak, “b-imps” on the Iow-energ side of the most intense peak. This Prominent peak consists of transitions among sindy , ionized configurations to fill a fluorine K-shell vacancy (i.e._ initial states like: [ItI,], [leg] and/or [2alg]) from one of the upper four occupied orbitals that are distributed in a range of about 6 eV [6]. Since the vertical ionization energies of the above orbitais are not known with certainty, a comparison of our computed assignment with the one suggested by experimenralists [7] should he!p in throwing some light on what we consider the essentially “diagram-
2.3. i%e ji’rroritze K, speclmn In examining the K-absorption spectrum from the fluorine atoms, we have already discussed [6] how the “localized” nature of these inner hofes lends to the existence, in MO LCAO parlance, of several IeveIs very close in energy but beIonging to different O,, irreducible representations, hence to the identification of scvera1 primary processes which can be described by the active-electron approximation. The recently measured
Table 3 Observed II, spectrum of fluorine in SF6 snd assigned computed
transitions -----------__L_
---___-___--
Observed bands (eVi
Computed
3
3
[ltlul -+ 12 e,] D very wcok, broad
= 650-658
--.
b 0.013
653.1
675.2
0.03
0.035
671.1
0.08
0.056
[2q,01 - 14tLul
671.7
697.7
0.5 1
0.60
667.6
699.9
0.23
0.25
--+ 15qgl
[Itlul
-+ Iltj_l -”
I2qg1
+ t5t1ui
700 677.1
704.6
0.32 0.94
2.00
[2@
d [lt2”1
676.2
705
1.00
2.30
Iltlul
+ I ItI,
678.9
706
1,oo
2.00
[ItI”
--+ [3 ccl
703.7
0.48
-_-c__--_.-a From ref. [ 151; b prcscn t work.
130
a 0.01
650.4
[It]“1
broad
b 678
- 13tluI
==612
% 677.6
655.3
11t1,1 -+ I4ol”lc
12qel
weak shoulder
intense,
Transition moments (arbitrary units)
trnnsitions (ev)
674.7
--.-.
--
1.90
_-.L--
VoIume 1 ‘i, number molecular
1 November
CHEMICAL PHYSICS LETTERS
I
levels into a totally-symmetric
low-lying
vir-
tual MO (la;), which appear both because of vibronic distortions and superposition of other symmetryallowed excitations in the same energy range. Table 4 collects both the esperimental lines (labelled a,b and c) and the sugested configurations involved in the transitions. They do not appear in the solid-target spectra, where the rather diffuse (large F-function COefficients) initial MO’s are ol~viousIy drastically deformed by crystalline interactions [28].
(ii) A rather sharp, medium-intensity
group generated
by transitions (dipole-allowed) from top bonding orbit& into some of the lowest-lying excited bound states which are effectively described here by our computed, lowest-lying virtual orbit&. The surrounding field effect appears accordingly less pronounced in the experiments (see table 4) and the generally broader bands correspond to the rmmerous allowed transitions among the closely spaced levels, typical of this molecular system. (iii) The broad, undulating features appearing on the high-energy side of the previous peaks (and whicl: are labelled (Y,P and 7 in table 4). are assigned to the multiple-excitation and/or ionization processes already described earlier and for which the use of the sudden approximation for computing transition probabilities wouId more properly require direct inclusion of correlation for the initial, ground-state, configuration [4],
1972
bound, of this highly symmetric moiecule. Their outer orbit& (in the independent-particle approxim= tion) are in fact most likely to be still rather localized around the central S and mainly supported by t!ie “electrostatic” potential from the charge distribution of the undistorted ground-state wavefunction, for the first non-zero multipole for SF6 is the 24-pole (and its molecular polarizabihty is considered rather small [30] ), thus strongly reducing the distortion contribution from the travelling electron. This appears to be the case, for instance, from its very-low-energy scavenging properties exhibited in electron-attachment experiments [9,30] and already discussed above. It follows, then, that the few SW virtual orbitals included in the calculations of this note (and which can be qualitatively looked at as eigensolutions for an “undistorted” negative ion [32] ) are particularly effective in mapping out those “physical” one-particle states taking part in X-ray excitation and/or ionization processes.
