Session V35: Focus Session: DFT VII: Time-Dependent Processes I: Driven Systems

Towards the ab-initio description of photo-induced processes

Excitons are prominent features in the optical spectra of periodic solids and molecular aggregates. Time-dependent density functional theory should, in principle, be able to describe excitonic effects. However, with standard functionals for the exchange-correlation (xc) kernel f$_{xc}$, such as adiabatic LDA and adiabatic GGA, excitonic features are completely absent. The construction of improved functionals for f$_{xc}$ yielding excitons has a long history. Here we propose a new parameter-free approximation for the xc kernel through an algorithm in which the exact Dyson equation for the response is solved self-consistently with an approximate expression for the kernel in terms of the dielectric function [PRL \textbf{107}, 186401 (2011)]. We apply this to the calculation of optical spectra for various small bandgap (Ge, Si, GaAs, AlN, TiO2, SiC), large bandgap (C, LiF, Ar, Ne) and magnetic (NiO) insulators. The calculated spectra are in very good agreement with experiment for this diverse set of materials, highlighting the universal applicability of the new kernel. These optical spectra are calculated with clamped nuclei. However, in a variety of optical phenomena, the coupling between electronic and nuclear motion plays an important role. Prominent examples are the process of vision and photo-synthesis. Standard approximations such as Ehrenfest dynamics, surface hopping, or nuclear wave-packet dynamics only partially capture the occurring non-adiabatic effects. As a first step towards a full ab-initio treatment of the coupled electron-nuclear system, we deduce an exact factorization of the complete wavefunction into a purely nuclear part and a many-electron wavefunction which parametrically depends on the nuclear configuration. We derive formally exact equations of motion for the nuclear and electronic wavefunction [PRL \textbf{105}, 123002 (2010)]. These exact equations lead to a rigorous definition of time-dependent potential energy surfaces as well as time-dependent geometric phases.   

Exact factorization of the time-dependent electron-nuclear wavefunction: Time-dependent potential energy surface

We have recently proved an exact decomposition of the electronic and nuclear degrees of freedom (Phys, Rev. Lett. 105 123002 (2010)) and introduced a set of coupled equations of motion for the electrons and nuclei that describe the evolution of the complete electron-nuclear system. The nuclear equation is particularly apealing being a Schroedinger equation with a time-dependent potential energy surface (TDPES) and a time-dependent vector potential as rigorous concepts, mediating the coupling between the nuclear and the electronic degrees of freedom in a formally exact way. By studying physically different cases, we demonstrate that the TDPES is a powerful tool to investigate molecular processes.   

Exact factorization of the full electron-nuclear wavefunction: A quantum-classical study

It was recently shown in [1] that the solution of the time-dependent Schr\"{o}dinger equation for a molecular system can be exactly factorized to an electronic and a nuclear contribution. In [1], the authors derived exact equations of motion for the coupled evolution of the electronic and nuclear wavefunctions, which are a good starting point to develop approximations, systematically. Based on this exact decomposition of the electron and nuclear motion, we present a quantum-classical scheme for the coupled electron-nuclear dynamics. Nuclear degrees of freedom evolve along a classical trajectory, affecting electronic motion and inducing quantum transitions, which in turn alter nuclear dynamics. Applications of the proposed method to model systems will be presented.\\[4pt] [1] A. Abedi, N.T. Maitra and E.K.U. Gross, \textsl{Phys. Rev. Lett.} \textbf{105} 123002 (2010).   

Time-dependent density functional theory for open quantum systems

We present the extension of time-dependent density functional theory (TDDFT) to the realm of open quantum systems (OQS). OQS-TDDFT allows a first principles description of electronic systems undergoing non-unitary dynamics due to coupling with a bath, such as that arising from molecular vibrations, solvent degrees of freedom or photon modes of the electromagnetic field. We first prove extensions of the Runge-Gross and van Leeuwen theorems to OQS-TDDFT, which rigorously establish it as a formally exact theory. We then discuss development of approximate OQS-TDDFT functionals, exact conditions on these functionals, as well as future challenges. Finally, we will discuss the application of OQS-TDDFT in obtaining broadened absorption spectra.   

Time-Dependent Electron Localization Functions, TDELF's, for Molecular Ionization and Harmonic Generation in Intense Laser Pulses

The nonlinear nonperturbative response of N2,CO2,OCS,CS2 are studied numerically by solutions of Kohn-Sham (KS) orbital equations in the presence of few cycle intense I$>$10$^{14}$ W/cm$^2$, 800nm laser pulses. It is found generally that ionization rates depend on different functionals and ionization also occurs from inner-shell KS orbitals .This is sensitive to laser-molecule orientation as predicted earlier [1]. Ionization rate maxima correspond to the alignment of maximum KS orbital densities with the laser polarization instead of orbital ionization potentials,Ip. These results are corroborated through time analysis of TDELF's where ionization occurs from lone pair or bond regions of the corresponding molecule at various times during the pulses. Time frequency analysis of Harmonic Generation spectra allow for identification of recollision times of ionized electrons with the parent ion.\\[4pt] [1] EF Penka, AD Bandrauk, Phys Rev A81, 023411(2010); 84, 035412(2011).   

