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Ionization of fluoromethanes: CHF3 and CF4. A Greens̀ function study and an (e, 2e) spectroscopic investigation
Volumr 90, numbcr 6
CHlXSIIC,\L
IONIZATION OF FLUORO~~TH~ES: A GREENS FICTION
PHSSICS LLTTLRS
CHF, AND CF4_
STUDY AND AN (e, le) SFECTROSCOPICINVESTIGATION
R. CAMBI, G. CIULLO. A. SG~fELLOTTl, F. TARANTELLI DlFurIinietrtodt Citmrrr4. iittwcrstt~ dt Penqt4, 06100 Put~gut, it&) and
R. FANTONI. A. GIARDINI-GUIDONI, hi. ROSI F and R TIRIBELLI EM EA
ex C&&V. Ccruro ,bxronole dl Fr4sc;rrr 0001-f Frascarr. Rorrtc, Irol.r-
Reccrrcd 10 Alay 1982. rn final form -I June 1982
1. Introduction
1112gas pha~
The high-resolutton photoelectron spectra of Ruoroeompounds have already been reported in the hterature and mtrrpreted m terms of molecular structure on an e~per~ent~ b&s [l--71. Tf~eorettc~ predictions have also been made for many of the molecules of thts famdy with different methods, such as SCF. Xo, HAM/3 nnd in the frame of the Green’s iunctron
fokmahsm [Sj. With the aim of obtatnirtg more detaded structural mfomatron, we have undertaken the study of the fluorinated series of m4rhanr by means of electron camcrdence (e, 7e) spectroscopy, together with theorettcel predictions via the Green’s functron theory. Prevtous results on CH,, CH3F and CH,F,, hereafter referred to as I, showed good agreemenlb;tween theoretical predictions and espertment, including a good description of the breakdown of the onepartrcle model for mner-lymg vfenee tomzatrons [9]. In this work we have periormed Green’s function calculations on the remaining terms of the series, that is CHF, and CF+ Complete binary (e, 2e) spectra m * On bavr irom Dlpsrttmenro 06100 Peru$ta, kdy.
dl Chimxa.
Unwcrrnl
di Pcrug~a.
are reported for both molecules together wtth angular momentum dtstrrbutrons ior some orbrtsfs of CF,. Prevrously e~per;illent~~y obtsmed PES IPs are also compared ivtth theorettcal predrcttons for both mofecules
1. Theoretical background
in many-body physics, a dtrrcr connectron IS found between the tonvation spectrum of a molecule and the oru+psrtrcle Green’s functton, provided that the experiments are carned out II high mctdent energy relative to the tonkttion threshold [ IO]. In thus case, the two-panrclc (iour mdrcas) hole-parttslu propagator m the fommla for the transitlon probabllfry P(w) can be replxed by the one-psrttck advanced Gi;(w) (more prec~scly both are present wnh then unsginary part). Indeed. due to the presence of an mfiiitcsimal imagmary tq tn the dcnommators of its spectral representatton, Im G,;(U) assumes 3 6-iunction behaviour and can mclude one of the two 6 -function factors of the golden role for the transrtton probabdtty.P(w) can thus be wrttten as
c.r,j %IN [c;; fw -
E. -
1$]6(w - .&) _
tn wluch the rematmng &(o - E,) factor accounts for the cncrglr conservatton law and the T are tontzatton m3tra elements [IO]. It 1s w12l.lknown that the smgularttles (poles) of G,;(U) represent the 1Ps oi the nl~ny-body system. In the region of high incident energy Eo, and when G,(w) = 0 ior t *I (dtagonal G mar&), the height ratio of two hnes for the same orbital tonization COWctdcs wnh the ratio of the correspondmg numerators tn rhe propagator (pole strengths) and the Green’s iunction 1s directly capable of a complete mterpretation of the spectrum In the full nondtagonal COP thts is no longer true, but m general 111sG matri. happens to bc almost dfagona_land the sum oi the dtap onal
rcstdues can r&tsonabiy be taken a~ playtng the same role as the pole strengths of the dta~on~ case. in the present ConlputatIon, moreover, the results of the nondzrgonal problem show the typical “diagond” bchavtour, tn that each tontzatton borrows mtenstty from 3 smgle one-electron state, li only dtagonal restdues20.01 are considered. The method of rcsolurton of the equatlons involved for the determination of poles and mtensittes can be found elsewhere [10-l-2]. The computattons were made n-t the Iph-TDA full non~ta~on~ appro~~~tton, with the same basts set asemployed m I. In the present case, in fact, the 2phTDA results appear to be closer to the experimentaT values than their GF counterparts (see below), even for the outer valence tonizatlons, though the dtiferenccs are obvtously small. Bmary (c, 2e) spectroscopy (wrth htgh mcrdent clcctron energy and high momentum transfer) allows one to measure the IPs and transnton probabihties tn J wide energy range, yielding a valuable check on the data predtcted by the Zph-TDA calculattons. In the out~f-plane ~mmet~c kinematics the plane wave mtpulse appro.~mation (PWA) holds f 13-151 for the relatm (e, 7e) cross sectron, which becomes proportional to the product of the h&f-off-shell lllott factor (d2a/dR& and the square modulus of the Fourier transfoml of the overlap between the mirlal neutral state 10”) and the fmal ionic state I@:): 446
Since in the PWIA the momentum is transferred to the ton only through the removal of an electron, q is equal and opposite to the momentum of the initially bound electron trt the one-electron approxtmation for the target. if the target is descrtbed in the Hartree-Fock approxtrnatron as an antisyrnmetrtzed product of a oneparticle orbitaf [ $,j and a remainder, that ts as k,$r) = I$,) l#,n>,one obrams TFk’,cii)l’= ~,~)~~,where p,@i) is the momentum denstty associated with the oneelectron orbttal l$,(f)).KF represents the probabthry of populating the X ioruc state when one electron is ejected out of the I$,) orbttal. Both energy spectra and electron momentum distnbutlons (EMD) can be dctermtned tn (e, 2e) cxpertments by varying the separation energy at fixed momentum, or measurtng the angular correlation between the final elecrrons at fmed separation energy, respecttvety [13-S]. The fe. Ze) exper~ents were carried out as discussed m 1.