Acknowledgement I am very grateful to Professor U. Lamanna for substantial computational help and to Professor C. Guidotti for several illuminating discussions on the programs employed.
4. Conclusions It is certainly surprising that, in spite of the crude computations involved in the present description, another set of experimental data from ?he X-ray-region spectra of SF6 can be reasonably explained via the SCF orbit&, both occupied and virtual, computed for the ground-state configuration. Simiiar results have recently been attained for the BP, molecule [29], where
GTF
orbitals
expansion, although seemed substantially
were
used
for the wavefunction
the experiments available there fewer in number and in range
covered. We feel, however, that SF6 constitutes a particularly fortunate example for testing even medium-qualib SCF wavefunctions of.the LCAO type, since the iovvest-lying virtual orbit& obtained in the self-consistent process afford here a particularly good description of the first few real excite.d states, bound and pseudo-
132
.:..
References D.A. Shirley, ed., Eiectran spxtroscopy (NorthHoll~d, Amsterdam, 1972), and referezxes therein. T. iberg, Phys. Rev. 156 (1957) 35. M.0 Krause, T.A. Carlson and R.D. Disumkcs, Phys. Rev. 170 (1958) 37. T.A. Cxlson, hl.0. Krause and W.E. hloddcman, J. Phys.
(Paris)
c3
(1971)
102.
J.L. Dehmer, J. Chem. Phys. 56 (1972) 4496. F.A. Gianturco, G. Guidotti and U. Lamanna, J. Chhzm. Phys. (1972), V.I. Ncfcdov, W.M. Hi&am 642. R.N. Compton,
to bc published. J. Struct. Chem. ! 1 (1970) 272. and R.E. Fos, J. Chem. Phys. 25 (1956)
L.G. Christophorou, G.S. Hurst and P. W. Reinhardt, J. Chem. Phys. 45 (1966) 4634. H.S.1’7. Massey, Negative ions (Cambridge Univ. Press, London, 1950).
Volume
17, number
1
CHEMICAL PHYSICS LETTERS
A.W. Weiss and hf. Krauss, J. Chem. Phys. 52 $1970) 4363. [ 121 hi. Krauss and FM. hiics, Phys. Rev. A 1 (1970) 1592. fll]
P.G. Burke and F.A. Ginnturco, in preparation. F.A. Gianturco, C. Guidotti, U. Lrima~na and R. hlocct, Chrm. Phys Letters IO (1971) 269. R.E. La Villa, to be published. L.C. Parratt, Phys. Rev. SO (1936) 1. D.F. Lawrence: and D.S. Urch, Spectrochim. Acta 25B (1970) 30.5. T.A. CarIson and hl. Krause, J. Chem. Phys. 56 (1972) 3 2Q6_ R. Marine, J. Chcm. Phys. 52 (1470) 5733. A.E. Lindh and 0. Lundquist, Axkiv hlat. Astron. Fys. 18 (1924) 3. F.A. Gianturco and C.A. Coutson, Mol. Phys. 14 (1968) 223. D.W. Fischer and L.W. Bran, 3. Appl. Phys. 36 (1965; 534. F.A. &ntUrcc, J. Phys. 31 119613) 614.
1 November
(241 D.J. Candlin, Proc. Phys. See. (London)
1972
A68 (1955)
322. [Z] L.G. Parratt, Rev. Mod. Phys. 31 (1959) 616. [ 261 D. Blschschmidt, R. Hnensel, E.E. Koch, U. Nielsen and T. Sagawa, Chem. Phys. titters I4 (1972) 33. [ 271 K. Siegbahn, C. Nordling. A. Fahlman, R. Nordberg, K. Hamrin, J. Hedmw, G. Johansson, T. Ocrgmark, S. Karlsson, 1. Lindgren and 5. Lindberg, Nova Actn Reg. Sot. Sci. Uppsala Ser. iV, 20 (1967). 1281 J.&f. Ziman, Principles of the theory of s&ids (CCambridge Univ. Press, London, 1965). 1291 B. Codioli, V. Pincelli, E. Tosatti. U. Fano and f.L. Dehemcr. Phys. Rsv. Letters, submitted for publication. f30j A. Merzcnbcrg, WI ICPEAC Abstracts, cds. LX. Branscomb et al.
