Session W35: Focus Session: DFT VIII: Time-Dependent Processes II: Excitations

Watching excitons move: the time-dependent transition density matrix

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.   

A minimal TDDFT model for excitons

Optical processes in insulators and semiconductors, including excitonic effects, can be accurately described with linear-response TDDFT, provided one uses suitable exchange-correlation kernels. We have developed a conceptually and computationally simple formalism for calculating exciton binding energies with TDDFT, based on a two-band approximation. This formalism is implemented in a one-dimensional Kronig-Penney model, and we discuss the requirements for excitonic binding in this model. The performance of different types of exchange-correlation kernels (long- versus short-ranged, adiabatic versus nonadiabatic) is analyzed, with a particular emphasis on the excitonic Rydberg series.   

Nonlinear ultrafast optical response in organic molecular crystals

We analyze possible nonlinear excitonic effects in the organic molecule crystals by using a combined time-dependent DFT and many-body approach. In particular, we analyze possible effects of the time-dependent (retarded)interaction between different types of excitations, Frenkel excitons, charge transfer excitons and excimers, on the electric and the optical response of the system. We pay special attention to the case of constant electric field and ultrafast pulses, including that of four-wave mixing experiments. As a specific application we examine the optical excitations of pentacene nanocrystals and compare the results with available experimental data.[1] Our results demostrate that the nonlinear effects can play an important role in the optical response of these systems. [1] A. Kabakchiev, ``Scanning Tunneling Luminescence of Pentacene Nanocrystals'', PhD Thesis (EPFL, Lausanne, 2010).   

Electronic and dielectric properties of organic photovoltaic compounds from first principles

The initial step towards the design of organic photovoltaic (OPV) devices from first principles is to predict the electronic spectra and dielectric responses of molecular and polymer OPV compounds to quantitative accuracy [{\it Phys. Rev. B} {\bf 71}, 041306 (2005)]. To date, determining the frontier levels and dielectric properties of materials within conventional density-functional theory approximations has been elusive. To address current limitations, orbital-dependent density-functional methods, namely, hybrid density-functional theory (hybrid-DFT) and self-interaction-corrected density-functional theory (SIC-DFT) approximations, represent promising alternatives. In this presentation, we provide a critical comparison of hybrid-DFT and SIC-DFT functionals in determining electronic energies for families of OPV materials. We demonstrate that SIC-DFT based upon Koopmans' condition [{\it Phys. Rev. B} {\bf 82}, 115121 (2010)] is apt at describing donor and acceptor levels within 0.1-0.4 eV and 0.2-0.6 eV relative to experiment. Furthermore, SIC-DFT dielectric responses for semiconducting polymers are predicted in close agreement with more expensive wave-function methods, thereby allowing the accurate and computationally tractable description of donor-acceptor molecular complexes.   

Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density functional theory (TDDFT) must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a frequency-dependent discontinuity of the XC kernel which diverges in the dissociation limit. This divergency compensates for the exponentially small overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction.   

Density Functional Resonance Theory: The Complex Density Function, Orbital Energies and Lifetimes, and Results for Simple Systems

Density Functional Resonance Theory (DFRT) is a recently developed complex-scaled version of ground-state Density Functional Theory (DFT) for metastable systems. This work is a detailed study of the formalism itself, its consequences and its application. The meaning of the complex ``density'' function, which is used as the primary variable, is discussed along with its possible application to study the reactivity of metastable systems. In addition, orbital energies and lifetimes are defined and related to physical quantities. Finally, results for energies and lifetimes are presented for simple systems.   

Meta-GGA-based adiabatic time-dependent density-functional theory

The local-density approximation (LDA) to the ground-state density functional theory (DFT) is well known to allow for a generalization to the time-dependent case [1]. The assumption of the adiabaticity of the process greatly simplifies the theory. The further extension of the time-dependent DFT (TDDFT) to the generalized gradient approximation (GGA) is trivial. Here we address lifting the adiabatic TDDFT to the third rung of the ``Jacobs ladder'' [2] : We work out the kinetic energy density dependent (meta-GGA) TDDFT formalism. The new theory possesses remarkable properties not present in LDA and GGA: (i) It is non-local with respect to the particle density; (ii) In the case of bulk semiconductors, it supports the 1/q$^2$ singularity of the exchange-correlation kernel, where q is the wave-vector, the latter being important to reproduce the excitonic effect. We also present illustrative calculations of the optical absorption in semiconductors [3]. \\[4pt] [1] A. Zangwill and P. Soven, Phys. Rev. A, 21, 1561 (1980).\\[0pt] [2] J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).\\[0pt] [3] V. U. Nazarov and G. Vignale, Phys. Rev. Lett. 107, 216402(2011).   

Describing electronic excitations using electron-hole density functional theory (eh-DFT)

The electron-hole interaction play a crucial role in calculating optical properties of atoms, molecules, clusters and solids. In this talk, the density functional treatment of electron-hole quasiparticle interaction will be presented in the framework of electron-hole density functional theory(eh-DFT). The electron-hole correlation functional plays a central role in accuracy of any eh-DFT calculations. In the present work, the development of eh-correlation functional using the eh-reduced density matrix will be presented. Benchmark calculation using the developed functional will be compared with HF, full CI, R12-full CI, and explicitly correlated Hartree-Fock calculations. Exciton binding energies in CdSe quantum dots have been calculated and the eh-DFT results will be compared with experimental and pseudopotential+CI results. Discussion on construction of electron-hole adiabatic connection curve (ACC) using density-constrained minimization will be presented and the results from the ACC will be compared with eh-DFT calculations. Finally, similarity and difference between the GW+Bethe-Salpeter method and eh-DFT approach for treating electron-hole interaction will be presented.   

