Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Zhu, Ying; Herbert, John M.

doi:10.1063/1.5004675

Cited by 55 publications

(92 citation statements)

References 66 publications

(121 reference statements)

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“…[4] As an alternative to the linear extrapolation scheme described above, an exponential PC scheme has also been suggested recently. [16] Another popular technique for time integration uses the modified midpoint unitary transformation (MMUT) approach which preserves the time reversal symmetry. [17] In contrast to the above schemes (SCF and PC), MMUT requires only one Fock matrix construction per time step.…”

Section: Predictor-corrector Schemementioning

confidence: 99%

“…However, it only allows for very small time steps. [16] Furthermore, the above schemes, allow to check on-the-fly for divergence of the propagation which is not the case for MMUT. [16] 3…”

Section: Predictor-corrector Schemementioning

confidence: 99%

“…[6,9] Due to its increasing popularity, RT-TDDFT has been implemented in several software packages like GAUSSIAN, NWCHEM, OCTOPUS, QBOX, Q-CHEM, SIESTA, etc. [4,7,8,[10][11][12][13][14][15][16][17][18][19][20][21][22] One of the limitations of RT-TDDFT is that the exchange correlation part of the Kohn-Sham (KS) matrix is generally non-local in both space and time. It is also formally a functional of the initial wave function and the entire history of the density.…”

Section: Introductionmentioning

confidence: 99%

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Real‐time time‐dependent density functional theory using density fitting and the continuous fast multipole method

2020

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An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the selfconsistent field as well as the predictor-corrector time integration schemes. The Coulomb contribution to the Kohn-Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two-and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.

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Section: Predictor-corrector Schemementioning

confidence: 99%

“…However, it only allows for very small time steps. [16] Furthermore, the above schemes, allow to check on-the-fly for divergence of the propagation which is not the case for MMUT. [16] 3…”

Section: Predictor-corrector Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Real‐time time‐dependent density functional theory using density fitting and the continuous fast multipole method

2020

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“…That said, for large systems the finite-∆t error may be more easily controllable as compared to errors engendered by truncation of the excitation space in LR-TDDFT, because the former can be reduced with smaller time steps and longer propagation time, whereas enlarging the excitation space may encounter hardware (i.e., storage) limitations. Because the TDKS and LR-TDDFT approaches are formally 20,[25][26][27] and operationally 38,39 equivalent in the limit of a weak perturbation to the ground-state density, the TDKS approach can be used to reveal the true TDDFT spectrum in the absence of any truncations.…”

Section: Introductionmentioning

confidence: 99%

Broadband X-Ray Absorption Spectra from Time-Dependent Kohn-Sham Calculations

Zhu¹,

Alam²,

Herbert

2021

Preprint

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We present a protocol for calculation of K-edge x-ray absorption spectra using time-dependent Kohn-Sham (TDKS) calculations, also known as "real-time" time-dependent density functional theory (TDDFT). In principle, the entire absorption spectrum (at all wavelengths) can be computed via Fourier transform of the time-dependent dipole moment function, following a perturbation of the ground-state density and propagation of time-dependent Kohn-Sham molecular orbitals. In practice, very short time steps are required to obtain an accurate spectrum, which increases the cost, but the use of Pade approximants significantly reduces the length of time propagation that is required. Spectra that are well converged with respect to the corresponding linear-response (LR-)TDDFT result can be obtained with < 10 fs of propagation time. Use of complex absorbing potentials helps to remove artifacts at high energies that otherwise result from the use of a finite atom-centered Gaussian basis set. Benchmark results, comparing TDKS to LR-TDDFT, are presented for several small molecules at the carbon and oxygen K-edges, demonstrating good agreement with experiment without the need for specialized basis sets. Whereas LR-TDDFT is a reasonable approach to obtain the near-edge structure, that approach requires hundreds of states and quickly becomes cost prohibitive for large systems, even when the core\slash valence separation approximation is used to remove most of the occupied states from the excitation manifold. We demonstrate the cost-effective TDKS approach by application to a copper dithiolene complex, where binding of a ligand is detectable via shifts in the sulfur K-edge.

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“…We refer the reader to the Refs. [7][8][9] for a general introduction, and make a quick summary here (some of the following ideas have been tested in combination with TDDFT [10][11][12][13][14][15][16][17][18][19][20][21] ):…”

Section: Introductionmentioning

confidence: 99%

Propagators for Quantum-Classical Models: Commutator-Free Magnus Methods

Pueyo

Blanes

Castro

2020

J. Chem. Theory Comput.

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We consider the numerical propagation of models that combine both quantum and classical degrees of freedom -usually, electrons and nuclei, respectively. We focus, in our computational examples, on the case in which the quantum electrons are modeled with time-dependent density-functional theory, although the methods discussed below can be used with any other level of theory. Often, for these so-called quantum-classical molecular dynamics models, one uses some propagation technique to deal with the quantum part, and a different one for the classical equations. While the resulting procedure may in principle be consistent, it can however spoil some of the properties of the methods, such as the accuracy order with respect to the time step or the preservation of the equations geometrical structure. Few methods have been developed specifically for hybrid quantum-classical models. We propose using the same method for both the quantum and classical particles, in particular one family of techniques that proves to be very efficient for the propagation of Schrödinger-like equations: the (quasi)-commutator

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Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

Cited by 55 publications

References 66 publications

Real‐time time‐dependent density functional theory using density fitting and the continuous fast multipole method

Real‐time time‐dependent density functional theory using density fitting and the continuous fast multipole method

Broadband X-Ray Absorption Spectra from Time-Dependent Kohn-Sham Calculations

Propagators for Quantum-Classical Models: Commutator-Free Magnus Methods

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