Electronic structure of small fluorocarbon clusters FpCn

(p = 1, 2) observed in secondary ionic mass

spectrometry (SIMS). I. Stabilities

M. Leleyter

To cite this version:

M. Leleyter. Electronic structure of small fluorocarbon clusters FpCn (p = 1, 2) observed insecondary ionic mass spectrometry (SIMS). I. Stabilities. Journal de Physique, 1987, 48 (11),pp.1963-1973. <10.1051/jphys:0198700480110196300>. <jpa-00210639>

HAL Id: jpa-00210639

https://hal.archives-ouvertes.fr/jpa-00210639

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinee au depot et a la diffusion de documentsscientifiques de niveau recherche, publies ou non,emanant des etablissements d’enseignement et derecherche francais ou etrangers, des laboratoirespublics ou prives.

1963

Electronic structure of small fluorocarbon clusters FpCn (p = 1, 2)observed in secondary ionic mass spectrometry (SIMS). I. Stabilities

M. Leleyter (*)

Groupe de Physique Théorique, Faculté des Sciences, 33, rue Saint-Leu, 80039 Amiens Cedex, France

(Reçu le 16 f6vrier 1987, révisé le 26 mai 1987, accept6 le 30 juin 1987)

Résumé. - Les intensités d’émission des ions secondaires FpC+n (p = 1-4) et FpC-n (p =1, 2) émis par une ciblede téflon (polytétra-fluoroéthylène) sous bombardement primaire par des ions Ar+ de 6,5 keV, présentent desoscillations très marquées suivant la parité du nombre n d’atomes de carbone. Les maximums ont lieu quand nest impair pour FpC+n (p = 1-3) et quand n est pair dans les autres cas (p = 4 ; ions négatifs). On interprète lesalternances des ions FpC+n et FPC-n (p = 1, 2) avec un calcul CNDO dans le modèle de la chaîne linéaireCn analogue à celui de Pitzer et Clementi. On trouve alors que les stabilités relatives des agrégats linéaires sontles plus fortes pour les ions FC+2+k+ 1, F2C+2k+ 1,FC-2k et F2C-2k, ce qui est en très bon accord avec la « règle decorrespondance » entre les émissions des différents ions et leurs stabilités relatives. En outre, dans le cas deschaines F2Cn, le calcul montre que ce sont les isomères dissymétriques qui donnent le meilleur accord avec lesrésultats expérimentaux.

Abstract. - The intensities of emission of FpC+n (p = 1-4) and FpC-n (p =1, 2) secondary ions given by a targetmade of teflon (polytetra-fluoroethylene) under a primary bombardment of 6.5 keV Ar+ ions, show a verystrong even-odd effect according to the parity of the number n of carbon atoms. Maxima occur when n is oddfor FpC+n (p = 1-3) and when n is even in the other cases (p = 4 ; negative ions).The alternations of FpC+n and FpC-n (p = 1, 2) are interpreted with a CNDO calculation by means of the

model of the linear Cn chain similar to the Pitzer and Clementi model. It is then found that the stabilities of thelinear clusters are the greatest for FC+2k+1, F2C+2k+1 and for FC-2k and F2C-2k ions. This agrees with the« correspondence rule » between the emissions of various ions and their stabilities and electronic properties.Besides, in the case of F2Cn chains, the calculation shows that the disymmetrical isomers are in the bestagreement with the experimental data.

J. Physique 48 (1987) 1963-1973 NOVEMBRE 1987,

Classification

Physics Abstracts36.40 - 31.20N - 79.20N

1. Introduction.

The existence of alternations in emission intensitiesof secondary polyatomic ions XI or X- (generally n 10) ejected from a target under primary ionicbombardment, has been shown for several years.Intensities I (Xn ) are enhanced for a given parity ofthe atom number n [1-3]. The phenomenon can veryoften be interpreted from the so-called « parityrule » which states that the emission intensities ofions X’ (or Xn ) are the largest ones when the

(*) Also Laboratoire de Physique des Solides, associdau CNRS (LA 2), Bitiment 510, Université Paris-Sud,91405 Orsay Cedex, France.

number of valence electrons of the correspondingions is odd (cases of Li, Cu, Ag, Cr,..., etc.). Therule is frequently still valid for heteronuclear ionssuch as XnYp [4].

However, when the secondary ions are emittedfrom carbon or some carbides, the parity rule thenfails since there are alternations in the intensities

I (C+n ) or I (MPCn ) though the valence electron

number keeps the same parity whatever n (for givenp) [5]. Yet, it can be remarked that the emission

spectra of MpC’ ions have almost the same aspectwhatever the kind of experiment: SIMS [5] or SSMS[6] (spark source mass spectrometry) or field

evaporation, etc. Now the two factors which can

govern the ion emission are the emission mechanism

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198700480110196300

1964

and the stability, that is the binding energy of theemitted cluster. Since the emission mode only leadsto a monotonic effect on the emission probability ofa polyatomic ion (the bigger the ion, the weaker itsemission probability), the only factor which couldlead to the appearance of so pronounced alternationsin the intensities I (MpC;) is the stability of thecorresponding aggregates.From this reasoning, we have been induced in

preceeding studies [7-9] to state another simple rulewhich also governs the secondary ion emission ; it isthe « correspondence rule » : « secondary inten-sities-stabilities » which can be written as follows :when the secondary emission intensities of clustersXn show oscillations in which the aggregates of agiven parity are the most abundant, the relativestabilities of these aggregates are the largest too.

