Electronic Dynamics by Ultrafast Pump Photoelectron Detachment

Article pubs.acs.org/JPCA

Electronic Dynamics by Ultrafast Pump Photoelectron Detachment Probed by Ionization: A Dynamical Simulation of Negative−Neutral− Positive in LiH− B. Mignolet,† R. D. Levine,*,‡,§ and F. Remacle*,†,‡ †

Department of Chemistry, B6c, University of Liège, B4000 Liège, Belgium The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel § Department of Chemistry and Biochemistry, University of California Los Angeles, Los Angeles, California 90095, United States ‡

ABSTRACT: The control of electronic dynamics in the neutral electronic states of LiH before the onset of significant nuclei motion is investigated using a negative−neutral− positive (NeNePo) ultrafast IR pump−attoescond pulse train (APT) probe scheme. Starting from the ground state of the anion (LiH−), multiphoton ultrafast electron detachment and subsequent excitation of the neutral by a few femtosecond intense IR pulse produces a non-equilibrium electronic density in neutral LiH. The coherent electronic wave packet is then probed by angularly resolved photoionization to the cation by an APT generated from a replica of the pump IR pulse at several time delays. Realistic parameters for the pump and the APT are used. Several NeNePo schemes are simulated using different IR carrier frequencies, showing that the delay between the successive attosecond pulses in the train can be used as a filter to probe the different pairs of states present in the coherent electronic wave packet produced by the pump pulse. The dynamical simulations include the pump and the probe pulses to all orders by solving the time-dependent Schrödinger equation using a coupled equation scheme for the manifolds of the anion, neutral, and cation subspaces. We show that an incomplete molecular orientation of the molecule in the laboratory frame does not prevent probing the electronic density localization by angularly resolved photoelectron maps.

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INTRODUCTION Attosecond science is in constant development, as seen from recent reviews.1−3 Ultrafast pump−probe schemes using a few femtosecond intense IR pulse and an attosecond pulse train (APT) generated by high harmonic generation (HHG) from the same IR pulse are becoming available for characterizing electronic dynamics and charge migration in molecular systems.4−6 In the experiments proposed up to now, charge migration is most often probed by detecting a charged fragment. This detection scheme necessarily implies that the nuclei motion has coupled to the electron dynamics. For this reason, the experimental results are often complex to interpret.7 Recently, however, dynamical simulations on N2 showed that if the dissociation is ultrafast and occurs within half a vibrational period, nuclear dynamics can be an accurate probe for electronic motion.8 Our aim is to investigate if it is possible to tune the nonequilibrium electronic density resulting from the excitation by a short intense optical pulse before the electrons couple to nuclear motion so as to control the subsequent dynamics that leads to a reaction.9 It is therefore essential to design schemes for probing charge migration at the purely electronic level, before the onset of significant nuclei motion. We have shown that angularly resolved photoionization at different delay times is a good probe of the spatial localization of the electronic density. Typically, pump−probe schemes involve the neutral © 2014 American Chemical Society

and cation molecular states, or in the case of charge-directed reactivity,10,11 three charged states, because the pump is tailored to create a non-equilibrium charge density in the cation by local ionization that is probed by a second ionization to the dication states. In this paper, we extend the IR pump−APT probe scheme discussed in refs 12−15 to negative−neutral−positive (NeNePo) starting from the ground state (GS) of the LiH anion. In that scheme, the vertical photodetachment of the electron from the LiH anion by the pump pulse creates a superposition of excited states of the neutral that is subsequently probed by ionization to the cation. The experimental challenge for studying LiH and its charged species resides in its high vapor pressure, which makes it difficult to bring it into the gas phase. However, the photoelectron spectrum of the anion was reported.16 In the NeNePo scheme shown in Figure 1, the few femtosecond IR pump pulse used for vertically detaching the electron from the LiH anion also excites the electronic states of the neutral and produces a coherent electronic wave packet. The electronic dynamics is then probed by an APT generated Special Issue: Franco Gianturco Festschrift Received: May 9, 2014 Revised: June 15, 2014 Published: June 17, 2014 6721

