Downloaded by guest on September 24, 2021 h enfil fteeetos h positions The in electrons. moving the particles of charged field mean classical the as modeled are nuclei while qiiru oiin n values. and from distorted positions be equilibrium may spreads systems, and maxima excited density highly electron where representing for well-suited is description atcpt ncvln,inc utcne,adee ealcbond- to metallic ing; even flexibility and the multicenter, ionic, them covalent, in giving participate variable, continuously are electrons asinwv packets: wave Gaussian atomic surface. of propa- the composition from and and desorbed electrons relaxes species how of excitation energies determine Auger the we an affects way, gates which this over In distance surface. the dif- the at below and surface depths diamondoid ferent the at processes, both secondary electrons accompanying core of ionizing and dynamics Auger primary electron-nuclear the coupled both the hydrogen-terminated study We from (1). desorb surfaces to species other and protons, causing hydrides, occur, processes Dur- secondary (5). time, this femtoseconds after and several of ing over ejection the all with electron, together valence hole, another core the into of collapse electron the valence to a leads electron core a of ionization process, Auger G orbitals Gaussian floating | dynamics molecular fermionic | field force electron diamond hydrogenated the wave the in simulate electrons we C systems, of nanoparticle large dynamics in decay breaking packet Auger bond subsequent to and 2008) ionization lead 19, core September review how for understand (sent To 2008 1, December III, Goddard A. William 91125 by CA Contributed Pasadena, Technology, of Institute California Center, Simulation Process and III Materials Goddard A. William and Su T. Julius dynamics packet wave from derived chemistry Auger-induced of Mechanisms w.nsog/ci/di/1.03/pnas.0812087106 / 10.1073 / doi / cgi / www.pnas.org hsdmntae hti sfail osuyteceityof molecular classical chemistry for analysis used the and those dynamics. to study simulation simplicity in to using comparable systems tools feasible large-scale is excited it highly that demonstrates (2006) This A, with consistent Laikhtman [Hoffman heating, A, experiments remote to desorption via photon-stimulated hydrides from surface results cause the from ionizations emitted core be Auger deeper direct a whereas through protons mechanism, and fragments carbon of emission r,a ela ohsai opeso n yai shock dynamic and C nanoparticle diamond hydrogenated compression a in static both the- as high-level (4). well with experiments dense agreement as warm excellent of ory, molecu- found properties a and thermodynamic used previously (eFF), the hydrogen, We compute field electrons. to includes force processes, eFF that electron excited model the dynamics highly lar developed large-scale have atomic in we and dynamics involved electron semiconductor the mechanisms to determine par- relevant To (1), (2) (3). surfaces systems fabrication covalent at large processes in chemical ticularly induce plasmas or ions, neF l lcrn,vlneadcr,aemdlda spherical as modeled are core, and valence electrons, all eFF, In erpr o h plcto feFt td ue processes Auger study to eFF of application the now report We p 0 V nue yeegtcpoos electrons, photons, excited energetic by highly induced how eV) concerning (∼100 states remain uncertainties reat x,i (r ) and ∝ p i s,i 197 exp r h orsodn ojgt oet.This momenta. conjugate corresponding the are H 112 − efidta ufc oeinztoscause ionizations core surface that find We . hsCnesMater Condens Phys J s 1 i 2 − 2 p s i s,i i (r − 1 197 x i ) H 2 x 112 i · n sizes and 18:S1517–S1546]. exp[ip .I the In 1A). (Fig. x,i · s i r fthe of ], ieszs n otistreprmtr e orpouethe reproduce CH as to such set molecules parameters small of three geometries contains respec- ground-state their and as well sizes, as electrons, tive