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Herbert JM, Zhu Y, Alam B, Ojha AK. Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response. J Chem Theory Comput 2023; 19:6745-6760. [PMID: 37708349 DOI: 10.1021/acs.jctc.3c00673] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/16/2023]
Abstract
We simulate X-ray absorption spectra at elemental K-edges using time-dependent density functional theory (TDDFT) in both its conventional linear-response implementation and its explicitly time-dependent or "real-time" formulation. Real-time TDDFT simulations enable broadband spectra calculations without the need to invoke frozen occupied orbitals ("core/valence separation"), but we find that these spectra are often contaminated by transitions to the continuum that originate from lower-energy core and semicore orbitals. This problem becomes acute in triple-ζ basis sets, although it is sometimes sidestepped in double-ζ basis sets. Transitions to the continuum acquire surprisingly large dipole oscillator strengths, leading to spectra that are difficult to interpret. Meaningful spectra can be recovered by means of a filtering technique that decomposes the spectrum into contributions from individual occupied orbitals, and the same procedure can be used to separate L- and K-edge spectra arising from different elements within a given molecule. In contrast, conventional linear-response TDDFT requires core/valence separation but is free of these artifacts. It is also significantly more efficient than the real-time approach, even when hundreds of individual states are needed to reproduce near-edge absorption features and even when Padé approximants are used to reduce the real-time simulations to just 2-4 fs of time propagation. Despite the cost, the real-time approach may be useful to examine the validity of the core/valence separation approximation.
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Affiliation(s)
- John M Herbert
- Department of Chemistry & Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
- Chemical Physics Graduate Program, The Ohio State University, Columbus, Ohio 43210, United States
| | - Ying Zhu
- Department of Chemistry & Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
- Chemical Physics Graduate Program, The Ohio State University, Columbus, Ohio 43210, United States
| | - Bushra Alam
- Department of Chemistry & Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Avik Kumar Ojha
- Department of Chemistry & Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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Moitra T, Konecny L, Kadek M, Rubio A, Repisky M. Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy. J Phys Chem Lett 2023; 14:1714-1724. [PMID: 36757216 PMCID: PMC9940299 DOI: 10.1021/acs.jpclett.2c03599] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.
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Affiliation(s)
- Torsha Moitra
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Marius Kadek
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physics, Northeastern University, Boston, Massachusetts 02115, United States
- Algorithmiq
Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics (CCQ), The Flatiron Institute, 162 Fifth Avenue, New York New York 10010, United States
- Nano-Bio
Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco, 20018 San Sebastian, Spain
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, 84104 Bratislava, Slovakia
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Ye L, Wang H, Zhang Y, Liu W. Self-Adaptive Real-Time Time-Dependent Density Functional Theory for X-ray Absorptions. J Chem Phys 2022; 157:074106. [DOI: 10.1063/5.0106250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Real-time time-dependent density functional theory (RT-TDDFT) can in principle access the whole absorption spectrum of a many-electron system exposed to a narrow pulse. However, this requires an accurate and efficient propagator for the numerical integration of the time-dependent Kohn-Sham equation. While a low-order time propagator is already sufficient for the low-lying valence absorption spectra, it is no longer the case for the X-ray absorption spectra (XAS) of systems composed even only of light elements, for which the use of a high-order propagator is indispensable. It is then crucial to choose a largest possible time step and a shortest possible simulation time, so as to minimize the computational cost. To this end, we propose here a robust AutoPST approach to determine automatically (Auto) the propagator (P), step (S), and time (T) for relativistic RT-TDDFT simulations of XAS.
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Affiliation(s)
| | - Hao Wang
- Shandong University - Qingdao Campus, China
| | | | - Wenjian Liu
- Qingdao Institue for Theoretical and Computational Sciences, Shandong University, China
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