Insights From Exact Exchange-Correlation Kernels

Abstract

The exact exchange-correlation (xc) kernel $f_{\mathrm{xc}}(x,x^{\prime },\omega )$ of linear response time-dependent density functional theory is computed over a wide range of frequencies, for three canonical one-dimensional finite systems. Methods used to ensure the numerical robustness of $f_{\mathrm{xc}}$ are set out. The frequency dependence of $f_{\text{xc}}$ is found to be due largely to its analytic structure, i.e. its singularities at certain frequencies, which are required in order to capture particular transitions, including those of double excitation character. However, within the frequency range of the first few interacting excitations, $f_{\mathrm{xc}}$ is approximately frequency independent, meaning the exact adiabatic approximation $f_{\mathrm{xc}}(\omega =0)$ remedies the failings of the local density approximation and random phase approximation for these lowest transitions. The key differences between the exact $f_{\mathrm{xc}}$ and its common approximations are analyzed, and cannot be eliminated by exploiting the limited gauge freedom in $f_{\mathrm{xc}}$. The optical spectrum benefits from using as accurate as possible an $f_{\mathrm{xc}}$ and ground-state xc potential, while maintaining exact compatibility between the two is of less importance.

References in corpus (26)

• Progress in Time-Dependent Density-Functional Theory
• Time-dependent density functional theory: Past, present, and future
• Excitonic effects in solids described by time-dependent density functional theory
• Perspectives on double-excitations in TDDFT
• Excitations in time-dependent density-functional theory
• Assessment of exchange-correlation functionals for the calculation of dynamical properties of small clusters in TDDFT
• Bound excitons in time-dependent density-functional-theory: optical and energy-loss spectra
• Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_{xc}(r) of the homogeneous electron gas
• Charge-Transfer in Time-Dependent Density Functional Theory
• The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems
• Excitonic optical spectrum of semiconductors obtained by time-dependent density-functional theory with the exact-exchange kernel
• A brief compendium of time-dependent density-functional theory
• Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory
• Linear density response function within the time-dependent exact-exchange approximation
• Accurate Ground State Energies of Solids and Molecules from Time Dependent Density Functional Theory
• Long-range excitations in time-dependent density functional theory
• Challenging Adiabatic Time-dependent Density Functional Theory with a Hubbard Dimer: The Case of Time-Resolved Long-Range Charge Transfer
• Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels
• Exact time-dependent density-functional potentials for strongly correlated tunneling electrons
• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory
• Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms
• Linear response time-dependent density functional theory of the Hubbard dimer
• Exact Density-Functionals with Initial-State Dependence and Memory
• Nonadiabatic Time-Dependent Spin-Density Functional Theory for strongly correlated systems
• Exact exchange-correlation kernels for optical spectra of model systems
• Comparison of local density functionals based on electron gas and finite systems

Cited by in corpus (4)

• Non-Adiabatic Approximations in Time-Dependent Density Functional Theory: Progress and Prospects
• A Snapshot of Time-Dependent Density-Functional Theory
• Excitonic effects in time-dependent density functional theory from zeros of the density response
• Accurate Total Energies from the Adiabatic-Connection Fluctuation-Dissipation Theorem