133
1 Novemkr
CHEMICAL PHYSICS LETTERS
1972
ELECTRONIC PROPERTIES OF SULPHUR HEXAFLUORIDE. OPTICAL ABSORPTION AND X-RAY EMISSION FROM SCF MO LCAO COMPUTATIONS F.A. GIANTURCO .!kborarorio di Chimica Quantistica ed Energetica Mokcoiare de1 C.N.R., Piso, Ital)
Rcccived
31 Jzly 1972
The enhanced lines and frequent lack of evidence for Rydtxxg structures, already discussed in a past paper on !hc X-ray absorption spectra of this molccuk, are here again interpreted for optical absorption as originating from “shake-up” and skke-off’ processes among computed SCF 510 LCAO levels. Similar mcchxkms, 9s well as oneelectron jumps are invoked for S and F tluorcsccncc spectra (Iin and I$) where they also a!!ow for 3 qualitative one-to-one correspondence between tile excited multiple ions involved and the computed “many-hole” confi_eurations. The electron-scavenger properties of SFc are suggested to be mainly responsible for the moderate success of the rather crude model eipto&d here for coGputnti;k.
1.
Introduction
An increasingly large amount of experimental and theoretical evidence has recently been gathered on the effects of inner- and outer-electron excitations in simple molecular systems [l] . Thus, it has been generally accepted that, when photoionization occurs in an inner shell, an electron in an outer, bound, orbital can be excited by the sudden change of the initial po-
tential due to the loss of a shielding electron [2]. The transitions
are therefore
governed
by “monopole”
sc-
lection rules and good agreement is found with cxperimcnts when Hnrtree-Fock (HF) single-electron wavefunctions are employed [3] , Moreover, when photoionization occurs in the outer shell, another electron in a bound orbital with similar “atomic” features can also undergo excitation, a fact which is explained theoretically only when intra- and inter-shell correlations arc explicitly included in the initial-state wavefunctions [4]. For more complex molecular systems it has also been demonstrated that extensive excitation occurs simultaneously with phot.oionization, but a complete understanding of its nature is still awaited for, even though several theoretical attempts have appeared recently [S-7].
In t’le present note we focus our attention on one of the most popular model-systems for the above processes, i.e., the sulphur hexatluoridc octahedral molecule. The interest in such a compound was prompted, among other reasons, by its unusual behaviour in electron-attachment experiments using monoenergetic electrons [8,9] . In fact, it was found there that the electron-attachment process !eading to the formation of SF; occurs over an extremely narrow energy range and with an exceptionally large cross section. This largely precludes the possibility that these ions result from radiative capture, for which the cross section would be about 1O-5 times smaller [ 10) and, in any case, would not be confined to such a narrow energy range. The process occurring must be one in which the electron is captured to a nearly “stationary” SF6,
the surplus
energy
will be distributed
over a great
number of modes of motion and break-up can only occur when this energy is concentrated in a suitable mode, before which considerable time may elapse [91. In a qualitative way, one may say that the effective potential generated outside the molecule by the outer e!ectrons charge distribution (chiefly fluorine lone-pairs, in chemical jargon) is here capable of supporting a few, closely spaced, bound states which, in 127
Volume
17, number
CHEMICAL
I
PHYSICS
2. Emission
turn, ORE hopes to describe convincingly via the Iowest-lying virtual orbit& generated by an SCF MO LCAO description of the ground state wavefunction
This has provided us with a satisfactory picture for the N; scattering resonance at = 2.0 eV, mainly assigned to a shape resonance of an incident d-wave electron [IZ], and it is in the process of being extended to more general, non-linear, molecular systems [ 131 for which a fairly adequate description of the groundstate wavefunction is availabie in the HF scheme. Moreover, the feasibility of our compured w.f. of the SF6 ground-state configuration for describing several of its experimenta properties has already been tested in some previous papers [G, 141, where ESCA ionization energies, K- and L-absorption spectra from both sulphur and fluorine atoms have been reported and discussed. We extend here the study to the computed assignments for some recently measured fluorescence lines [!5], with the aim of both continuing to test our wavefunction and of pointing out, at the same time, the multi-electron nature of the rearrangement processes following an inner-ionization or excitation in molecular systems of such complexity. All compu‘tations were performed within the sudden approximatioh described elsewhere [6,2 l] .