dx.doi.org/10.1021/jp504592f | J. Phys. Chem. A 2014, 118, 6721−6729

The Journal of Physical Chemistry A

Article

Figure 2. Time and frequency domain views of the filtering action of the APT. (a) In the time domain, when the beating period between two states of the coherent superposition (black line) corresponds to periodicity (TIR/2m) of the APT (red line), the same phase relations in the coherent wave packet are probed by each pulse of the train. When this is not the case, different phase relations are probed by each pulse. (b, c) In the frequency domain, when ℏωij = 2mℏωIR, there is an interference between the ionization pathways of the two states i and j to the same final state. The beating of the two states, i and j, is therefore reflected in the angular distributions measured at the energies of the above threshold ionization (ATI) peaks in the photoelectron spectrum. (d) The Fourier transform of an APT is a frequency comb in which the peaks are separated by 2ℏωIR. In the case of an APT generated by an 800 nm laser (Figure 1), the peaks are separated by 3.1 eV.

Figure 1. Scheme of the NeNePo pump−probe in LiH−. (a) LiH− oriented or partially oriented (cos2 θ = 0.7) in the laboratory frame, the IR pump pulse and the APT probe. The time delay between two attopulses of the APT is half the period of the IR pulse, TIR/2, so that it could be generated by HHG from a replica of the IR pump pulse. The train has a Gaussian envelope of 10 fs. (b) Level structure of the anion, neutral, and cation manifolds of LiH, as well as the excitation schemes for the pump and probe pulses. The GS of the anion, 13 neutral states, and the GS of cation are retained in the dynamical simulations. Each neutral and cationic state carries an ionization continuum. The arrows represent the energy of one photon of the pump (red) or probe (blue) pulse and indicate which states are accessed. The IR pump pulse accesses the states of the neutral by photodetachment and subsequent IR multiphoton excitation and induces ionization to the GS of the cation. Because the probe pulse is an APT, there are several frequencies corresponding to an odd number of IR photons. Interferences between the ionization pathways of two neutral states to the same final state occur when their transition frequency corresponds to an even number of IR photons.

electronic states that is probed. When the coherence in the nonstationary wave packet leads to localization in different parts of the molecule as a function of time, the beating of the anisotropy parameter reflects the variation of the spatial localization of the electronic density. Typically, characterizing the spatial localization of the electronic wave packet requires measuring angularly resolved photoelectron distributions. The LiH molecule is ideal for implementing a NeNePo scheme because the permanent dipole of the neutral is large enough (2.11 a.u.) to allow for the dipole bound electronic states of the anion which have been experimentally16 and computationally characterized.20−22 In the case of LiH, the geometry of the GS is not very different from that of the neutral20−22 so the dynamics in the excited states of the neutral is not very different from that induced when exciting the neutral GS. Potentially, however, when the equilibrium geometries of the two charged states are different, detaching an electron vertically can allow launching non-equilibrium electronic dynamics in regions of nuclei configurations of the neutral that could lead to fast reactivity. In the numerical simulations discussed below, we use realistic parameters for the pump IR and the APT probe pulses that are experimentally feasible. We show that for these realistic parameters, the pattern of the ATI peaks produced by the APT probe is robust and not obscured by the background due to the unavoidable photoionization of the high excited states of the neutral that can occur during the pump pulse. The methodology used to compute the electronic dynamics is given in details in refs 10 and 19 and summarized in Electronic Dynamics and Photoionization in the NeNePo Pump−Probe Scheme; in addition, the essential details about the electronic structure of the LiH anion are presented in Field Free Stationary States of the LiH Anion, Neutral, and Cation. Both the anion and the neutral GS have strong dipole moments and can be oriented.23−25 We first report results for a perfectly oriented system. Then, to be closer to experimental capabilities,

