A density functional theory based comparative study of hybrid photoemissions from Cl@C60, Br@C60 and I@C60
Dakota Shields, Ruma De, Esam Ali, Mohamed E Madjet, Steven T Manson, Himadri S. Chakraborty
aa r X i v : . [ phy s i c s . a t m - c l u s ] M a r EPJ manuscript No. (will be inserted by the editor)
A density functional theory based comparative study of hybridphotoemissions from Cl@C , Br@C and I@C Dakota Shields , Ruma De , Esam Ali , Mohamed E Madjet , Steven T Manson , and Himadri S. Chakraborty Department of Natural Sciences, D.L. Hubbard Center for Innovation, Northwest Missouri State University, Maryville, Mis-souri 64468, USA, e-mail: [email protected] Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, P.O. Box 34110, Doha, Qatar Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia, USAReceived: date / Revised version: date
Abstract.
Photoionization from atom-C hybrid levels in halogen endufullerene molecules, Cl@C ,Br@C and I@C , are calculated using a linear response density functional method. Both the ordinaryelectron-configuration where the open shell halogen is at the center of C and the stable configurationafter the atom receives an electron from C to form a closed shell anion are considered. Similar groundstate hybridization is found for all three systems while, in general, a slight weakening of the effect is noticedafter the electron transfer. At lower photon energies, cross sections of the outer hybrid levels attain iden-tical shapes from enhancements driven by the C plasmon resonances, while the higher energy emissionsremain distinguishable from the differences in atomic responses. These results further show near insensi-tivity to the choice of a configuration. The inner hybrid cross sections in general exhibit similar overallstructures, although differ in details between molecules. However, for these states the results significantlydiffer before and after the electron transfer – a feature that can be useful to experimentally determine thereal configuration of the molecules via photoelectron spectroscopy. PACS.
XX.XX.XX No PACS code given
Spectroscopic research on solid phase and gas phase endo-fulerenes – an atom or a smaller molecule taken captive in-side a fullerene [1] – is important to generate a knowledgerepository. This may find fundamental use in prospectiveapplications of these nanosystems which include quantumcomputations [2,3], organic photovoltaics [4], supercon-ductivity [5] and biomedical sciences [6]. Merged beamtechniques were employed at the ALS at Berkeley to probephotoionization properties of atomic endofullerenes exper-imentally [7,8,9]. It may be possible in future to employphotoelectron spectroscopy techniques [10] to access level-selective measurements as well.Theoretical model studies of the photoresponse of closed-shell atomic endofullerenes are aplenty; some accounts canbe found in the review articles Refs. [11] and [12]. Studieshave regularly predicted hybridization between a variedhigh-lying orbitals of the atom and the fullerene [13,14,15,16,17]. The photoionization process of these hybrid or-bitals, being rich in dynamical character from admixingspectral signatures of both the atom and the fullerene,are special for spectroscopic studies.Endofullerenes with open-shell atoms, in contrast, arestudied rather scantily. On the other hand, due to the exis-tence of unpaired electrons, there are attractive fundamen- tal interests in such systems. These include long spin relax-ation times in N@C [18] while enhancement and diminu-tion in hyperfine coupling, respectively, in P@C [19] andexotic muonium@C [20]. For an atom with one outer-shell vacancy other secondary processes can be inducedif energetically accessible. For instance, the transfer of afullerene electron to fill in the atomic vacancy. This willlikely result into a stable electronic configuration due tothe formation of a closed shell atomic anion. If this con-figuration is an excited configuration of the system thenit will result into a metastable molecular state. Of course,the realistic ground state of the compound may as wellbe a mixture of both the configurations, before and af-ter the electron transfer. Therefore, the comparison ofthe photoionization properties between these two diabati-cally unique configurations, particularly of the hybrid lev-els with a focus on