peaks
-----_I_-_~-Espcrimcntal
bands
a
Assigned
spectra
The above main line has already been assigned to a dipole-allowed process of filling in the 1s-electron vacancy (from now on designated as a [Is] state) on the central atom by one of t!!e tlu valence orbit& with iarge sulphur $-function contributions [G] . \hat appears to be possible from these additional experiments is the suggestion that the principal part of the whole spectrum is associated to “diagrammatic” transitions to final states with single vacancies in the three tlil binding orbit& [ 171. Thus, the calculated transitions from our SCF wavefunction, in the sudden approximation, are reported in the upper part of table 1. They also seem in qualitative agreement with experiments when the re-
Table 1 transitions --
and computed
for sulph~~r K:p lines in SF6 [eV) Transition (arbitrary
transitions
broad
2448.5
[lqgl
-
very strong, sharp
2467.1
IlQ!
weak
2472.5
[lqgl
2444
2463
shoulder
very weak vcly
wea!c
aFromrcf. MO’S.
128
[lSJ;b
c k=2p
cl,
J
nsgiveninref.
moments units)
c
b medium,
November 1972
When both photons and electrons were employed as exciting sources [ 151 , the experimental spectra for the moiecule in the gas phase exhibited one sharp, intense, peak (2467.1 cV> flanked by two other small ones (at 2448.5 eV and 2472.5 eV respectively). OnIy the electronzxcited spectra presented what were termed “resonance radiation” phenomena, i.e., a low broad peak at 2444 eV and a low shoulder at abol;t 2463 eV j15].
IllI*
Experimental
1
LETTERS
d
2480
0.11
0.10
0.27
- [4tl”1
2501
0.36
0.56
0.49
-
[5tlul
2509
0.07
0.30
0.14
(la;;
t;,,)
-+(3t
(I,;;
tf”)’
[l.S];c
[3tlul
c
k=2p
(4t;;
c&
;:
-
< lo+
t;u)
2472
f?“)
2497
c 1o-3
2499
<
from
present
wavefunction;
d dipole
matrix
elements
from
1o-3
present
Volume 17, number I
1 November
CHEMICAL PHYSICS LETTERS
lative computed intensities+ are concerned [ 191. In addition to ionization caused by the one-electron processes involved in the initial photoelectron ejection, it is an established fact [4] that several additional ionizations can occur by electron “shake-off” accompanying photoionization and by multiple Auger processes. Moreover, “shake-up” phenomena are also invoked to exp!ain the presence of additional emission peaks in the ener,T region of strong absorption maxirna [3 l] _It therefore follows that the computed virtual MO’s of the present mo!ecule, already fcund reliable for explaining the observed absorption spectra, can here be called upon for assigning the broad “bumps” detected with electron sources [ 1.51. This is shown in table 1 and again reasonable agreement is found with observations. It should be mentioned, however, that the narrow spacings among the top vzilence orbit& and the lowest-!ying virtual MO’s [6] permit several symmetry-allowed transitions to fall very close to each other: this means that the assignments reported in the table should be considered as indicative of only some of the most likely rearrangemen t processes [ 16, IS] . When a Z,p-electron is removed from the central atom, another fluorescence transition involving singleparticle excitation can take place, the vacancy being filled by tile outer orbit& allowed by electric dipole selection rules. In the SF, molecule, two intense broad bands (at 153 and 162 eV respectively) have been dEtected in the enerw region of the sulphur L, 3 fluorescence line and their assi&nments invoked as &idence for d-orbital participation in sulphur bonding [ 15) . This means that the suggested transitions involve final-state configurations holding one vacancy in an MO with large sulphur 3s- and 3d-contributions. Our two most intense computed excitaticns (with transition moments N in the dipole approximation) are the following:
[2 t1,(2p)]
+ [5 alg(3s)] at 170eV (AI= 0.27),
12 t,,(Zp)]
+ [3 e,(3d)]
at 177 eV (N = 0.20)
and are in fair agreement with the observed separations between the two broad lines of La Villa’s measurements [ 151. It is obvious, however, that other i I70r the various merits of the approximations c and d of the table, set refs. [ I _ 15,191.