between overlap the of function (see electrons exclu- of ods Pauli pairs spin-dependent between a acts and that sion electrons, smaller for larger is nraea h aepce sdsotdadsoe.I u simple our of variation In possible slowed. the for and account distorted we model, is packet wave the as increase i,adB and LiH, n”mto seetossrn n xadi ieoe time. over size in “breath- expand a and with shrink but take electrons We classically, as move motion electrons ing” and nuclei i.e., 09b h ainlAaeyo cecso h USA the of Sciences of Academy National The by 2009 © ntesronigbnst aeiwr ofiltehl.O h four the Of hole. the fill to inward race to bonds surrounding electrons the down-spin in the induces which nanoparticle, At the of state. carbon hole valence 1s two a a zero, time into continuously evolving state hole il,teefciems eue otetu lcrnms,btin but mass, singularities, electron near true particularly the potentials, to poten- reduces anharmonic harmonic mass In effective semiconductors. the in tials, transport electron of ory iuain o utpefixed multiple for simulations ed opriual ipeeutoso oin(6): motion of equations simple particularly to leads potential harmonic locally a assuming and equation Schrodinger h uhr elr ocnito interest. 1 of conflict no declare authors The paper. and the research; wrote performed J.T.S. W.A.G. research; and J.T.S. designed W.A.G. and J.T.S. contributions: Author tncercnes(o tmti ed oa ro f15%). of error an to leads this atom H cusps (for form to centers functions nuclear Gaussian by at single underbound of HF ability are bound, limited from electrons the properly from and core are eV electrons and 17.7 CC CH Hence, and eV. but 13.8, 18.5 and 237, 17.5, eFF of 305, electrons from CC Hartree–Fock have and of CH, we 1s, energies ethane, the the for eFF orbitals: with Boys-localized of compared (HF) energies be Potential 1B). may (Fig. electrons similar theory naturally profiles functional density segregate electron density with to to shells, electrons valence and the core the causes into hydrocarbons, potential and Pauli diamond respect For eFF with parameters. energy electron overall the the to minimizing dynamics, by electron efficiently damped more from or obtained be may states Ground Results sum. pairwise exchange a with as (9), estimated float- theory energy (FSGO) initio accurate orbital ab Gaussian of potential spherical version ing time-dependent Pauli and a approximate an using with as systems 8), condensed that (7, enough methods dynamics lar (4). studied systems all for and owo orsodnesol eadesd -al [email protected]. E-mail: addressed. be should correspondence whom To h aitna nldseetottc,akntceeg which energy kinetic a electrostatics, includes Hamiltonian The usiuigteaoeepeso notetime-dependent the into expression above the Substituting i.2sosfraC a for shows 2 Fig. molecu- fermionic of elaboration an as viewed be may eFF o h ealdeeg xrsin.TePuiptnili a is potential Pauli The expression). energy detailed the for m elec 2 H b; PNAS lcrnwt onsi srmvdfo h central the from removed is spin down with electron ob nefciems,a ntesmcasclthe- semiclassical the in as mass, effective an be to 6 dp d h aaeesaetesm o l electrons, all for same the are parameters The . p s x /dt /dt aur 7,2009 , 27 January =− 196 =−∇ H ∂ 112 V x V /∂ aoatcetednmc facore a of dynamics the nanoparticle m , s, elec p x p . = s = Z m o.106 vol. (3m elec > x a edsrbd or described; be can 1 ˙ elec aeil n Meth- and Materials m /4) elec 0,probably ∼20%, o 4 no. s ˙ yperforming by m 1001–1005 4 elec ,C 2 may H V 6 ,

CHEMISTRY Fig. 1. The hydrogen-terminated diamond nanoparticle C197H112 used as a model system. (A) At the red sites, carbon core electrons are individually ionized and Auger dynamics are studied. (B) Comparison of electron densities between eFF and density functional theory (B3LYP/6-311g**) along a carbon–hydrogen bond in methane, and along a carbon–carbon bond in ethane.