understanding the interplay betweenthe two configuration modes, can be uniquely interesting.Using a density functional theory (DFT) framework, a re-cent study of Cl@C has been conducted by us to explorethe molecule’s hybrid emission behavior [21]. The naturalnext step is to study endofullerenes with larger halogenatoms which we report in this paper. Detailed results ofsingle-photoiozation from the atom-fullerene hybrid levelsof Cl@C , Br@C and I@C are compared and analyzedin detail. Dakota Shields et al.: A DFT study of hybrid photoemission among Cl@, Br@ and I@C Closed-shell Ar, Kr or Xe being chemically inert, al-most certainly locate at the center of the spherical C .We first treat the barely open-shell Cl, Br and I at thecenter of C within a spherical framework. We call themthe ordinary configurations. A reactive halogen atom isvery likely to capture an electron from C which willlikely bring the compound to a more stable configurationby forming closed-shell Cl − , Br − or I − . Therefore, we alsoconsider systems of Cl − @C , Br − @C , I − @C pro-duced by the transfer of a C electron to fill in the Cl,Br and I valence shell. There has been experimental ev-idence, based on laser desorption mass spectroscopy, ofC with a single Cl − inside [22]. While it is expectedthat the polarization interaction of the ion can inducesome offset in its position from the center of C , a DFTcalculation with Born-Oppenheimer molecular dynamicsindicates that this offset is quite small for Cl − and al-most zero for Br − within neutral C [23]. Earlier studiesshowed only small effects of the cage polarization exceptvery close to the ionization threshold [24]. Likewise, a rel-atively weak effect on the process from a small offset ofthe atomic location was predicted [25]. Therefore, we treatCl − @C , Br − @C , I − @C assuming spherical ge-ometry as well. We then compare the hybrid photoioniza-tion for these stable configurations with those for ordinaryconfigurations. The details of the theoretical schemes are described inRef. [14] and more recently in Ref. [21]. Choosing the pho-ton polarization along the z -axis, the photoionization dipoletransition cross section in a linear response approximationof time-dependent DFT is given by, σ nℓ → kℓ ′ ∼ |h ψ k ℓ ′ | z + δV | φ nℓ i| . (1)Here k is the momentum of the continuum electron, z isthe one-body dipole operator, φ nl is the single electronbound wavefunction of the target level, and ψ k l ′ is therespective outgoing dipole-allowed continuum wavefunc-tion, with l ′ = l ± δV represents the complex inducedpotential that accounts for electron correlations within thelinear response of the electrons to the photon field. Thecomputation of δV involves determining photon energydependent induced change in the electron density to beobtained by varying the ground state potential with re-spect to the ground state electron density as described inRef. [26].We model the bound and continuum states, and theground state potential, using the independent particle DFTapproximation that utilizes the Leeuwen-Baerends (LB)exchange-correlation functional [27]. This functional in-volves the gradient of the electron density in the schemedescribed earlier [28]. A core of 60 C ions for C isconstructed by smearing the total positive charge over aspherical shell with known molecular radius R = 6 .
70 a.u.(3 . A ) [10] and thickness ∆ . The Kohn-Sham equationsfor the system of 240 C electrons (four valence 2 s p Table 1.
Ionization potential (IP) and electron affinity (EA)calculated. The values in the parenthesis are NIST data.IP (eV) EA (eV)Cl 13.9 (13.0; Ref. [31]) 4.15 (3.60; Ref. [32])Br 13.0 (11.8; Ref. [33]) 4.10 (3.36; Ref. [34])I 11.8 (10.5; Ref. [33]) 4.06 (3.06; Ref. [35]) electrons from each carbon atom), plus all electrons of thecentral atom/ion, are then solved self-consistently. Thevalues of ∆ and a pseudo potential used are determinedboth by requiring charge neutrality and obtaining the ex-perimental value [29] of the first ionization threshold ofC . ∆ = 2 .