In the case of carbon clusters Cn studied overtwenty years ago by Pitzer and Clementi (P.C.) withthe Huckel method [10], then by ourselves with amethod derived from that of P.C. and also with theCNDO approximation [5], and more recently byEwing and Peiffer with ab initio calculations [11] onlinear Cn chains, the experimental alternations arearising from the fact that the « Fermi level » (orHOMO : highest occupied molecular orbital) lies ina band of degenerate 7T molecular orbitals. There-

fore, according to the parity of n, this level is eitherhalf-filled (with 2 electrons) or full-filled (with 4electrons). Besides we have been able to show thatthe alternations vanish if the correlation effects aretaken into account [12].

This saw tooth behaviour is observed not only forCn, but also when the Cn clusters include some

impurities. We already studied the cases of transitionimpurities such as Fe, Ni, Cr or Ti [8, 9, 13] or anormal element such as H [5, 7] and we saw that avery important factor to explain the « parity » of theionic current alternations is the electronegativity ofthe « impurity ». Here we shall consider thefluorocarbon aggregates FpCn obtained by SIMS too.Fluorine is a normal element of very large elec-

tronegativity. It is therefore interesting to examinehow the electronic charge transfers take place be-tween the « impurity » F and the C,, cluster and howthe F electronegativity is acting on the stabilities andthe energy levels of the clusters.

In order to determine the electronic structures and

properties of the FpCn aggregates, we use here thesimple model of the linear chain of carbon on whichare engrafted one or several fluorine atoms. Ourmethod is the same as for TiCn and VCn [9, 14]. Weshall recall below the reasons for this choice. How-ever let us note that when n is lower than 6, theCn aggregates are generally more stable (they have alarger binding energy) when they are in the linearshape (case of sp hybridization) [5]. The onlyexception could be C4 since the calculation of

Whiteside et al. [15] shows that the rhombus shape isslightly more stable (0.26 eV) than the linear shape.Besides, the molecules with carbon atoms detectedin interstellar clouds are always linear, even if thereare about 10 carbon atoms [16]. Finally the last abinitio calculations of Raghavachari and co-workerson C6 [17] have shown that linear structures withequal bond lengths are among the most stable ones.

In this paper, we begin first to recapitulate theexperimental results about the FpC’ and FpCn ions(Sect. 2). Then, in section 3, we analyse with thehelp of CNDO approximation, the electronic struc-tures of these aggregates against n, only for

p =1 and 2, and we compare the experimentalcurves to the theoretical results obtained from theelectronic properties of FCn and F2Cn. We study themolecular orbital (M.O.) dispositions of the chainstoo, which allows us to understand where the

experimental alternations come from. The theory ofF3Cn and F4Cn clusters will be dealt with in anotherpaper as well as the study against p. In the followingpaper (II), we shall analyse the charge transfers

throughout the chain.

2. Experimental results.

2.1 EXPERIMENTAL CONDITIONS. - Here we recallour results [18] obtained by bombardment with aprimary beam of 6.5 keV impinging on a targetmade of « teflon », a (CF2)n-polymer (or P.T.F.E.).Teflon is a very good insulator. So it has been madeconducting by covering the target with a thin foil ofaluminium produced by evaporation, to allow thecharges brought by the primary beam to flow away.However, despite the conducting layer, the chargescause some problems in the negative ion study : theintensity of F- ion current is indeed so high that thealuminium layer and the part of the target aroundthe impinging point are instantaneously pulverized,so the primary and secondary ion beams becomeunstable and some discharges may occur. As a

result, we were not be able to measure the exactvalue of the ratio of the current intensities I (FpCn )and I (F- ).The ionic microanalyzer CAMECA IMS-300 of

Castaing-Slodzian was used to analyse and recordthe secondary ion FPCn currents. The apparatusmass resolution is 300 in normal use conditions andthe limit of the m/e ratio for the secondary ions isabout 260. The primary beam density is about 50 AImm . On the spectra, the intensity of everypolyatomic ion is derived from that of the main peakby an isotopic distribution of C in the ion.The results can be shared in two classes according

as the variable under consideration is either thecarbon atom number n, or the fluorine atom number

p in FpC;.