electrons, only one (green) wins; the others bounce away from the Fig. 3B shows the atomic composition of fragments emitted now-filled core. One electron (red) feels the strongest repulsion, from the nanoparticle after Auger excitation at different sites causing it to break free as an Auger electron, only to be trapped (using melec = mp). An outer layer excitation produces hydro- 20 fs later in the particle ∼3 Å away, with its energy dissipated gen and carbon fragments with yields of 0.67 C, 0.17 CH, and 0.02 among the other electrons of the solid (not shown in the figure). CH2 per core ionization. Subsurface excitations, however, release only one species, the hydride ion H−. This remote bond breaking The other two electrons (blue and purple) stay in bonds to the − same nucleus, but remain highly excited, even after 50 fs. is a strange phenomenon, and to understand why it occurs for H , In these dynamics we set melec = mp(roton), which leads to a core hole lifetime τ = 3.8 ± 0.9 fs for CH4 (300 K, 500 trajectories), comparable to the experimental value τexpt = 7.9 ± 1.0 fs (10), = based on linewidth. Using melec mp/1, 836 (mass√ of an electron) leads to τ = 0.09 ± 0.02 fs, smaller by nearly 1/ 1, 836. Aside from an overall time-scaling, changing melec does not change the basic events observed: core hole filling, ejection of a secondary electron, and excitation of neighboring electrons. When electrons escape the nanoparticle, their size increases linearly with time, as expected from a free particle wave packet, and we consider them to be ionized when their size exceeds 5 bohr. Fig. 3A shows the energy distribution of ejected electrons, obtained from 990 trajectories initiated by ionizing each of the six sites shown in Fig. 1. Nearly all of the ejected electrons (95–98%), both fast and slow, originate from the valence shell of the core ionized atom. Here using melec = mp (which leads to a reason- able core hole lifetime) leads to excessive dissipation, suppressing the emission of fast Auger electrons. But using melec = mp/1, 836 leads to a proper fast Auger peak for core excitation of atoms within three layers of the diamondoid surface. The eFF Auger peak appears at a too-low energy, 95 eV [(eFF, outer surface) versus 263 eV (experiment, diamond surface (11))], due primarily to the reduced IP of the C(1s) electrons in eFF,which leaves less energy available for the Auger process. In addition, some of the energy is trapped in a core exciton (60–80 eV). Even so, the key features of the energy spectrum are correct. For exam- ple, in addition to the Auger peak, we find emission of low-energy electrons (0–10 eV) that appear to be the excited but non-Auger electrons of Fig. 2; similar energy distributions (4–8 eV) have been observed experimentally (12). Fig. 2. Single Auger trajectory after ionization of a carbon core electron A hallmark of Auger spectroscopy is its surface selectivity, which at the center of the diamond nanoparticle (melec = mp). Valence electrons exists because secondary electrons emitted >5 Å below the sur- surrounding the core hole with the same spin as the ionized core electron are face are trapped and not detected (13). Indeed we observe no highlighted in red, green, blue, and purple. (A) Distance of valence electrons fast Auger peak when diamondoid carbons >3 Å below the sur- from the core hole, showing the green electron filling the core hole, the red electron being ejected (and trapped after 20 fs, not shown), and the blue face are ionized (our diamondoid has a radius of 6.5 Å). We and purple electrons being excited. (B) Potential energy of valence and core find that trapped Auger electrons dissipate their energy away to electrons, showing the conversion of the green electron from a valence to a surrounding bulk electrons over tens of femtoseconds. core electron.

1002 www.pnas.org / cgi / doi / 10.1073 / pnas.0812087106 Su and Goddard Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 ue rdcs (B products. Auger nayeeto inl ugsigta yrdswr released sec- were the hydrides dependence with that complex well suggesting correlated a signal, mechanism. that electron had Auger energy ondary signal direct photon a ion incident via with suggest- hydride emitted energy, the electron were However, a incident protons predominantly the insensitive that was to was ing signal relative detector ion protons function (the proton causing step The desorbed level, species). be core neutral to the to experi- ions near recent hydride exposed energies a was and with surface with