Kohn-Sham self-interaction correction in real time

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

Analyzing Excitation-Energy Transfer Based on the Time-Dependent Density Functional Theory in Real Time

Excitation-energy transfer is a key step in processes such as photosynthesis that convert light into other forms of energy. Time-dependent density functional theory (DFT) in real time is ideal for the first-principles simulation of such processes due to its computational efficiency. We here demonstrate how real-time DFT can be used for analyzing excitation-energy transfer from first-principles. We discuss several measures of energy transfer that are based solely on the time-dependent density, are well founded in the DFT framework, allow for intuitive understanding and visualization, and reproduce important limiting cases of an analytical model. We demonstrate their usefulness in calculations for model systems, both with static nuclei and in the context of DFT-based Ehrenfest dynamics.

Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Self-interaction correction, electrostatic, and structural influences on time-dependent density functional theory excitations of bacteriochlorophylls from the light-harvesting complex 2

First-principles calculations offer the chance to obtain a microscopic understanding of light-harvesting processes. Time-dependent density functional theory can have the computational efficiency to allow for such calculations. However, the (semi-)local exchange-correlation approximations that are computationally most efficient fail to describe charge-transfer excitations reliably. We here investigate whether the inexpensive average density self-interaction correction (ADSIC) remedies the problem. For the systems that we study, ADSIC is even more prone to the charge-transfer problem than the local density approximation. We further explore the recently reported finding that the electrostatic potential associated with the chromophores' protein environment in the light-harvesting complex 2 beneficially shifts spurious excitations. We find a great sensitivity on the chromophores' atomistic structure in this problem. Geometries obtained from classical molecular dynamics are more strongly affected by the spurious charge-transfer problem than the ones obtained from crystallography or density functional theory. For crystal structure geometries and density-functional theory optimized ones, our calculations confirm that the electrostatic potential shifts the spurious excitations out of the energetic range that is most relevant for electronic coupling.

Molecular excitations from meta-generalized gradient approximations in the Kohn-Sham scheme

Meta-Generalized Gradient Approximations (meta-GGAs) can, in principle, include spatial and temporal nonlocality in time-dependent density functional theory at a much lower computational cost than functionals that use exact exchange. We here test whether a meta-GGA that has recently been developed with a focus on capturing nonlocal response properties and the particle number discontinuity can realize such features in practice. To this end, we extended the frequency-dependent Sternheimer formalism to the meta-GGA case. Using the Krieger-Li-Iafrate (KLI) approximation, we calculate the optical response for the selected paradigm molecular systems and compare the meta-GGA Kohn-Sham response to the one found with exact exchange and conventional (semi-)local functionals. We find that the new meta-GGA captures important properties of the nonlocal exchange response. The KLI approximation, however, emerges as a limiting factor in the evaluation of charge-transfer excitations.

First-Principles Modeling of Electronic Stopping in Complex Matter under Ion Irradiation

Electronic stopping refers to the dynamical energy-transfer process to electrons in matter from highly energetic charged particles such as high-velocity protons. We discuss recent progress in theoretical studies of electronic stopping in condensed matter under ion irradiation, focusing on modern electronic structure theory's role in enabling the study of electronic excitation dynamics that result from the energy transfer. In the last few decades, first-principles simulation approaches based on real-time time-dependent density functional theory have greatly advanced the field. While linear response theory is widely used to study electronic stopping processes, especially for simple solids, novel first-principles dynamics approaches now allow us to study chemically complex systems and also yield detailed descriptions of electronic excitations at the molecular scale. Outstanding challenges for further advancement of electronic stopping modeling are also discussed from the viewpoint of electronic structure theory.

Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional

Three properties of the exact energy functional of DFT are important in general and for spectroscopy in particular, but are not necessarily obeyed by approximate functionals. We explain what they are, why they are important, and how they are related yet inequivalent.

Identifying Electronic Modes by Fourier Transform from δ-Kick Time-Evolution TDDFT Calculations

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.

Shrinking Self-Interaction Errors with the Fermi-Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation

The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. In this article we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew [ J. Chem. Phys. 2014, 140, 121103] for performing self-interaction free calculations in density functional theory based on Fermi orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with the standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for practical density functional calculations without SIE.

Time-Dependent Multicomponent Density Functional Theory for Coupled Electron-Positron Dynamics

Electron-positron interactions have been utilized in various fields of science. Here we develop time-dependent multicomponent density functional theory to study the coupled electron-positron dynamics from first principles. We prove that there are coupled time-dependent single-particle equations that can provide the electron and positron density dynamics, and derive the formally exact expression for their effective potentials. Introducing the adiabatic local density approximation to time-dependent electron-positron correlation, we apply the theory to the dynamics of a positronic lithium hydride molecule under a laser field. We demonstrate the significance of the coupling between electronic and positronic motion by revealing the complex positron detachment mechanism and the suppression of electronic resonant excitation by the screening effect of the positron.

Charge transfer in time-dependent density functional theory

Charge transfer plays a crucial role in many processes of interest in physics, chemistry, and bio-chemistry. 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.

The adiabatic strictly-correlated-electrons functional: kernel and exact properties

We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.

Using optimally tuned range separated hybrid functionals in ground-state calculations: consequences and caveats

Optimally tuned range separated hybrid functionals are a new class of implicitly defined functionals. Their important new aspect is that the range separation parameter in these functionals is determined individually for each system by iteratively tuning it until a fundamental, non-empirical condition is fulfilled. Such functionals have been demonstrated to be extremely successful in predicting electronic excitations. In this paper, we explore the use of the tuning approach for predicting ground state properties. This sheds light on one of its downsides - the violation of size consistency. By analyzing diatomic molecules, we reveal size consistency errors up to several electron volts and find that binding energies cannot be predicted reliably. Further consequences of the consistent ground-state use of the tuning approach are potential energy surfaces that are qualitatively in error and an incorrect prediction of spin states. We discuss these failures, their origins, and possibilities for overcoming them.

Universal dynamical steps in the exact time-dependent exchange-correlation potential

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially nonlocal and time nonlocal dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of nonequilibrium dynamical situations relevant for modeling of photochemical or physical processes: field-free evolution of a nonstationary state, resonant local excitation, resonant complete charge transfer, and evolution under an arbitrary field. A lack of these steps in the usual approximations yields inaccurate dynamics, for example, predicting faster dynamics and incomplete charge transfer.

Negative differential resistance in a hybrid silicon-molecular system: resonance between the intrinsic surface-states and the molecular orbital

It has been a long-term desire to fabricate hybrid silicon-molecular devices by taking advantages of organic molecules and the existing silicon-based technology. However, one of the challenging tasks is to design applicable functions on the basis of the intrinsic properties of the molecules, as well as the silicon substrates. Here we demonstrate a silicon-molecular system that produces negative differential resistance (NDR) by making use of the well-defined intrinsic surface-states of the Si (111)-√3 × √3-Ag (R3-Ag/Si) surface and the molecular orbital of cobalt(II)-phthalocyanine (CoPc) molecules. From our experimental results obtained using scanning tunneling microscopy/spectroscopy, we find that NDR robustly appears at the Co(2+) ion centers of the CoPc molecules, independent of the adsorption configuration of the CoPc molecules and irrespective of doping type and doping concentration of the silicon substrates. Joint with first principle calculations, we conclude that NDR is originated from the resonance between the intrinsic surface-state band S(1) of the R3-Ag/Si surface and the localized unoccupied Co(2+)d(z(2)) orbital of the adsorbed CoPc molecules. We expect that such a mechanism can be generally used in other silicon-molecular systems.