Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

131 p.

Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals.

Time-dependent density functional theory (TDDFT) has broad application in the study of electronic response, excitation and transport. To extend such application to large and complex systems, we develop a reformulation of TDDFT equations in terms of non-orthogonal localized molecular orbitals (NOLMOs). NOLMO is the most localized representation of electronic degrees of freedom and has been used in ground state calculations. In atomic orbital (AO) representation, the sparsity of NOLMO is transferred to the coefficient matrix of molecular orbitals (MOs). Its novel use in TDDFT here leads to a very simple form of time propagation equations which can be solved with linear-scaling effort. We have tested the method for several long-chain saturated and conjugated molecular systems within the self-consistent charge density-functional tight-binding method (SCC-DFTB) and demonstrated its accuracy. This opens up pathways for TDDFT applications to large bio- and nano-systems.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nanoelectronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master equation with the well-known time-dependent density functional theory. The key ingredients of this paper include (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e., the device); and (iii) the construction of Kohn-Sham master equations for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOMs) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along with the propagation of the Kohn-Sham master equation and the EOMs of the auxiliary functions.

Time-dependent R -matrix theory for ultrafast atomic processes

We describe an ab initio nonperturbative time-dependent R-matrix theory for ultrafast atomic processes. This theory enables investigations of the interaction of few-femtosecond and -attosecond pulse lasers with complex multielectron atoms and atomic ions. A derivation and analysis of the basic equations are given, which propagate the atomic wave function in the presence of the laser field forward in time in the internal and external R-matrix regions. To verify the accuracy of the approach, we investigate two-photon ionization of Ne irradiated by an intense laser pulse and compare current results with those obtained using the R-matrix Floquet method and an alternative time-dependent method. We also verify the capability of the current approach by applying it to the study of two-dimensional momentum distributions of electrons ejected from Ne due to irradiation by a sequence of 2 as light pulses in the presence of a 780 nm laser field.

Density-potential mapping in time-dependent density-functional theory

The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schroedinger equation with a potential that depends nonlocally on the wave function.

Ultra-fast spin dynamics in the 2s2p^2 configuration of C^+ studied by time-dependent R-matrix theory

We employ time-dependent R-matrix theory to study ultra-fast dynamics in the doublet 2s2p(2) configuration of C+ for a total magnetic quantum number M = 1. In contrast to the dynamics observed for M = 0, ultra-fast dynamics for M = 1 is governed by spin dynamics in which the 2s electron acts as a flag rather than a spectator electron. Under the assumption that m(S) = 1/2, m(2s) = 1/2 allows spin dynamics involving the two 2p electrons, whereas m(2s) = -1/2 prevents spin dynamics of the two 2p electrons. For a pump-probe pulse scheme with (h) over bar omega(pump) = 10.9 eV and (h) over bar omega(probe) = 16.3 eV and both pulses six cycles long, little sign of spin dynamics is observed in the total ionization probability. Signs of spin dynamics can be observed, however, in the ejected-electron momentum distributions. We demonstrate that the ejected-electron momentum distributions can be used for unaligned targets to separate the contributions of initial M = 0 and M = 1 levels. This would, in principle, allow unaligned target ions to be used to obtain information on the different dynamics in the 2s2p(2) configuration for the M = 0 and M = 1 levels from a single experime

Atomic harmonic generation in time-dependent R-matrix theory

We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity, or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390-nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code, finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.

Time-dependent density functional theory study of charge transfer in collisions

We study the charge transfer between colliding ions, atoms, or molecules, within time-dependent density functional theory. Two particular cases are presented, the collision between a proton and a Helium atom, and between a gold atom and a butane molecule. In the first case, proton kinetic energies between 16 keV and 1.2 MeV are considered, with impact parameters between 0.31 and 1.9 angstrom. The partial transfer of charge is monitored with time. The total cross-section is obtained as a function of the proton kinetic energy. In the second case, we analyze one trajectory and discuss spin-dependent charge transfer between the different fragments.

Macroscopic limit of time-dependent density-functional theory for adiabatic local approximations of the exchange-correlation kernel

Time-dependent density-functional theory is a rather accurate and efficient way to compute electronic excitations for finite systems. However, in the macroscopic limit (systems of increasing size), for the usual adiabatic random-phase, local-density, or generalized-gradient approximations, one recovers the Kohn-Sham independent-particle picture, and thus the incorrect band gap. To clarify this trend, we investigate the macroscopic limit of the exchange-correlation kernel in such approximations by means of an algebraical analysis complemented with numerical studies of a one-dimensional tight-binding model. We link the failure to shift the Kohn-Sham spectrum of these approximate kernels to the fact that the corresponding operators in the transition space act only on a finite subspace.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

The solution of the time-dependent Schrodinger equation for systems of interacting electrons is generally a prohibitive task, for which approximate methods are necessary. Popular approaches, such as the time-dependent Hartree-Fock (TDHF) approximation and time-dependent density functional theory (TDDFT), are essentially single-configurational schemes. TDHF is by construction incapable of fully accounting for the excited character of the electronic states involved in many physical processes of interest; TDDFT, although exact in principle, is limited by the currently available exchange-correlation functionals. On the other hand, multiconfigurational methods, such as the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach, provide an accurate description of the excited states and can be systematically improved. However, the computational cost becomes prohibitive as the number of degrees of freedom increases, and thus, at present, the MCTDHF method is only practical for few-electron systems. In this work, we propose an alternative approach which effectively establishes a compromise between efficiency and accuracy, by retaining the smallest possible number of configurations that catches the essential features of the electronic wavefunction. Based on a time-dependent variational principle, we derive the MCTDHF working equation for a multiconfigurational expansion with fixed coefficients and specialise to the case of general open-shell states, which are relevant for many physical processes of interest. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3600397]

Time-dependent R-matrix theory applied to two-photon double ionization of He

We introduce a time-dependent R-matrix theory generalized to describe double-ionization processes. The method is used to investigate two-photon double ionization of He by intense XUV laser radiation. We combine a detailed B-spline-based wave-function description in an extended inner region with a single-electron outer region containing channels representing both single ionization and double ionization. A comparison of wave-function densities for different box sizes demonstrates that the flow between the two regions is described with excellent accuracy. The obtained two-photon double-ionization cross sections are in excellent agreement with other cross sections available. Compared to calculations fully contained within a finite inner region, the present calculations can be propagated over the time it takes the slowest electron to reach the boundary.

Harmonic generation by noble-gas atoms in the near-IR regime using ab initio time-dependent R-matrix theory

We demonstrate the capability of ab initio time-dependent R-matrix theory to obtain accurate harmonic generation spectra of noble-gas atoms at near-IR wavelengths between 1200 and 1800 nm and peak intensities up to 1.8 × 10^(14) W/cm^(2). To accommodate the excursion length of the ejected electron, we use an angular-momentum expansion up to Lmax=279. The harmonic spectra show evidence of atomic structure through the presence of a Cooper minimum in harmonic generation for Kr, and of multielectron interaction through the giant resonance for Xe. The theoretical spectra agree well with those obtained experimentally.