diamond photons compared hydrogenated to performed a be where analysis, can (14), This ment the trajectories, protons. and 410 bonds the over the with of associated lengths charges the tracking adamantane, ionized of ionization. number core large each to relatively exposed a is because bonds study, CH to convenient is cule fteAgrpoesi dmnae(C adamantane in process Auger the of tmccmoiino rget eaae rmtennpril fe 0f,weetetrsod o odt ecniee rknaea follows: as are broken considered be to H bond and a H for for not is thresholds but size the its where if fs, ionized 50 considered after is electron nanoparticle an the where from motions), (t separated translational ps d fragments 1.0 + over 1s of (radial performed carbon energies composition was equilibration a kinetic Atomic The snapshots, electron 1. the Fig. ejected in from of shown ps; sites Histogram Auger 0.5 different last six the the and over K 300 at snapshots 990 from 3. Fig. uadGoddard and Su at present charge instantaneous the on based categories 4. Fig. ihteeetdpoos optdasmn hta lcrni on oapoo fi satisfies it if proton a to bound is electron an that assuming computed protons, ejected the with ula-lcrndsac and distance nuclear-electron CC i.4sostefamnainoe ieo Hbnsi core- in bonds CH of time over fragmentation the shows 4 Fig. > . ,d Å, 2.5 yrgndsrto ehnssotie rmtaetre fcr-oie adamantane core-ionized of trajectories from obtained mechanisms desorption Hydrogen jce lcrnadaoi rgetsaitc rmtennpril.Ageae vr590idpnetAgrtaetre ftenanoparticle, the of trajectories Auger independent 5,940 over Aggregated nanoparticle. the from statistics fragment atomic and electron Ejected CH > niettemlzdpout.(C products. thermalized Indirect ) . ,d Å, 1.8 + eeaie h ealdeeto motions electron detailed the examined we , HH > s abnhdoe itneoe ie h ouain r eaae noH into separated are populations The time. over distance Carbon-hydrogen figures ) (Lower (bohr). size electron the is . .Cagsascae ihtedsre yrgn r nlzdi oedphb sn h rcdr ulndi i.4. Fig. in outlined procedure the using by depth more in analyzed are hydrogens desorbed the with associated Charges Å. 1.5 10 H 16 rdcsfo eodr impact. secondary from Products ) .Ti ml mole- small This ). lcrnwsisatnosyrmvd n ue yaiswspoaae o 0f ( fs 50 for propagated was dynamics Auger and removed, instantaneously was electron t 0 s 1 rjcoiswr osdrd(0 ) vrwih66hdoeswr jce.( ejected. were hydrogens 676 which over K), (300 considered were trajectories 410 fs; 100 = aha seFg 4C Fig. (see a pathway from come atoms non-Auger from (76%), ejected gens hydrides as mostly emitted experiment. are with hydrogens consistent the the this nuclei that denote separating the find We approach the electrons 4B). to external Fig. no bound (see and remain times, motion all electrons thermal at the nuclei from electrons; result (32%) the these of of Most (34%), atoms. excited atoms hydrogen or (63%) protons experiment. with as consistent emitted are (see gens atom this Auger-excited In the 4A). to Fig. attached were adamantane from an as electrons secondary involving mechanism intermediary. indirect an via oee,w lofidta ml ecnae(% fhydro- of (7%) percentage small a that find also we However, non-Auger from originated hydrogens emitted other The (61%) ejected hydrogens most that find simulations Our (C E nuc ietAuger direct 10 PNAS H −elec 16 .I hsptwy nectdvlneelectron valence excited an pathway, this In ). ).( =− itiuino hre associated charges of Distribution figures ) Upper aur 7,2009 , 27 January Erf ( aha,temjrt ftehydro- the of majority the pathway, √ 2R /s)R nietthermal indirect s,wt npht extracted snapshots with as), 5 = < . ate,where hartree, −0.6 o.106 vol. oratr5 fs. 50 after bohr >5 eodr impact secondary aha,and pathway, t o 4 no. as). 1 = Direct A) + R /H sthe is 1003 (A) (B − )

CHEMISTRY from the Auger process smashes into a carbon–hydrogen bond, Materials and methods causing the charge around the proton to increase momentarily Full Hamiltonian for the Electron Force Field. The overall energy is a sum of (shown as H2− in Fig. 4), along with the bond to fragment, with the Hartree product kinetic energy, Hartree product electrostatic energy, and a pairwise sum that approximates the effect of the Pauli principle a proton scattered in one direction (88% of cases), along with (antisymmetrization): two electrons in other directions. Because line-of-sight targeting is required, only hydrogens one bond separated from the Auger E = Eke + Enuc·nuc + Enuc·elec + Eelec·elec + EPauli site depart via this mechanism. which can be broken down further as follows, where s are the electron Experimentally, it has been observed that protons produced via i sizes, xij are the interelectron distances, and Rij are the nuclear-nuclear and photon-stimulated desorption (PSD) on hydrogenated diamond nuclear-electron distances: are emitted with a doubly peaked kinetic energy distribution (14). 3 1 We interpret these two classes of protons as originating from direct Eke = 2 s2 Auger versus secondary impact pathways, with direct Auger pro- i i tons ejected more slowly because of the presence of electrons that Zi Zj Enuc·nuc = Rij linger in the bond over the core hole lifetime. i