Applying state-of-the-art signal processing to time-dependent density functional theory

Real-time time-dependent density functional theory (TDDFT) is a computationally efficient method that can be used to calculate optical absorption spectra, circular dichroism spectra, and other properties including non-linear ones. These properties are often obtained via time-propagation methods, and a discrete Fourier transform is used to convert from the time domain to the frequency domain. However, a Fourier transform requires long time propagations to resolve spectra, especially if they contain closely-spaced frequencies. Instead, we apply a state-of-the-art signal processing technique known as compressed sensing to the spectral analysis of electron dynamics. Compared to a Fourier transform, compressed sensing provides higher-resolution absorption spectra with shorter propagation times. In the systems we study, the method requires about 80\% less time series data to obtain comparable frequency resolution, thus reducing total computational cost by approximately a factor of five. By combining the computational efficiency and parallelizability of real-time TDDFT for large systems with the dramatic reduction in simulation time enabled by compressed sensing, we increase the feasibility of studying electron dynamics in large biological molecules and organic photovoltaics.   

Density Functional Theory Investigation of Tunable Surface Composition of CdS Quantum Dots

It has recently been observed that surface composition of CdS QDs greatly affects photoluminescence. Band edge emission is quenched in sulfur terminated CdS QDs and recovered when QDs were cadmium terminated. However, in all cases the absorption spectra remained relatively unchanged. To understand the origin of this phenomenon, the density of states in a stoichiometric, Cd rich, and S rich dots was investigated using density functional theory (DFT). It was found the in the S rich system states within the band gap were introduced, providing a channel for non-radiative electronic relaxation. Gap states were also introduced in the Cd rich system compared to the stoichiometric system, but a significant band gap remained in even the most Cd rich systems. Finally, time dependent (TD)DFT was used to calculate the spectra of the various systems. It was found that created gap states were largely optically inactive. Therefore the new states would not participate in optical absorption or emission, but could participate in electron phonon relaxation. This study clarifies the role of surface defects in QD optical properties and provides a route for tuning those optical properties by controlling surface composition.   

First-Principles Approach to Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

A first-principles density functional theory (DFT)-based approach is developed [1] to determine chemical contributions to surface-enhanced Raman spectroscopy (SERS) for molecular adsorbates on metal surfaces. While SERS applications are often directed at sensing trace amounts of chemical species, quantitative calculations of how Raman spectra of molecules are altered on chemisorption [1], coupled to experiments, can contribute significantly to our understanding of the electronic structure of the metal-adsorbate interface. For two adsorbates on Au -- benzene thiol and trans-1,2-two(4-pyridyl) ethylene (BPE) -- DFT calculations of the static Raman tensor demonstrate a strong mode-dependent modification of Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential. Based on our calculations, we introduce a straightforward analysis to extract ``chemical enhancement'' from measurements, and demonstrate how SERS spectra of BPE change as a function of the relative fraction of BPE molecules chemisorbed to the substrate.\\[4pt] [1] Zayak et al, Phys. Rev. Lett. 106, 083003 (2011)   

Electron-Hole Pairs during Adsorption Dynamics of O$_2$ on Pd(100) -- Exciting or not?

{\it Ab initio} modeling can provide important atomistic insights into the dynamics of elementary reaction steps in heterogeneous catalysis. But already an apparently simple example like the adsorption of O$_2$ on a frozen Pd(100) surface brings up several fundamental challenges: The corresponding six-dimensional potential energy surface (PES) is required, and excitations of electron-hole (eh) pairs as well as the transition from the $^3\Sigma_{\rm g}^-$ spin-triplet in the gas phase to a singlet-like state of adsorbed oxygen might require to go beyond the Born-Oppenheimer approximation. We tackle the PES by neural network interpolation, based on a coordinate transformation that correctly includes and exploits the underlying symmetry. Classical molecular dynamics thereon yields the initial sticking coefficient in good agreement with experimental data. Scrutinizing this result, we calculate spin-resolved eh pair spectra for several trajectories of different statistical relevance using a computationally appealing perturbative approach building on time-dependent DFT.\footnote{J. Meyer and K. Reuter, New J. Phys. {\bf 13}, 085010 (2011)} Although non-adiabatic energy losses do not exceed 5\% of the chemisorption energy, their importance for the spin transition is finally discussed.   

Self-consistent GW calculations with basis of dominant products

Hedin's $GW$ approximation (GWA) is a well known method to study charged excitations in electronic systems with a moderate computational cost [1]. Already one-shot GWA delivers a considerable improvement if compared with Green's functions from density-functional theory (DFT). However, the one-shot results are dependent on the used starting point. This unphysical dependence can be eliminated by iterating a $GW$ calculation to self-consistency. We implemented self-consistent GWA for molecules [2], within our original framework of dominant products basis. We use the DFT calculation by SIESTA code as starting point. The framework allowed to calculate Green's functions on a fine frequency mesh for such small molecules as benzene. We demonstrate the level of independence on starting point achievable within pseudo-potential framework, validating the implementation. Effects of the self-consistency on the interacting Green's function will be discussed along with different levels of self-consistency and mixing schemes. Finally, we compare the self-consistency with so-called quasi-particle self-consistent $GW$ [3]. \\[0pt] [1] F.Aryasetiawan, O.Gunnarsson, Rep. Prog. Phys. 61, 237 (1998).\\[0pt] [2] D.Foerster, P.Koval, D.Sanchez Portal, J. Chem. Phys. 135, 074105 (2011).\\[0pt] [3] T.Kotani, M.van Schilfgaarde, S.V.Falleev, Phys. Rev. B 76, 165106 (2007).