Ultrafast transfer and transient entrapment of photoexcited Mg electron in Mg@C60
Mohamed El-Amine Madjet, Esam Ali, Marcelo Carignano, Oriol Vendrell, Himadri S. Chakraborty
aa r X i v : . [ phy s i c s . a t m - c l u s ] D ec Ultrafast transfer and transient entrapment of photoexcited Mg electron in Mg@C Mohamed El-Amine Madjet, ∗ Esam Ali, Marcelo Carignano, Oriol Vendrell, and Himadri S. Chakraborty † Department of Natural Sciences, D.L. Hubbard Center for Innovation,Northwest Missouri State University, Maryville, Missouri 64468, USA Department of Biomedical Engineering, Northwestern University, Evanston, IL 60208, USA Theoretical Chemistry, Institute of Physical Chemistry & Centre for Advanced Materials,Heidelberg University, Im Neuenheimer Feld 229 & 225, 69120 Heidelberg,Germany
Electron relaxation is studied in endofullerene Mg@C , after an initial localized photoexcitationin Mg, by nonadiabtic molecular dynamics simulations. To ensure reliability, two methods areused: i) an independent particle approach with a DFT description of the ground state and ii) HFground state with many-body effects for the excited state dynamics. Both methods exhibit similarrelaxation times leading to an ultrafast decay and charge transfer from Mg to C within tens offemtoseconds. Method (i) further elicits a robust transient-trap of the transferred electron that candelay the electron-hole recombination. Results shall motivate experiments to probe these ultrafastprocesses by two-photon transient absorption spectroscopy in gas phase, in solution, or as thin films. Synthesis, extraction and isolation methods of endo-fullerenes with encapsulated atoms/molecules are fast de-veloping [1, 2]. Time domain spectroscopy of these stable,symmetric systems can test advances in laboratory tech-niques and access real time novel processes of fundamen-tal and applied interest. Due to their exceptional proper-ties, progression of technology piggybacks fullerene andendofullerene materials through applications in molecu-lar devices [3, 4], energy storage [5] and conversion[6, 7].Photoinduced charge transfer (CT) is a key processin organic photovoltaics whose donor-acceptor complexesare predominantly based on fullerene materials. This isbecause a fullerene molecule can be chemically tuned bychoosing its endohedral core [8] or exohedral ligands in-cluding polymers [9, 10] to control light absorption ef-ficiency and carrier transport. Upon absorbing a pho-ton, the energy converts to an exciton that either disso-ciates into free carriers or recombines depending on theelectron-hole separation and excitonic binding energy. Ofcourse, the dissociation is preferred for photovoltaics [11].Thus, the decay and transfer of a “hot” electron from onelocation of the molecular material to another is a funda-mental sub-process of this mechanism [12–16]. Therefore,gaining insights into the CT dynamics by addressing asimpler prototype system is very important.These ultrafast processes occur on the femtoseconds(fs) to picoseconds (ps) time-scale and are driven by thestrong coupling between ionic and electronic degrees offreedom. Frameworks based on nonadiabatic moleculardynamics (NAMD), therefore, are appropriate for pro-viding accurate, comprehensive descriptions of the pro-cesses [12, 17]. A powerful experimental technique toprobe such dynamics is the ultrafast transient absorp-tion spectroscopy (UTAS) [18] using fs pulses or, morerecently, attosecond pulses for greater resolution [19, 20].Indeed, photoinduced charge migration has been mea-sured in the time domain for fullerene-based polymerizedfilms [15] and heterojunctions [16], and also for bulks [21]and nanorods [22]. However, these systems are large and, consequently, the relaxation pathways may intermix withconcurrent processes that can wash out, mask or cam-ouflage spectral information on fundamental CT mech-anisms, including access to prominent transient events.