of columns b,
“diagrammatic”
transitions
could
be involved
1972
in the
relevant energy region, e.g., those from the 4a1,(3s), 2ep(3d) and 1tZB(3d) valence orbit& [6] , although any experiment discriminating among them is still a long way off. 2.2. 711esitlphctr K, spectiwn As early as fifty years ago, Lindh and Lundquist [20] first showed that the sulphur K-X-ray spectrum could be affected by bonding. Since then, many studies have been made showing chemical effects on both positions and intensities of K, iines in sulphur compounds, and simple theoretical models have been suggested for correlating these shifts with the localized charge on the relevant atoms [21] i. A similar series of results has been obtained for the satellite lines to the parent K, fluorescence transition [ 22, 231 and the assignments generally suggested for ihese lines are here employed
to interpret
the experimenta!
findings
on the SF, molecule.
Thus, while the main peak of the unresolved o1 ,2 doublet at 2309.3 eV [2J is attribufed to a singleparticle transition of the type [K] -+ [L2,3], the most intense of the peaks on its high-energy side is assigned to single-electron transitions from KL double vacancy states, narneIy [KL] -+ [L’] . For atomic systems with L-,C-coupling treatment of involved multiplets, such transitions should give rise to a fiveline group for all possible final states after rearrangement [2,25], although in a molecular environment the above “channel indices” are hardly behaving as “good” quantum numbers. The identification of a, cu3 and cy4 was therefore made by analogy with the relative positions and intensity of similar satellite lines of other sulphur K, spectra in the literature [24], and the results collected in table 2. Here again the square bracket notation indicates the one- or two-hole configuration and the upper indices the spin multiplicities. The general agreement with the experimental line separations, in spite of the crudeness of the “frozen orbitaI” approximation, seems to suggest that once more
f The K&,,: experimental shift provides here a net Char!$ on sulphur of+2.38 when the semi-empirical equation from ref. (21 j is used. The calculated net charge (in the hlullikcn sense [32]) with the present L141.
wavefdnction
was found to be +2.36
Volume
17, number
1
1 November
CHEMICAL PHYSICS LETTERS
1972
Trible 2
Experimental R, spectrum and computed transitions for sulphur in SF6 Observed line a)
------
Esperimcntal energy (eV) s) _...-- -----_-_-_
-___
Computed ______
a1 ,’
2309.3
a’
2317.8
l[lsLg
a3
2322.7
3[1qg
2325.4 _--_.----__----
Lllsfg -_-_---------.__-----
a4 --
transition
"1 lq&
(eV) -
~--
- ?2qul
2331
3qgl
+ LDqg2tLuI
2346
3s]cl
-+3[3qS2tlul
2353
2tLu] -L L[2t;J
2357
n) From ref. [ 15] .
the MO scheme for these “monopole” ionizations provides us with a fairly realistic physical picture what happens in SF6.