3. Results and discussion 3.1.
CHFj
Fluoroform ISa 34efectron cloud-shell molecule wtth C,, symmetry, which has been reduced to the abelian C, m the computations. Of the 47, molecular orbitats resulting from the SCF computation, 21 (13 of whtch occupied) have been deemed active in the computation of the Zph-TDA expansion. The four inner shells (Is on C and F) have been kept frozen. The ionization energies and their relative intensities are shown in table 1 together with the experimental PES iomzatton potentials. Only pole strength vrdues20.01 are reported. Energy levels have been computed within the ‘Iph-TDA frame, except for la2 which is the only orbital not appearing with a’ symmetry in the C, subgroup. Since this is an outer valence ionization, energy and pole strength have been computed in the computationally less expensive GF approxtrnation [ 161, based on a third-order truncatron of the graphical Abnlcosov series, improved by a renormahzation procedure to take higher-
Volume 90,
number 6
Table 1 IPs as determrned
CHIXICAL
by tfte Zph-TDA non-dugon~
PflYSfCS LKTKRS
appro\tm3tton
CHFS
/D August 1981
Only pole strcngtbs
>0 01 arc reported.
Values m cV
cr4
0rbit.d
c\p.a)
Hr
Zph-TDA
pofu strcngthb)
orbIt
c\p 3)
NT
I!@-TDA
631
13 8 15 5 16 2 17 a LO.7
16 63 18.39 1850 19 69 22.87,
I4 88 16 05 (Cl-) 16.11 17.08 30 59
0.93 0 92 (CT) 091 090 090
111 4tz qa1
16 2 17 4 IS 5 ” 1 25 1
1911 19 67 31 35 21.90 38 1-I
16.74 17.45 1859 22.54 25 68 35 83 36.89
21.43 2s 06 31 30 40.80 41 00 41 05 41x 4113 41 70 41 83 4192 41.98 41.07 42 1-l 11.19 J? 31 42.-C 42 77
0.89 OS? 001 001 002 00’ 001 004 0 33 003 00-t 001 0 01 oo’t 002 001 0.03 002
-712
10 3
46 61
41 33 415.5 42 16 42.51 4265 42 13
43 19 43 55 43 63 43 65 43 75 46 10 46 39 46.35 46 53 47 07
006 0 17 007 0.06 001 001 003 0.X 0 04 0 05
132 je 4e 3c
5%
10.7
-1%
24 4
23 78 77 46
,e
39 2
45.28
331
42.0
4s 19
le 3t:!
41.90 4199
331
43 8
SO49
43.06 43 31 13 55 4361 36.35 16 66 16 S5 4107 4164 5100 43 23 45 19 45 71 45 97 37 62 17.91 19 58 51.15 $4 00 6261
pole stWl!gh b) 092 09’
091 0.90 088 00’ 001 001 001 005 002 0 II 0.13 t-JO6 002 009 ‘01 00-1 007 002 00-T 0.0’ 003 001 001 001 0 18 003 001 00-I 0 30 0 14 00 00’ 001
scr = 336 740 (au)
E'O'
b, As c\pkincd m the text. the computationsacre mzdc tn the Tuff oondiagon?l Zph-TDA ~ppto~rmar~on in the prSsen1 dmx, ho&cover, each lute bonows tntenuty from one lontzation only and fhc slims oi the dqoxtf ro~tdues comctdr: wzth the usox1 pofr: strengths oi the dtztgonxf compu~~on
order graphs parttally mto account [ 10, pp. 2692733. As noted above, according to a feature of the present calculattons, an improved value could be expetted in the 2ph-TDA model, even if the basis set was completely etiausted in the GF case.
The Iph-IDA results for the 6al, Se, 4e snd 3e Jeveis (outer vaJence electrons) show excellent greement with the experimental PES values, wJuJe a dE ference of0.7 eV ISfound for the 5q rontwrion. AJJof these iomzations appear to be essentially one-particle 4.47
V&m
40.