Mg 3 s Mg 3 p C HOMOC LUMO h n Ionization edge
LUMO+17LUMO+14LUMO+6LUMO+3 h n FIG. 1. (Color online) Mg@C molecular orbital energies(relative to C HOMO) at the DFT/B3LYP level of the-ory (see text). The Mg 3 s → p photoexcitation and sub-sequent CT decay are illustrated. Isosurface plots of Mg3 s , LUMO+20 (Mg 3 p -type), LUMO+17 and LUMO+14 areshown. From both theoretical and experimental standpoints,Mg@C serves as an excellent benchmark system tostudy the ultrafast relaxation and charge separation ofan exciton in contact with an organic matrix. (i) It fea-tures a “surgical” photoexcitation at a local site. (ii)It showcases a pristine relaxation dynamics, consistingof the photoelectron’s transfer to an entirely differentsite. (iii) Its dynamics upon photoexcitation proceedsthrough potentially long-lived intermediate states, simi-larly as in transient charge-trappings [23]. Fig. 1 delin-eates these points and displays the molecular orbital ener-gies of Mg@C as obtained in the present DFT descrip-tion. Notice how the valence Mg 3 s level occurs isolatedwithin the C band gap and thus can be conveniently ex-cited by a UV pump pulse to Mg 3 p - a level which splitsinto LUMO+19 to LUMO+21, each retaining predomi-nant Mg character (Fig. 2). This happens owing to thelifting of the three-fold degeneracy of p states due to thesymmetry-breaking interaction with C . These excitedstates, localized on Mg, are the initial states of our sim-ulation. Nonradiative decay, driven by electron-phononcouplings, then becomes the dominant decay process; nointercoulombic decay (ICD) channel [24, 25] exists, sincethe Mg excitation energy is lower than the C ioniza-tion energy (IE). This ultrafast relaxation is the subjectof our simulations and can be followed by a time-delayedprobe pulse in UTAS. As the photoelectron decays toLUMO+17, the first pure C state (Fig. 1), an atom-to-C CT occurs. This CT is complete and irreversible,and thus offers a clean and well defined event for exper-imental measurements. Decaying further, the electronlands on LUMO+14 and experiences a transient hold-updue to a wide energy gap right below this state whichhinders the subsequent decay. Consequently, the lifetimeof the LUMO+14 population is predicted to be longerthan for nearby states. Even though there are gaps be-low LUMO+6 and LUMO+3 in Fig. 1, their peak popu-lations never grow enough due to significant slowdown.We describe first the simulations performed with an in-dependent particle (IP), molecular orbital description ofthe electrons. The ground-state geometry optimizationof Mg@C is conducted at the B3LYP/6-311+G ∗∗ levelof theory using Gamess [26, 27]. For the empty C op-timized structure, this produces an accurate descriptionof the band gap, 2.72 eV, close to reference values formolecular C [29, 30]. Moreover, the calculated differ-ence of 5.15 eV between the C IE and electron affinityclosely agrees with the difference of these quantities mea-sured, respectively, by electron impact mass spectrome-try [31] and high-resolution photoelectron imaging [32].Accounting for the known up-shift of DFT energies [33],our computed free Mg IE matches the NIST value of 7.65eV. This energy being close to the C IE ensures that Mg3 s in Mg@C moves up into the C band gap (Fig. 1)from higher screening by C electrons.From the optimized structure of Mg@C , we conductMD simulations in the NVT ensemble at 300 K with avelocity-rescaling thermostat. Isosurface plots in Figs. 1-3 are obtained from the final structure of the NVT equi-libration run. A production run starts in the NVE en-semble and extends to 3 ps. All MD simulations areconducted using the CP2K [34] and B3LYP hybrid func-tional. The time-dependent population is obtained byaveraging over 20 initial configurations and 1000 surface hopping trajectories for each configuration. The DFT-D3dispersion correction of Grimme is employed to accountfor the dispersion interactions [35, 36]. The QMflows-namd [37] module interfaced with CP2K is employed tocompute electronic structure properties ( φ j , ǫ j ) and toobtain electron-phonon nonadiabatic couplings (NACs) d jk [38], d jk = D φ j | ~ ∇ R H | φ k E ǫ k − ǫ j ∂ ~R∂t , (1)where H and ~R are the electronic Hamiltonian and nu-clear coordinate. Evidently, NACs can enhance by (i)larger orbital overlaps, (ii) narrower energy separations,and (iii) faster nuclear velocities. The energies and NACsare then used to perform the NAMD simulations usingthe PYXAID package; for details, see Ref. [39–42]. FIG. 2. Time evolutions of the decay and transfer popula-tion fractions after three initial excitations to LUMO+21 (a),LUMO+20 (b) and LUMO+19 (c), corresponding to Mg 3 p τ de ) and transfer ( τ tr )times shown