TDDFT for nonlinear phenomena of light-matter interactions

Despite the success of linear-response schemes to describe excitations of many electron systems,many physical processes stemming from the interaction of light with matter are nonlinear in nature. In this talk we will address the problems and open questions related to the description of this phenomena with the goal of providing a sound description of laser-induced-population processes within TDDFT. Through the exact solution of a few electron system interacting with a monochromatic laser we highlight some common deficiencies of all adiabatic density functionals within time-dependent density-functional theory to handle photoinduced processes leading to population changes of many-body states. One prototype case is Rabi oscillations between the ground and an excited state when a monochromatic laser with a frequency close to the resonance is applied. All adiabatic functionals are not able to discern between resonant and nonresonant (detuned) Rabi oscillations. Only the inclusion of an appropriate memory dependence can correct the fictitious time-dependence of the resonant frequency. We extend this description to dynamical induced charge transfer processes and many body tunneling. Adiabatic functionals will fail similarly in the description of all processes involving a change in the population of states. We will show our recent advances in deriving a new memory-dependent functional. The description of photo-induced processes in chemistry, physics, and biology and the newfield of attosecond electron dynamics and high-intense lasers all demand fundamental functional developments going beyond the adiabatic approximation.   

Performance of the exact adiabatic density functional to describe Rabi physics

Through the exact solution of few-electron systems interacting with a monochromatic laser we study the performance of adiabatic density functionals within time-dependent density-functional theory (TDDFT) to reproduce Rabi oscillations. The non-linear dynamics of the Kohn-Sham (KS) system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We illustrate this effect by comparing the exact time-dependent many-body solution of a He-atom in one dimension and a few-site Hubbard model with the solution of TDDFT-KS equations for different adiabatic exchange-correlation functionals. Preventing the detuning introduces a new strong condition to be satisfied by approximate new xc-functionals.   

Curing pathologies of TDDFT with semiclassical electron correlation

Time-dependent density functional theory (TDDFT) has been identified as a prime candidate for describing the dynamics of atoms and molecules in strong laser fields. It would be especially useful in predicting the highly non-intuitive fields needed in the optimal control problem for photonic reagents. However TDDFT encounters a number of problems when simulating these systems, both in the functional approximation of the exchange and correlation potentials, but also for observables of interest, such as momentum distributions or ionization probabilities. Recently a method to overcome some of these problems was proposed[1], whereby an auxiliary semiclassical dynamics calculation produces a correlation potential, which is then used to drive a density-matrix propagation. This method incorporates memory, initial-state dependence, changing occupation numbers, all of which are known issues for TDDFT. In this talk we build on previous work[2] and examine this scheme for a number of model 1D systems including calculations for strong field dynamics, optimal control, non-sequential ionization, and double excitations [1] A.K. Rajam, I. Raczkowska,and N.T. Maitra, Phys. Rev. Lett. 105, 113002 (2010). [2] P. Elliott and N.T. Maitra, J. Chem. Phys. 135, 104110 (2011).   

Quantum dynamics integrators in a plane-wave implementation of time-dependent density functional theory

In order to develop our understanding of various dynamical phenomena in materials at the electronic-structure level, computational methods based on first-principles theory are indispensable. Such approaches can make significant contributions to improving materials for a wide range of applications reaching from photovoltaic cells to nuclear reactors. Time-dependent density functional theory is an efficient approach for describing the real-time quantum dynamics of electronic systems. However, the numerical integration of the time-dependent Kohn-Sham equations, i.e., including a density-dependent effective Hamiltonian, is highly non-trivial. We studied various integrators for propagating the single-particle wave functions explicitly in time, in order to achieve a highly-scalable implementation based on plane-waves and pseudo-potentials. We show that the fourth-order Runge-Kutta scheme is conditionally stable and accurate within this framework. Moreover, the application of our scheme to a system consisting of several hundreds of electrons unveils its excellent scalability and, hence, its applicability for large-scale simulations.   

The effect of cusps in time-dependent quantum mechanics

Spatial cusps in initial wavefunctions can lead to non-analytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor-expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time-analytic.   

Demonstration of the Gunnarsson-Lundqvist theorem and Lack of Hohenberg-Kohn Theorem for Excited States

By considering two noninteracting fermions in a 1-D infinite square well we demonstrate the following: (a) The GL theorem is satisfied for the lowest excited triplet state. There exists only one potential for this density so that the HK theorem is satisfied for this lowest excited state configuration. (b) For the second excited triplet state, there exists no other potential with the original orbital configuration that reproduces the density. However, (c) for the second excited triplet state, there exist other potentials with orbital configurations different from the original that reproduce the density. Thus, there is no HK theorem for this and other excited states. The orbitals of the other set of potentials are related to the original orbitals by a rotation. The exact new eigenvalues, and solutions for the potentials and orbitals including near and at the boundaries are provided.