46 a.u. (1 . A ) thus obtained closely agreewith the value extracted from measurements [10]. Withinthe same framework, we also selectively omit either theatom (anion) or C (C ) to obtain the correspondingempty C (C ) and free atomic (anionic) results. Forempty fullerenes the model describe two single electronbands in the ground state with one of σ (no radial node)and another of π (one radial node) character [28].In the density functional model as in the current study,one may adjust the parameters of the functional, or use adifferent functional, to force accurate ground state proper-ties [30]. However, we could not find a unique set of param-eter values of our LB functional to work for both free Cl,Br, I and empty C . Therefore, we have used the set, thatis successful for C , for the endohedral composite-systemsas well. The same parametric values were also used to cal-culate results of atomic anions and C included in thediscussion. But these values, for instance, overestimate Clionization potential of NIST database [31] by about 7%.They further produce an electron affinity of 4.15 eV asopposed to the measured value of 3.6 eV [32] for Cl. Thesame level of small inaccuracies are also noted for Br andI, that can be seen in Table I. But these small inaccuraciesshould not take away much from the main results of thisstudy which explores the dominant effects of C . One useful way to describe hybridization in electronic statesof a multi-member system is the assessment of both thelevel energy separation and the wavefunction overlap be-tween states of the participating members. Both the de-crease of the former and the increase of the latter favorhybridization. To that end, Fig. 1 presents detailed en-ergy information as obtained from the current calcula-tions. Note that from the orthogonality of wavefunctionsin spherical systems, only states with same angular mo-mentum can hybridize. The left side of Fig. 1(a) presentsthe empty C p level energy and np energies of X = Cl,Br and I. We use Coulomb notation for the atomic levelsand harmonic oscillator notation for the C levels. Notethat the np binding energy systematically decreases going akota Shields et al.: A DFT study of hybrid photoemission among Cl@, Br@ and I@C (cid:16)(cid:21)(cid:19)(cid:16)(cid:20)(cid:24)(cid:16)(cid:20)(cid:19)(cid:16)(cid:24)(cid:16)(cid:21)(cid:19)(cid:16)(cid:20)(cid:24)(cid:16)(cid:20)(cid:19)(cid:16)(cid:24) (cid:38) (cid:25)(cid:19) (cid:3)(cid:21)(cid:83)(cid:38)(cid:79)(cid:3)(cid:22)(cid:83) (cid:37)(cid:85)(cid:3)(cid:23)(cid:83) (cid:44)(cid:3)(cid:24)(cid:83) (cid:38)(cid:79)(cid:14)(cid:38) (cid:25)(cid:19) (cid:38)(cid:79) - (cid:38) (cid:25)(cid:19) (cid:37)(cid:85) - (cid:38) (cid:25)(cid:19) (cid:37)(cid:85)(cid:14)(cid:38) (cid:25)(cid:19) (cid:44)(cid:14)(cid:38) (cid:25)(cid:19) (cid:44) - (cid:38) (cid:25)(cid:19) (cid:38) (cid:25)(cid:19)(cid:14) (cid:3)(cid:21)(cid:83)(cid:38)(cid:79) - (cid:3)(cid:22)(cid:83) (cid:37)(cid:85) - (cid:3)(cid:23)(cid:83) (cid:44) - (cid:3)(cid:24)(cid:83) (cid:38)(cid:79) - (cid:14)(cid:38) (cid:25)(cid:19)(cid:14) (cid:38)(cid:79) - - (cid:38) (cid:25)(cid:19)(cid:14) (cid:37)(cid:85) - - (cid:38) (cid:25)(cid:19)(cid:14) (cid:37)(cid:85) - (cid:14)(cid:38) (cid:25)(cid:19)(cid:14) (cid:44) - (cid:14)(cid:38) (cid:25)(cid:19)(cid:14) (cid:44) - - (cid:38) (cid:25)(cid:19)(cid:14) (cid:37) (cid:76) (cid:81)(cid:71) (cid:76) (cid:81)(cid:74) (cid:3) (cid:72) (cid:81) (cid:72) (cid:85) (cid:74)(cid:92) (cid:3) (cid:11) (cid:72) (cid:57) (cid:12) (cid:11)(cid:68)(cid:12)(cid:11)(cid:69)(cid:12) (cid:38) (cid:25)(cid:19) (cid:3)(cid:43)(cid:50)(cid:48)(cid:50) Fig. 1. (Color online) Valence np level binding energies of freehalogen atoms (a) and anions (b), and that of the 2 p levels ofempty C (a) and C (b) are drawn on the left side. Thecorresponding symmetric and antisymmetric hybrid levels ofthe compound X@C (a) and X − @C (b) are presented onthe right side. Electron transition energies from C HOMO tothe halogen’s np hole are indicated on panel (b). from Cl to I thereby increasing the energy separation from2 p C . It is then expected that 2 p of the C cation willget more bound while the energy levels of the X − anionswill become less bound compared to their neutral counter-parts. This is seen on the the left side of Fig. 1(b), where itis evident that the loosening of np levels going from Cl − to I − is almost negligible. Furthermore, the np energiesof anions are practically the electron affinity values of theneutrals (Table I). Energies of the resultant hybrid states,for both X@C and X − @C configurations of compos-ite systems, are given on the right sides of both panelswhere + and - signs represent symmetric (bonding) andantisymmetric (antibonding) hybrids respectively. It is in-teresting to note that for both configurations the higherbinding energy (inner) hybrid levels have practically thesame binding energy. On the other hand, for each configu-ration the outer hybrid levels systematically move higherfrom Cl to I, while the X@C configuration shows anweaker change with an overall lower binding.As noted above, the configuration of simply placinga neutral halogen at the center of a neutral C is or-dinary. For C , due to large cloud of 240 delocalizedelectrons, the ground state structure is insensitive to thelocation of the hole among the molecular levels. Likewise,for X − @C the level energies and wavefunctions of pureC and hybrid states are found to be independent of atwhich C orbital the hole is situated. Let us consideran electron transition from the highest occupied (HOMO)level of C of binding energy -7.52 eV to the outer np of Cl+C Cl - +C Cl 3pCl - Radial coordinate (a.u.) -0.8-0.400.4 Cl - C Cl - - C Cl 3pCl - R a d i a l w a v e f un c ti on ( a . u . ) (a)(b) C R i R o Fig. 2. (Color online) Radial symmetric (a) and antisymmetric(b) hybrid wavefunctions of Cl@C versus Cl − @C . Forboth the molecules the 3 p level of the free atom Cl and anionCl − hybridizes with the 2 p level of, respectively, empty C and C . Corresponding wavefunctions of free Cl and Cl − are displayed, while that of only C is shown on panel (a).The inner ( R i ) and outer ( R o ) radii of the C shell are shownon panel (a). Br - C Br - - C Br+C Br - +C Radial coordinate (a.u.) -0.8-0.400.4
I+C I - +C I - C I - - C R a d i a l w a v e f un c ti on ( a . u . ) (a)(b) Fig. 3. (Color online) Radial hybrid wavefunctuions of Br@C versus Br − @C (a) and I@C versus I − @C (b) systems. Dakota Shields et al.: A DFT study of hybrid photoemission among Cl@, Br@ and I@C X of electron affinity (see Table I) which is the np bind-ing energy of X − as noted above. These transitions areindicated in Fig. 1(b). The resulting configuration withthe HOMO vacancy will have the minimum total energyand, therefore, will be the ground state configuration forX − @C . This does not even take into account the extrabinding associated with the electrostatic Coulomb attrac-tion between X − and C . Despite the electron affinityof Cl being less than the ionization potential of C (seeabove), this extra binding is what that will enable theionic compound to bind. Therefore, this ground state con-figuration of Cl − @C should be stable and abundantlyformed. Simultaneously, if this energy is still higher thanthe total energy of X@C , then the configuration will bemetastable and of significant spectroscopic interest. Oneway to probe the physical situation is to conduct pho-toelectron spectroscopic measurements that may test thestate selective ionization results described in the followingsubsection.The Radial wavefunctions corresponding to two con-figurations of the Cl system are presented in Fig. 2 withpanel (a) and (b) for, respectively, symmetric and anti-symmetric hybrids. In both panels the 3 p wavefunctionsof Cl and Cl − and that of 2 p for C are shown. Note that2 p is π -type fullerene state. For the hybrid states, a some-what weakening of hybridization is noted in going fromCl@C to Cl − @C . However, the extent of hybridiza-tion still achieved for Cl − @C in spite of very largeseparation [Fig. 1(b)] between free Cl − and empty C states is surprising at a first look. However, some outwardradial shift (Fig. 2) of 3 p wavefunction, Cl − versus Cl,and a small inward shift of 2 p of C compared to C (not shown), likely advantaged the mixing. The situationis qualitatively similar for Br and I systems whose hybridwavefunctions are presented in Fig. 3(a) and 3(b) respec-tively. Note, however, that due to the two-node characterof the Br (Br − ) 4 p wavefunction, its symmetric combina-tion with one-node C (C ) 2 p will have one less nodethan the antisymmetric combination to become the innerhybrid, while for Cl 3 p and I 5 p having one and threenodes reverse this order. Finally, the hybrid states can besymbolically expressed as, | X ± C i = | φ ± i = η ± | φ np X i ± η ∓ | φ p C i (2)for X@C , and the same for X − @C with X and C re-placed by X − and C . Here η + = √ α and η − = √ − α where α is the mixing parameter that renders the hybridstates orthonormal. Cross sections calculated in linear response time-dependentDFT for the outer hybrid levels for both configurations arepresented in in Fig. 4 with panels (a), (b) and (c), respec-tively, for Cl, Br and I composites. Several narrow reso-nances are due to the many autoionizing resonance chan-nels, driven by Auger and inter-Coulombic decay (ICD)