are extracted by curve fittings (see text) and thefit curves for the decay are shown by the dashed lines. The simulations of the dynamics of Mg@C start froma localized excitation of Mg 3 s to each of the 3 p states,LUMO+21, LUMO+20, and LUMP+19, by photon en-ergies of 5.69 eV, 5.67 eV, and 5.59 eV respectively. Fig. 2presents the time evolution of the relaxations. From theinitial excited state, the hot electron quickly spreads tothe other two states of the 3 p degeneracy owing to theirstrong NACs from large orbital overlaps [Eq. (1)] beforethe electron transfers to lower states. The time evolutionof the population fractions of the initial states are plot-ted in the panels of Fig. 2. Their decay times ( τ de ) areevaluated by fitting to the sum of an exponential and aGaussian decay function, as 15.6 fs, 15.4 fs and 19.0 fsrespectively. τ de for LUMO+19 is a bit longer because inthis case the initial sputter of population to LUMO+20and LUMO+21 turns around to feed LUMO+19 back.While LUMO+17 is found to be the first dominant C state on the decay path, LUMO+18 is an atom-C hy-brid state. Thus, in order to estimate the atom to C electron transfer time ( τ tr ) from a given initial excitedstate, we add up the population of the three 3 p statesand half of that of hybrid LUMO+18. The resultant cu-mulative curves, representing the transfer dynamics, arealso included in Fig. 2. Fittings yield the values of τ tr tobe 39.7 fs, 36.5 fs, and 28.2 fs respectively. The slowertransfer trend going from the higher to lower initial statepoints to the fact that the higher the excitation the longerthe electron takes to evacuate the Mg region. Further,one may visualize the original electron-hole pair in Mgas a local exciton, while the exciton after the electrontransfers to the cage with a hole at Mg 3 s is a nonlocal exciton. Therefore, τ tr also corresponds to the ultrafastconversion time from a local to a nonlocal exciton, lead-ing to the generation of carriers. Vibronic coupling sup-presses the electron-hole recombination owing to energydissipation to the vibrational modes of C . In solid C ,the exciton biding energy has a large value ∼ plus decay functions are used to fit the curvesto extract the trapping times ( τ ) of 202 fs, 227 fs and 230fs respectively. Again, the electron residing somewhatlonger in the atomic zone when excited to a higher statefeeds LUMO+14 for a longer time. This fact is reflectedfrom an earlier time ( t max ) of 88 fs at the maximumpopulation of LUMO+14 when the electron was initiallyexcited to LUMO+19. The similar t max values of about108 fs for the other two cases occur likely because of thecomplexity of the dynamics. Only after 100 fs the LUMOstarts to gain population and reaches about 30% at 500fs (Fig. 3). This significant slowdown at the band edgeis due to additional slowing effects induced by the gapsbelow LUMO+6 and LUMO+3. However, like the pop-ulation peak of LUMO, that of LUMO+6 and LUMO+3are so low that it will likely be difficult to measure them.We note that such intermittent gaps in C unoccupiedlevels were found in other calculations [33]. Thus, withthe reliability of the B3LYP functional, the prediction of FIG. 3. (Color online) Time evolutions of the populationfractions of the trapper state LUMO+14 and the band edgeLUMO after initial excitations to LUMO+19 (a), LUMO+20(b) and LUMO+21 (c). The excited state decays are alsoshown. The lifetime ( τ ) and the time ( t max ) of maximumpopulation of LUMO+14 are extracted by curve fittings; thefit curves are shown as the dashed lines. a strong population trap atop the first gap on the decaypath must be realistic.The computation scheme used above in the IP frame-work neglected the electron-electron and electron-holeinteractions. To account for the many-electron effects,we now apply a method where the dynamics of ex-cited (many-electron) states are computed using on-the-fly NAMD simulations as implemented in our CDKT [44]tool interfaced with Gamess-US [26, 27]. Excited stateenergies and gradients are calculated at the CIS/SBKJClevel analytically as implemented in Gamess-US. Thenon-adiabatic couplings are described by a Landau-Zener(LZ) approximation [44]. The computational costs arefurther reduced by using an effective core potential(ECP) basis set, namely SBKJC [28], instead of an all-electron basis. The accuracy of the SBKJC basis set isascertained by comparing the excited state energies andoscillator strengths with those calculated using the all-electron basis set 6-31G for the first 200 singlet excitedstates and also using hybrid functional PBE0 in TDDFT.The insertion of Mg inside C induces a blue shift ofthe bright states of empty C . For the optimized struc-ture, the