[3] of
emission spectrum in the fluorine K, energy region [ 151 exhibited again some broad, weak, “b-imps” on the Iow-energ side of the most intense peak. This Prominent peak consists of transitions among sindy , ionized configurations to fill a fluorine K-shell vacancy (i.e._ initial states like: [ItI,], [leg] and/or [2alg]) from one of the upper four occupied orbitals that are distributed in a range of about 6 eV [6]. Since the vertical ionization energies of the above orbitais are not known with certainty, a comparison of our computed assignment with the one suggested by experimenralists [7] should he!p in throwing some light on what we consider the essentially “diagram-
2.3. i%e ji’rroritze K, speclmn In examining the K-absorption spectrum from the fluorine atoms, we have already discussed [6] how the “localized” nature of these inner hofes lends to the existence, in MO LCAO parlance, of several IeveIs very close in energy but beIonging to different O,, irreducible representations, hence to the identification of scvera1 primary processes which can be described by the active-electron approximation. The recently measured
Table 3 Observed II, spectrum of fluorine in SF6 snd assigned computed
transitions -----------__L_
---___-___--
Observed bands (eVi
Computed
3
3
[ltlul -+ 12 e,] D very wcok, broad
= 650-658
--.
b 0.013
653.1
675.2
0.03
0.035
671.1
0.08
0.056
[2q,01 - 14tLul
671.7
697.7
0.5 1
0.60
667.6
699.9
0.23
0.25
--+ 15qgl
[Itlul
-+ Iltj_l -”
I2qg1
+ t5t1ui
700 677.1
704.6
0.32 0.94
2.00
[2@
d [lt2”1
676.2
705
1.00
2.30
Iltlul
+ I ItI,
678.9
706
1,oo
2.00
[ItI”
--+ [3 ccl
703.7
0.48
-_-c__--_.-a From ref. [ 151; b prcscn t work.
130
a 0.01
650.4
[It]“1
broad
b 678
- 13tluI
==612
% 677.6
655.3
11t1,1 -+ I4ol”lc
12qel
weak shoulder
intense,
Transition moments (arbitrary units)
trnnsitions (ev)
674.7
--.-.
--
1.90
_-.L--
VoIume 1 ‘i, number molecular
1 November
CHEMICAL PHYSICS LETTERS
I
levels into a totally-symmetric
low-lying
vir-
tual MO (la;), which appear both because of vibronic distortions and superposition of other symmetryallowed excitations in the same energy range. Table 4 collects both the esperimental lines (labelled a,b and c) and the sugested configurations involved in the transitions. They do not appear in the solid-target spectra, where the rather diffuse (large F-function COefficients) initial MO’s are ol~viousIy drastically deformed by crystalline interactions [28].
(ii) A rather sharp, medium-intensity
group generated
by transitions (dipole-allowed) from top bonding orbit& into some of the lowest-lying excited bound states which are effectively described here by our computed, lowest-lying virtual orbit&. The surrounding field effect appears accordingly less pronounced in the experiments (see table 4) and the generally broader bands correspond to the rmmerous allowed transitions among the closely spaced levels, typical of this molecular system. (iii) The broad, undulating features appearing on the high-energy side of the previous peaks (and whicl: are labelled (Y,P and 7 in table 4). are assigned to the multiple-excitation and/or ionization processes already described earlier and for which the use of the sudden approximation for computing transition probabilities wouId more properly require direct inclusion of correlation for the initial, ground-state, configuration [4],
1972
bound, of this highly symmetric moiecule. Their outer orbit& (in the independent-particle approxim= tion) are in fact most likely to be still rather localized around the central S and mainly supported by t!ie “electrostatic” potential from the charge distribution of the undistorted ground-state wavefunction, for the first non-zero multipole for SF6 is the 24-pole (and its molecular polarizabihty is considered rather small [30] ), thus strongly reducing the distortion contribution from the travelling electron. This appears to be the case, for instance, from its very-low-energy scavenging properties exhibited in electron-attachment experiments [9,30] and already discussed above. It follows, then, that the few SW virtual orbitals included in the calculations of this note (and which can be qualitatively looked at as eigensolutions for an “undistorted” negative ion [32] ) are particularly effective in mapping out those “physical” one-particle states taking part in X-ray excitation and/or ionization processes.
Acknowledgement I am very grateful to Professor U. Lamanna for substantial computational help and to Professor C. Guidotti for several illuminating discussions on the programs employed.