1004 www.pnas.org / cgi / doi / 10.1073 / pnas.0812087106 Su and Goddard Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 jce lcrn,w okeetoswt size with KE electrons quantity the took calculated we electrons, Energies. ejected Electron Ejected of Histogram interactions included that terms energy eFF electron. tra- the that the all with of over course the summing over by electron jectory each for energies potential the computed epromddnmc rmtoegoere vr5 s(iese,1as) 1 step, (time fs 50 over geometries those for from dynamics performed We r n optddnmc akadwt -stm tp o i.2 Fig. For step. time 5-as a geome- with inverted starting we backward non-core-ionized zero, dynamics the time computed of before and velocities points center try electron for the size and trajectory (with with nuclear a electrons trajectory the create any To Auger be zero. single to time a electrons at of valence course took We the ionized). over hole core the V rjcoyoe . s(iese,5a)with as) nuclei 5 an step, integrating the (time and giving ps velocities, geometry, 1.0 over initial energy-minimized trajectory of an NVE at distribution with nanoparticle Maxwell–Boltzmann starting a diamond by the K NVE equilibrated the 300 We in integrated ensemble. were trajectories (microcanonical) Individual Process. the algorithm. out Auger Verlet velocity printed the and of orbitals, Dynamics valence and performed orbitals. core ethane, localized used the the of we wavefunc- of of geometry energies purposes, frozen the localization comparison optimize these Boys to For of a 7.0 ethane. Jaguar energies ionized in the and HF/6-311g** ethane between i.e., difference tions, a as energy uadGoddard and Su . s eto 9 npht trglritras rmteesnapshots, these From intervals. regular 990 at 1s generated snapshots carbon 990 removed took we we ps; 0.5 freedom. of degrees ste r nitnusal atce,bti h aeta neeto is electron an that case the in well-defined, but speaking particles, strictly indistinguishable not is are electron they single a as of momentum or tion ffedm ecmue h eprtr yuigtevra expression virial the using by temperature the computed degrees We all between freedom. partitioned properly of energy with ( temperature distribution final velocity rect initial the of temperature m 2 3 .FotA 16)Fotn peia asinobtlmdlo oeua tutr.I. structure. molecular of model orbital Gaussian of spherical simulation Floating packet (1967) Wave AA (2007) Frost G fermions. Zwicknagel C, 9. for Toepffer P-G, dynamics Reinhard Molecular B, Jakob (2000) J 8. Schnack H, dynamics. semiclassical Feldmeier to approach 7. Time-dependent (1985) (1975) JF EJ Tyson dense Heller A, warm Christie of 6. MD, modelling Baker dynamics M, electron Thompson Excited (2007) 5. III WA Goddard JT, Su 4. des- HP, electron/photon-stimulated Gillis in effects 3. interaction Covalent applica- (1982) and DE principles Ramaker desorption: Electron-stimulated 2. (1991) JT Yates RD, Ramsier 1. k elec ete xrce npht fteeulbimtaetr vrtelast the over trajectory equilibrium the of snapshots extracted then We epotdtepstoso h aec lcrn eaieto relative electrons valence the of positions the plotted we 2A, Fig. For B m T opttoa rcdr.LHa nexample. an as LiH procedure. Computational hydrogen. dense 72:655–688. 