1965

2.2 FpCn IONS AGAINST n.

2.2.1 Positive ions. - They give rise to 4 families ofFpCn ions (Fig. 1)- FCn (n = 0 to 11) ; for n = 4 and n =10, the

corresponding ions have not been detected becausethe intensities are below the sensibility limit of ourapparatus.- F2C’ (n = 0 to 5) ;- F3C+ (n = 1 to 5) ; F3 and F3C’ have

intensities too weak to be detected ;- F4C+ (n = 2 to 6) ; here again, F4+, F4C+ and

F4C+ have too weak intensities.

Fig. 1. - SIMS relative intensities of FpCn ions (p =1-4) emitted by a teflon (PTFE) target against n, thenumber of carbon atoms. Primary ions are 6.5 keVAr+ ions. The target is covered with a thin Al layer.

In figure 1, experimental intensities I (FpCn ) rela-tive to I (FC+) when p = 1 to 3 and relative to

I (F4C!) when p = 4, are drawn versus n. The

curves show a very large even-odd effect as a

function of the carbon atom number n. The firstthree families have very intense currents when n isodd. On the contrary, F4C+ ions should rather showa change in the alternations since the currents aremore intense this time when n = 2, 4 and 6, andF4C+ and F4C5 ions are even not detected.

2.2.2 Negative ions (Fig. 2). - Despite the beamstability problem above-mentioned, we could ob-serve, on the spectrum of negative ions, FCn ionswith n = 1 to 5 and F2Cn with n = 0 to 4.

Intensities again show very strong alternationswith the parity of n, but this time the maxima takeplace, for « even » ions. The peaks are particularlyhigh for FC2 and F2C2 ions, whereas, for instance,F2C- and F2C5 ions are so weak that they are notdetected.We can notice that, as in all our previous experi-

Fig. 2. - SIMS relative intensities of FpCn ions (p = 1-2)emitted by a teflon (PTFE) target against n, the number ofcarbon atoms. Primary ions are 6.5 keV Ar+ ions. The

target is covered with a thin Al layer.

ments on XCn ions [18], « even » ions are always themost frequent ones.

2.3 FpC’ IONS versus p, THE FLUORINE ATOM NUM-BER. - In figure 3 we show the relative intensities

I (FpC’ )II (FC+ ).For FpC+ and FPCI ions, the intensity curves

present, as in the variations versus n, a saw-toothedbehaviour with a large enhancement when p is odd.The other families (n = 2, 4, 5) show a less evidentaspect. Yet, one can see, on the FPCI ions, a

maximum in p = 4 with 2 minima in p = 3 and 5. It

Fig. 3. - SIMS relative intensities of FpCn = Y; ions

(n = 1-5) emitted by a teflon (PTFE) target against p, thenumber of fluorine atoms.

1966

could be deduced that it corresponds to 2 consecutivereversings of the alternations as a function of the pparity, the first one occurring when going fromFPC’ to FPC’ , and the second one from FpC’ to

FpC3 . At last, FPCI and FPC5’ ions have a maximumin p = 2 and p = 3, respectively but there is no moreperiodicity.

3. Electronic properties of FC nand F 2C n chains.

3.1 THEORETICAL MODEL AND PARAMETER

CHOICE. - We come now to the study of theelectronic structure of the clusters. Here, as an-

nounced in the introduction, we only deal with themodel of linear carbon chains having at one end one(or more) fluorine atom.For the carbon chain, it corresponds to the case of

sp hybridization [5]. It is well known that in almostall the cases, the linear shape is the most stable onefor Cn when n is less than 6. However, as noticedpreviously [16], the interstellar HCxN molecules arelinear even for x values as large as 11, so that thismodel seems plausible for values of n large enough.In the same way, it is likely that K2C2 n molecules arelinear too [19] contrary to what Ewing et al. [11] saidabout carbon molecules. Besides, this more simplestructure of the clusters has the advantage of allow-ing easier comparisons of relative stabilities for

clusters of consecutive n, which is not the case whenthe shapes are 2- or 3-dimensional and where thereare singular values of n which give rise to very stablegeometries with « magic » numbers of atoms (e.g.tetrahedron, bicapped pentagon, etc.). Moreover,as noted in the introduction, recent work on

C6 [17] has pointed out that the linear structure

containing cumulene type bonding:C=C=C=C=C=C: is lower in energy than the

triacetylenic form . C==C-C==C-O=C. , and eventhan the cyclic symmetric benzene-like structure

[20].As a matter of fact, our purpose here is to try to

find again the experimental trends and not to lookfor the most stable geometries of the clusters. Wetherefore computed the total energies ET(n), El (n )of the FCn, FCn , F2Cn and F2C’ clusters with the

well known semiempirical CNDO/2 method [21] forthe following linear chains

F-(C=-C)k , F-(O=C)k-F (n = 2 k ) (shapesmarked (b) in tables in Appendix A), and for non-linear chains

The CNDO technique, which only takes account ofthe valence electrons of the atoms, does not givecorrect values of molecular energies, but we needonly to compare, energies of clusters of consecutiven, so the defect of the method has no influence onthe conclusions which can be drawn from the study.