nuntber fi
CHEIIICAL
PHk SICS
procesjzs. the first orbital for whtch some satelhte structure is predtcted being the mtermedtate m energy -tat. As has been found in many analogous sttuations, the 7e ievet (at 39.13 eV) is shtfted by the computation towards htgh energies. The computations show a complete breakdown of the one.puticle model, the ma~unum mtensity being 0 34 for the line at 41.70 eV. . The smc can be said for the 3at orbttal for which the mstn peaks he at 13.55 (0.17) and 16X (02-t). the ca~erimental rake betng 42.00 cV. The sphtttng of the 33t orbttai was not observed tn prevtous ESCA wxk [j,s] because of resolution and since tn the stunphng at htglt q (q >-kr; ‘) p?rkrnted by ESCA, the contributtons from the 33t orbit31 are very low . ft is to be noted, m add&ton, that in ref. I.51no net breakdown phenomenon ISassumed and each inner band ISreproduced as a convolutton of two peaks only, our expcrunentsl and theorettcal results show, on the contrary, that the sphtttttg of the irttt?nsity over very many shakeup states ISa dtstincttve feature of the 33t and le iontzations
Ftg 1. lanuatwn
LCTTtRS
The measured and theoretuxtllp reconstructed energy spectra (with an overah resolution of 1.7 ev) are reported in fig. I ut a boding energy range up to 50 eV for two drfferent scatterutg a.ngIes.The convolution procedure used has been eupltied m detatl in ref. [16]. IFS and pole strengths are those obtained from GF and Zph-TDA data of table 1. The relative intenstties are wetghted by the theorettcal momentum denstttes correspondmg to io~ations out of each sm~e-pa~tcle orbttal. While tn f&. la, at q = 0.1 UC’, only totally symmetric states contrtbute to the spectrum, at q = 09cG t (fig. lb), contrtbuttons from alI the tune vaknce orbitals appear. The spectrum show different bands, dtvtded in two main groups; the First one dertves from ~ontzattons that are almost pure in character in that they show no significant breakdown structute. The second one comprises many dtfferent shake.up states gtvtng rise to a wade profiie whose shape strongly depends on the q at which the measurements are made. As fig. 1 clearly shows, not even a resolution as good as 1.7 eV can completely separate each iontc state, etther in the
energy jpcctn oTCHF3 St q = O.l$ (a), and q = 0.9a$ @) result Tot la2 1~1 (xc text)].
calcukuedon the bassof the?ph-TtIA resultsIGr
20 Au~usr1982
Top r\pcnrnental
data.
bottom: Yme spectn 35
Volume 90. number 6
CHCCMICAL PHYSICS LCTT’CRS
out~~ost valence region, when the vrbrationa~ structure of the states is taken into account 181, or in the ~e~ost valence shell, where, as noted above, 2e and 3a, intensities are ~t~bu~d over a large number of contiguous lmes. It is worth noting, m th& respect, the behaviour of the 3al orbital, split into main peaks, ~3 eY apart, when observed with an 1.7 eV energy resolution. This behaviour IS predicted by the ~lculatlons, which nevertheless do not account for the satelhre lmes from the 3a, observed at higher energies. 3.3 CF, Carbon retra!Iuorlde ISa 42-electron system with T, symmetry, reduced to the abehan Czv III the computattons. The orbrtal space has been truncated to 24 acflve orbltals, 16 of which are occupied. The five core orbitals Is on C and F hake been excluded from the active set. The IPs are shown in table 1 tog&her with their pole strengths(>,O_Ol only).The computed values are in agreement with the e~per~ent~ fidlngs from 1t i to 4at The computations show non-neglrgible satellite structures startmg from the 4at orbital. Also m this case the computed 2t2 band ISshifted towards high
energies, its rn~~a being located at 42.65 and 42 73 eV (\vrth mten~ttes 0.1 I and 0.13 respectively). As for CHF,, thrs fs due to mherent hmttations of the ZphIDA method which takes is-110account only smgk excitation shake-up processes, and to the basis set whxh ISunable IO reproduce satisfactorily high-lying I%i p States. The 33, level ISeven more drspiaed tb,u~ 3t2, 11smaximum lymg = 4 eV apart from the experimental value (43.8 eV), though a srgmficant hne is found at 45.19 eV (0.18). In fig. 2 (e, 2e) measured energy spectra, taken at Iwo different scattering angles, are reported and compared with the results of table 1. The cakulatcd spccrrum accounts for the experimental energy resolution of 2.6 eV. Due to the close proGrnrty of the iomc states, the CF, spectra appear 3s formed by only three large bands. The first (centered at =Z18 eV) and the second (centered at 5.25 eV) take contrtburtons fram three and fwo mam pe3ks. respectively (I tt ,4tt, It? and 3t2, 4at), each of them carrying almost ail the intensity of a sm~e-panicle ro~atlon. On the other hand, the third band (centered at = 42 eV) is relevant to states artsing from io~atron processes in the innermost valence shell and appears as a broad structure
\-
0
00
Fe. 2 lonu3tion encr~y specu~ of CF4 at q = 0 25 a;’ (a), and q = 0 9 a-lo (b). JS calcuhted on the basis of the Zph-IDA results
20
so
1. ‘0
‘\-. 501‘
*I.
Top. experuncnral datt3, bottom’ r*lmL‘spcc~n
113
Volume 90. number 6
CHEMICAL PHYSICS LETTERS
20 August I982
IS
10
s
0
0
1
2 qta,'t
of
T& 3. EMD’s CF+ mew.trsd at d&crent eh &ucs and compared wth the cslculsted contrlbutrons from al! ihe Statej convoluted by theenergy resolution.
m whxh several lnes of small mten~ty and of dtifer-
ent ongin can be convoluted. As observed III I, in ref. [ 161 and m the case of CHF,, a large number of ntellire lines appear m the region near 40 eV, where ionization OUIof molecular orbit& mamly of atomic IsF character 1sproduced. The overaLlshape of the bands ISwell reproduced both at q = 0.25 and 09 noI, apart From the sit&t in the 40-50 eV region referred to above. Mth the aim of extracting more mformation, some angular d~tnbu~lons measured at surtable chosen separation energy (EJ vahses are reported in fig. 3, together with the theoretical predictions. In fig. 4 we show the Iinenr momentum denuties associated with each SCF molecular orbital, that is with 450
cun-tls
fsohd Itnes), obtnmed bJ’ =ctudlnL!
