Kernel Of Time-dependent Density Functional Theory Research Articles

Combining mBJ exchange potential and bootstrap kernel of TDDFT to compute optical spectra of solids

One of the fundamental challenges in calculating the optical properties of crystalline materials is the accurate description of exciton effects so as to make it computationally viable for studying large systems. We combine the modified Becke-Johnson (mBJ) exchange potential and bootstrap kernel (BSK) of time-dependent density functional theory (TDDFT) to compute the imaginary part of the dielectric function of a variety of semiconductors and insulators (Si, GaAs, NiO, TiO2, LiF, LiCl, SrTiO3 and NaMgF3). The results are compared with the experimental data available in the literature. We also compute their dielectric functions using the random phase approximations (RPA) to verify the effect of the BSK method on the optical spectra of these compounds. We conclude that TDDFT+BSK+mBJ calculations can determine the optical spectra of the solids in good agreement with the experimental data (except for small-energy gap materials such as Si and GaAs) with low computational cost, and using a fully ab initio procedure.

Predictive optical photoabsorption of Ag24Au(DMBT)18 - via efficient TDDFT simulations.

We report a computational study via time-dependent density-functional theory (TDDFT) methods of the photo-absorption spectrum of an atomically precise monolayer-protected cluster (MPC), the Ag24Au(DMBT)18 single negative anion, where DMBT is the 2,4-dimethylbenzenethiolate ligand. The use of efficient simulation algorithms, i.e., the complex polarizability polTDDFT approach and the hybrid-diagonal approximation, allows us to employ a variety of exchange-correlation (xc-) functionals at an affordable computational cost. We are thus able to show, first, how the optical response of this prototypical compound, especially but not exclusively in the absorption threshold (low-energy) region, is sensitive to (1) the choice of the xc-functionals employed in the Kohn-Sham equations and the TDDFT kernel and (2) the choice of the MPC geometry. By comparing simulated spectra with precise experimental photoabsorption data obtained from room temperature down to low temperatures, we then demonstrate how a hybrid xc-functional in both the Kohn-Sham equations and the diagonal TDDFT kernel at the crystallographically determined experimental geometry is able to provide a consistent agreement between simulated and measured spectra across the entire optical region. Single-particle decomposition analysis tools finally allow us to understand the physical reason for the failure of non-hybrid approaches.

Design of auxiliary systems for spectroscopy.

The Kohn-Sham system is the prototypical example of an auxiliary system that targets, in principle exactly, an observable like the electronic density without the need to calculate the complicated many-body wavefunction. Although the Kohn-Sham system does not describe excited-state properties directly, it also represents a very successful strategy guideline for many spectroscopy applications. Here we propose a generalization of the Kohn-Sham idea. In many situations one is interested only in limited answers to specific questions, whereas in state-of-the-art approaches a lot of information is generally calculated that is not needed for the interpretation of experimental spectra. For example, when the target is a spectrum S(ω) like the optical absorption of a solid, within time-dependent density-functional theory (TDDFT) one calculates the whole response function χ(r,r',ω). Analogously, within many-body perturbation theory (MBPT) one calculates the whole one-particle Green's function G(r,r',ω), while only the total spectral function A(ω) is needed for angle-integrated photoemission spectra. In this contribution, we advocate the possibility of designing auxiliary systems with effective potentials or kernels that target only the specific spectral properties of interest and are simpler than the self-energy of MBPT or the exchange-correlation kernel of TDDFT. In particular, we discuss the fundamentals and prototypical applications of simplified effective kernels for optical absorption and spectral potentials for photoemission, and we discuss how to express these potentials or kernels as functionals of the density.

Power Series Approximation for the Correlation Kernel Leading to Kohn-Sham Methods Combining Accuracy, Computational Efficiency, and General Applicability.

A power series approximation for the correlation kernel of time-dependent density-functional theory is presented. Using this approximation in the adiabatic-connection fluctuation-dissipation (ACFD) theorem leads to a new family of Kohn-Sham methods. The new methods yield reaction energies and barriers of unprecedented accuracy and enable a treatment of static (strong) correlation with an accuracy of high-level multireference configuration interaction methods but are single-reference methods allowing for a black-box-like handling of static correlation. The new methods exhibit a better scaling of the computational effort with the system size than rivaling wave-function-based electronic structure methods. Moreover, the new methods do not suffer from the problem of singularities in response functions plaguing previous ACFD methods and therefore are applicable to any type of electronic system.

Studies of spuriously shifting resonances in time-dependent density functional theory.

Adiabatic approximations in time-dependent density functional theory (TDDFT) will in general yield unphysical time-dependent shifts in the resonance positions of a system driven far from its ground-state. This spurious time-dependence is explained in Fuks et al. [Phys. Rev. Lett. 114, 183002 (2015)] in terms of the violation of an exact condition by the non-equilibrium exchange-correlation kernel of TDDFT. Here we give details on the derivation and discuss reformulations of the exact condition that apply in special cases. In its most general form, the condition states that when a system is left in an arbitrary state, the TDDFT resonance position for a given transition in the absence of time-dependent external fields and ionic motion is independent of the state. Special cases include the invariance of TDDFT resonances computed with respect to any reference interacting stationary state of a fixed potential, and with respect to any choice of appropriate stationary Kohn-Sham reference state. We then present several case studies, including one that utilizes the adiabatically exact approximation, that illustrate the conditions and the impact of their violation on the accuracy of the ensuing dynamics. In particular, charge-transfer across a long-range molecule is hampered, and we show how adjusting the frequency of a driving field to match the time-dependent shift in the charge-transfer resonance frequency results in a larger charge transfer over time.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem.