Let us recall that, since the cluster geometry, inthe cumulene type chain, is the same whatever n, itis possible to easily see the influence of the n parityon the stability of a given cluster ; indeed whengoing from a (n - 1 )-atom cluster to the next onewith n atoms, one only adds one extra carbon atomand one extra C-C bond. In Appendix A, we givethe various results we got for the above shapes andalso the energies Ei (n) found by moving the

fluorine atoms through the carbon chain in FCn andF2Cn.The parameters for C and F used in the computa-

tions are the standard ones given by Pople andBeveridge [21]. They are given in table I. The C-Cand F-F distances are the experimental equilibriumones of C2 and F2 [22]. The C-F distance wasdetermined by taking the average of C-C and F-Fdistances, and the value is very close to the C-F

distance in CF4 [22].

Table I. - CNDO input parameters (in eV) usedfor the fluorocarbon aggregates (Refs. [21], [22]).

In the cumulene type chain, we have supposedthat the distances are constant whatever n and the

cluster charge. Thus the ionization energies andelectron affinities obtained in the calculations arethe « vertical » values and not the « ther-

modynamical » ones in the sense of Simons and

Smith [23] as we shall see below when we give theirdefinitions. For the polyacetylenic form, the alternat-ing bond lengths C-C = 1.376 A and C=C =1.205 A are those given for diacetylene by Herzberg[24]. Fi ally, for the non linear shapes, the bondangle KT = 108.0° was taken from F2CO molecule[24] .

3.2 RESULTS OF THE CNDO CALCULATIONS ON

THE CLUSTER ENERGIES. - The energy values are

given in the Appendix A. Here we present the

results by introducing the quantities L1n, An -:’ whichare defined by Aq = IE!f(n) - E!f(n -1)1 ] where

q = 0, + 1 or - 1 is the cluster charge. An is nothing

1967

but the energy increase of the FpCn -1 moleculewhen one extra C atom and one extra C-C bond areadded.Table II sums up the results obtained for the main

isomers of the FCn and F2Cn aggregate and figures 4and 5 show the evolution against n of ..1% for

FCn chains and these of An’ and An for the possibleisomers of F2Cn (F2Cn and FCnF).

Table II. - Parity of the computed alternations

(when they exist) of the an obtained for differentcluster formulae (see text). (a) : cumulene typemolecule ; (b) : acetylenic type chain (only if n =2 k). For F2Cn, the forms are arranged in increasingorder of the stabilities. The only shapes which repro-duce the experimental alternations for the 2 chargestates are the less stable ones (at the CNDO level andwithout any optimization) (top of the F2Cn Table).

3.2.1 FCn chains. - The variations of dn against nis characterized by very pronounced oscillations withenhancement for odd n (positive ions) or for even n(negative ions). From figure 4 (with only one kind ofisomer for the two shapes which give very similarbehaviours), it is thus possible to deduce that a

FCI (respectively FC;) ion is more stable for odd n(respectively even n).

Indeed, for the positive ions, figure 4 shows thatmore energy is gained when a (FC2 k + 1 )+ cluster is

built from a (FC2 k)+ than when a (FC2 k)+ is built

from a (FCz k - 1) +. Therefore the ions are morestable when n is odd than when n is even.

This reasoning is valid for negative ions too, butwith an inverse parity of n.As a consequence, if we assume, as we said in

introduction, that the possible effect of an emissionmechanism of the ions only gives rise to a monotonicdecrease with n of the emission probability of aFpCn cluster [5], we can then make a comparisonbetween the curves of the dn and the correspondingexperimental ones in figures 1 and 3. Accordinglywe get a fairly good agreement between experimentand the computation of the FCn chain properties.

Fig. 4. - Evolution against n, the carbon atom number,of the quantities 4j (q = -1, 0, + 1) calculated in theCNDO approximation for the linear chains FCn , FCn andFCn .

Let us notice too that the values of dn given in theAppendix A show that only the aggregates withfluorine at one end of the Cn chain have the samebehaviour as experiment. For the other linear isom-ers (CkFCn-k)’ there are almost no more periodicalternations of the dn , or energies ET (n ) are muchweaker. This corresponds to much less stable shapes.Therefore, it is the reason why, for negative ions, weonly dealt with the FCn shape.

In figure 4, we have also drawn the curves for theAn of neutral FCn chains and it appears that theiroscillations, of the same kind as those of FCn ions,are much weaker. We shall see later that a first

attempt of explanation can be found from thetheoretical ionization energy values (§ 3.3.1.2).3.2.2 F2Cn chains. - From figure 5, where only thecumulene type chain curves have been drawn since

polyacetylenic forms give no alternations for positiveions, it can be observed that the results are verydifferent according to the kind of isomers which isunder consideration.

