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Shepard C, Zhou R, Bost J, Carney TE, Yao Y, Kanai Y. Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT. J Chem Phys 2024; 161:024111. [PMID: 38984957 DOI: 10.1063/5.0211238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Accepted: 06/19/2024] [Indexed: 07/11/2024] Open
Abstract
The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.
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Affiliation(s)
- Christopher Shepard
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Ruiyi Zhou
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - John Bost
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Thomas E Carney
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
| | - Yi Yao
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
- Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
- Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
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2
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Mattiat J, Luber S. Comparison of Length, Velocity, and Symmetric Gauges for the Calculation of Absorption and Electric Circular Dichroism Spectra with Real-Time Time-Dependent Density Functional Theory. J Chem Theory Comput 2022; 18:5513-5526. [PMID: 36041170 DOI: 10.1021/acs.jctc.2c00644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A velocity and symmetric gauge implementation for real-time time-dependent density functional theory (RT-TDDFT) in the CP2K package using a Gaussian and plane wave approach is presented, including the explicit gauge-transformed contributions due to the nonlocal part of pseudopotentials. Absorption spectra of gas-phase α-pinene are calculated in length and velocity gauges in the long-wavelength approximation for the application of a δ pulse in linear and full order. The velocity gauge implementation is also applied to a solvated uracil molecule to showcase its use within periodic boundary conditions (PBC). For the calculation of the expectation value of the electric dipole moment in PBC, both the velocity representation and the modern theory of polarization give equivalent absorption spectra if a distributed reference point is used for the nonlocal term of the velocity operator. The discussion of linear response theory takes place in a unified framework in terms of linear response functions in propagator notation, distinguishing the parts of the linear response functions associated with perturbation and response. To further investigate gauge dependence, electric circular dichroism (ECD) spectra of α-pinene were calculated either as magnetic response to an electric field perturbation, in length or velocity gauge, or as electric response to a magnetic field perturbation in the symmetric gauge. Both approaches, electric and magnetic perturbations, have been found to yield equivalent ECD spectra.
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Affiliation(s)
- Johann Mattiat
- Department of Chemistry, University of Zurich, Zurich 8057, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Zurich 8057, Switzerland
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3
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Dreyer CE, Coh S, Stengel M. Nonadiabatic Born Effective Charges in Metals and the Drude Weight. PHYSICAL REVIEW LETTERS 2022; 128:095901. [PMID: 35302830 DOI: 10.1103/physrevlett.128.095901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
In insulators, Born effective charges describe the electrical polarization induced by the displacement of individual atomic sublattices. Such a physical property is at first sight irrelevant for metals and doped semiconductors, where the macroscopic polarization is ill defined. Here we show that, in clean conductors, going beyond the adiabatic approximation results in nonadiabatic Born effective charges that are well defined in the low-frequency limit. In addition, we find that the sublattice sum of the nonadiabatic Born effective charges does not vanish as it does in the insulating case, but instead is proportional to the Drude weight. We demonstrate these formal results with density functional perturbation theory calculations of Al and electron-doped SnS_{2} and SrTiO_{3}.
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Affiliation(s)
- Cyrus E Dreyer
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York, 11794-3800, USA
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
| | - Sinisa Coh
- Materials Science and Mechanical Engineering, University of California, Riverside, California 92521, USA
| | - Massimiliano Stengel
- Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, 08193 Bellaterra, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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4
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Mattiat J, Luber S. Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods. Helv Chim Acta 2021. [DOI: 10.1002/hlca.202100154] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Johann Mattiat
- Department of Chemistry University of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland
| | - Sandra Luber
- Department of Chemistry University of Zurich Winterthurerstrasse 190 CH-8057 Zurich Switzerland
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5
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Hekele J, Yao Y, Kanai Y, Blum V, Kratzer P. All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework. J Chem Phys 2021; 155:154801. [PMID: 34686041 DOI: 10.1063/5.0066753] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [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) is an attractive tool to model quantum dynamics by real-time propagation without the linear response approximation. Sharing the same technical framework of RT-TDDFT, imaginary-time time-dependent density functional theory (it-TDDFT) is a recently developed robust-convergence ground state method. Presented here are high-precision all-electron RT-TDDFT and it-TDDFT implementations within a numerical atom-centered orbital (NAO) basis function framework in the FHI-aims code. We discuss the theoretical background and technical choices in our implementation. First, RT-TDDFT results are validated against linear-response TDDFT results. Specifically, we analyze the NAO basis sets' convergence for Thiel's test set of small molecules and confirm the importance of the augmentation basis functions for adequate convergence. Adopting a velocity-gauge formalism, we next demonstrate applications for systems with periodic boundary conditions. Taking advantage of the all-electron full-potential implementation, we present applications for core level spectra. For it-TDDFT, we confirm that within the all-electron NAO formalism, it-TDDFT can successfully converge systems that are difficult to converge in the standard self-consistent field method. We finally benchmark our implementation for systems up to ∼500 atoms. The implementation exhibits almost linear weak and strong scaling behavior.
