ultrafast charge migration in xuv photoexcited phenylalanine...

Ultrafast Charge Migration in XUV Photoexcited Phenylalanine: AFirst-Principles Study Based on Real-Time Nonequilibrium Green’sFunctionsE. Perfetto,†,‡ D. Sangalli,† A. Marini,† and G. Stefanucci*,‡,§

†CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Via Salaria Km 29.3, I-00016Monterotondo Scalo, Italy‡Dipartimento di Fisica, Universita ̀ di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy§INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy

*S Supporting Information

ABSTRACT: The early-stage density oscillations of the electronic charge inmolecules irradiated by an attosecond XUV pulse takes place on femto- orsubfemtosecond time scales. This ultrafast charge migration process is a centraltopic in attoscience because it dictates the relaxation pathways of the molecularstructure. A predictive quantum theory of ultrafast charge migration shouldincorporate the atomistic details of the molecule, electronic correlations, andthe multitude of ionization channels activated by the broad-bandwidth XUVpulse. We propose a first-principles nonequilibrium Green’s function methodfulfilling all three requirements and apply it to a recent experiment on thephotoexcited phenylalanine amino acid. Our results show that dynamicalcorrelations are necessary for a quantitative overall agreement with theexperimental data. In particular, we are able to capture the transient oscillationsat frequencies 0.15 and 0.30 PHz in the hole density of the amine group as wellas their suppression and the concomitant development of a new oscillation atfrequency 0.25 PHz after ∼14 fs.

Photoinduced charge transfer through molecules is theinitiator of a large variety of chemical and biologicalprocesses.1−5 Remarkable examples are the charge separation inphotosynthetic centers, photovoltaic blends, and catalytic triadsor the radiation-induced damage of biological molecules. Thesephenomena occur on time scales of several tens of femto-seconds to picoseconds, and, in general, the coupling ofelectrons to nuclear motion cannot be discarded.6−8 However,the density oscillations of the electronic charge following anattosecond XUV pulse precede any structural rearrangementand take place on femto- or subfemtosecond time scales. Thisearly-stage dynamics is mainly driven by electronic correla-tions,9 and it is usually referred to as ultrafast charge migration.Charge migration dictates the relaxation pathways of themolecule, for example, the possible fragmentation channels ofthe cations left after ionization.10 Understanding andcontrolling this early-stage dynamics has become a centraltopic in ultrafast science11,12 as it would, in principle, allow usto influence the ultimate fate of the molecular structure.The subfemtosecond electron dynamics in photoexcited or

photoionized molecules can be probed in real-time with anumber of experimental techniques, for example, high-harmonic spectroscopy,13 laser streaking photoemission,14 or(fragment) cation chronoscopy.10,15,16 On the theoretical side,the description of ultrafast charge migration in attosecond XUV

ionized molecules is a complex problem because the parentcation is left in a coherent superposition of several many-electron states.5 In fact, the XUV-pulse bandwidth is as large astens of electronvolts, thus covering a wide range of ionizationthresholds. The resulting oscillations of the charge density dotherefore depend in a complicated manner on the electronicstructure of the molecule and on the profile parameters of thelaser pulse (intensity, frequency, duration).Understanding ultrafast charge migration at a fundamental

level inevitably requires a time-dependent (TD) quantumframework able to incorporate the atomistic details of themolecular structure. The numerical solution of the TDSchrödinger equation (SE) in the subspace of carefully selectedmany-electron states is certainly feasible for atoms, but itbecomes prohibitive already for diatomic molecules. Fortu-nately, many physical observables require only knowledge ofthe TD charge density n(r, t) (or the single-particle densitymatrix ρ(r, r′, t)) rather than the full many-electron wavefunction. Density functional theory (DFT) and its TDextension17,18 are first-principles methods having n(r, t) asbasic variable. TD-DFT calculations scale linearly with the

Received: January 4, 2018Accepted: March 1, 2018Published: March 1, 2018

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number of electrons (against the exponential scaling ofconfiguration interaction calculations), and it has beensuccessfully applied to study ultrafast charge migration duringand after photoionization in a number of molecules.19−25