by HHG from a replica of the IR pump pulse that ionizes the molecule to the LiH cation. The pulses in an APT are separated in time by TIR/2 where TIR = 2π/ℏωIR is the period of the IR field of carrier frequency ωIR used for the HHG process.17 When a system is photoionized by an ATP, above threshold ionization (ATI) peaks18 spaced by 2ℏωIR are present in the photoelectron spectrum (PES).17 We have recently proposed19 an IR pump−APT probe scheme for characterizing the purely electronic dynamics in LiH neutral molecule, starting from the neutral GS. We showed that varying the delay between the pulses of the APT can be used to filter out a particular transition frequency present in the neutral coherent electronic wave packet, provided that TIR/2 corresponds to 2π/ℏωij where ωij is the transition frequency for the pair of electronic states i and j of the wave packet that is targeted. In general, the transition frequency between the two states must correspond to an even number of IR photons. In the energy domain, the filtering results from the interference between two photoionization pathways, the ionization of the state i by m IR photon and the ionization of the j state by (m − 2n) photons (Figure 2) to the same ionized state (same energy and angular distribution). The ionization anisotropy parameter obtained from the angularly resolved photoelectron distribution computed at various delay times at the energy of the ATI peaks therefore beats with a frequency that is the same as that of the pair of 6722



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At each time step of the numerical integration, the timedependent wave function is written as a superposition over the field free states of the three manifolds, 1 = Q + P1 + P2:

we investigate the effect of a partial orientation of the molecular frame in the laboratory frame, taking a value of cos2 θ = 0.7, see Figure 1. Such an averaging is heavy computationally because the electronic dynamics has to be run for each new orientation of the molecular frame with respect to the laboratory frame. This is computationally feasible because LiH is a few-electron molecule.

Ψ(r, t ) = c anion(t )Ψanion(r) +

i

+

■

∑∑∑ m

ELECTRONIC DYNAMICS AND PHOTOIONIZATION IN THE NENEPO PUMP−PROBE SCHEME The electronic dynamics is computed by solving the timedependent electronic Schrö dinger equation (TDSE), iℏ dΨ(r,t)/dt = H(r,t)Ψ(r,t) at the equilibrium geometry of the anion for the manifolds of the three charged states (anion, neutral, and cation) using a coupled equation scheme.11,26 Details about the methodology implemented for three coupled manifolds can be found in ref 10. The interaction between the pulses and the molecule is described in the dipole approximation and included in the electronic Hamiltonian, H(r,t), used to solve the TDSE so that all orders of the interaction by the strong electric fields are taken into account: n

H (r , t ) =

N

n

∑ 1 ∇i 2 − ∑ ∑ i=1 n

2

α=1 i=1

Zα + R ux

n

n

∑∑ i

i>j

(1)

i

where r are the electronic coordinates, Riα the electron− nucleus distances, n the number of electrons, and N the number of nuclei. E(t) = −dA(t)/dt is the time dependent electric field that corresponds to the pump and probe pulses: 2 E(t ) = Epumpf0,pump exp[− (t − t pump)2 /σpump ]

⎡ 2(t − t pump)sin(ωpumpt ) ⎤ ⎢cos(ωpumpt ) − ⎥ + Eprobe 2 ⎢⎣ ⎥⎦ ωpumpσpump ⎤ ⎡ ⎢ ⎛ iTIR ⎞2 2 ⎥ ⎟ /σ ∑ exp⎢−⎜⎝t − probe ⎥ 2 ⎠ i=1 ⎥⎦ ⎢⎣ ∞

2

f0,probe exp[− (t − t probe)

2 /σenv ]

iT ⎡ ⎤ 2 t − 2IR sin(ωprobet ) ⎥ ⎢ cos( ω t ) − probe ⎢ ⎥ 2 ωprobeσprobe ⎢⎣ ⎥⎦

(

k1

k2

k1

cmcat, k1, k2(t )ψmcat(r)χk⊥ (r1)χk⊥ (r2) 1 2

(3)

