Response Functions in TDDFT: Concepts and Implementation

Strubbe, David A.; Lehtovaara, Lauri; Rubio, Ángel; Marques, Miguel A. L.; Louie, Steven G.

doi:10.1007/978-3-642-23518-4_7

Cited by 18 publications

(16 citation statements)

References 99 publications

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“…An alternate approach to linear response is not to solve for the response function but rather for its poles (the excitation energies ω k ) and residues (e.g. electric dipole matrix elements d k ) [74]. The polarizability is given by 35) and the absorption cross-section is…”

Section: Linear Response In the Electron-hole Basismentioning

confidence: 99%

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Andrade

Strubbe

Giovannini

et al. 2015

Phys. Chem. Chem. Phys.

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457

399

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Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

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Section: Linear Response In the Electron-hole Basismentioning

confidence: 99%

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Andrade

Strubbe

Giovannini

et al. 2015

Phys. Chem. Chem. Phys.

Self Cite

457

399

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“…not just the lowest excitations. Finally, another formulation to obtain response from TDDFT is the Sternheimer approach, also known as density functional perturbation theory, or coupled perturbed Kohn-Sham theory, that operates directly in frequency-space but avoids the calculation of many unoccupied orbitals by instead considering perturbations of the occupied orbitals in frequency-space [37][38][39].…”

Section: A Linear Response Tddftmentioning

confidence: 99%

Charge transfer in time-dependent density functional theory

Maitra

2017

J. Phys.: Condens. Matter

140

151

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Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and biochemistry. In many applications the size of the systems involved calls for time-dependent density functional theory (TDDFT) to be used in their computational modeling, due to its unprecedented balance between accuracy and efficiency. However, although exact in principle, in practise approximations must be made for the exchange-correlation functional in this theory, and the standard functional approximations perform poorly for excitations which have a long-range charge-transfer component. Intense progress has been made in developing more sophisticated functionals for this problem, which we review. We point out an essential difference between the properties of the exchange-correlation kernel needed for an accurate description of charge-transfer between open-shell fragments and between closed-shell fragments. We then turn to charge-transfer dynamics, which, in contrast to the excitation problem, is a highly non-equilibrium, non-perturbative, process involving a transfer of one full electron in space. This turns out to be a much more challenging problem for TDDFT functionals. We describe dynamical step and peak features in the exact functional evolving over time, that are missing in the functionals currently used. The latter underestimate the amount of charge transferred and manifest a spurious shift in the charge transfer resonance position. We discuss some explicit examples.

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“…Neither Sternheimer approach [38][39][40][41] , nor real-time propagation 14 need calculation of unoccupied states. They also have a favourable scaling of O(N 2 ) with the system size N as compared, for example, to O(N 3 ) for the sum over states (Refs.…”

Section: Numerical Solution Of Liouville Equationmentioning

confidence: 99%

“…The commutator [r,ρ] corresponding to i∂ kρk in reciprocal space is determined in the present paper within the k · p theory 38,40,41 (see equations on pages 2 and 3 Supplementary information). The polarizability α 0νµ in the absence of the magnetic field and the contribution α νµ,γ to the polarizability in the presence of the magnetic field (α νµ = α 0νµ +α νµ,γ B γ ) are obtained from the current response as…”

Section: Numerical Solution Of Liouville Equationmentioning

confidence: 99%

Orbital magneto-optical response of periodic insulators from first principles

et al. 2019

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Magneto-optical response, i.e. optical response in the presence of a magnetic field, is commonly used for characterization of materials and in optical communications. However, quantum mechanical description of electric and magnetic fields in crystals is not straightforward as the position operator is ill defined. We present a reformulation of the density matrix perturbation theory for timedependent electromagnetic fields under periodic boundary conditions, which allows us to treat the orbital magneto-optical response of solids at the ab initio level. The efficiency of the computational scheme proposed is comparable to standard linear-response calculations of absorption spectra and the results of tests for molecules and solids agree with the available experimental data. A clear signature of the valley Zeeman effect is revealed in the continuum magneto-optical spectrum of a single layer of hexagonal boron nitride. The present formalism opens the path towards the study of magneto-optical effects in strongly driven low-dimensional systems.arXiv:1806.09886v4 [cond-mat.mtrl-sci]

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Response Functions in TDDFT: Concepts and Implementation

Cited by 18 publications

References 99 publications

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Charge transfer in time-dependent density functional theory

Orbital magneto-optical response of periodic insulators from first principles

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