the same orbitais as in the Green’s function perturbation expansion. In the theoretreat angular distributions of fig. 3. each momentum density of fig. 4 is weighted by the ?-ph-TDA pole strengths and by the percentage contribution of each line at the chosen q,_ by taking into account the gaussian energy resolution of the apparatus. It should be noted that a sin& orbital contribution (4at) was detected onIy at q, = 27 eU (iig. 3~). Significant in this respect is the agreement found with the SCF description of the 4aI orbital, which involves essentially the bonding comb~ation of 3,sCand 2pF. Good agreement with thy theoretical predictlons is also obtained for the data taken at q, = 7_0eV (fg. 3b), where the 3t2 orbital gives by far the most important contnbution. This is not suquisiig
CHCMfCAt
Volume 90, number 6
0 24
PH’l SICS LETTERS
11,
515
008 0 :i’\\ 0
GE
16
2.I
32
01
GA
03
03
I.2
31,
02
02
01
01
0 ~ 0
Tg
08
Ii
24
32
4. EblDs of CF4 v&xc-shzU
since the 3t, orbital mvolvr?sthe annbonding combination of the same orbitals as 41,. The rather satisfactory fit in the measurement at eh = 17 eV confkms the augment of the present c~eulatton for the outer levels Itt ~4t2 and le. The data reported m figs. 3d and 3e show the typical behaviour of the innermost valence band. The comparison between experimental data and theoretical predlctions has been done in this case after having shifted the calculated band to the left by 4 eV (see above). The HF description of the ionization would f& to fit the angular distribution measurements whatever shift in energy one could introduce_ On the other hand, as figs. 3d and 3e clearly show, the agree-
0 I!!l!L0
GO
fi
24
32
orbuals OScomputed by SCT wsvrfunct~onr
ment ISgood when contributrons irom different satelhte hnes are included as predicted by the manybody Green’s function cakulation,
4. Concluding
remarks
‘Thepresent computation confms that, even for rather complex molecular systems, the Green’s functlon methods, and their related approximate graphcal expansions, are well suited for the description of the iomzation processes; in particular the breakdown phenomenon for inner valence orbitais is qualitatively weil described by the Zph-TDA approbation_ The 451
~oiun~e 90, number 6
CJ+EMCAL
PHYSKS
(e, 12) spectroscopy ptovldrs extra mformatlon by measurmg the electron momentum distrtbutton for each smgle molecular orbrral and shows it to be more sensitwe to the molecular symmetry in the mnial sratc and to the nature of the chemical bond, than other spccttoscopies, Ike PES, even d these are coupled wth angulardlstnbutlon measuremenrs.
(41 S Kasumata
[6] [7j
[9]
Gckno~ ledgement [ 101 [I 1J [l?,]
References 1131 1 I J D \V Turner, C Bahcr. X C Bzd.cr and C R Brundlr. hloleculsr phorelectron spccttoicopy (Wdey-lntcrsc~snce, New York, 1970). [ 21A IV Potts, MJ. Lcmpha. D C Srrecr and WC Pr~cc. Phd Trans. Roy Sot. (London) A268 (!970) 59.
[ 31
R N Duon, (1971)611.
J N XlurreU snd B Narayan. Llol
Phys. 10
and K;. Kimun,
46 (1973) i341. IS] M S. Bsnna end D
[S]
We gratefully acknowledge Professor W. von Nfessen ior prowding the computer programs, and the k&an CNR for fiiancisl support.
10 Au@st
LIXI’ERS
[J-I]
[ 151 [ 161
BuiJ Chem
Sot
1982
Japan
A Shuley,Chcm. Phys Lacers 33 (1975) 411. L. Karlsson, R. Jardrny, 1. Msttsson,I--T. Chwi and K Siqbshn, PhysIca ScrIpta 16 (1977) 225. C R Brundlc. hf B Robm snd H Basch, I Chcm Phys 53 (1970) 2196. G. B~crr, 1. Asbrmk and W van Nvswn, J. Electron Spcctry. Reht. Phenom. 23 (1981) 281 R Csmbl, G. CMlo. A SgnmclJotta. F. fanntel, R. Fantom, A. CwduuGuidonr and A. Srrgto, Chcm Phys. Letters 80 (1981) 195. L S. Ccdcrbaum and W Domcke, Advan. Chem. Phys 36 (1977) 205. J. Schtrmrr and L S. Cederbaum, J. Phys 811 (1978) 1889. W uon Ntessen. L S. Ccderbaum and W Domcke. m Escttcd states III qwntum chemistry, cds C.t\ Ntcolxdes and D.R Beck (Reidel, Doidrtchr, 1978). IE. McCarthy and E. W&gold, Phys Rept. 27C (1976) 275. R.Camrllxu, A. GurduuGuzdom, I E. McCarthy and G. Strfam, Phys Rev. 17A (1978) 1631. E. \\egold and 11. McCarthy, Adban. At Mol. Phys 1-f (1978) 127. R. Fantom, A. C~ardtntGu~dom. R Tlrtbellt, R Cambi. G CmUo, A. SgimelIottl and F Tarantclh, hlol Phys II
(1982) 1.