Q is the projector on the (n + 1 = 5) electron field-free stationary GS of the anion, Ψanion: Q = |Ψanion⟩⟨Ψanion|. The continuum subspace of the neutral (P 1 ) is built of ⊥ antisymmetrized products |Ψneut i , χk1⟩ of the (n = 4) electron field free state of the neutral (|Ψneut i ⟩) and of the wave function of the electron in channel i |χ⊥k1⟩ that is a plane wave normalized on a box and orthogonalized to the molecular orbitals.27,28 The imposed orthogonalization ensures that P1Q = 0. The stationary field-free states of continuum subspace of the cation (P2) are built in a similar fashion of antisymmetrized products ⊥ ⊥ cat |Ψcat m ,χk1,χk2⟩, where |Ψm ⟩ are the n − 1 field free stationary states of the cation and |χ⊥k1⟩ and |χ⊥k2⟩ orthogonalized plane waves so that P1P2 = QP2 = 0.19,29 The ionization continua are discretized so that each ionized electron (χ⊥k1) of energy |k1|2/2 and orientation k1/|k1| is defined by a point in 3D. This spherical grid is more efficient than sampling on a Cartesian grid for building the angularly resolved photoelectron distributions. The main role of the dipole coupling in eq 1 is to induce the photoionization process that couples subspaces Q and P1 and P1 and P2. We assume that there is no direct coupling between the anion and cation states, which is realistic for the strengths and the wavelengths of the pulses that we use in the simulations below. We do take into account the electronic dynamics induced by the dipole coupling within each subspace. The first pulse detaches an electron from the GS of the anion, excites the states of the neutral, and ionizes the high excited states of the neutral to the cation. After a delay (τ), the APT pulse ionizes the coherent superposition of states of the neutral to the cation. We show below that in spite of the ionization to the cation that is occurring during the pump pulse, because of the ATI peaks produced by the APT in the photoelectron spectrum, one can have a clear signal for the probe that is not covered by the ionization from the pump. Details about the computations of the matrix elements of the coupled equation scheme can be found in refs 10 and 19. The photoionization matrix elements reduce to a one-electron integral over a Dyson orbital30−32 that represents the wave function of the ionized electron. Two kinds of Dyson orbitals are involved here: those describing the wave function of the photodetached electron, which is computed as the overlap between the n + 1 electron GS of the anion and an n electron state of the neutral i and those between the neutral and (n − 1) electron cation states.33 In each case, the photoionization matrix elements takes the form −E(t)∫ Dyson ⊥ rχk2 , involving the dipole coupling between an drϕim for an ionization orthogonalized plane wave and the ϕDyson im from the neutral state i to the cationic state m. The coupling between the remaining electrons and the ionized electron that can induce internal state dynamics in the states of the neutral is neglected.34,35 The cation-ionizing electron coupling is expected to play a more important role in tunnel ionization36,37 than in the photoionization processes considered here.

1 − E (t ) rij

∑ ri

⊥ neut ∑ ∑ cineut , k1 (t )Ψ i (r)χk1 (r1)

)

(2)

In eq 2, Epump and Eprobe are the direction of the electric field of pump and probe pulses in the laboratory frame and f 0,pump or f 0,probe their strength, respectively. tpump and σpump characterize the Gaussian envelope of the pump pulse, and ωpump is its carrier frequency. The probe is a train of attopulses in a Gaussian envelope (Figure 1) in which σprobe is related the duration of the train and tprobe to the pump−probe delay. Each attopulse of the train has the same carrier frequency (ωprobe) and same duration (σprobe). The pulses have the shape of a cosine oscillating in a Gaussian envelope. Because the electric field is defined from the time-derivative of the vector potential, there is a second term in the bracket of eq 2 that makes the integral of the electric field go to zero once the pulse is over even for pulses with less than one optical period in the envelope. This term is small if the duration of the pulse is large in comparison with the period of the carrier frequency. 6723



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Dyson Figure 3. (a) Dyson orbital between the GS of the anion (GS−) and the GS of the neutral, ϕGS − −GS, and between the GS of the anion and the first ∑ Dyson excited state of the neutral, ϕGS−−I∑. (b) Computed photodetachment widths, Γ, from the GS of the anion to the 3 lowest ∑ states of the neutral. The photoionization widths are computed as in ref 31 for a polarization along z and a field strength of 0.01 a.u.