10 100 -3 -2 -1 Cl - +C Cl+C Cl - -3 -2 -1 Br - - C Br - C Br -
10 100
Photon energy (eV) -3 -2 -1 I - +C I+C I - C r o ss s ec ti on ( a . u . ) (a)(b)(c) Fig. 4. (Color online) Photoionization cross sections of theouter hybrid electron in Cl@C versus Cl − @C (a), Br@C versus Br − @C (b), and I@C versus I − @C (c). Thecross section of the outer np ionization of the correspondingfree anion is also presented on each panel for comparisons. process [17], that exist in the endofullerenes due to levelsin the fullerene molecule that are not there in free atoms.In any case, comparing the curves with the np cross sec-tions of free X (not shown) and X − , which are practi-cally same over these energies, indicates plasmon drivenenhancements at lower photon energies up to 30 eV [13,16,36,37]. In the framework of interchannel coupling due toFano [38], the correlation-modified matrix element of thephotoionization of X ± C can be written perturbativelyas [16,21], M ± ( E ) = D ± ( E )+ X nℓ Z dE ′ h ψ nℓ ( E ′ ) | | r ± − r nℓ | | ψ ± ( E ) i E − E ′ D nℓ ( E ′ )(3)in which the single electron (uncorrelated) matrix element,that is the matrix element without δV in Eq. 1, is D ± ( E ) = h ks ( d ) | z | φ ± i (4)and | ψ nl i in the interchannel coupling integral is the (con-tinuum) wavefunction of the nℓ → kℓ ′ channel. Taking thehybridization into account, the channel wavefunctions in akota Shields et al.: A DFT study of hybrid photoemission among Cl@, Br@ and I@C -5 -4 -3 -2 -1 Cl - - C Cl - C C -5 -4 -3 -2 -1 Br - +C Br+C C Photon energy (eV) -5 -4 -3 -2 -1 I - - C I - C C C r o ss s ec ti on ( a . u . ) (a)(b)(c) Fig. 5. (Color online) Same as Fig. 4 but for the photoioniza-tion of the inner hybrid levels.
Eq. 6 become | ψ ± i = η ± | ψ np X i ± η ∓ | ψ p C i (5)Substituting Eqs. (2) and respective Eqs. (5) in Eq. 6,and noting that the overlap between a pure X (X − ) anda pure C (C ) bound state is negligible, we separatethe atomic and fullerene contributions to the integral toget the full (correlated) matrix element for X ± C andX − ± C levels as, M ± ( E ) = η ± M np X(X − ) ( E ) ± η ∓ M p C (C +60 ) ( E ) (6)where the first and second terms, respectively, on the righthand side describes interchannel coupling effects of atomicand fullerene ionization channels.A large number of fullerene channels, which are verystrong due to the photoionization of plasmon resonances,exist at lower energies. Through the second term in Eq. 6,these channels couple with the np emissions of comparablestrengths from X and X − (Fig. 4). This explains the almostsimilar cross sections in broad shapes and magnitudes overthese energies making the results insensitive to the choiceof the system or the configuration. The broad shoulderstructures above 20 eV is likely the effect of the higherenergy plasmon resonance [39]. Note, however, that thelevels of X − ± C open at lower photon energies since they bind weakly (Fig. 1). Further note that the oppositesymmetry of Cl and I versus Br endofullerenes, pointedout above, bears little effect on the results.As the plasmonic effect weakens with increasing en-ergy, the cross sections (Fig. 4) largely follow their freeatom (ion) curves, since the first term of Eq. 6 begins todominate. The results also show a series of oscillations.These oscillations are a consequence of a well-known mul-tipath interference mechanism [40] due to the cavity struc-ture of C which was modeled earlier in detail in Ref. [41].Since the free Cl, Br and I results are distinctly differentat higher energies primarily due to the occurrence of vari-ous Cooper minima, the outer hybrid results also maintaindifferences. However, owing to the cross sections of X ver-sus X − being so close, results are seen to be essentiallyindependent to the choice of the configuration. Fig. 5 delineates results of the emissions from the innerhybrid level. Since these channel opens above 15 eV, theeffect of the giant plasmon only exists over a small energyrange above the ionization threshold, although the effectsof the higher energy plasmon linger on slightly further inenergy. We, however, note significant differences betweenthe choice of configuration at these lower energies which,however, tend to match at the intermediate energy range.Due to the stronger fullerene charter of these levels (seeFigs. 