CHlXSIIC,\L
IONIZATION OF FLUORO~~TH~ES: A GREENS FICTION
PHSSICS LLTTLRS
CHF, AND CF4_
STUDY AND AN (e, le) SFECTROSCOPICINVESTIGATION
R. CAMBI, G. CIULLO. A. SG~fELLOTTl, F. TARANTELLI DlFurIinietrtodt Citmrrr4. iittwcrstt~ dt Penqt4, 06100 Put~gut, it&) and
R. FANTONI. A. GIARDINI-GUIDONI, hi. ROSI F and R TIRIBELLI EM EA
ex C&&V. Ccruro ,bxronole dl Fr4sc;rrr 0001-f Frascarr. Rorrtc, Irol.r-
Reccrrcd 10 Alay 1982. rn final form -I June 1982
1. Introduction
1112gas pha~
The high-resolutton photoelectron spectra of Ruoroeompounds have already been reported in the hterature and mtrrpreted m terms of molecular structure on an e~per~ent~ b&s [l--71. Tf~eorettc~ predictions have also been made for many of the molecules of thts famdy with different methods, such as SCF. Xo, HAM/3 nnd in the frame of the Green’s iunctron
fokmahsm [Sj. With the aim of obtatnirtg more detaded structural mfomatron, we have undertaken the study of the fluorinated series of m4rhanr by means of electron camcrdence (e, 7e) spectroscopy, together with theorettcel predictions via the Green’s functron theory. Prevtous results on CH,, CH3F and CH,F,, hereafter referred to as I, showed good agreemenlb;tween theoretical predictions and espertment, including a good description of the breakdown of the onepartrcle model for mner-lymg vfenee tomzatrons [9]. In this work we have periormed Green’s function calculations on the remaining terms of the series, that is CHF, and CF+ Complete binary (e, 2e) spectra m * On bavr irom Dlpsrttmenro 06100 Peru$ta, kdy.
dl Chimxa.
Unwcrrnl
di Pcrug~a.
are reported for both molecules together wtth angular momentum dtstrrbutrons ior some orbrtsfs of CF,. Prevrously e~per;illent~~y obtsmed PES IPs are also compared ivtth theorettcal predrcttons for both mofecules
1. Theoretical background
in many-body physics, a dtrrcr connectron IS found between the tonvation spectrum of a molecule and the oru+psrtrcle Green’s functton, provided that the experiments are carned out II high mctdent energy relative to the tonkttion threshold [ IO]. In thus case, the two-panrclc (iour mdrcas) hole-parttslu propagator m the fommla for the transitlon probabllfry P(w) can be replxed by the one-psrttck advanced Gi;(w) (more prec~scly both are present wnh then unsginary part). Indeed. due to the presence of an mfiiitcsimal imagmary tq tn the dcnommators of its spectral representatton, Im G,;(U) assumes 3 6-iunction behaviour and can mclude one of the two 6 -function factors of the golden role for the transrtton probabdtty.P(w) can thus be wrttten as
c.r,j %IN [c;; fw -
E. -
1$]6(w - .&) _
tn wluch the rematmng &(o - E,) factor accounts for the cncrglr conservatton law and the T are tontzatton m3tra elements [IO]. It 1s w12l.lknown that the smgularttles (poles) of G,;(U) represent the 1Ps oi the nl~ny-body system. In the region of high incident energy Eo, and when G,(w) = 0 ior t *I (dtagonal G mar&), the height ratio of two hnes for the same orbital tonization COWctdcs wnh the ratio of the correspondmg numerators tn rhe propagator (pole strengths) and the Green’s iunction 1s directly capable of a complete mterpretation of the spectrum In the full nondtagonal COP thts is no longer true, but m general 111sG matri. happens to bc almost dfagona_land the sum oi the dtap onal
rcstdues can r&tsonabiy be taken a~ playtng the same role as the pole strengths of the dta~on~ case. in the present ConlputatIon, moreover, the results of the nondzrgonal problem show the typical “diagond” bchavtour, tn that each tontzatton borrows mtenstty from 3 smgle one-electron state, li only dtagonal restdues20.01 are considered. The method of rcsolurton of the equatlons involved for the determination of poles and mtensittes can be found elsewhere [10-l-2]. The computattons were made n-t the Iph-TDA full non~ta~on~ appro~~~tton, with the same basts set asemployed m I. In the present case, in fact, the 2phTDA results appear to be closer to the experimentaT values than their GF counterparts (see below), even for the outer valence tonizatlons, though the dtiferenccs are obvtously small. Bmary (c, 2e) spectroscopy (wrth htgh mcrdent clcctron energy and high momentum transfer) allows one to measure the IPs and transnton probabihties tn J wide energy range, yielding a valuable check on the data predtcted by the Zph-TDA calculattons. In the out~f-plane ~mmet~c kinematics the plane wave mtpulse appro.~mation (PWA) holds f 13-151 for the relatm (e, 7e) cross sectron, which becomes proportional to the product of the h&f-off-shell lllott factor (d2a/dR& and the square modulus of the Fourier transfoml of the overlap between the mirlal neutral state 10”) and the fmal ionic state I@:): 446
Since in the PWIA the momentum is transferred to the ton only through the removal of an electron, q is equal and opposite to the momentum of the initially bound electron trt the one-electron approxtmation for the target. if the target is descrtbed in the Hartree-Fock approxtrnatron as an antisyrnmetrtzed product of a oneparticle orbitaf [ $,j and a remainder, that ts as k,$r) = I$,) l#,n>,one obrams TFk’,cii)l’= ~,~)~~,where p,@i) is the momentum denstty associated with the oneelectron orbttal l$,(f)).KF represents the probabthry of populating the X ioruc state when one electron is ejected out of the I$,) orbttal. Both energy spectra and electron momentum distnbutlons (EMD) can be dctermtned tn (e, 2e) cxpertments by varying the separation energy at fixed momentum, or measurtng the angular correlation between the final elecrrons at fmed separation energy, respecttvety [13-S]. The fe. Ze) exper~ents were carried out as discussed m 1.