In the case of positive ions, only the disymmetricalF2Cn isomers (linear or not), give rise to the samebehaviour as the experimental curves with an maxi-ma for odd n (with more pronounced alternations inthe linear case). The FCNF+ isomers, on the con-

trary, show very weak aperiodical variations of thean curve. It can be noted that the most stable

isomers do not necessarily give the largest alterna-

1968

Fig. 5. - Evolutions against n of the quantities 4/ (leftpart of the figure) and An (right part of the figure)calculated in the CNDO approximation for the linear

F2Cn and FCnF± chains.

tions and can even lead to no alternation at once

(Tab. II).For negative ions, both linear species of isomers

have the same alternations with maxima for even n,while the non linear F2Cn isomers give reversedalternations, but the linear F2Cn chains show a veryimportant phenomenon, which is not the case for

FCnF- . So, if we take the emission attenuation withincreasing atom number of the cluster, into accountwe can deduce that the curve of the F2Cn chains iscloser to the experimental one. In the next section,the analysis of the energy levels will make us

understand this result in a very simple way.

3.3 ENERGY LEVEL ANALYSIS. - Figures 6 and 7represent the composition of the molecular orbitals(M.O.) of FC3 chain and of F2C3 and FC3F chains,that is the values of their projections on the s or patomic orbitals (A.O.), with the indication of theproportion in every component which comes fromthe fluorine atom (or to the 2 F atoms). The 1TM.O.which are doubly degenerate (for linear shapes) areshown by a double dash. Polyacetylenic isomers leadto M.O. dispositions very close to those of figures 6and 7 ; so they are not represented.

3.3.1 FCn chains.3.3.1.1 M.O. disposition. - If we consider theseclusters as linear Cn chains with a foreign terminalatom, we can observe that the results of the CNDOcalculation (Fig. 6) are analogous to those which arededuced from the above-quoted Pitzer and Clementimodel (P.C.) [25], a similarity which we have

already used in preceeding papers [9, 13].For the FCn chain, the fluorine atom binds to one

of the 2 « surface » o,, levels of the Cn chain ; this

Fig. 6. - CNDO calculated structure of the energy levelsof the FC3 chain and composition of the molecular orbitals(M.O.) as a function of the atomic orbitals (A.O.). In boldlines, the degenerate 7T levels. The M.O.s which mainlyproject upon the A.O.s of the F atom are indicated by theF index. U is one of the 2 « surface » levels which arisefrom the dangling bonds at the ends of the Cn chain, thesecond one is here replaced by the 2 M.O.s uL(F-C) andU AL (F-C) (see text).

gives rise to 2 per M.O., O"L(F-C) and 0" AL(F-C)(Fig. 6) both in CNDO and in the P.C. model. Thelevel distribution of FCn chains roughly becomes asfollows :

- a bonding spL band of n + 1 full up a levels

(2 n + 2 electrons), that is the n -1 levels of

Cn + O"L(F-C) + the SCRF level which almost exclu-

sively projects upon the 2s A.O. of fluorine ;- the remaining « surface » level o-, with 2 elec-

trons ;- then the 7r band with n + 1 doubly degenerate

levels (the n’1T M.O. of Cn + the p’1T level of

fluorine). It is only partially filled with 2 n + 3

electrons ;- finally, the antibonding SpAL band with n

empty cr M.O. (the n - 1 M.O. coming from

Cn + 0" AL(F-C». ·As a result, the Fermi level (HOMO) of the

aggregate falls in the 7r band as in the case of thelinear Cn chains mentioned in the introduction, andthis fact gives rise to the stability alternations withthe n parity. If n is even, the Fermi level accommo-dates 3 electrons, but only one electron if n is odd.Therefore, if we assume that taking away oneelectron does not change the above distribution ofenergy levels, the HOMO for FC+ is full when n is

odd, and a complete shell always corresponds to a

1969

Fig. 7. - Calculated structure of the energy levels of the F2C3 chain (left of the figure), the FC3F chain (middle part ofthe figure) and the non linear F2C3 molecule (right part of the figure) and composition of the levels against the A.O. s. Inbold lines, the degenerate 1T levels (except for the non linear molecule where the degeneracy is raised ; the « 1T» levelsare then marked with a bracket). The M.O.s which mainly project upon the A.O.s of the F atom are indicated by the Findex. For F2C3, a, holds for one of the 2 « surface » levels which arise from the existence of dangling bonds at the endsof the Cn chain, the second terminal level of the Cn chain is replaced by the 2 M.O.s uL(F-C) and U AL(F-C). ForFC3F, there is no more crt level, the second one is indeed replaced by 2 extra uL(F-C)2 and U AL(F-C)2Ievels (see text).

more stable configuration. On the contrary, if n is

even, the Fermi level of FCn is only half-filled, sothe stability is weaker.

Let us notice that, in the case of figure 6, HOMOand LUMO are the same 7T M.O. However, thecalculation uses unrestricted Hartree-Fock method

(U.H.F.), so HOMO which is a 7r level with one aspin electron, lies under the other w level (LUMO)of the same M.O., corresponding to J3 spin, which isempty.