4. Conclusions It is certainly surprising that, in spite of the crude computations involved in the present description, another set of experimental data from ?he X-ray-region spectra of SF6 can be reasonably explained via the SCF orbit&, both occupied and virtual, computed for the ground-state configuration. Simiiar results have recently been attained for the BP, molecule [29], where
GTF
orbitals
expansion, although seemed substantially
were
used
for the wavefunction
the experiments available there fewer in number and in range
covered. We feel, however, that SF6 constitutes a particularly fortunate example for testing even medium-qualib SCF wavefunctions of.the LCAO type, since the iovvest-lying virtual orbit& obtained in the self-consistent process afford here a particularly good description of the first few real excite.d states, bound and pseudo-
132
.:..
References D.A. Shirley, ed., Eiectran spxtroscopy (NorthHoll~d, Amsterdam, 1972), and referezxes therein. T. iberg, Phys. Rev. 156 (1957) 35. M.0 Krause, T.A. Carlson and R.D. Disumkcs, Phys. Rev. 170 (1958) 37. T.A. Cxlson, hl.0. Krause and W.E. hloddcman, J. Phys.
(Paris)
c3
(1971)
102.
J.L. Dehmer, J. Chem. Phys. 56 (1972) 4496. F.A. Gianturco, G. Guidotti and U. Lamanna, J. Chhzm. Phys. (1972), V.I. Ncfcdov, W.M. Hi&am 642. R.N. Compton,
to bc published. J. Struct. Chem. ! 1 (1970) 272. and R.E. Fos, J. Chem. Phys. 25 (1956)
L.G. Christophorou, G.S. Hurst and P. W. Reinhardt, J. Chem. Phys. 45 (1966) 4634. H.S.1’7. Massey, Negative ions (Cambridge Univ. Press, London, 1950).
Volume
17, number
1
CHEMICAL PHYSICS LETTERS
A.W. Weiss and hf. Krauss, J. Chem. Phys. 52 $1970) 4363. [ 121 hi. Krauss and FM. hiics, Phys. Rev. A 1 (1970) 1592. fll]
P.G. Burke and F.A. Ginnturco, in preparation. F.A. Gianturco, C. Guidotti, U. Lrima~na and R. hlocct, Chrm. Phys Letters IO (1971) 269. R.E. La Villa, to be published. L.C. Parratt, Phys. Rev. SO (1936) 1. D.F. Lawrence: and D.S. Urch, Spectrochim. Acta 25B (1970) 30.5. T.A. CarIson and hl. Krause, J. Chem. Phys. 56 (1972) 3 2Q6_ R. Marine, J. Chcm. Phys. 52 (1470) 5733. A.E. Lindh and 0. Lundquist, Axkiv hlat. Astron. Fys. 18 (1924) 3. F.A. Gianturco and C.A. Coutson, Mol. Phys. 14 (1968) 223. D.W. Fischer and L.W. Bran, 3. Appl. Phys. 36 (1965; 534. F.A. &ntUrcc, J. Phys. 31 119613) 614.
1 November
(241 D.J. Candlin, Proc. Phys. See. (London)
1972
A68 (1955)
322. [Z] L.G. Parratt, Rev. Mod. Phys. 31 (1959) 616. [ 261 D. Blschschmidt, R. Hnensel, E.E. Koch, U. Nielsen and T. Sagawa, Chem. Phys. titters I4 (1972) 33. [ 271 K. Siegbahn, C. Nordling. A. Fahlman, R. Nordberg, K. Hamrin, J. Hedmw, G. Johansson, T. Ocrgmark, S. Karlsson, 1. Lindgren and 5. Lindberg, Nova Actn Reg. Sot. Sci. Uppsala Ser. iV, 20 (1967). 1281 J.&f. Ziman, Principles of the theory of s&ids (CCambridge Univ. Press, London, 1965). 1291 B. Codioli, V. Pincelli, E. Tosatti. U. Fano and f.L. Dehemcr. Phys. Rsv. Letters, submitted for publication. f30j A. Merzcnbcrg, WI ICPEAC Abstracts, cds. LX. Branscomb et al.
133