3. Results and discussion 3.1.
CHFj
Fluoroform ISa 34efectron cloud-shell molecule wtth C,, symmetry, which has been reduced to the abelian C, m the computations. Of the 47, molecular orbitats resulting from the SCF computation, 21 (13 of whtch occupied) have been deemed active in the computation of the Zph-TDA expansion. The four inner shells (Is on C and F) have been kept frozen. The ionization energies and their relative intensities are shown in table 1 together with the experimental PES iomzatton potentials. Only pole strength vrdues20.01 are reported. Energy levels have been computed within the ‘Iph-TDA frame, except for la2 which is the only orbital not appearing with a’ symmetry in the C, subgroup. Since this is an outer valence ionization, energy and pole strength have been computed in the computationally less expensive GF approxtrnation [ 161, based on a third-order truncatron of the graphical Abnlcosov series, improved by a renormahzation procedure to take higher-
Volume 90,
number 6
Table 1 IPs as determrned
CHIXICAL
by tfte Zph-TDA non-dugon~
PflYSfCS LKTKRS
appro\tm3tton
CHFS
/D August 1981
Only pole strcngtbs
>0 01 arc reported.
Values m cV
cr4
0rbit.d
c\p.a)
Hr
Zph-TDA
pofu strcngthb)
orbIt
c\p 3)
NT
I!@-TDA
631
13 8 15 5 16 2 17 a LO.7
16 63 18.39 1850 19 69 22.87,
I4 88 16 05 (Cl-) 16.11 17.08 30 59
0.93 0 92 (CT) 091 090 090
111 4tz qa1
16 2 17 4 IS 5 ” 1 25 1
1911 19 67 31 35 21.90 38 1-I
16.74 17.45 1859 22.54 25 68 35 83 36.89
21.43 2s 06 31 30 40.80 41 00 41 05 41x 4113 41 70 41 83 4192 41.98 41.07 42 1-l 11.19 J? 31 42.-C 42 77
0.89 OS? 001 001 002 00’ 001 004 0 33 003 00-t 001 0 01 oo’t 002 001 0.03 002
-712
10 3
46 61
41 33 415.5 42 16 42.51 4265 42 13
43 19 43 55 43 63 43 65 43 75 46 10 46 39 46.35 46 53 47 07
006 0 17 007 0.06 001 001 003 0.X 0 04 0 05
132 je 4e 3c
5%
10.7
-1%
24 4
23 78 77 46
,e
39 2
45.28
331
42.0
4s 19
le 3t:!
41.90 4199
331
43 8
SO49
43.06 43 31 13 55 4361 36.35 16 66 16 S5 4107 4164 5100 43 23 45 19 45 71 45 97 37 62 17.91 19 58 51.15 $4 00 6261
pole stWl!gh b) 092 09’
091 0.90 088 00’ 001 001 001 005 002 0 II 0.13 t-JO6 002 009 ‘01 00-1 007 002 00-T 0.0’ 003 001 001 001 0 18 003 001 00-I 0 30 0 14 00 00’ 001
scr = 336 740 (au)
E'O'
b, As c\pkincd m the text. the computationsacre mzdc tn the Tuff oondiagon?l Zph-TDA ~ppto~rmar~on in the prSsen1 dmx, ho&cover, each lute bonows tntenuty from one lontzation only and fhc slims oi the dqoxtf ro~tdues comctdr: wzth the usox1 pofr: strengths oi the dtztgonxf compu~~on
order graphs parttally mto account [ 10, pp. 2692733. As noted above, according to a feature of the present calculattons, an improved value could be expetted in the 2ph-TDA model, even if the basis set was completely etiausted in the GF case.
The Iph-IDA results for the 6al, Se, 4e snd 3e Jeveis (outer vaJence electrons) show excellent greement with the experimental PES values, wJuJe a dE ference of0.7 eV ISfound for the 5q rontwrion. AJJof these iomzations appear to be essentially one-particle 4.47
V&m
40.
