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Application of the Real-Time Time-Dependent Density Functional Theory to Excited-State Dynamics of Molecules and 2D Materials

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Application of the Real-Time Time-Dependent Density Functional Theory to Excited-State Dynamics of Molecules and 2D Materials J. Phys. Soc. Jpn. Downloaded from journals.jps.jp by 77.230.156.210 on 02/07/18 Journal of the Physical Society of Japan 87, 041016 (2018) Special Topics https://doi.org/10.7566/JPSJ.87.041016 New ab initio Approaches to Exploring Emergent Phenomena in Quantum Matter Application of the Real-Time Time-Dependent Density Functional Theory to Excited-State Dynamics of Molecules and 2D Materials Yoshiyuki Miyamoto1,2+ and Angel Rubio3,4 1Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Tsukuba, Ibaraki 305-8568, Japan 2TASC Graphene Division, Tsukuba, Ibaraki 305-8565, Japan 3Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany 4Nano-Bio Spectroscopy Group and ETSF, Universidad del País Vasco, CSIC-UPV=EHU-MPC, 20018 San Sebastián, Spain (Received April 8, 2017; accepted July 11, 2017; published online January 26, 2018) We review our recent developments in the ab initio simulation of excited-state dynamics within the framework of time-dependent density functional theory (TDDFT). Our targets range from molecules to 2D materials, although the methods are general and can be applied to any other finite and periodic systems. We discuss examples of excited-state dynamics obtained by real-time TDDFT coupled with molecular dynamics (MD) and the Ehrenfest approximation, including photoisomerization in molecules, photoenhancement of the weak interatomic attraction of noble gas atoms, photoenhancement of the weak interlayer interaction of 2D materials, pulse-laser-induced local bond breaking of adsorbed atoms on 2D sheets, modulation of UV light intensity by graphene nanoribbons at terahertz frequencies, and collision of high-speed ions with the 2D material to simulate the images taken by He ion microscopy. We illustrate how the real-time TDDFT approach is useful for predicting and understanding non-equilibrium dynamics in condensed matter. We also discuss recent developments that address the excited-state dynamics of systems out of equilibrium and future challenges in this fascinating field of research. to control the chemical reactions of molecules16–18) has also 1. Introduction been demonstrated, and the amount of products obtained Density functional theory (DFT)1,2) can be used for from a laser-induced chemical reaction was used as feedback predicting material properties by dealing with the complex to tune the pulse shape to maximize the product yield.19) exchange correlation of many-body electronic systems as a Structural changes in solids caused by femtosecond lasers functional of the electron charge density. The one-to-one have also been reported.20–22) Furthermore, the development relation between charge density and external potential holds of a short-pulse high-intensity laser source enabled us to for the electronic ground state. This one-to-one relation was fabricate nanoscale patterns in materials in a controlled extended to time-dependent systems, resulting in time- manner,23) although the underlying physics was not well dependent density functional theory (TDDFT),3) which has understood. become a powerful tool for studying excited-state dynamics The ultrafast dynamics cannot be directly explained by in many-body interacting systems. thermal equilibrium dynamics; electrons are excited and are Instead of the direct solution of the time-dependent Kohn– not steady but transient with a finite lifetime before decaying Sham equation,3) into lower-energy states (non-radiative decay). The pump- @ ðr;tÞ probe experiments require a full dynamical non-equilibrium iħ n ¼ HKSðr;tÞ ðr;tÞ; ð1Þ description of a combined electronic-ionic system. The @t n present review will address some aspects of this issue. It the main technique for the excited-state calculation remained may be a good approximation to treat electronic excited states perturbation theory using the imaginary time scheme to by introducing an electron temperature of several thousand compute the real-space dielectric response function4,5) until kelvin alongside the lattice temperature.24) However, this the benefit of real-time propagation of electrons in computing approximation does not hold after laser excitation, as has the (non-linear) optical responses was demonstrated.6) In been measured experimentally.25) If the real-time dynamics of KS equation (1), nðr;tÞ and H ðr;tÞ represent the time- electrons can be considered throughout the simulation, the dependent Kohn–Sham orbitals of the n-th state and the non-equilibrium dynamics triggered by a strong laser can be Hamiltonian, respectively. The direct solution of the Kohn– treated. Sham equation was also applied to excited-state molecular In contrast, the DFT first-principles MD approach within dynamics (MD)7–9) within the Ehrenfest approximation.10) the excited-state Born–Oppenheimer approximation assumes Photoexcited ultrafast dynamics within 1 ps (1 ps = the electronic states are steady states [obtained by