62:1544–1555. York). New (Wiley, matter. plasma. direct-current helium orption. tions. = elec = m N ufSiRep Sci Surf = p nuc 1 hsRvLett Rev Phys ,836. /1, a c ehA Tech Sci Vac J tal. et m × p n vr50 over and , × 19)Lweeg lcrnehne thn fS(0)i hydrogen in Si(100) of etching electron-enhanced Low-energy (1995) 6 hsRvE Rev Phys i 12:243–378. = 1 2 m ,90idpnetsatn oeinzdgeometries. core-ionized starting independent 940 5, 99:185003. i v lcrn rmtestssoni i.1 hs we Thus, 1. Fig. in shown sites the from electrons 1(2):1137–1144. i 2 where , = 76:036406. × plPy Lett Phys Appl 2 1 ,836 1, m elec epromdeFdnmc yuiga using by dynamics eFF performed We i (v stknoe l ula n electronic and nuclear all over taken is −1/2 x 2 + ocmuetekntceege of energies kinetic the compute To s(iese,1 step, (time fs v 66(19):2475. y hmPhys Chem J 2 + v 0 ) eotie cor- a obtained we K), ∼600 z 2 m oratr5 s then fs, 50 after bohr >5 ) ue lcrnSpectroscopy Electron Auger elec + 2 1 47:3707–3713. = · × 4 3 m m p ,836 1, yvrigthe varying By . elec e o Phys Mod Rev v s 2 −1/2 hmPhys Chem J h posi- The . . bohr >0.5 s for as) B ,we w tm r once ftedsac ewe hmflsblwathresh- a below falls them between distance distance: the old if connected algorithm: are following atoms the using two by fragments molecular into nuclei effectively of ration Fragments. Atomic be Ejected of can Composition Atomic it electrons, other wavefunction. the from of space out” “factored phase in well-separated 8 ntkM 18)Siuae desorption. processes. Stimulated (1984) atomic ML in Knotek interaction Post-collisional 18. (1989) SA Sheinerman MU, systems. covalent Kuchiev in states final Auger 17. Localized (1982) RR decay. Rye JA, Auger Kelber core-hole DR, Jennison by desorption Ion 16. (1978) PJ Feibelman ML, Knotek 15. 4 ofa ,LihmnA(06 htnsiuae eopino yrgnfo dia- from hydrogen of desorption stimulated Photon (2006) path A mean-free Laikhtman Inelastic A, A Hoffman (2005) Jablonski B, 14. Lesiak M, Vanecek J, Potmesil J, Zemek 13. 2 si M risyI 19)Fn tutr ntescnayeeto msinpa for peak smission electron secondary the in structure Fine (1998) IL Krainsky VM, Asnin 12. 1 risyI,AnnV,Ptko G oglM(97 ue pcrsoyo hydro- of spectroscopy Auger (1997) M Foygel AG, Petukhov VM, Asnin IL, Krainsky 11. HM, Köppe 10. itdwt h rtna 0f yuigaptnileeg threshold: energy potential a using by fs asso- 50 electrons of at number proton E the the computed and with above, ciated procedure Species. the Hydrogen using Ejected trajectory. on each Charges of the end count the then at We types atoms. fragment of different group of each other; number of each composition from elemental classes the disconnected mine distinguish to analysis class ue rjcoisit H into trajectories Auger Time. over Distances Bond Carbon–Hydrogen outlined procedure the using by proton bond above. CH the the computed with then We associated above. charge procedure on the dynamics using performed by and snapshots K, core-ionized 300 at geometries adamantane of Protons. distribution Bond Carbon–Hydrogen the with Associated Charges a peak. interaction finding proton–electron and the energies, demarcated potential clearly that electron–nuclei elec- value of find selected histograms to was rough threshold plotting criterion energy a by optimum energy with The proton. away potential the far with above associated too trons the or large applying too then ones threshold, eliminating system, the in trons and distance sdcmuigfclte tLsAao ainlLb opromthe perform to Labs National Alamos Los at We calculations. Projects Materials). facilities dynamics Research Optimized computing Real Advanced (Predicting used Defense Research (Advanced the Naval Energy of and of Agency/Office Department Computing) States and United the Simulation by supported was CH work the averaged then category. We each ACKNOWLEDGMENTS. fs. in trajectories 100 the at all present over proton distance bond bond CH the on charge nuc −elec o hsUsp Phys Sov B Rev Phys Lett odsrae i oelvlecttos udmna rcse n plctosto applications and processes fundamental studies. excitations: surface core-level via surfaces mond surfaces. diamond nanocrystalline at electrons of imn rsa ih(0)ngtv lcrnafiiysurface. affinity electron negative (100) with crystal diamond eae imn surfaces. diamond genated A Rev 40:964–967. =− 53:4120–4126. s d 25:1384–1387. R 1 tal. et steeeto ie o ahpoo,w cne vralelec- all over scanned we proton, each For size. electron the is CC Erf 32:569–587. hsCnesMatter Condens Phys J > 19)Hg-eouinC1s C High-resolution (1996) √ . Å, 2.5 s 2R PNAS etakH .Gli o epu icsin.This discussions. helpful for Gillis P. H. thank We < + d hsRvB Rev Phys /H CH . ates where hartrees, −0.6 aur 7,2009 , 27 January > − . Å, 1.8 aeoisbsdo h instantaneous the on based categories 56:13529–13534. 18:S1517–S1546. d e rgPhys Prog Rep efudhdoe rget by fragments hydrogen found We HH hteeto pcr fmethane. of spectra photoelectron > esprtdteadamantane the separated We plPy Lett Phys Appl . Å; 1.5 edvd ie configu- given a divide We R o.106 vol. 47:1499–1561. stenuclear-electron the is (ii ) plPy Lett Phys Appl s nequivalence an use 87:262114. egnrtda generated We o 4 no. (iii ) hsRev Phys 73:3727. deter- 1005 Phys (i )

CHEMISTRY