Session K31: Advances in Density Functional Theory V

\textbf{Ultrafast Laser-Induced Demagnetization: Identifying the Mechanism with Real-Time TDDFT}

In the past 2 decades several experiments have demonstrated the laser-induced demagnetization of ferromagnetic solids in less than 100 femto-seconds. This is orders of magnitude faster than the present-day magnetic-field-based technology. To shed light on the underlying microscopic mechanism, we have performed an ab-initio study of Fe, Co, Ni and Cr in short laser pulses, using real-time non-collinear time-dependent spin density functional theory (TDDFT). We show [1] that the demagnetization proceeds in two distinct steps: First, a fraction of the electrons is excited without much change in the total spin polarization. In a second step, the spin magnetic moment of the remaining localized d-electrons decreases through spin-flip transitions induced by spin-orbit coupling. For pulse lengths of a few femto-seconds, the whole process of demagnetization happens in less than 50 femto-seconds. For antiferromagnetic Heusler compounds, such as Mn$_{\mathrm{3}}$Ga and Ni$_{\mathrm{2}}$MnGa, an even faster process is found where magnetic moment is transferred from one sublattice to the other. Employing a combination [2] of TDDFT with Optimal Control Theory, we furthermore demonstrate how the demagnetization process can be controlled with suitably shaped laser pulses. Finally, we assess the influence of the approximation used for the exchange-correlation (xc) functional by comparing non-collinear LSDA results with a novel xc functional [3] that exerts a local exchange-correlation torque. \begin{enumerate} \item K. Krieger, J.K. Dewhurst, P. Elliott, S. Sharma, E.K.U. Gross, JCTC\textbf{ 11, }4870 (2015). \item A. Castro, J. Werschnik, E.K.U. Gross, Phys. Rev. Lett. \textbf{109}, 153603 (2012). \item F.G. Eich, E.K.U. Gross, Phys. Rev. Lett. \textbf{111}, 156401 (2013). \end{enumerate}   

Real-time dynamics of Hubbard-type model systems via a combination of the Kadanoff-Baym formalism with adiabatic TDDFT

We propose a description of nonequilibrium systems via a simple protocol that combines DFT-exchange-correlation potentials with self-energies of many-body perturbation theory. The approach, aimed to avoid double counting of interactions, is tested against exact results in Hubbard-type systems, with respect to interaction strength, perturbation speed/inhomogeneity, and system dimensionality/size. In many regimes, we observe good agreement with the exact results, and an improvement over the pure adiabatic local TDDFT or the pure Second-Born NEGF approximations. We also address the reasons behind the residual discrepancies, and briefly discuss possible directions for future work.   

Electronic stopping in liquid water from first principles: An application of large-scale real-time TDDFT simulations

Electronic stopping describes the transfer of energy from a highly-energetic charged particle to electrons in a material. This process induces massive electronic excitations via interaction between the material and the highly localized electric field from the charged particle. Understanding this phenomenon in condensed matter systems under proton irradiation has implications in various modern technologies. First-principles simulations, based on our recently-developed large-scale real-time time-dependent density functional theory approach, provide a detailed description of how electrons are excited via a non-equilibrium energy transfer from protons on the attosecond time scale. We apply this computational approach to the important case of liquid water under proton irradiation. Our work reveals several key features of the excitation dynamics at the mesoscopic and molecular levels which support a clearer understanding of the water radiolysis mechanism under proton irradiation. Importantly, we will demonstrate a first-principles determination of the energy transfer rate, (i.e. electronic stopping power) in liquid water, and a comparison to existing empirical models will be presented. We will conclude by discussing how the exchange-correlation approximation influences the calculation of the electronic stopping power.   

Electrical conductivity of metals from real-time time-dependent density functional theory

In this presentation, I will discuss how to apply real-time electron dynamics to study electronic currents in crystalline systems and, in particular, how to use this method to predict electrical conductivities in different regimes. This approach presents many interesting theoretical challenges associated to the representation of bulk systems as infinitely periodic. For example, in order to induce electronic currents in the system, we use a gauge transformation that allows us to include finite electric fields in the simulation. We have implemented this approach using time-dependent density functional theory (TDDFT). This implementation allows us to induce, measure and visualize the current density as a function of time, in simulations with thousands of electrons (hundreds and even thousands of atoms). We have found that real-time TDDFT can describe how currents naturally decay in metals. From this dissipation process we can directly calculate the frequency-dependent conductivity, including the direct current (DC) conductivity that is not accessible from linear-response approaches like Kubo-Greenwood.   