3.3.1.2 Ionization energies and electron affinities.- The ionization energies are EI n =ET (n ) - ET(n) and the electron affinities are here« thermodynamically » defined by the differencebetween the final and the initial state energy, that is

AEn = ET (n) - ET(n).The values of these quantities, given by the

CNDO calculation, show oscillations with the n

parity too (Fig. 8). In this figure the absolute valuesof the HOMO energy versus n for FCn (cumulenetype isomers) are also drawn. It can be seen that

these values are very close to those of EI n. Thismeans that Koopmans’ theorem is rather good in thepresent case.We can thus verify that odd aggregates are easier

to be positively ionized and that, on the contrary, fornegative ions, the even aggregates correspond to themost negative values of AEn and therefore allow thelargest energy gains to be obtained. In the case of

Fig. 8. - Ionization energies EI n, electron affinities

AE,, and absolute values of the energy of HOMO calcu-lated in CNDO against n for the linear FCn chains.

other carbonaceous clusters such as VCn [14], wesaw that the EI n and the dn vary in an opposite way,

1970

but only the alternations of the i1: agree with

experimental data on VC+ (in this case, moreover,the oscillations are not well marked).For the FC+ ions, the relative stabilities i1: and

the ionization energies EI n, that is the 2 quantitieswhich may play a role in the emission, both act, atonce, in the same sense and favour the odd ions.This double effect no doubt allows us to understand

why the FCn alternations are so evident when

compared to those of other carbides such as

VC+. It would almost be possible to get a rule aboutthe emission of some kinds of ions, that is to say :when both stabilities and ionization energies are

acting in the same sense, the saw-toothed behaviouris very important, and when the 2 factors are actingin opposite senses, the alternations are weakened.However, their « parity » still remains governed bythe variations of the relative stabilities i1:.

In the case of FCn ions, as for VCn ions [14], theoscillations of the AEn act exactly as those of therelative stabilities An by favouring the even-n ions.If the same rule as before for positive ions is appliedto negative ions, it becomes easy to understand whythe FC2" k emission is considerably more intense thanthe (FC2 k + 1)- one.The preponderant factors which govern the ion

emission - the relative stabilities i1: or i1; - canthus be considered in both cases as enhanced by thealternations of EI n or AEn-

3.3.2 Chains with 2 fluorine atoms. - We haveexamined the 3 kinds of isomers, the symmetricaland disymmetrical (linear and non linear) clusters.The results are quite different.3.3.2.1 F2Cn chains (left and right parts of Fig. 7). -From figure 7 it can be seen that the M.O. disposi-tions are very similar for the 2 disymmetrical isomersF2C3. Therefore to make the comparisons easier wehave kept the same notations of u and 7T M.O. forboth linear and non-linear forms although they areno longer valid for molecules of C2 v symmetry.For the disymmetrical isomers, because of the

very large value of the fluorine bonding parameter130 (which is a way of taking the considerable Felectronegativity into account), everything seems tohappen as if there were an F2 molecule bound to theCn chain, whose levels would lie much deeper in theenergy scale than the Cn levels. These levels are theuL(F-F) and u AL(F-F) levels in figure 7 (left part).They are essentially made of projections of s A.O. ofthe fluorine. For non-linear F2C3, the disposition isquite similar with bonding and antibonding M.O.projecting upon s A.O. of the 2 fluorine and the

adjacent C atoms. Besides, as for FCn molecules,there are still the 2 bonding M.O. uL(F-C) and0’-AL(F-C). They are chiefly of pa type and arise alsofrom the combination of aUt level of Cn with the

pcrp A.O. of the intermediate fluorine atom (linearcase) or with the per? A.O. of the 2 F atoms (non-linear case). We therefore find the following arrange-ment of the F2C,, levels :- a bonding spL band of n + 2 full up a levels

(that is to say the n - 1 levels of Cn + uL(F-F) +uL(F-C) + the other pUF level) to which can beadded the F2 antibonding level CrAL(F-F) (deepenough to be filled up too), then at last n + 3 levelsaccommodating 2 n + 6 electrons ;- the remaining U t level which corresponds to

the free end of the Cn chain, with 2 electrons ;- the 7T band with n + 2 degenerate levels,

arising from the n + 2 atoms of the cluster, which arepartially filled with 2 n + 6 electrons (the chain as awhole has indeed 4 n + 14 electrons) ;- finally the antibonding SpAL band with n empty

a levels, that is the n - 1 M.O. of the Cn chain +U AL(F-C).Let us notice however that our notation for

naming the M.O. is a little approximate : for in-

stance, the uL(F-C) M.O. is especially projectedupon both F and C adjacent atoms, but not ex-clusively, as we shall be able to see when we examinethe electronic charge distribution (paper II). But thenotations are very useful to clarify the role of thevarious M.O.