Although TD-DFT is an exact reformulation of the TD-SE, inpractice, all simulations are carried out within the adiabaticapproximation, that is, by using the equilibrium DFT exchange-correlation (xc) potential evaluated at the instantaneous densityn(r, t). The adiabatic approximation lacks dynamical exchange-correlation effects that often play a major role in chargemigration processes. For instance, ultrafast charge migration indifferent polypeptide molecules would not be possible withoutdynamical correlations.26−28 Double (or multiple) excita-tions29,30 and ionizations,31 long-range charge transferexcitations,32−34 image-charge quasi-particle renormaliza-tions,35−37 and Auger decays38 are other processes missed bythe adiabatic approximation.We take a step forward and propose a first-principles

approach that shares with TD-DFT the favorable (power-law)scaling of the computational cost with the system size but at thesame time allows for the inclusion of dynamical correlations ina systematic and self-consistent manner. The approach is basedon nonequilibrium Green’s functions (NEGF) theory31,39−45

and at its core is the (nonlinear) equation of motion for thesingle-particle density matrix ρ in the Kohn−Sham (KS) basis.The NEGF method is applied to revisit and complement the

TD-DFT analysis of ultrafast charge migration in thephenylalanine amino acid reported in ref 10; see Figure 1 for

an illustration of the molecular structure. In the experiment theultrafast electron motion is activated by an ionizing XUV 300-aspulse, and it is subsequently probed by a vis−NIR pulse. Theprobe causes a second ionization of the phenylalanine thateventually undergoes a fragmentation reaction. The yield Y(τ)of immonium dications is recorded for different pump−probedelays τ. The data show that for τ ≲ 14 fs the yield oscillateswith a dominant frequency Ω0exp ≈ 0.14 PHz (1 PHz = 1015 Hz)and a subdominant one Ω2exp ≈ 0.3 PHz. For τ ≳ 14 fs, instead,Y(τ) oscillates almost monochromatically at the frequency Ω1exp

≈ 0.24 PHz. Reference 10 and other works46 suggest that theyield of immonium dications shares common features with theTD hole density on the amine group NH2 (see Figure 1),driven by the action of the XUV only. This relation is alsosuggested by other experimental studies on 2-phenylethyl-N,N-dimethylamine, and it is based on the hypothesis that to forman immonium dication the probe pulse is absorbed by electronson the NH2. The TD-DFT calculation of ref 10 partiallyconfirms this hypothesis, finding that the NH2 hole densityoscillates mainly at frequency Ω2DFT ≈ 0.36 PHz for τ ≲ 14 fsand Ω1DFT ≈ 0.25 PHz for τ ≳ 14 fs. However, in addition to themismatch between Ω2exp and Ω2DFT, no clear evidence of theslow dominant oscillation at frequency Ω0exp was found.The main finding of this work is that the inclusion of

dynamical correlations through the proposed NEGF approachis crucial to achieve a quantitative overall agreement with theexperimental data. In particular, dynamical correlations areresponsible for the appearance of a dominant oscillation atfrequency Ω0 ≈ 0.15 PHz, for the renormalization of the highfrequency Ω2 (∼0.34 PHz in mean-field and ∼0.30 PHz inNEGF), and for the transition at delay τ ≈ 14 fs frombichromatic to monochromatic behavior with frequency Ω1 ≈0.25 PHz.We examine the most abundant conformer of the amino acid

phenylalanine,10 which consists of a central CH unit linked toan amine group (−NH2), a carboxylic group (−COOH), and abenzyl group (−CH2C(CH)5). We consider a linearly polarizedXUV pulse with a weak peak intensity Ipump = 5 × 10

11W/cm2

(ensuring a linear response behavior), central photon energyωpump = 30 eV, and duration τpump = 300 as (with a sin

2

envelope) yielding photon energies in the range ∼(15, 45) eV.Because the phenylalanine molecules of the experimentallygenerated plume are randomly oriented, we perform calcu-lations for light polarization along the x, y, and z directions andaverage the results. The XUV-induced ionization and thesubsequent ultrafast charge migration are numerically simulatedusing the CHEERS@Yambo code47−49 that solves the NEGFequation for the single-particle density matrix ρ(t) in KS basisat fixed nuclei. Multiple ionization channels are taken intoaccount by an exact embedding procedure for the KScontinuum states, while dynamical correlations enter througha collision integral, which is a functional of ρ at all previoustimes. Details of the theoretical method and numericalimplementation are provided in the Supporting Information.To highlight the role of dynamical correlations, we solve the