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Affiliation(s)
- Joscha Hekele
- Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
| | - Yi Yao
- Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - Volker Blum
- Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - Peter Kratzer
- Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, 47057 Duisburg, Germany
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6
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Shepard C, Zhou R, Yost DC, Yao Y, Kanai Y. Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation. J Chem Phys 2021; 155:100901. [PMID: 34525811 DOI: 10.1063/5.0057587] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.
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Affiliation(s)
- Christopher Shepard
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, USA
| | - Ruiyi Zhou
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, USA
| | - Dillon C Yost
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
| | - Yi Yao
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, USA
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, USA
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7
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Mattiat J, Luber S. Time Domain Simulation of (Resonance) Raman Spectra of Liquids in the Short Time Approximation. J Chem Theory Comput 2020; 17:344-356. [DOI: 10.1021/acs.jctc.0c00755] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Johann Mattiat
- Department of Chemistry, University of Zurich, Zurich 8057, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Zurich 8057, Switzerland
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8
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Mattiat J, Luber S. Vibrational (resonance) Raman optical activity with real time time dependent density functional theory. J Chem Phys 2019; 151:234110. [DOI: 10.1063/1.5132294] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- Johann Mattiat
- Department of Chemistry, University of Zurich, Zurich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Zurich, Switzerland
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9
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Mattiat J, Luber S. Electronic circular dichroism with real time time dependent density functional theory: Propagator formalism and gauge dependence. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2019.110464] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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10
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Silva J, Milne BF, Nogueira F. Theoretical Investigation of Single-Molecule Sensing Using Nanotube-Enhanced Circular Dichroism. J Phys Chem A 2018; 122:5666-5670. [DOI: 10.1021/acs.jpca.8b03676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jaime Silva
- CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal
| | - Bruce F. Milne
- CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal
- Coimbra Chemistry Centre, Department of Chemistry, University of Coimbra, Rua Larga, 3004-535 Coimbra, Portugal
- Nano-Bio Spectroscopy Group, University of the Basque Country (UPV-EHU), Centro Joxe Mari Korta, Avenida de Tolosa, 72, 20018 Donostia-San Sebastian, Spain
| | - Fernando Nogueira
- CFisUC, Department of Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal
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11
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Kim P, Ryoo JH, Park CH. Breakdown of the Chiral Anomaly in Weyl Semimetals in a Strong Magnetic Field. PHYSICAL REVIEW LETTERS 2017; 119:266401. [PMID: 29328719 DOI: 10.1103/physrevlett.119.266401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Indexed: 06/07/2023]
Abstract
The low-energy quasiparticles of Weyl semimetals are a condensed-matter realization of the Weyl fermions introduced in relativistic field theory. Chiral anomaly, the nonconservation of the chiral charge under parallel electric and magnetic fields, is arguably the most important phenomenon of Weyl semimetals and has been explained as an imbalance between the occupancies of the gapless, zeroth Landau levels with opposite chiralities. This widely accepted picture has served as the basis for subsequent studies. Here we report the breakdown of the chiral anomaly in Weyl semimetals in a strong magnetic field based on ab initio calculations. A sizable energy gap that depends sensitively on the direction of the magnetic field may open up due to the mixing of the zeroth Landau levels associated with the opposite-chirality Weyl points that are away from each other in the Brillouin zone. Our study provides a theoretical framework for understanding a wide range of phenomena closely related to the chiral anomaly in topological semimetals, such as magnetotransport, thermoelectric responses, and plasmons, to name a few.