2 and 3), causing their lower average-magnitudes,the oscillatory features are found to be more intense com-pared to the outer hybrid cases. Note that the cross sec-tions for the two choices of the configurations begin tofall off significantly again past 70 eV with the results forX − @C staying lower.In Fig. 5 we further compare the results with the crosssection of the 2 p level of C which shows sharper oscil-lations with very rapid fall-off due to the absence of anyatomic type steady emission [21,42]. This comparison ex-hibits a stronger non-oscillatory background strength forinner hybrid emissions that largely weakens the sharpnessof the oscillations. The reason for this is the contribu-tions to the amplitude from the atomic region owing tothe structures that exist there in the wavefunction dueto the hybridization, as can be seen in Figs. 2 and 3.This can be understood in the dipole acceleration gaugeformalism of the ionization amplitude which involves thepotential gradient [43]. The derivative of the Coulomb-type potential at the center is large, since ddr ( − /r ) = r .As a result, even a small probability density at the center(due to hybridization) can create significant contributionsto the matrix element. This will be more prominent athigher energies. Therefore, electron probability densities,however small, at the central region receive strong recoilforce from the Coulombic potential ridge to augment thematrix element. Dakota Shields et al.: A DFT study of hybrid photoemission among Cl@, Br@ and I@C Using a DFT methodology with the LB exchange corre-lation functional, ground state atom-C single electronhybrid levels of p angular momentum character are pre-dicted for Cl, Br and I centered endofullerene molecules.Single electron dipole photoionization of these systems areinvestigated within the framework of linear response time-dependent DFT. While the degree of hybridization in allthree molecules is found similar, the effect somewhat re-duces after a C electron transfers to occupy the halogenvacancy producing likely a more stable configuration. Forthe outer hybrid states the ionization response over theplasmonic range of the spectra is almost indistinguishableamong all systems, including before and after the elec-tron transitions, barring the detailed structures of nar-row autoionizing resonances. At higher energies likewise,while little sensitivity arises from the electron’s relocal-ization, the confined halogen’s character dominates theionization of the outer hybrid. The ionization of the in-ner hybrid levels at lower energies, in contrast, modifiessubstantially upon the electron transfer. This differencediminishes considerably at intermediate energies to againbecome important as the energy further increases. Ion-ization for these hybrids, even though of dominant C character, however, draws some extra strength from theatomic zone. The details of these differences and simi-larities, along with the delineation of the actual electronconfiguration of the molecules, are excellent candidate forstudy via photoelectron spectroscopic experiments.The C ion core is smeared over a jellium sphere inour model that freezes bond vibrations. A moot questiontherefore remains. Can the oven temperature of about800 K to produce fullerene vapor wash out the broaderstructures discussed in this paper? Sample temperaturecan affect the situation in two ways: (i) coupling of theelectronic motion with the temperature-induced vibrationmodes of the ion core [44] and (ii) fluctuation of the clus-ter shape around the shape at absolute zero [45]. How-ever, as shown in Ref. [26], it required a convolution ofthe theoretical results to add a width less than 1 eV tocompare with photoionization measurements of gas phaseC . This width is rather miniscule in comparison withenergy resolution of about 5-10 eV required to measurebroad structures in Figs. 4 and 5. Therefore, thermal vi-brations, while will likely smooth the autoionizing spikes,will not qualitatively alter the key results presented. ACKNOWLEDGEMENT:
The research is supported bythe US National Science Foundation Grant No. PHY-1806206(HSC) and the US Department of Energy, Office of Science, Ba-sic Energy Sciences, under award DE-FG02-03ER15428 (STM).
Author Contributions:
STM and HSC conceived theproblem; MEM and HSC designed and implemented theresearch; DS, RD and EA contributed to the computa-tions, while all authors contributed to the analysis of theresults; RD, STM and HSC primarily worked to write themanuscript.
References
1. A.A. Popov, S. Yang, and L. Dunsch, Endohedral fullerenes,Chem. Rev. , 5989 (2013).2. W. Harneit, C. Boehme, S. Schaefer, K. Huebner, K. For-tiropoulos, and K. Lips, Room temperature electronic detec-tion of spin coherence in C , Phys. Rev. Lett. , 216601(2007).3. C. Ju, D. Suter, and J. Du, An endohedral fullerene-basednuclear spin quantum computer, Phys. Lett. A 375, (2011).4. R.B. Ross, C.M. Cardona, D.M. Guldi, S.G. Sankara-narayanan, M.O. Reese, N. Kopidakis, J. Peet, B. Walker,G.C. Bazan, E.V. Keuren, B.C. Holloway, and M. Drees, En-dohedral fullerenes for organic photovoltaic devices, NatureMaterials , 208 (2009).5. A. Takeda, Y. Yokoyama, S. Ito, T. Miyazaki, H. Shimotani,K. Yakigaya, T. Kakiuchi, H. Sawa, H. Takagi, K. Kitazawa,and N. Dragoe, Superconductivity of doped Ar@C , Chem.Commun. , 912 (2006).6. J.B. Melanko, M.E. Pearce, and A.K. Salem, Nanotechnol-ogy in Drug Delivery , edited by M.M. de Villiers, P. Aramwit,and G.S. Kwon (Springer, New York, 2009) 105.7. A. M¨uller, S. Schippers, M. Habibi, D. Esteves, J.C. Wang,R.A. Phaneuf, A.L.D. Kilcoyne, A. Aguilar, and L. Dun-sch, Significant redistribution of Ce 4 d oscillator strength ob-served in photoionization of endohedral Ce@C +82 ions, Phys.Rev. Lett. , 133001 (2008).8. A.L.D. Kilcoyne, A. Aguilar, A. M¨uller, S. Schippers, C.Cisneros, G. Alna’Washi, N.B. Aryal, K.K. Baral, D.A. Es-teves, C.M. Thomas, and R.A. Phaneuf, Confinement reso-nances in photoionization of Xe@C , Phys. Rev. Lett. ,213001 (2010).9. R.A. Phaneuf, A.L.D. Kilcoyne, N.B. Aryal, K.K. Baral,D.A. Esteves-Macaluso, C.M. Thomas, J. Hellhund, R. Lom-sadze, T.W. Gorczyca, C.P. Balance, S.T. Manson, M.F. Ha-soglu, S. Schippers, and A. M¨uller, Probing confinement res-onances by photoionizing Xe inside a C molecular cage,Phys. Rev. A , 053402 (2013).10. A. R¨udel, R. Hentges, H.S. Chakraborty, M.E. Madjet, andJ.M. Rost, Imaging delocalized electron clouds: Photoioniza-tion of C in Fourier reciprocal space, Phys. Rev. Lett. ,125503 (2002).11. H.S. Chakraborty and M. Magrakvelidze, Many-electronresponse of gas-phase fullerene materials to ultraviolet andsoft X-ray photons, From Atomic to Mesoscale: the Roleof Quantum Coherence in Systems of Various Complexities ,edited by S. Malinovskaya and I. Novikova (World Scientific,Singapore, 2015) p. 221.12. V.K. Dolmatov, Photoionization of atoms encaged inspherical fullerenes,
Theory of Confined Quantum Systems:Part two, Advances in Quantum Chemistry , edited by J.R.Sabin and E. Braendas (Academic Press, New York, 2009),Vol. 58, pp. 13-68.13. H.S. Chakraborty, M.E. Madjet, T. Renger, J.-M. Rost,and S.T. Manson, Photoionization of hybrid states in endo-hedral fullerenes, Phys. Rev. A , 061201(R) (2009).14. M.E. Madjet, T. Renger, D.E. Hopper, M.A. McCune,H.S. Chakraborty, J.-M Rost, and S.T. Manson, Photoion-ization of Xe inside C : Atom-fullerene hybridization, giantcross-section enhancement, and correlation confinement res-onances, Phys. Rev. A , 013202 (2010).akota Shields et al.: A DFT study of hybrid photoemission among Cl@, Br@ and I@C d states in Zn@C , Phys.Rev. A , 053201 (2012).16. M.H. Javani, R. De, M.E. Madjet, S.T. Manson, and H.S.Chakraborty, Photoionization of bonding and antibonding-type atom-fullerene hybrid states in Cd@C vs Zn@C , J.Phys. B , 175102 (2014).17. M.H. Javani, J.B. Wise, R. De, M.E. Madjet, S.T. Man-son, and H.S. Chakraborty, Resonant Auger-intercoulombichybridized decay in the photoionization of endohedralfullerenes, Phys. Rev. A , 063420 (2014).18. J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, K.Porfyrakis, S.A. Lyon, and G. A. D. Briggs, Environmen-tal effects on electron spin relaxation in N@C , Phys. Rev.B , 085418 (2007).19. C. Knapp, N. Weiden, H. Kass, K.