All-electron time-dependent density functional theory with finite elements: Time-propagation approach

Lehtovaara, Lauri; Havu, Ville; Puska, Martti J.

doi:10.1063/1.3651239

Cited by 20 publications

(23 citation statements)

References 50 publications

(49 reference statements)

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“…However, the second observation is that the strong peak shifts to a higher energy position after we strengthen the artificial absorption, which is negative for a simulation. A similar phenomenon has been also reported in [18]. To deliver a reliable result, an appropriate setup is needed to balance the above two kinds of effect of the mask function.…”

Section: Calculation Of Photoabsorption Spectrasupporting

confidence: 58%

“…For three dimensional simulations, Lehtovaara et al extend their all-electron finite element solver for the Kohn-Sham equation [17] to the RT-TDKS case [18]. Excellent numerical results can be observed there.…”

Section: Introductionmentioning

confidence: 85%

“…Recently, a new negative imaginary kinetic energy (NIK) method is proposed in [18]. This method is one kind of PML method, with some modifications from the standard PML implementation.…”

Section: The Absorbing Boundary Conditionsmentioning

confidence: 99%

“…To reduce the condition number and accelerate the convergence, a preconditioning process becomes necessary. In [18], an effective preconditioner, (α A + T ) −1 , is presented. Here α is a constant, A is the mass matrix, and T is the stiff matrix.…”

Section: An Algebraic Multigrid Solver For the Complex Symmetric Systemmentioning

confidence: 99%

“…Excellent numerical results can be observed there. To generate an appropriate mesh, an elegant method is introduced in [17,18], say, the mesh is created by merging highly nonuniform but symmetric atomic meshes to a global, nonuniform, and unstructured mesh. Similar mesh generation methods can also be observed from [29,25].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

Bao

Liu

2015

Journal of Computational Physics

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Section: Calculation Of Photoabsorption Spectrasupporting

confidence: 58%

Section: Introductionmentioning

confidence: 85%

“…Recently, a new negative imaginary kinetic energy (NIK) method is proposed in [18]. This method is one kind of PML method, with some modifications from the standard PML implementation.…”

Section: The Absorbing Boundary Conditionsmentioning

confidence: 99%

Section: An Algebraic Multigrid Solver For the Complex Symmetric Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

Bao

Liu

2015

Journal of Computational Physics

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Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

Kamban

Christensen

Søndergaard

et al. 2020

Physica Status Solidi (b)

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A finite-difference time-domain (FDTD) scheme with perfectly matched layers (PMLs) is considered for solving the time-dependent Schrödinger equation and simulating the laser-induced ionization of two systems: 1) an electron initially bound to a 1D δ potential and 2) excitons in carbon nanotubes (CNTs). The performance of PMLs based on different absorption functions is compared, where slowly growing functions are found to be preferable. PMLs are shown to be able to reduce the computational domain, and thus the required numerical resources, by several orders of magnitude. This is demonstrated by testing the proposed method against an FDTD approach without PMLs and a very large computational domain. It is shown that PMLs outperform the well-known exterior complex scaling (ECS) technique for short-range potentials when implemented in FDTD. For long-range potentials such as in CNTs, however, ECS performs better than PMLs when propagating over many periods.

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A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

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The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all-electron electronic structure calculations in general-the linear combination of atomic orbitals (LCAO) method-is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform allelectron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.atomic calculations, density functional theory, diatomic calculations, fully numerical electronic structure theory, Hartree-Fock | INTRODUCTIONThanks to decades of development in approximate density functionals and numerical algorithms, density functional theory [1,2] (DFT) is now one of the cornerstones of computational chemistry and solid-state physics. [3][4][5] Since atoms are the basic building block of molecules, a number of popular density functionals [6][7][8][9][10] have been parametrized using ab initio data on noble gas atoms; these functionals have been used in turn as the starting point for the development of other functionals. A comparison of the results of density-functional calculations to accurate ab initio data on atoms has, however, recently sparked controversy on the accuracy of a number of recently published, commonly used density functionals. [11][12][13][14][15][16][17][18][19][20][21] This underlines that there is still room for improvement in DFT even for the relatively simple case of atomic studies.The development and characterization of new density functionals require the ability to perform accurate atomic calculations. Because atoms are the simplest chemical systems, atomic calculations may seem simple; however, they are in fact sometimes surprisingly challenging. For instance, a long-standing discrepancy between the theoretical and experimental electron affinity and ionization potential of gold has been resolved only very recently with high-level ab initio calculations. [22] Atomic calculations can also be used to formulate efficient starting guesses for molecular electronic structure calculations via either the atomic density [23,24] or the atomic potential as discussed in Ref. [25].

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All-electron time-dependent density functional theory with finite elements: Time-propagation approach

Cited by 20 publications

References 50 publications

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

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