of positive charge, the dipole moment of the anion is negative (−2.21 a.u.), whereas it is positive for the neutral. Unlike for neutrals, the value of the dipole moment for anions is not independent of the origin and orientation of the molecular frame. Excited states of the anion were computed at the CAS-SCF average level using the same active space and basis set. At this level, the first excited state is not bound and has excitation energy of 0.70 eV, above the ionization potential of LiH−. At the CCSDT level, the first excited state is reported to be slightly bound, by 0.002 eV.22 Using a basis set with a larger number of diffuse functions decreases significantly the excitation energy (to 0.50 eV) but does not bring it below the IP. In the dynamical simulations reported below, we consider only the ground state of the anion because the pump pulse photoionizes promptly the anion rather than exciting it. The 40 lowest electronic states of the neutral have been computed in CAS-SCF average with four active electrons and the same active and basis set at the equilibrium geometry of the anion. The excitation energies of the excited states are close to the ones computed at the equilibrium geometry of the neutral (Table 1) because the potential energy curves are very shallow.21,22 The values of the transition dipoles are also very

We integrate numerically the TDSE using a sixth-order Runge−Kutta algorithm and an electronic basis of the GS of the anion, 13 neutral electronic states (7Σ and 3Π), and the electronic GS of the cation. The neutral and cation subspaces, P1 and P2 include one and two discretized continua, respectively. For each state of the neutral, we use a grid of 600 points for the continuum states χ⊥k1, and for the cation, an additional 800 grid points for χ⊥k2 are added. In total, at each time step of 1.2 × 10−4fs, 487 801 coupled equations are integrated.

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FIELD FREE STATIONARY STATES OF THE LIH ANION, NEUTRAL, AND CATION The field free electronic states, transition densities, and transition dipoles of each charged species of LiH are computed using the multiconfiguration complete active space−spin adapted configuration function (CAS-SCF) methodology as implemented in MOLPRO.38 To implement the coupled equation scheme efficiently, the three charge states have to be described by the same atomic basis set and number of active molecular orbitals in the CAS procedure. Of the anion, neutral, and cation, it is the electronic structure of the anion that requires the highest level of electronic structure theory. We obtain a good agreement with previous works at the MRCISD +Q level21 and CCSDT level22 for the electronic structure of the anion keeping the same atomic Gaussian basis set, 6-311+ +G(2df, 2p), and same number of 29 active molecular orbitals orbitals (13σ,7πx,7πy, and 2δ) as in our previous work.39 For each species, all the electrons are included in the active space, meaning 5 for the anion, 4 for the neutral, and 3 for the cation. The equilibrium interatomic distance computed for the anion at this level is 1.672 Å and is 0.074 Å longer than the equilibrium bond length of the neutral. Both equilibrium distances are in good agreement with previous computations (1.668 Å in ref 21 and 1.660 in ref 22) and with the experimental value of 1.724 ± 0.025.16 The computed vertical and adiabatic electron affinities are 0.304 and 0.301 eV, respectively, also in good agreement with the experimental value of 0.342 ± 0.01216 and the adiabatic computed values: 0.332 eV at the MRCISD+Q level21 and 0.327 eV at the CCSDT level.22 In the anion, the additional electron is added into a very diffuse orbital of the lithium, thereby significantly modifying the charge distribution. In the molecular frame shown in Figure 3, in which the origin is attached to the center

Table 1. Comparison of the Values of the Excitation Energies of the 13 Lowest States of LiH Neutral Computed at the Equilibrium Geometry of the Neutral and Cation at the CAS (4,29) Average Level, with Gaussian Basis Set 6311++G(2df, 2p) transition dipole moments with the GS excitation energies (eV) neutral states GS 1ES 2ES 3ES 4ES 5ES 6ES 1ES 2ES 3ES 6724

Σ Σ Σ Σ Σ Σ Π Π Π

μz

μx or μy

geom. neutral

geom. anion

geom. neutral

geom. anion

geom. neutral

geom. anion

0.00 3.11 5.24 5.69 6.17 7.12 7.22 3.87 5.73 7.21

0.00 3.07 5.20 5.65 6.12 7.07 7.19 3.83 5.68 7.16

2.10 −1.39 −0.48 −0.14 0.67 0.30 0.89 0.0 0.0 0.0

2.11 −1.42 −0.48 −0.15 0.69 0.29 0.88 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 −1.67 0.21 −0.06