nuntber fi
CHEIIICAL
PHk SICS
procesjzs. the first orbital for whtch some satelhte structure is predtcted being the mtermedtate m energy -tat. As has been found in many analogous sttuations, the 7e ievet (at 39.13 eV) is shtfted by the computation towards htgh energies. The computations show a complete breakdown of the one.puticle model, the ma~unum mtensity being 0 34 for the line at 41.70 eV. . The smc can be said for the 3at orbttal for which the mstn peaks he at 13.55 (0.17) and 16X (02-t). the ca~erimental rake betng 42.00 cV. The sphtttng of the 33t orbttai was not observed tn prevtous ESCA wxk [j,s] because of resolution and since tn the stunphng at htglt q (q >-kr; ‘) p?rkrnted by ESCA, the contributtons from the 33t orbit31 are very low . ft is to be noted, m add&ton, that in ref. I.51no net breakdown phenomenon ISassumed and each inner band ISreproduced as a convolutton of two peaks only, our expcrunentsl and theorettcal results show, on the contrary, that the sphtttttg of the irttt?nsity over very many shakeup states ISa dtstincttve feature of the 33t and le iontzations
Ftg 1. lanuatwn
LCTTtRS
The measured and theoretuxtllp reconstructed energy spectra (with an overah resolution of 1.7 ev) are reported in fig. I ut a boding energy range up to 50 eV for two drfferent scatterutg a.ngIes.The convolution procedure used has been eupltied m detatl in ref. [16]. IFS and pole strengths are those obtained from GF and Zph-TDA data of table 1. The relative intenstties are wetghted by the theorettcal momentum denstttes correspondmg to io~ations out of each sm~e-pa~tcle orbttal. While tn f&. la, at q = 0.1 UC’, only totally symmetric states contrtbute to the spectrum, at q = 09cG t (fig. lb), contrtbuttons from alI the tune vaknce orbitals appear. The spectrum show different bands, dtvtded in two main groups; the First one dertves from ~ontzattons that are almost pure in character in that they show no significant breakdown structute. The second one comprises many dtfferent shake.up states gtvtng rise to a wade profiie whose shape strongly depends on the q at which the measurements are made. As fig. 1 clearly shows, not even a resolution as good as 1.7 eV can completely separate each iontc state, etther in the
energy jpcctn oTCHF3 St q = O.l$ (a), and q = 0.9a$ @) result Tot la2 1~1 (xc text)].
calcukuedon the bassof the?ph-TtIA resultsIGr
20 Au~usr1982
Top r\pcnrnental
data.
bottom: Yme spectn 35
Volume 90. number 6
CHCCMICAL PHYSICS LCTT’CRS
out~~ost valence region, when the vrbrationa~ structure of the states is taken into account 181, or in the ~e~ost valence shell, where, as noted above, 2e and 3a, intensities are ~t~bu~d over a large number of contiguous lmes. It is worth noting, m th& respect, the behaviour of the 3al orbital, split into main peaks, ~3 eY apart, when observed with an 1.7 eV energy resolution. This behaviour IS predicted by the ~lculatlons, which nevertheless do not account for the satelhre lmes from the 3a, observed at higher energies. 3.3 CF, Carbon retra!Iuorlde ISa 42-electron system with T, symmetry, reduced to the abehan Czv III the computattons. The orbrtal space has been truncated to 24 acflve orbltals, 16 of which are occupied. The five core orbitals Is on C and F hake been excluded from the active set. The IPs are shown in table 1 tog&her with their pole strengths(>,O_Ol only).The computed values are in agreement with the e~per~ent~ fidlngs from 1t i to 4at The computations show non-neglrgible satellite structures startmg from the 4at orbital. Also m this case the computed 2t2 band ISshifted towards high
energies, its rn~~a being located at 42.65 and 42 73 eV (\vrth mten~ttes 0.1 I and 0.13 respectively). As for CHF,, thrs fs due to mherent hmttations of the ZphIDA method which takes is-110account only smgk excitation shake-up processes, and to the basis set whxh ISunable IO reproduce satisfactorily high-lying I%i p States. The 33, level ISeven more drspiaed tb,u~ 3t2, 11smaximum lymg = 4 eV apart from the experimental value (43.8 eV), though a srgmficant hne is found at 45.19 eV (0.18). In fig. 2 (e, 2e) measured energy spectra, taken at Iwo different scattering angles, are reported and compared with the results of table 1. The cakulatcd spccrrum accounts for the experimental energy resolution of 2.6 eV. Due to the close proGrnrty of the iomc states, the CF, spectra appear 3s formed by only three large bands. The first (centered at =Z18 eV) and the second (centered at 5.25 eV) take contrtburtons fram three and fwo mam pe3ks. respectively (I tt ,4tt, It? and 3t2, 4at), each of them carrying almost ail the intensity of a sm~e-panicle ro~atlon. On the other hand, the third band (centered at = 42 eV) is relevant to states artsing from io~atron processes in the innermost valence shell and appears as a broad structure
\-
0
00
Fe. 2 lonu3tion encr~y specu~ of CF4 at q = 0 25 a;’ (a), and q = 0 9 a-lo (b). JS calcuhted on the basis of the Zph-IDA results
20
so
1. ‘0
‘\-. 501‘
*I.
Top. experuncnral datt3, bottom’ r*lmL‘spcc~n
113
Volume 90. number 6
CHEMICAL PHYSICS LETTERS
20 August I982
IS
10
s
0
0
1
2 qta,'t
of
T& 3. EMD’s CF+ mew.trsd at d&crent eh &ucs and compared wth the cslculsted contrlbutrons from al! ihe Statej convoluted by theenergy resolution.
m whxh several lnes of small mten~ty and of dtifer-
ent ongin can be convoluted. As observed III I, in ref. [ 161 and m the case of CHF,, a large number of ntellire lines appear m the region near 40 eV, where ionization OUIof molecular orbit& mamly of atomic IsF character 1sproduced. The overaLlshape of the bands ISwell reproduced both at q = 0.25 and 09 noI, apart From the sit&t in the 40-50 eV region referred to above. Mth the aim of extracting more mformation, some angular d~tnbu~lons measured at surtable chosen separation energy (EJ vahses are reported in fig. 3, together with the theoretical predictions. In fig. 4 we show the Iinenr momentum denuties associated with each SCF molecular orbital, that is with 450
cun-tls
fsohd Itnes), obtnmed bJ’ =ctudlnL!