either 10À12 s) have become a hot topic since the development of perturbation theory or constraint DFT (ΔSCF) techniques as the pump-probe measurement technique using femtosecond mentioned later]. However, this scheme is not generally lasers,11–13) and attosecond resolution has now been achiev- applicable for the case where non-adiabatic phenomena ed.14) For example, photoexcitation was found to cause the induced by the laser pulse play a pivotal role.26) Therefore, very fast cis–trans transition of retinal with a time constant a perturbation approach within the TDDFT scheme may be of 500 fs15) (1 fs = 1 Â 10À15 s), whereas this process was applicable27,28) unless the perturbation is strong. However, previously believed to take several picoseconds. The ability using real-time TDDFT for Ehrenfest dynamics appears to be 041016-1 ©2018 The Physical Society of Japan J. Phys. Soc. Jpn. Downloaded from journals.jps.jp by 77.230.156.210 on 02/07/18 J. Phys. Soc. Jpn. 87, 041016 (2018) Special Topics Y. Miyamoto and A. Rubio a useful approach, because electron dynamics are directly are negligible, non-equilibrium electron dynamics play an treated throughout the MD simulation. Therefore, transient important role in generating a terahertz (THz) signal dynamics, such as alternation of the potential energy surface (Sect. 3.5). Finally, we consider the high-speed collision of (PES) and modulation of the applied optical field, can be He+ with graphene to illustrate the mechanisms of secondary observed throughout the MD simulation. ion emission (Sect. 3.6), which has been applied in a new However, performing light-induced classical MD is an microscopic technique. approximation, and the appropriate choice of one of two classical MD approaches (Ehrenfest dynamics10) and surface 2. Computational Scheme hopping29)) was concluded to be system dependent,30) and Our main scheme is summarized in Ref. 41. The real-time that surface hopping is necessary when the system contains TDDFT calculations can be performed by using a plane-wave an avoided crossing in the PES. Trajectory-based methods, basis set7,8) and for periodic=non-periodic systems with a such as ab initio multiple spawning31) and Tully surface real-space grid.6,9) In the discussion below, all calculations hopping,29) can efficiently simulate non-adiabatic processes were performed with a plane-wave basis set using norm- once the appropriate Born–Oppenheimer potential energy conserving pseudopotentials42) in separable forms43) to surfaces (BOPESs) and non-adiabatic coupling constants express electron-ion interactions through the dynamics of (NACs) are provided. These BOPESs and NACs are, valence electrons. A numerically reliable scheme for solving however, extremely difficult to obtain for large systems, equation (1) is the split-operator method,44,45) in which the and there is a great demand for practical methods that avoid time propagator [exponential of HKSðr;tÞ] is expressed as calculating the BOPESs and NACs. A leading method for products of exponentials of the kinetic energy operator, local describing the dynamics of large electron-nuclear systems is potential, and non-local part of the pseudopotentials. Several TDDFT coupled to classical nuclear trajectories through mathematical schemes for solving the time-dependent Kohn– Ehrenfest dynamics because of its favorable system-size Sham equation are reported in Ref. 46 for readers interested scaling. The Ehrenfest method with TDDFT has been in further details. A scheme to apply the split-operator successful for many applications, from photodissociation method to the plane-wave basis set and pseudopotential dynamics in small molecules9) to radiation damage in metals; method as well as keeping a self-consistent field is described its efficiency allows calculations on large systems for even in Refs. 7, 8, and 47. thousands of femtoseconds, as shown in one of the results Because the Kohn–Sham Hamiltonian [HKSðr;tÞ]isa presented in this overview. functional of charge density ðr;tÞ, consisting of the sum of – KSðr;tÞ Full quantum trajectory methods describe full nuclear the norm of Kohn Sham orbitals, n , for all occupied quantum effects on the fly, but require an exhaustive states, a self-consistent relation between the time propagator knowledge of the BOPES landscape.32–34) In addition, the and the Kohn–Sham orbital must be maintained throughout ring-polymer phase space was shown to provide a practical the real-time propagation. To maintain this self-consistent MD framework to approximate the effects of quantum relation, a predictor-corrector algorithm must be used, in fluctuations, including zero-point oscillation and tunneling which the time variation of the Hartree-exchange–correlation effects (see the review in Ref. 35 for details of this method). potential is extrapolated and interpolated by a railway Recently, two alternative frameworks have been developed smoothing scheme (see Refs. 7, 8, and 47 for more detail). to describe non-adiabatic nuclear MD by either an exact Ionic forces are computed by the Hellmann–Feynman factorization of the many-body electron-nuclear wave force scheme,48) and the MD simulation is performed.
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