-P. Dinse, B. Piet-zak, M. Waiblinger, and A. Weidinger, Electron paramag-netic resonance study of atomic phosphorus encapsulatedin [60]fullerene, Molecular Physics , 999 (1998); online(2011).20. O. Donzelli, T. Briere, and T. P. Das, Location of muo-nium and hydrogen in C60 fullerene and associated electronicstructure and hyperfine properties, Hyperfine Interactions , 19 (1996).21. D. Shields, R. De, M.E. Madjet, S.T. Manson, and H.S.Chakraborty, Photoemission from hybrid states of Cl@C before and after a stabilizing charge transfer, J. Phys. B (Un-der review) arXiv:1907.04881 [physics.atm-clus]22. L. Zhu, S. Wang, Y. Li, Z. Zhang, H. Hou, and Q. Qin,Evidence for fullerene with single chlorine anion inside, Appl.Phys. Lett. , 702 (1994).23. P. Ravinder and V. Subramanian, Studies on the encap-sulation of various anions in different fullerenes using den-sity functional theory calculations and Born-Oppenheimermolecular dynamics simulation, J. Phys. Chem. A , 11723(2011).24. V.K. Dolmatov and S. T. Manson, Interior static polar-ization effect in A@C photoionization, Phys. Rev. A ,023422 (2010).25. A.S. Baltenkov, V.K. Dolmatov, S.T. Manson, A.Z.Msezane and V.A. Pikhut, Trends in near-threshold pho-toionization of off-the-center endohedral atoms, Phys. Rev.A , 043202 (2003).26. M.E. Madjet, H.S. Chakraborty, J.M. Rost, and S.T. Man-son, Photoionization of C : a model study, J. Phys. B ,105101 (2008).27. R. Van Leeuwen and E. J. Baerends, Exchange-correlationpotential with correct asymptotic behavior, Phys. Rev. A ,2421 (1994).28. J. Choi, E.H. Chang, D.M. Anstine, M.E. Madjet, and H.S.Chakraborty, Effects of exchange-correlation potentials onthe density-functional description of C versus C , Phys.Rev. A , 023404 (2017).29. J. de Vries, H. Steger, B. Kamke, C. Menzel, B. Weisser,W. Kamke, I.V. Hertel, Single-photon ionization of C - andC -fullerene with synchrotron radiation: determination ofthe ionization potential of C , Chem. Phys. Lett. , 159(1992).30. L.N. Anderson, M. Bele’en Oviedo, and B.M. Wong, Accu-rate electron affinities and orbital energies of anions from anonempirically tuned range-separated density functional the-ory approach, J. Chem. Theory Comput. , 1656 (2017). 31. A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASDTeam, NIST Atomic Spectra Database (ver. 5.6.1), (2018).32. U. Berzinsh, M. Gustafsson, D. Hanstorp, A. Klinkm¨uller,U. Ljungblad, and A.-M. Martensson-Pendrill, Isotope shiftin the electron affinity of chlorine, Phys. Rev. A , 231(1995).33. D.R. Lide (Editor), Ionization potentials of atoms andatomic ions in Handbook of Chem. and Phys., 10-211 (1992).34. C. Blondel, P. Cacciani, C. Delsart, and R. Trainham, HighResolution Determination of the Electron Affinity of Fluorineand Bromine using Crossed Ion and Laser Beams, Phys. Rev.A, 1989 , 3698 (1989).35. R.J. Pelaez, C. Blondel, C. Delsart, and C. Drag, Pulsedphotodetachment microscopy and the electron affinity of io-dine, J. Phys. B , 125001 (2009).36. M.E. Madjet, H.S. Chakraborty, and S.T. Manson, Giantenhancement in low energy photoemission of Ar confined inC , Phys. Rev. Lett. , 243003 (2007).37. M.H. Javani, H.S. Chakraborty, and S.T. Manson, Valencephotoionization of noble-gas atoms confined in the fullereneC , Phys. Rev. A , 053402 (2014).38. U. Fano, Effects of configuration interaction on intensitiesand phase shifts, Phys. Rev. , 1866 (1961).39. S.W.J. Scully, E.D. Emmons, M.F. Gharaibeh, R.A. Pha-neuf, A.L.D. Kilcoyne, A.S. Schlachter, S. Schippers, A.M¨uller, H.S. Chakraborty, M.E. Madjet, and J.M. Rost, Pho-toexcitation of a volume plasmon in C ions, Phys. Rev.Lett. , 065503 (2005).40. J.-P. Connerade, V.K. Dolmatov, and S.T. Manson, Onthe nature and origin of confinement resonances, J. Phys. B , 2279 (2000).41. M.A. McCune, M.E. Madjet, and H.S. Chakraborty, Re-flective and collateral photoionization of an atom inside afullerene: Confinement geometry from reciprocal spectra,Phys. Rev. A , 011201(R) (2009).42. M.A. McCune, M.E. Madjet, and H.S. Chakraborty,Unique role of orbital angular momentum in subshell-resolved photoionization of C , J. Phys. B , 201003(2008).43. A. Potter, M.A. McCune, R. De, M.E. Madjet, and H.S.Chakraborty, Probing photoelectron multiple interferencesvia Fourier spectroscopy in energetic photoionization ofXe@C , Phys. Rev. A , 033201 (2010).44. G.F Bertsch and D. Tom´anek, Thermal line broadening insmall metal clusters, Phys. Rev. B62