NEGF equation in the (mean-field) Hartree−Fock (HF)approximation and in the (beyond mean-field) second Born(2B) approximation. The latter has been shown to be accuratefor equilibrium spectral properties50 and total energies51 ofseveral molecules. More importantly for the present work, the2B approximation faithfully reproduces the nonequilibriumbehavior of finite and not too strongly correlated systems (likethe phenylalanine molecule considered here). This evidenceemerges from benchmarks against numerically exact simu-lations in 1D atoms and molecules,52 quantum wells,53 weaklycorrelated Hubbard and extended Hubbard nanoclusters,54−59

the Anderson model at finite bias,60 and photoexcited donor−acceptor tight-binding Hamiltonians.61 The fixed nucleiapproximation is not expected to be too severe either (this isconfirmed a posteriori by Figure 2). Considering the molecularstructure in Figure 1, the time-dependent variation of theelectronic charge on the amine group is due to electron flowthrough the N−C bond. The N−C stretching mode is medium-

Figure 1. Molecular structure of the most abundant conformer of thephenylalanine molecule; see ref 10. Black spheres represent carbonatoms; gray spheres, hydrogen atoms; blue sphere, nitrogen; and redspheres, oxygen. The amine group NH2 is contained in a light-yellowcubic box.

The Journal of Physical Chemistry Letters Letter

DOI: 10.1021/acs.jpclett.8b00025J. Phys. Chem. Lett. 2018, 9, 1353−1358

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weak and it has a period of about 25−30 fs; hence the electrondynamics up to 30 fs is not too disturbed by this mode.Furthermore, nonadiabatic couplings become less importantwhen the cationic wavepacket is a linear combination of severalmany-electron states spread over a broad energy range. This isprecisely the situation of the experiment in ref 10 because thebandwidth of the ionizing XUV is as large as 30 eV.After ionization, the coherent superposition of cationic states

is characterized by several femtosecond and subfemtosecondoscillations. Following the suggestion of refs 10 and 46, we havecalculated the TD charge Namine(t) on the amine group byintegrating the electron density in the light-yellow box shown inFigure 1. The box was carefully chosen to give the correctnumber of valence electrons in equilibrium, that is, Namine(0) =7. By analogy to the analysis of ref 10, we perform a sliding-window Fourier transform of the relative variation of Namine(t)with respect to its time-averaged value ⟨Namine⟩

∫τ ω δ̃ = ω τ− − −N t N t( , ) d e e ( )i t t tamine d ( ) / amined 2 02 (1)

where δNamine(t) ≡ Namine(t) − ⟨Namine⟩ and t0 = 10 fs. Theresulting spectrograms are shown in Figure 2 panels b (2B) andc (HF). The theoretical spectra are compared with thespectrogram of the experimental yield in panel a. The latterhas been obtained as in eq 1 after replacing δNamine(t) with theyield Y(t) taken from ref 10.The agreement between the 2B spectrogram and the

experimental one is astounding. For τd ≲ 15 fs they bothexhibit two main structures at almost the same frequencies: Ω0≈ 0.15 PHz and Ω2 ≈ 0.30 PHz (theory), Ω0exp ≈ 0.14 PHz andΩ2exp ≈ 0.30 PHz (experiment). Remarkably, the 2B calculationreproduces the relative weight as well, with the peak at lowerfrequency being much more pronounced. At τd ≈ 15 fs abichromatic−monochromatic transition occurs, and again the2B frequency Ω1 ≈ 0.25 PHz is very close to the experimentalone Ω1exp ≈ 0.24 PHz. Of course, as we are comparing the TDamine density with the TD yield of immonium dications, aquantitative agreement in terms of peak intensities, delays, andso on cannot, in principle, be expected. Nonetheless, our resultsstrongly corroborate the hypothesis of ref 10, according towhich the two quantities are tightly related. In Figure 3 we

display snapshots of the real-space distribution of the molecularcharge at three times corresponding to a maximum, consecutiveminimum, and then maximum of Namine(t) before (top) andafter (bottom) the transition at τd ≈ 15 fs. The dominantoscillations at frequency Ω0 ≈ 0.15 PHz (period 6.7 fs) and Ω1≈ 0.25 PHz (period 4.0 fs) are clearly visible. Interestingly, theperiodic motion of the charge on the amine group is notfollowed by other regions of the molecule. This is a furtherindication of the role played by the quantity Namine(t) inpredicting the probe-induced molecular fragmentation.The impact of dynamical correlations can be clearly

appreciated in Figure 2c, where the spectrogram resultingfrom the mean-field HF approximation is shown. Overall, theagreement with the experimental spectrogram is rather poor.We have a single dominant frequency Ω1HF ≈ 0.26 PHz

Figure 2. Spectrograms of (a) experimental yield Y(τ) of immoniumdications (row data from figure S4 of ref 10.) (b,c) Variation δNamine(t)of the charge on the amine group calculated within the 2Bapproximation (b) and HF approximation (c). All spectrograms areobtained by performing a Fourier transform with a sliding Gaussianwindow-function of width 10 fs centered at delay τd (vertical axis); seeeq 1.