0.0 0.0 0.0 0.0 0.0 0.0 0.0 −1.68 0.20 −0.07



Article

Figure 4. Population of the anion, neutral and cationic states as a function of time for (a) an 800 nm (ωpump = 0.0570 a.u.; f 0,pump = 0.01 a.u.; and σpump = 150 a.u.), (b) 1275 nm (ωpump = 0.0355 a.u.; f 0,pump = 0.0125a.u.; and σpump = 200 a.u.), and (c) 1064 nm (ωpump = 0.0428 a.u.; f 0,pump = 0.0125 a.u.; and σpump = 150 a.u.) IR pump pulse. The parameters correspond to a duration of 6.0 fs for 800 and 1064 nm and to 7.9 fs for the 1275 nm IR pulse. The pump pulse (red) is polarized linearly in the x−z plane of the laboratory frame so that both Σ and Π states can be accessed by the pump pulse. The probe pulse (blue) is composed of identical XUV attopulses of 0.3 fs (ωprobe is 9th harmonic of the IR pump pulse; f 0,probe = 0.0125 a.u.; and σprobe = 8 a.u.) separated by TIR/2 and polarized along z. The APT has a Gaussian envelope of 8 fs (σenv = 200) for the 800 nm experiment and 12 fs for the 1275 and 1064 nm experiments (σenv = 300). Only the states with a population larger than 1% are labeled. (d−f) Photoelectron spectra (PES). The photoelectron spectrum computed at the end of the pump−probe simulation is composed of an intense peak at low kinetic energies (see insets) that comes from the photoionization of the neutral during the pump pulse and of sharp ATI peaks separated by 2ℏωIR at higher kinetic energies that result from the probe by the pulse train. Dyson The Dyson orbital ϕGS − −GS is very diffuse. Therefore, the photoionization width for the ionization of the GS of the anion to the GS of the neutral is large (Figure 3b) and corresponds to a very short photodetachment lifetime of 0.4 fs (for the 800 nm IR pump pulse). Therefore, the LiH− anion photoionizes almost completely to the GS of the neutral even for a weak pulse. The photodetachment widths to the excited states of LiH neutral are small in comparison to the ionization to the GS (see Figure 3b). Furthermore, only one IR photon is required to photoionize the anion to the GS of the neutral, whereas 2 or 3 photons are required to photoionize to the excited states of the neutral. Once the GS of the neutral is accessed by

similar. In the dynamical simulations, we retained the seven lowest Σ states and the three lowest Π states that are below the ionization potential in the subspace P1, meaning 13 states in total. The other excited states do not play a significant role in the dynamics. The Dyson orbitals for the ionization of the ground state of the anion to the two lowest states of the neutral are shown in Figure 3a. The Dyson orbitals for photodetachment to higher excited states of the neutral have a norm close to zero; therefore, the photodetachment yield to these higher states is very small. 6725



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Figure 5. Probing the localization of the electronic density by the anisotropy parameter (a−d) 800 nm and (e−h) 1275 nm IR pump experiments (see panels a and b of Figure 4). The anisotropy parameter is reported in a heat map as a function of the pump−probe delay, τ, and kinetic energy of the ionized electron, ε, (panels b and f). (c,g) Anisotropy parameter integrated over the kinetic energies of the main ATI peaks of the PES shown in panels a and b. At these kinetic energies, the dipole moment (d and h) oscillates with a frequency that is the same as that of the anisotropy parameter.