The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation approximations.

Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. A 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density-functional theory

We identify the key property that the exchange-correlation (XC) kernel of time-dependent density-functional theory must have in order to describe long-range charge-transfer excitations. We show that the discontinuity of the XC potential as a function of particle number induces a space- and frequency-dependent discontinuity of the XC kernel that diverges as $r\ensuremath{\rightarrow}\ensuremath{\infty}$. In a combined donor-acceptor system, the same discontinuity compensates for the vanishing overlap between the acceptor and donor orbitals, thereby yielding a finite correction to the Kohn-Sham eigenvalue differences. This mechanism is illustrated to first order in the Coulomb interaction.

The Absorption of Diamondoids from Time-dependent Density Functional Calculations

ABSTRACTDiamondoids are small diamond nanocrystals with perfect hydrogenated surfaces. Recent absorption measurements showed that the spectrum of diamondoids exhibit features that are not understood from the theoretical point of view, e.g. optical gaps are only slightly larger than the gap of bulk diamond which runs against the quantum confinement effect. Previous calcula-tions, even beyond standard density functional theory (DFT), failed to obtain the experimental optical gaps (Eg) of diamondoids. We show that all-electron time-dependent DFT (TD-DFT) calculations including the PBE0 hybrid functional in the TD-DFT kernel are able to provide quantitatively accurate results. Our calculations demonstrate that Rydberg transitions govern the low energy part of the absorption spectrum, even for relatively large nanodiamonds result-ing in low Eg. Since the optical gap of these diamondoids lies in the ultraviolet spectral re-gion, we investigated whether simple adsorbates of the surface are able to shift the gap towards the infrared region. We found that a double bonded sulfur atom at the surface results in a sub-stantial gap reduction.

Optical absorption of diamond nanocrystals fromab initiodensity-functional calculations

Absorption spectrum of small nanodiamonds, i.e., diamondoids has been recently measured exhibiting features that are not understood. Previous calculations, even beyond standard density-functional theory (DFT), failed to obtain the experimental optical gaps $({E}_{\text{g}})$ of diamondoids. We show that all-electron time-dependent DFT (TD-DFT) calculations including hybrid functional in the TD-DFT kernel are able to provide quantitatively accurate results. Our calculations demonstrate that Rydberg transitions are characteristic even for relatively large nanodiamonds resulting in low ${E}_{\text{g}}$. The nonmonotonic size dependence of ${E}_{\text{g}}$ is explained by symmetry considerations.

Reconstructing the adiabatic exchange-correlation kernel of time-dependent density-functional theory

The interacting and the Kohn-Sham static density-density response functions for different one-dimensional two-electron singlet systems are reconstructed numerically. From their inverse we obtain the exact static exchange-correlation kernel. This quantity represents the adiabatically exact approximation of the frequency-dependent exchange-correlation kernel that is crucial for time-dependent linear density-response theory. We investigate its performance for nonlocal perturbations and analyze its sum rule properties. We also compute the adiabatically exact transition energies that follow from the static kernel within linear-response theory.

Double excitations in finite systems

Time-dependent density-functional theory (TDDFT) is widely used in the study of linear response properties of finite systems. However, there are difficulties in properly describing excited states, which have double- and higher-excitation characters, which are particularly important in molecules with an open-shell ground state. These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchange-correlation (xc) kernel, the calculated excitation energies have a strict single-excitation character and are fewer than the real ones. A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character. We introduce a frequency-dependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems. In order to achieve this, we use the Bethe-Salpeter equation with a dynamically screened Coulomb interaction W(omega), which can describe these excitations, and from this we obtain the xc kernel. Using a two-electron model system, we show that the frequency dependence of W does indeed introduce the double excitations that are instead absent in any static approximation of the electron-hole screening.

Autoionizing resonances in time-dependent density functional theory

Autoionizing resonances that arise from the interaction of a bound single-excitation with the continuum can be accurately captured with the presently used approximations in time-dependent density functional theory (TDDFT), but those arising from a bound double excitation cannot. In the former case, we explain how an adiabatic kernel, which has no frequency-dependence, can yet generate the strongly frequency-dependent resonant structures in the interacting response function, not present in the Kohn-Sham response function. In the case of the bound double-excitation, we explain that a strongly frequency-dependent kernel is needed, and derive one as an a posteriori correction to the usual adiabatic approximations in TDDFT. Our approximation becomes exact for an isolated resonance in the limit of weak interaction, where one discrete state interacts with one continuum. We derive a "Fano TDDFT kernel" that reproduces the Fano lineshape within the TDDFT formalism, and also a dressed kernel, that operates on top of an adiabatic approximation. We illustrate our results on a simple model system.

Including nonlocality in the exchange-correlation kernel from time-dependent current density functional theory: Application to the stopping power of electron liquids

We develop a scheme for building the scalar exchange-correlation (XC) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time-dependent current density functional theory (TDCDFT) and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. As an application of this general scheme, we calculate the dynamical XC contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.

Exact exchange kernel for time-dependent density-functional theory

An exact expression for the exchange kernel of time-dependent density-functional theory, the frequency-dependent functional derivative of the exchange potential with respect to the density, is derived. The expression is simple enough to be applied in practice. A simple and transparent derivation of the coupled Kohn–Sham equation of time-dependent density-functional theory is given. Modified coupled Kohn–Sham equations are presented that are especially well suited for an “exact-exchange” treatment of excitation energies, polarizabilities, and other linear response properties. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 265–277, 1998