Figure 3. Snapshots of the real-space distribution of the molecularcharge at three times corresponding to a maximum, consecutiveminimum, and then maximum of δNamine(t) before (top) and after(bottom) the transition at τd ≈ 15 fs. The snapshots highlight the twomost prominent oscillations at Ω0 ≈ 0.15 PHz (period 6.7 fs) and Ω2≈ 0.25 PHz (period 4.0 fs) observed in the correlated spectrogram ofFigure 2b. Hole excess (blue) and electron excess (red) are withrespect to the reference density obtained by averaging ρ(t) over thefull real-time simulation.



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appearing at τd ≈ 12 fs. Subdominant structures of frequenciesΩ0HF ≈ 0.12 PHz and Ω2HF ≈ 0.34 PHz exist, too, but are notvisible.In fact, the height of the corresponding peaks is at least 2.5

times smaller than that of the dominant one (see also Figure5c). In the Supporting Information we display the 3D plot of allthree spectrograms to better appreciate the relative weight ofthe various structures.To get further insight into the dynamics of ultrafast charge

migration, let us denote by HFm, m = 1, ..., 32, the HF orbitalsof the 64 valence electrons of the phenylalanine (orderedaccording to increasing values of the HF energy; hence HF32 isthe HOMO). In NEGF calculations the HF basis is specialbecause the HF orbitals are fully occupied or empty in the HFapproximation and hence these are the reference orbitals toidentify correlation effects like double or multiple excitations.41

In Figure 4a we have singled out those HFm with a sizable

amplitude on the amine group. We show the square modulus oftheir wave functions along with the value (upper-left corner) ofthe respective spatial integrals over the light-yellow box ofFigure 1. Figure 4b contains the Fourier transform of the single-particle density matrix ρij(t) for the most relevant excitationsHFi ↔ HFj. We display separately two spectral regions, oneclose to Ω0 = 0.15 PHz (left) and the other close to Ω2 ≈ 0.30

PHz (right). The results have been obtained using the 2B andHF approximations and by averaging over the three orthogonalpolarizations of the XUV pulse (more details are provided inthe Supporting Information). The low-frequency Ω0 is due tothree (almost) degenerate excitations, namely, HF13 ↔ HF14,HF18 ↔ HF19, and HF19 ↔ HF20, and the left panel ofFigure 4b shows the sum of them. In HF these excitations areslightly red-shifted, Ω0HF = 0.12 PHz, and the correspondingpeak is hardly visible in the spectrogram of Figure 2c.Dynamical (2B) correlations substantially redistribute thespectral weight and give rise to a renormalization of ∼0.03PHz (0.12 eV), moving the low frequency much closer to theexperimental value. The high-frequency Ω2 is due to theexcitation HF29 ↔ HF30. The involved HF orbitals are thosewith the largest amplitude on the amine group, in agreementwith ref 10. In the HF calculation the HF29↔ HF30 excitationoccurs at Ω2HF ≈ 0.34 PHz (TD-DFT predicts a slightly largervalue ∼0.36 PHz10), and, as the low-frequency excitation, it isnot detected by the spectrogram; see Figure 2c. The effect ofdynamical (2B) correlations is to split Ω2HF into a doublet withΩ2+ ≈ 0.38 PHz and Ω2 ≈ 0.30 PHz, suggesting that theunderlying excitations are actually double excitations.41,54

Moreover, the redistribution of spectral weight makes visibleonly the structure at Ω2, in excellent agreement with theexperimental spectrogram. We mention that the centraldominant frequency Ω1 = 0.25 PHz (see Figure 2) dependsonly weakly on electronic correlations because it occurs atalmost the same energy and delay τd in the 2B, HF, and TD-DFT.10 In our simulations this frequency should be assigned tothe HF18 ↔ HF20 excitation. See the Supporting Informationfor more details.We finally address the transition around 10−15 fs leading to

the suppression of the structures at Ω0 and Ω2 and theconcomitant development of the central structure at Ω1. Weconsider the 2B and HF curve δNamine(t) shown in Figure 5(dotted) and perform two different trichromatic fits with thefunction ∑i=02 Ai sin(Ωit + ϕi) in the time intervals (0 fs, 12.5fs) and (12.5 fs, 38 fs); see blue and red curves, respectively.The fitting parameters are the amplitudes and phases, whereasthe frequencies are Ωi in 2B, panel a, and ΩiHF in HF, panel b.