interference is between ionization pathways by n and (n + 4) photons. The simulated dynamics for the NeNePo scheme with an IR pump of 800, 1275, and 1064 nm and the corresponding APT probing are compared in Figure 4. The 800 nm example aims at probing the beating GS-1Σ, and the 1275 nm the beating GS1Π. The 1064 nm IR pump simulation should not probe any coherent superposition of states because there is no beating period corresponding to the time-delay between two attopulses in a 1064 nm APT. The simulations start from the GS of the anion. At the beginning of the pulse, the anion photoionizes almost instantaneously to the ground state of the neutral. Then multiphoton transitions occur between the GS of the neutral and excited neutral states, as well as photoionization to the cation. When the pump pulse is over, there is almost no population in the anion, except in the 800 nm case (Figure 5a) where 10% are left; for the two other wavelengths, Figure 4b,c, the population in the anion state is close to 0. In the neutral manifold, a coherent superposition of the GS of the neutral and the lowest Σ and Π states is built for the three IR pulses except for the 800 nm where the population in the 1Π state is very small. The population in the higher neutral excited states is very small for all cases because once these states are accessed, they photoionize almost instantaneously to the cation. There is therefore a significant contribution of the photoionization of neutral LiH to the cation during the pump pulse. As can be seen from the insets in Figure 4d−f, the contribution of the pump pulse to the photoelectron spectrum (PES) is large near the threshold and decays exponentially at larger kinetic energies, which allows one to distinguish the photoionization due to the pump pulse from that induced by the APT probe. The ionization potential of LiH neutral is 7.65 eV. The APT has a central wavelength equal to the ninth harmonic of the IR pump pulse (about 14 eV for a 800 nm pump pulse; see Figure

photodetachment, while the IR pump pulse is on, multiphoton transitions between the GS of the neutral and higher excited states can occur, as well as the photoionization of the neutral. All these processes are taken into account in the dynamical simulations reported below. The same active space and atomic basis set was used to compute the five lowest Σ and Π states of the cation. The lowest excited state has a Π symmetry and is 11 eV above the ground state of the cation. For the dynamical simulations, we considered only the ground state in the subspace P2.

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DYNAMICAL SIMULATION OF THE NENEPO PUMP−PROBE SCHEME The simulations of the NeNePo scheme are run with realistic parameters for the pump and probe pulses that could be applied experimentally. We first discuss results for an oriented molecule in the laboratory frame using three different carrier frequencies of the IR pump pulse, 800, 1275, and 1064 nm, showing how the periodicity of the APT generated from a replica of the pump can be used as a filter to identify the states present on the coherent electronic wave packet of the neutral. We then investigate the effect of a partial orientation of the molecular frame with respect to the laboratory frame on the patterns of the photoelectron angular distributions. The GS-1Σ transition frequency is 3.07 eV (see Table 1 for excitation energies). For probing the GS-1Σ beating in the coherent wave packet of the neutral, we need IR photon of 1.54 eV, which correspond to a 800 nm carrier frequency. For probing the beating GS-1Π with the interference between the two pathways that differ by 2 IR photons, we need a 640 nm laser. However, ATP are usually generated by HHG using IR pulse with a wavelength longer than 800 nm. The GS-1Π coherence could be probed an APT generated from an IR field with the double wavelength (1275 nm). In that case, the 6726



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the 800 nm experiment, the APT probes the beating GS-1Σ in which the electronic density is moving along the z axis. At kinetic energies corresponding to the ATI peaks of the PES, Y(ε,τ) oscillates with the same period as the dipole moment along z in the 800 nm case because it is the GS-1Σ beating (Figure 5c,d) and with dipole moment along x for the GS-1Π beating (Figure 5g,h). In the case of the 1064 nm IR pump (Figure 6), the time delay between two APTs does not correspond to any multiple beating period of a given pair of states in the coherent superposition. Even though an ATI structure appears in the PES, the angular distribution is isotropic and independent of the pump−probe delay even at the energy of the ATI peaks. We investigated the effect of a partial orientation of the molecular frame with respect to the laboratory frame on the variation of the anisotropy parameter for the 800 nm experiment. We run the simulations for an oriented molecule and a set of 13 randomly oriented molecules with a value of cos2 θ equal to 0.7. The results of the averaging of the anisotropy parameter integrated on the ATI peaks of the photoelectron spectrum are shown in Figure 7. For kinetic