With the above disposition of the energy levels,we can then see that if n is odd as in figure 7, the 7rlevels of F2Cn, and in particular the Fermi levelHOMO, are full whereas, if n is even, this M.O.

only accommodates 2 electrons and then is half-

filled. It is therefore normal, after what has beensaid above (Sect. 3.3.1.1) to generally find a largerstability of neutral chains FzCz k + l’ ·3.3.2.2 FCNF symmetrical chains. - In the symmet-rical isomer case (middle part of figure 7), the

symmetry of the molecule has some degeneracies ofthe various levels arisen and the sketch is very closeto that of the FCn levels. The only difference isrelative to the second U level of chain Cn whichdisappears too since it contributes to the building ofthe second group of M.O. which are projecting uponthe adjacent F and C atoms. Therefore the arrange-ment of the levels becomes the following :- the bonding spL band still contains n + 3 full a

levels : the n - 1 levels of Cn + the 2 sUF levels ofeach fluorine atom + the 2 uL(F-C) levels arising, asspecified above, from the combination of the

2 o-t t « surface » levels of Cn with the 2 PUF of thefluorine atoms ;- the n + 2 7T level band now accommodating

2 n + 8 electrons ;- the antibonding spAL band with n + 1 empty

levels : the n - 1 of Cn + the 2 levels U AL (F-C ).We can see that the Fermi level is now full if n is

even, thus the neutral FCNF chains are more stable

1971

for even n (Tab. A.II in Appendix). However, thisresult does not seem to agree with the experimentaldata. It can be noticed about the energies ET (n ) orET (n ) given in Appendix that there is a filled upantibonding a level in the disymmetrical isomercase ; this may explain why the energy values arelarger (in absolute value) for the FCNF symmetricalisomer which have no filled antibonding level. Wethus might think that the symmetrical isomers aremore stable ; however, they do not agree with theexperimental results, that is the very importantalternations with enhanced emission for odd n. This

might then be a limit of our simple interpretationmodel : as a matter of fact, it could be deduced thatsome factors leading to a larger global stability of thedisymmetrical clusters with respect to the symmetri-cal ones, have not been taken into account in ourmodel. Nevertheless, we shall restrict ourselves tothis model by only considering the relative stabilitiesfor a same series of isomers.

4. Conclusion.

In this paper, we recalled in detail the experimentalresults of SIMS of teflon which show a very pro-nounced preferential emission of (FpC2k+l )+ ions

for p = 1 to 4 and of (FPC2 k)- for p = 1 and 2, thatis alternations in the intensities of ionic currents withthe parity of the carbon atom number. We interpretthe results on the ions having 1 and 2 fluorine atomsfrom the stabilities of the corresponding aggregatesFpCn which present some oscillations against n too.From the theoretical model of the linear chain, we

use the CNDO approximation to carry out therelative stabilities of FpCn. We verify that the

phenomena come from the fact that the Fermi levelof the clusters always falls in the 7T band, and itsfilling well explains the stability oscillations. Thusthe CNDO technique, in spite of its well-knowndefects (too large values of the various energies)gives a good idea of the electronic structure of theclusters. Besides, the comparison of the experimen-tal results with the stability computations allows usto conclude that the disymmetrical isomers F2Cn arein the best agreement with the experimental data.Our study of FCn and F2Cn is naturally not

exhaustive, but the aim of this paper was to showthat when, as in the present case, the experimentaldata have remarkable properties of periodicity, it ispossible, by using a relatively simple technique, toget some information on the most likely geometriesof the clusters. The results of our CNDO calculationswould obviously have to be checked by more sophis-ticated computational methods by studying manypossible shapes for all successive values of n. Nevert-

heless, our calculations lead to a satisfactory in-

terpretation of experiment and we still verify ourcorrespondence rule between measured intensitiesand calculated stabilities. SIMS experiments thus

appear once more to give a good way of« measuring » the stabilities of small clusters belong-ing to a same family.

Acknowledgments.

The computations have been performed at theCentre Interrdgional de Calcul Electronique(C.I.R.C.E.) of the C.N.R.S. at the UniversiteParis-Sud (Orsay, France).

Appendix A.

Energies of various isomers of the linear FpC n(p = 1, 2) clusters.

A. 1 FC, CLUSTERS. - We give the total energiesEl (n) (q = 0, + 1 or - 1), the ionization energiesEI n and electron affinities AEn computed with theCNDO technique for the linear FCn clusters (upperpart of Tab. A.I). The polyacetylenic type moleculesare noted (b) in table A.I (middle).For the CkFCn - k isomers (lower part of Tab.

A.I), only the positive ion energies are given becauseit appears that the most stable ions are the

FCn ones. Besides, table A.I points out that onlythe FC£ isomers show enhancements of dn for agiven n parity (underlined values), that is for odd n.We can notice that C3FC+ n - 3 ions have the goodalternations too, but their total energies are muchweaker than those of FC+.