Development of an ab-initio calculation method for 2D layered materials-based optoelectronic devices

We report on the development of a novel first-principles method for the calculation of non-equilibrium nanoscale device operation process. Based on region-dependent $\Delta $ self-consistent field method beyond the standard density functional theory (DFT), we will introduce a novel method to describe non-equilibrium situations such as external bias and simultaneous optical excitations. In particular, we will discuss the limitation of conventional method and advantage of our scheme in describing 2D layered materials-based devices operations. Then, we investigate atomistic mechanism of optoelectronic effects from 2D layered materials-based devices and suggest the optimal material and architecture for such devices.   

The Time-Dependent Particle-Hole Map

The particle-hole map (PHM) is proposed as a new visualization tool to analyze electronic excitations in molecules in the time- or frequency domain, to be used in conjunction with TDDFT or other ab initio methods. The purpose of the PHM is to give detailed insight into electronic excitation processes which is not obtainable from local visualization methods such as transition densities, density differences, or natural transition orbitals. The PHM provides information on the origins, destinations, and coherences of charge fluctuations during an excitation process. In contrast with the transition density matrix, the PHM has a statistical interpretation involving joint probabilities of individual states and their transitions, and it is easier to read and interpret. We discuss and illustrate the properties of the PHM and give several examples and applications to excitations in one-dimensional model systems and in organic donor-acceptor systems.   

Exploiting initial-state dependence to improve the performance of adiabatic TDDFT

Although time-dependent density functional theory (TDDFT) descriptions of dynamics in non-equilibrium situations have seen exciting successes recently, there have also been studies that throw into doubt the reliability of the approximate exchange-correlation functionals to accurately describe the dynamics.~ Here we study exact exchange-correlation potentials for few electron systems, found using the global fixed-point iteration method [NRL]. We find that the size of dynamical correlation features that are missing in the currently-used adiabatic approximations depend strongly on the choice of the initial Kohn-Sham wavefunction. With a judicious choice, the dynamical effects can be small over a finite time duration, but sometimes they can get large at longer times.~ We also examine different starting points, in particular an orbital-dependent potential directly obtained from the Kohn-Sham hole [LFSEM14], ~for approximate xc functionals: instead of building on an adiabatic approximation.   

Studies of spuriously time-dependent resonances in TDDFT

Recently the failure of some exchange-correlation functionals to accurately ~capture non-perturbative dynamics in time-dependent density functional theory (TDDFT) was shown to be correlated with their violation of an exact condition [1]: that the resonance positions of the system remain fixed during the evolution.~ Closely related is the inconsistent prediction of excitation frequencies in linear response when the reference state is an excited state of the system. We discuss this and the effect on dynamics in a range of molecular systems, exploring system-size dependence of the violation. [1] ~Time-resolved spectroscopy in time-dependent density functional theory: An exact condition, J. I. Fuks, K. Luo, E. D. Sandoval, N. T. Maitra, Phys. Rev. Lett.~\textbf{114}, 183002 (2015).~   

Open Quantum Transport and Non-Hermitian Real-Time Time-Dependent Density Functional Theory

Sub-nanometer electronic devices are notoriously difficult to simulate, with the most widely adopted transport schemes predicting currents that diverge from experiment by several orders of magnitude. This deviation arises from numerous factors, including the inability of these methods to accommodate dynamic processes such as charge reorganization. A promising alternative entails the direct propagation of an electronic structure calculation, as exemplified by real-time time-dependent density functional theory (RT-TDDFT). Unfortunately this framework is inherently that of a closed system, and modifications must be made to handle incoming and outgoing particle fluxes. To this end, we establish a formal correspondence between the quantum master equation for an open, many-particle system and its description in terms of RT-TDDFT and non-Hermitian boundary potentials. By dynamically constraining the particle density within the boundary regions corresponding to the device leads, a simulation may be selectively converged to the non-equilibrium steady state associated with a given electrostatic bias. Our numerical tests demonstrate that this algorithm is both highly stable and readily integrated into existing electronic structure frameworks   

TDDFT-based local control theory for chemical reactions

In this talk I will describe the implementation of local control theory for laser pulse shaping within the framework of TDDFT-based nonadiabatic dynamics~\footnote{B. Curchod, T. Penfold, U. Rothlisberger, I. Tavernelli, Phys. Rev. A, 84, 042507, 2011}. The method is based on a set of modified Tully’s surface hopping equations and provides an efficient way to control the population of a selected reactive state of interest through the coupling with an external time-dependent electric field generated on-the-fly during the dynamics. This approach is applied to the investigation of the photoinduced intramolecular proton transfer reaction in 4-hydroxyacridine in gas phase and in solution~\footnote{B.F.E. Curchod, T. J Penfold, U. Rothlisberger, I.Tavernelli, Chem. Phys. Chem., 16, 2127, 2015}. The generated pulses reveal important information about the underlying excited-state nuclear dynamics highlighting the involvement of collective vibrational modes that would be neglected in studies performed on model systems. Finally, this approach can help to shed new light on the photophysics and photochemistry of complex molecular systems and guide the design of novel reaction paths.   