2), photoionizes the coherent superposition of states of the neutral to high kinetic energies (above 5 eV), and will lead to a clear pattern of ATI peaks separated by 2hvIr as can be seen from Figure 4 d−f. Except for the difference in the spacing of the ATI peaks, the photoelectron spectra shown in Figure 4d−f look rather similar. To uncover the interference dynamics in the coherent electronic wave packet built at the end of the pulse, one needs to resolve the angular distribution of the photoelectron at the energy of the ATI peaks, as explained above. We report the variation of the anisotropy parameter as a function of the pump−probe delay in Figure 5 for the 800 and 1275 nm IR pump pulse and in Figure 6 for the 1064 nm pump pulse.

Figure 7. Effect of a partial orientation on the variation of the anisotropy parameter as a function of the pump−probe delay for the main peaks of the PES in the 800 nm experiment (Figures 4a and 5b). Figure 6. Variation of the anisotropy parameter (b) and dipole moment (d) for the probe of the electronic dynamics induced by a 1064 nm IR pump pulse (Figure 4c). The anisotropy parameter for the electron ionized with a kinetic energy corresponding to the main peaks of the PES are shown in panel c. The dipole moment along x and z is oscillating, but not the anisotropy parameter because the time delay between two attopulses does not correspond to the beating period of any pair of states in the coherent superposition built at the end of the pump pulse (Figure 2a).

energies 3.5−5.0 eV and 9.5−11.0 eV (first and third peak in Figure 5a), the amplitude of the anisotropy parameter decreases by 10−20%, whereas for the kinetic energies between 6.5 and 8.0 eV (second peak in Figure 5a), the amplitude is decreased by at least 50%. In the case investigated here, the molecule therefore does not need to be perfectly oriented to be able to probe the motion of the electronic density that corresponds to a particular coherence in the electronic wave packet.

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The anisotropy parameter gives information about the angular distribution of the ionized electron at a given kinetic energy. It is computed as Y α / β (ε , τ ) =

CONCLUDING REMARKS Our numerical simulation demonstrate that the NeNePo pump−probe scheme can be implemented with experimentally realistic ultrashort pump−probe pulses. Probing the disequilibrium electronic density by angularly resolved photoelectron maps with a APT tuning to one of the coherence of the electronic wave packet built during the excitation step by the IR pulse is a reliable way to disentangle the components of the electronic wave packet. We also show that the scheme is robust with respect to a partial orientation of the molecule with respect to the molecular frame and to the background to the photoelectron spectrum due to unavoidable ionization during the pump pulse. Our simulations neglect the coupling to the nuclei. In view of the about 25 fs period of both the neutral and the anion, we do not expect a significant dephasing of the electronic wave packet due to vibronic coupling.40 The effect

(Yα(ε , t ) − Yβ(ε , t )) (Yα(ε , t ) + Yβ(ε , t ))

(4)

where Yα(ε,τ) and Yβ(ε,τ) are the ionization yields at the end of the simulation of electrons with a kinetic energy ε and an orientation α and β, respectively, at a pump−probe delay τ. For the 800 and 1064 nm experiment, Yα(ε,τ) and Yβ(ε,τ) are the ionization yields of electron with a negative, Y−z(ε,τ), and a positive, Y+z(ε,τ), orientation of the kz component, respectively. Therefore, we report Y−z/+z(ε,τ) in the heatmap of Figures 5 and 6. For the 1275 nm experiment, we report Y−x/+x(ε,τ) because the APT probes the beating between the GS-1Π that induces a motion of the electronic density along the x axis. In 6727



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that we report should therefore remain observable for delay times of a few tens of femtoseconds.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: rafi@fh.huji.ac.il. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS F.R. and B.M. gratefully acknowledge support of the Fonds de la Recherche Fondamentale Collective, FRFC 2.4545.12, and of the Fonds National de la Recherche Scientifique (FNRS, Belgium). F.R. and R.D.L. thank and acknowledge the support of the Einstein Foundation of Berlin.

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Electronic Dynamics by Ultrafast Pump Photoelectron Detachment

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