the same orbitais as in the Green’s function perturbation expansion. In the theoretreat angular distributions of fig. 3. each momentum density of fig. 4 is weighted by the ?-ph-TDA pole strengths and by the percentage contribution of each line at the chosen q,_ by taking into account the gaussian energy resolution of the apparatus. It should be noted that a sin& orbital contribution (4at) was detected onIy at q, = 27 eU (iig. 3~). Significant in this respect is the agreement found with the SCF description of the 4aI orbital, which involves essentially the bonding comb~ation of 3,sCand 2pF. Good agreement with thy theoretical predictlons is also obtained for the data taken at q, = 7_0eV (fg. 3b), where the 3t2 orbital gives by far the most important contnbution. This is not suquisiig
CHCMfCAt
Volume 90, number 6
0 24
PH’l SICS LETTERS
11,
515
008 0 :i’\\ 0
GE
16
2.I
32
01
GA
03
03
I.2
31,
02
02
01
01
0 ~ 0
Tg
08
Ii
24
32
4. EblDs of CF4 v&xc-shzU
since the 3t, orbital mvolvr?sthe annbonding combination of the same orbitals as 41,. The rather satisfactory fit in the measurement at eh = 17 eV confkms the augment of the present c~eulatton for the outer levels Itt ~4t2 and le. The data reported m figs. 3d and 3e show the typical behaviour of the innermost valence band. The comparison between experimental data and theoretical predlctions has been done in this case after having shifted the calculated band to the left by 4 eV (see above). The HF description of the ionization would f& to fit the angular distribution measurements whatever shift in energy one could introduce_ On the other hand, as figs. 3d and 3e clearly show, the agree-
0 I!!l!L0
GO
fi
24
32
orbuals OScomputed by SCT wsvrfunct~onr
ment ISgood when contributrons irom different satelhte hnes are included as predicted by the manybody Green’s function cakulation,
4. Concluding
remarks
‘Thepresent computation confms that, even for rather complex molecular systems, the Green’s functlon methods, and their related approximate graphcal expansions, are well suited for the description of the iomzation processes; in particular the breakdown phenomenon for inner valence orbitais is qualitatively weil described by the Zph-TDA approbation_ The 451
~oiun~e 90, number 6
CJ+EMCAL
PHYSKS
(e, 12) spectroscopy ptovldrs extra mformatlon by measurmg the electron momentum distrtbutton for each smgle molecular orbrral and shows it to be more sensitwe to the molecular symmetry in the mnial sratc and to the nature of the chemical bond, than other spccttoscopies, Ike PES, even d these are coupled wth angulardlstnbutlon measuremenrs.
(41 S Kasumata
[6] [7j
[9]
Gckno~ ledgement [ 101 [I 1J [l?,]
References 1131 1 I J D \V Turner, C Bahcr. X C Bzd.cr and C R Brundlr. hloleculsr phorelectron spccttoicopy (Wdey-lntcrsc~snce, New York, 1970). [ 21A IV Potts, MJ. Lcmpha. D C Srrecr and WC Pr~cc. Phd Trans. Roy Sot. (London) A268 (!970) 59.
[ 31
R N Duon, (1971)611.
J N XlurreU snd B Narayan. Llol
Phys. 10
and K;. Kimun,
46 (1973) i341. IS] M S. Bsnna end D
[S]
We gratefully acknowledge Professor W. von Nfessen ior prowding the computer programs, and the k&an CNR for fiiancisl support.
10 Au@st
LIXI’ERS
[J-I]
[ 151 [ 161
BuiJ Chem
Sot
1982
Japan
A Shuley,Chcm. Phys Lacers 33 (1975) 411. L. Karlsson, R. Jardrny, 1. Msttsson,I--T. Chwi and K Siqbshn, PhysIca ScrIpta 16 (1977) 225. C R Brundlc. hf B Robm snd H Basch, I Chcm Phys 53 (1970) 2196. G. B~crr, 1. Asbrmk and W van Nvswn, J. Electron Spcctry. Reht. Phenom. 23 (1981) 281 R Csmbl, G. CMlo. A SgnmclJotta. F. fanntel, R. Fantom, A. CwduuGuidonr and A. Srrgto, Chcm Phys. Letters 80 (1981) 195. L S. Ccdcrbaum and W Domcke, Advan. Chem. Phys 36 (1977) 205. J. Schtrmrr and L S. Cederbaum, J. Phys 811 (1978) 1889. W uon Ntessen. L S. Ccderbaum and W Domcke. m Escttcd states III qwntum chemistry, cds C.t\ Ntcolxdes and D.R Beck (Reidel, Doidrtchr, 1978). IE. McCarthy and E. W&gold, Phys Rept. 27C (1976) 275. R.Camrllxu, A. GurduuGuzdom, I E. McCarthy and G. Strfam, Phys Rev. 17A (1978) 1631. E. \\egold and 11. McCarthy, Adban. At Mol. Phys 1-f (1978) 127. R. Fantom, A. C~ardtntGu~dom. R Tlrtbellt, R Cambi. G CmUo, A. SgimelIottl and F Tarantclh, hlol Phys II
(1982) 1.