A.2 F2Cn CLUSTERS. - In table A.II are given thesame quantities E!j(n) (q = 0, 1 or - 1), En andAEn for the various kinds of linear isomers F2Cn andFCNF. The Ef(n) of the symmetrical isomers aregreater than the corresponding ones of F2Cn, particu-larly for the polyacetylenic forms, but they do notgive the right alternations of the dn (underlinedvalues). The energy values ET (n ) have been com-puted for the CkF2Cn - k chains too (Tab. A.III) andit can be seen that they are much weaker than thoseof F2Cn and moreover they show either alternationsof dn with enhancements for even n (a result

irrelevant to the experimental data) or no alterna-tions at all. Table A.IV deals with non-linear

F2Cn clusters, which are less stable than FCNF(though more stable than linear F2Cn chains), andmoreover, give wrong alternations for negative ions.

1972

Table A.I. - CNDO calculated energies, ionization energies and electron affinities of FCn clusters. Above,cumulene type linear structure ; middle, (b) = acetylenic chains ; below, some other isomers. The underlinedvalues show the maxima of the calculated quantities.Clusters FCn

Table A.II. - CNDO calculated energies, ionization energies and electron affinities of F2Cn and

FCnF clusters. (b) : triacetylenic chain ; the other molecules have cumulene type shapes.Clusters F2Cn

1973

Table A.III. - CNDO calculated energies of CkF2Cn - k positive ions.

Clusters F2Cn (end)

Table A.IV. - CNDO calculated energies of non-linear F2Cn positive ions (the 2 F atoms are bound to thesame terminal C atom).

Non-linear clusters

References

[1] LELEYTER, M., JOYES, P., Radiat. Eff. 18 (1973) 105.[2] RODRIGUEZ-MURCIA, H., BESKE, H. E. , Diss. JUL

1292, Kemforschungsanlage, Julich, Germany(1976).

[3] HORTIG, G., MULLER, M., Z. Physik 221 (1969) 119.[4] LELEYTER, M., JOYES, P., J. Phys. B 7 (1974) 516 ;

J. Phys. B 16 (1983) 671 ;LELEYTER, M., J. Physique Lett. (Paris) 43 (1982) L-

305 ; J. Microsc. Spectrosc. Electron. 9 (1984)461.

[5] LELEYTER, M., JOYES, P., J. Physique (Paris) 36(1975) 343.

[6] DORNENBURG, E., HINTENBERGER, H., Z. Natur-

forsch. 14a (1969) 765.[7] LELEYTER, M., Thèse de Doctorat d’Etat, Orsay

(France) (1975) (unpublished).[8] JOYES, P. , LELEYTER, M., HOAREAU, A., J. Physi-

que Lett. (Paris) 40 (1979) L-131.[9] LELEYTER, M., JOYES, P., ORTOLI, S. , Surf. Sci. 106

(1981) 292.[10] PITZER, K. S., CLEMENTI, E., J. Am. Chem. Soc. 81

(1959) 4477.[11] EWING, D. W., PPEIFFER, G. V., Chem. Phys. Lett.

86 (1982) 365.[12] JOYES, P., LELEYTER, M., J. Physique (Paris) 45

(1984) 1681.[13] LELEYTER, M., JOYES, P., CADEVILLE, M. C., J.

Phys. Chem. Solids 44 (1983) 779.[14] LELEYTER, M., J. Physique (Paris) 42 (1981) 1115.[15] WHITESIDE, R. A., KRISHNAN, R., DEFREES, D. J.,

POPLE, J. A., VON, R., SCHLEYER, P., Chem.Phys. Lett. 78 (1981) 538.

[16] LELEYTER, M., J. Physique Lett. (Paris) 46 (1985) L-915 and references therein.

[17] RAGHAVACHARI, K., WHITESIDE, R. A., POPLE, J.A., J. Chem. Phys. 85 (1986) 6623.

[18] LELEYTER, M., JOYES, P., Surf. Sci. 156 (1985) 800.[19] ROHLFING, E. A., COX, D. M., KALDOR, A., J.

Chem. Phys. 81 (1984) 3322.[20] The most stable structure of C6 is a cyclic

one with spins coupled in an antiferromagnetic-type manner.

[21] POPLE, J. A., BEVERIDGE, D. L., ApproximateMolecular Orbital Theory (McGraw Hill, NewYork) 1970.

[22] GRAY, H. B., Electrons and Chemical Bonding(Benjamin, New York) 1964.

[23] SIMONS, J., SMITH, W. D., J. Chem. Phys. 58 (1973)4899.

[24] HERZBERG, G., Molecular Spectra and MolecularStructure, tome III: Spectra of polyatomicmolecules (Van Nostrand Reinhold Co, NewYork) 1966, p. 633.

[25] Let us recall that, in the case of the

Cn chain, the P.C. model gives us the followingsuccession of levels in increasing energy order :

- a bonding spL band of n - 1 03C3, levels with2 n 2014 2 electrons ;

- 2 « surface » levels 03C3t (with 4 electrons), the

existence of which arising from the fact that theCn chain has a finite length, thus one danglingbond at each end ;

2014 then a band of n doubly degenerate 03C0 levels,accommodating 2 n 2014 2 electrons and

2014 at last an antibonding spAL band of n -1

empty 03C3 levels.