excitation of Mg corresponds to an energy of t=0 fs, S t=35.5 fs, S t=0 fs, S t=8 fs, S t FIG. 4. (Color online) Electron density difference (excited minus ground) of Mg@C with iso-density value of ± t = 0 for S and S , and the electron transfer forS in a molecular dynamics trajectory are shown. ∼ s → LUMO+21, LUMO+20, LUMO+19 excitations in the IPtreatment, and corresponds to the CIS (many electron)excited states: S , S and S . Fig. 4 shows the electrondensity difference, excited minus ground, for S and S at t = 0, where their localized Mg nature can be seen;the golden color encodes positive values while the greenis negative. The central negative lobes are due to thesubtraction of the ground Mg 3 s spherical density.Thirty nine singlet states (S -S ) are included in thesimulation and the classical equations of motion are inte-grated with the velocity Verlet algorithm. The trajectoryis propagated for 150 fs with time-steps of 0.5 fs for thevibrational dynamics. In our implementation of surface-hopping based on the LZ model, the momentum of thenuclei is re-scaled along the direction of the gradient dif-ference vector of the potential energy surfaces involvedin the transition to ensure the conservation of total en-ergy. After the initial ( t = 0) excitation of Mg, as illus-trated in Fig. 4 for S in a NAMD trajectory, the elec-tron population follows structural rearrangements drivennon-adiabatically by the electron-phonon couplings. Af-ter 35.5 fs, S decays to S to complete the electrontransfer to C . This is evident in the iso-density plot ofS where the negative values are localized on Mg andthe positive values are on the cage. Note also the plotat an intermediate time of 8 fs which denotes a hybrid state. The 35.5-fs transfer time is very close to the av-erage of three values of τ tr in Fig. 2. This suggests thatthe many-body dynamics, which dominates the plasmon-driven ionization spectra [45] at higher energies (XUV),is not important in the middle UV region of current in-terest. Furthermore, most of the excited states below S are found to be dark – a fact that favors a localized pho-toexcitation of Mg – and are only populated during therelaxation of the hot electron.Similar to our IP model, there are energy gaps betweenCIS excited states below S . These gaps ( ∼ for the experiment isby the ion implantation technique. C films can be ir-radiated by Mg ions [46] in a similar manner employedfor Li@C , which showed stability in the air after sub-limation [47]. The ion energy can be optimized to allowthe encapsulation and yet to minimize the destructionof fullerenes, so Mg@C can be isolated from the colli-sion debris. The air stability of the molecule will be achallenge owing to the oxidation state Mg @C − . Thiscan be mitigated by converting to a stable salt-form withMg @C cation and some stabilizing anion, as was ac-complished for Li@C [48]. For example, Ca@C wasproduced with a laser vaporization source and its pho-toelectron spectroscopy in gas-phase was performed [49].Due to the non-covalent interactions of Mg@C with itsenvironment, we believe that the essence of our resultswill remain valid also in solution or in thin films.To conclude, we simulated and analyzed the ultra-fast nonradiative relaxation process, driven by electron-phonon coupling (lattice thermalization), of a photoex-cited hot electron in an atom confined in C . Mg@C features a clean and uncluttered electron relaxation tothe outer C shell, possibly featuring a transient slow-down of the electron relaxation process in real time due tothe presence of large gaps in the spectrum of excited elec-tronic states. The possibility of inducing the initial exci-tation accurately within Mg makes this molecule an idealexample for ultrafast transient absorption spectroscopicstudies. Good agreement at early times between the twoemployed methods, with and without the many-body in-teractions, indicates that the ultrafast charge separationof the initial exciton with tens of femtoseconds driven byvibronic effects is a robust result. The study providesa reference to understand both experimental and the-oretical investigations on endofullerene derivatives withincreasing structural complications via functionalizationand we hope that the current research will motivate ex-perimental activities in the domain of ultrafast science.Computing time at Bartik High-Performance Comput-ing Cluster in Northwest Missouri State University is ac-knowledged. Dr. Felipe Zapata is acknowledged for helpand assistance with Qmflows code. We thank Dr. AlexeyPopov and Dr. Eleanor Campbell for encouraging dis-cussions on synthesis possibilities of Mg@C for futureexperiments. 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