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Affiliation(s)
- Pilkwang Kim
- Department of Physics, Seoul National University, Seoul 08826, Korea
| | - Ji Hoon Ryoo
- Department of Physics, Seoul National University, Seoul 08826, Korea
| | - Cheol-Hwan Park
- Department of Physics, Seoul National University, Seoul 08826, Korea
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12
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Andrade X, Strubbe D, De Giovannini U, Larsen AH, Oliveira MJT, Alberdi-Rodriguez J, Varas A, Theophilou I, Helbig N, Verstraete MJ, Stella L, Nogueira F, Aspuru-Guzik A, Castro A, Marques MAL, Rubio A. Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems. Phys Chem Chem Phys 2016; 17:31371-96. [PMID: 25721500 DOI: 10.1039/c5cp00351b] [Citation(s) in RCA: 192] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
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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Affiliation(s)
- Xavier Andrade
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA. and Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
| | - David Strubbe
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Umberto De Giovannini
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain
| | - Ask Hjorth Larsen
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain
| | - Micael J T Oliveira
- Unité Nanomat, Département de Physique, Université de Liège, Allée du 6 Août 17, B-4000 Liège, Belgium
| | - Joseba Alberdi-Rodriguez
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain and Dept. of Computer Architecture and Technology, University of the Basque Country UPV/EHU, M. Lardizabal, 1, 20018 Donostia-San Sebastian, Spain
| | - Alejandro Varas
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain
| | - Iris Theophilou
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Matthieu J Verstraete
- Unité Nanomat, Département de Physique, Université de Liège, Allée du 6 Août 17, B-4000 Liège, Belgium
| | - Lorenzo Stella
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, University Road, Belfast BT7 1NN, Northern Ireland, UK
| | - Fernando Nogueira
- Center for Computational Physics, University of Coimbra, Rua Larga, 3004-516 Coimbra, Portugal
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
| | - Alberto Castro
- Institute for Biocomputation and Physics of Complex Systems (BIFI) and Zaragoza Center for Advanced Modeling (ZCAM), University of Zaragoza, E-50009 Zaragoza, Spain and ARAID Foundation, María de Luna 11, Edificio CEEI Aragón, Zaragoza E-50018, Spain
| | - Miguel A L Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, Von-Seckendorff-Platz 1, 06120 Halle (Saale), Germany
| | - Angel Rubio
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, 20018 Donostia-San Sebastián, Spain and Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
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13
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Molteni E, Onida G, Tiana G. Conformational Dependence of the Circular Dichroism Spectra of Single Amino Acids from Plane-Waves-Based Density Functional Theory Calculations. J Phys Chem B 2015; 119:4803-11. [DOI: 10.1021/jp5118568] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- E. Molteni
- Department
of Physics, Università degli Studi di Milano, via Celoria
16, 20133 Milano, Italy
| | - G. Onida
- Department
of Physics, Università degli Studi di Milano, via Celoria
16, 20133 Milano, Italy
| | - G. Tiana
- Department
of Physics, Università degli Studi di Milano, via Celoria
16, 20133 Milano, Italy
- INFN, sezione
di Milano, via Celoria 16, 20133 Milano, Italy
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14
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Varsano D, Espinosa-Leal LA, Andrade X, Marques MAL, di Felice R, Rubio A. Towards a gauge invariant method for molecular chiroptical properties in TDDFT. Phys Chem Chem Phys 2009; 11:4481-9. [DOI: 10.1039/b903200b] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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15
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Chang E, Bussi G, Ruini A, Molinari E. Excitons in carbon nanotubes: an ab initio symmetry-based approach. PHYSICAL REVIEW LETTERS 2004; 92:196401. [PMID: 15169423 DOI: 10.1103/physrevlett.92.196401] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2003] [Indexed: 05/24/2023]
Abstract
The optical absorption spectrum of the carbon (4,2) nanotube is computed using an ab initio many-body approach which takes into account excitonic effects. We develop a new method involving a local basis set which is symmetric with respect to the screw-symmetry of the tube. Such a method has the advantages of scaling faster than plane-wave methods and allowing for a precise determination of the symmetry character of the single-particle states, two-particle excitations, and selection rules. The binding energy of the lowest, optically active states is approximately 0.8 eV. The corresponding exciton wave functions are delocalized along the circumference of the tube and localized in the direction of the tube axis.
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Affiliation(s)
- Eric Chang
- INFM National Center on NanoStructures and BioSystems at Surfaces (S3) and Dipartimento di Fisica, Università di Modena e Reggio Emilia, Via Campi 213/A, 41100 Modena, Italy
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16
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Pickard CJ, Mauri F. Nonlocal pseudopotentials and magnetic fields. PHYSICAL REVIEW LETTERS 2003; 91:196401. [PMID: 14611593 DOI: 10.1103/physrevlett.91.196401] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2003] [Indexed: 05/24/2023]
Abstract
We show how to describe the coupling of electrons to nonuniform magnetic fields in the framework of the widely used norm-conserving pseudopotential approximation for electronic structure calculations. Our derivation applies to magnetic fields that are smooth on the scale of the core region. The method is validated by application to the calculation of the magnetic susceptibility of molecules within density functional theory (DFT) in the local density approximation. Our results are compared with high-quality all-electron DFT results obtained using Gaussian basis sets and another recently proposed pseudopotential formalism.
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Affiliation(s)
- Chris J Pickard
- TCM Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom
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