Mixed Quantum-Classical Dynamics Methods for Strong-Field Processes: Multiple-trajectory Ehrenfest dynamics $+$ decoherence terms

The exact factorization of the electron-nuclear wave function [1, 2, 3] allows to define the time-dependent potential energy surfaces (TDPESs) responsible for the nuclear dynamics and electron dynamics. Recently a novel coupled-trajectory mixed quantum-classical (CT-MQC) approach based on this TDPES has been developed [4], which accurately reproduces both nuclear and electron dynamics. Here we study the TDPES for laser-induced electron localization with a view to developing a MQC method for strong-field processes [5]. We show our recent progress in applying the CT-MQC approach to the systems with many degrees of freedom. [1] A. Abedi, N. T. Maitra, E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010). [2] Y. Suzuki, A. Abedi, N. T. Maitra, K. Yamashita, E. K. U. Gross, Phys. Rev. A, 89, 040501(R) (2014). [3] A. Abedi, F. Agostini, Y. Suzuki, E. K. U. Gross, Phys. Rev. Lett. 110, 263001 (2013); F. Agostini, A. Abedi, Y. Suzuki, S. K. Min, N. T. Maitra, E. K. U. Gross, J. Chem. Phys., 142, 084303 (2015). [4] S. K. Min, F. Agostini, E. K. U. Gross, Phys. Rev. Lett.,115, 073001, (2015). [5] Y. Suzuki, A. Abedi, N. T. Maitra, E. K. U. Gross, Phys. Chem. Chem. Phys., 17, 29271 (2015).   

Nuclear Quantum Effects in the Dynamics of Biologically Relevant Systems from First Principles

Understanding the structure and dynamics of biomolecules is crucial for unveiling the physics behind biology-related processes. These molecules are very flexible and stabilized by a delicate balance of weak (quantum) interactions, thus requiring the inclusion of anharmonic entropic contributions and an accurate description of the electronic and nuclear structure from quantum mechanics. We here join state of the art density-functional theory (DFT) and path integral molecular dynamics (PIMD) to gain quantitative insight into biologically relevant systems. Our design of a better and more efficient approximation to quantum time correlation functions based on PIMD (TRPMD [1,2]) enables the calculation of ab initio TCFs with which we calculate IR/vibrational spectra and diffusion coefficients. In stacked polyglutamine strands (structures often related to amyloid diseases) a combination of NQE and H-bond cooperativity provides a small free energy stabilization that we connect to a softening of high frequency modes, enhanced by nuclear quantum anharmonicity [3]. [1] Rossi, Ceriotti, Manolopoulos, JCP {\bf 140}, 234116 (2014); [2] Rossi et al., JCP {\bf 141}, 181101 (2014); Rossi, Fang, Michaelides, JPCL {\bf 6}, 4233 (2015)   

Properties of the Schr\"{o}dinger Theory for Electrons in External Fields

We consider electrons in external electrostatic ${\boldsymbol{\cal{E}}} ({\bf{r}}) = - {\boldsymbol{\nabla}} v ({\bf{r}})$ and magnetostatic ${\bf{B}} ({\bf{r}}) = {\boldsymbol{\nabla}} \times {\bf{A}} ({\bf{r}})$ fields. (The case of solely an electrostatic field constitutes a special case.) Via the `Quantal Newtonian' first law for the individual electron we prove the following: (i) In addition to the external electric and Lorentz fields, each electron experiences an internal field representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, the kinetic energy, the density, and the magnetic field; (ii) the scalar potential $v ({\bf{r}})$ arises from a curl-free field and is thus path-independent; (iii) the magnetic field ${\bf{B}} ({\bf{r}})$ appears explicitly in the Schr\"{o}dinger equation in addition to the vector potential ${\bf{A}} ({\bf{r}})$; (iv) The Schr\"{o}dinger equation can be written to exhibit its intrinsic self-consistent form. (The generalization of the conclusions to time-dependent external fields via the `Quantal Newtonian' second law follows.)