Figure 4. (a) Real-space plot of the HF orbitals with sizable charge onthe amine group (see upper-left corner). (b) Fourier transform ofselected elements of the single-particle density matrix ρij(t) in the HFbasis for frequencies close to Ω0 (left) and Ω2 (right). The low-frequency Ω0 is due to three (almost) degenerate excitations, namely,HF13 ↔ HF14, HF18 ↔ HF19, and HF19 ↔ HF20, and the left plotshows ∑(i,j)|ρij(ω)| with (i,j) = (13, 14), (18, 19), (19, 20). The high-frequency Ω2 is due to the excitation HF29 ↔ HF30, and the rightplot shows |ρ29,30(ω)|. To obtain ρ(t) we have performed calculationsin the HF and 2B approximations for the three orthogonalpolarizations of the XUV pulse and then we have averaged the results.

Figure 5. (a,b) Relative variation δNamine(t) (×106) after filtering out

all oscillations faster than 0.4 PHz, obtained within the 2B and HFapproximations (dotted curves). Solid curves are trichromatic best fitsobtained with the function∑i=02 Ai sin(Ωit + ϕi) in the time window (0fs, 12.5 fs) (blue) and (12.5 fs, 38 fs) (red). (c) Best-fitted amplitudesAi (scaled by a factor 10

6) and phases ϕi.



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The values of Ai and ϕi are reported in panel c. We clearly see adramatic change of the fitted amplitudes across the transitionaround 10−15 fs, consistent with the spectrograms of Figure 2.In conclusion, we proposed a first-principles NEGF approach

to study ultrafast charge migration during and after the actionof an ionizing XUV pulse on the phenylalanine molecule.Multiple ionization channels of the initially correlated many-electron system were taken into account through an exactembedding procedure for the KS states in the continuum.Dynamical correlation effects were included at the level of theself-consistent second Born approximation, thus incorporatingdouble excitations and other scattering mechanisms in theelectron dynamics. The obtained results indicate that dynamicalcorrelations (and hence memory effects) are crucial to achieve aquantitative agreement with the experimental data. In fact,although the charge density oscillation of frequency Ω1 atdelays larger than τd ≈ 15 fs is captured even in HF, the mean-field results do not display any significant structure at smallerdelays. On the contrary, the correlated NEGF calculations showa substantial reshaping, characterized by the monochromatic-bichromatic transition Ω1 ↔ (Ω0,Ω2). All frequencies as well asthe delay of the transition are in excellent agreement with theexperiment. The overall similarity between the theoretical andexperimental spectrograms corroborates the existence of a tightrelation between the charge on the amine group and the yieldof immonium dications.We finally observe that the NEGF approach proposed here

can be extended in at least two different ways to include theeffects of nuclear motion The first is through the Ehrenfestapproximation, and it requires us to update the one-particle andtwo-particle integrals during the time-propagation. The secondstems from many-body perturbation theory, and it consists ofadding the Fan self-energy62 with equilibrium vibronicpropagators to the electronic correlation self-energy. Thesedevelopments allow for incorporating either classical effects orquantum harmonic effects, thus opening the door to studies ofa broader class of phenomena.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpclett.8b00025.

Method, numerical details, and further analysis (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Sangalli: 0000-0002-4268-9454G. Stefanucci: 0000-0001-6197-8043NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank P. Decleva for providing us with the nuclearcoordinates of the most abundant conformer of the phenyl-alanine molecule. G.S. and E.P. acknowledge EC fundingthrough the RISE Co-ExAN (grant no. GA644076). A.M., D.S.,and E.P. also acknowledge funding from the European Unionproject MaX Materials design at the eXascale H2020-EINFRA-2015-1, grant agreement no. 676598 and Nanoscience

Foundries and Fine Analysis-Europe H2020-INFRAIA-2014-2015, grant agreement no. 654360. G.S. and E.P. acknowledgethe computing facilities provided by the CINECA Consortiumwithin IscrC_AIRETID and the INFN17_nemesys projectunder the CINECA-INFN agreement.

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