Exact exchange-like electric response from a meta-generalized gradient approximation: A semilocal realization of ultranonlocality.

We review the concept of ultranonlocality in density functional theory and the relation between ultranonlocality, the derivative discontinuity of the exchange energy, and the static electric response in extended molecular systems. We present the construction of a new meta-generalized gradient approximation for exchange that captures the ultranonlocal response to a static electric field in very close correspondence to exact exchange, yet at a fraction of its computational cost. This functional, in particular, also captures the dependence of the response on the system size. The static electric polarizabilities of hydrogen chains and oligo-acetylene molecules calculated with this meta-GGA are quantitatively close to the ones obtained with exact exchange. The chances and challenges associated with the construction of meta-GGAs that are intended to combine a substantial derivative discontinuity and ultranonlocality with an accurate description of electronic binding are discussed.

Meta-generalized gradient approximations in time dependent generalized Kohn-Sham theory: Importance of the current density correction.

We revisit the use of Meta-Generalized Gradient Approximations (mGGAs) in time-dependent density functional theory, reviewing conceptual questions and solving the generalized Kohn-Sham equations by real-time propagation. After discussing the technical aspects of using mGGAs in combination with pseudopotentials and comparing real-space and basis set results, we focus on investigating the importance of the current-density based gauge invariance correction. For the two modern mGGAs that we investigate in this work, TASK and r2SCAN, we observe that for some systems, the current density correction leads to negligible changes, but for others, it changes excitation energies by up to 40% and more than 0.8 eV. In the cases that we study, the agreement with the reference data is improved by the current density correction.

Delocalized electronic excitations and their role in directional charge transfer in the reaction center of Rhodobacter sphaeroides.

In purple bacteria, the fundamental charge-separation step that drives the conversion of radiation energy into chemical energy proceeds along one branch-the A branch-of a heterodimeric pigment-protein complex, the reaction center. Here, we use first principles time-dependent density functional theory (TDDFT) with an optimally-tuned range-separated hybrid functional to investigate the electronic and excited-state structure of the six primary pigments in the reaction center of Rhodobacter sphaeroides. By explicitly including amino-acid residues surrounding these six pigments in our TDDFT calculations, we systematically study the effect of the protein environment on energy and charge-transfer excitations. Our calculations show that a forward charge transfer into the A branch is significantly lower in energy than the first charge transfer into the B branch, in agreement with the unidirectional charge transfer observed experimentally. We further show that the inclusion of the protein environment redshifts this excitation significantly, allowing for energy transfer from the coupled Qx excitations. Through analysis of transition and difference densities, we demonstrate that most of the Q-band excitations are strongly delocalized over several pigments and that both their spatial delocalization and charge-transfer character determine how strongly affected they are by thermally-activated molecular vibrations. Our results suggest a mechanism for charge-transfer in this bacterial reaction center and pave the way for further first-principles investigations of the interplay between delocalized excited states, vibronic coupling, and the role of the protein environment in this and other complex light-harvesting systems.

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.

Assessing density functional theory in real-time and real-space as a tool for studying bacteriochlorophylls and the light-harvesting complex 2.

We use real-time density functional theory on a real-space grid to calculate electronic excitations of bacteriochlorophyll chromophores of the light-harvesting complex 2 (LH2). Comparison with Gaussian basis set calculations allows us to assess the numerical trust range for computing electron dynamics in coupled chromophores with both types of techniques. Tuned range-separated hybrid calculations for one bacteriochlorophyll as well as two coupled ones are used as a reference against which we compare results from the adiabatic time-dependent local density approximation (TDLDA). The tuned range-separated hybrid calculations lead to a qualitatively correct description of the electronic excitations and couplings. They allow us to identify spurious charge-transfer excitations that are obtained with the TDLDA. When we take into account the environment that the LH2 protein complex forms for the bacteriochlorophylls, we find that it substantially shifts the energy of the spurious charge-transfer excitations, restoring a qualitatively correct electronic coupling of the dominant excitations also for TDLDA.

Linear response time-dependent density functional theory without unoccupied states: The Kohn-Sham-Sternheimer scheme revisited.

The Sternheimer approach to time-dependent density functional theory in the linear response regime is attractive because of its computational efficiency. The latter results from avoiding the explicit calculation of unoccupied orbitals and from the basic structure of the Sternheimer equations, which naturally lend themselves to far-reaching parallelization. In this article, we take a fresh look at the frequency-dependent Sternheimer equations. We first give a complete, self-contained derivation of the equations that complements previous derivations. We then discuss several aspects of an efficient numerical realization. As a worked example, we compute the photoabsorption spectra of small hydrogenated silicon clusters and confirm that for these the quality of the Kohn-Sham eigenvalues is more important than the effects of the exchange-correlation kernel. Finally, we demonstrate how triplet excitations can readily be computed from the Sternheimer approach.

Accurate Evaluation of Real-Time Density Functional Theory Providing Access to Challenging Electron Dynamics.

We demonstrate that electronic excitations and their transition densities can be obtained from real-time density functional theory calculations with great accuracy by relating the data from numerical propagation to the analytical form of the electronic response after a boost excitation. The latter is derived in this article. This approach facilitates quantitatively obtaining oscillator strengths, identifying excitations that carry very small oscillator strengths, and assessing electronic couplings from transition densities based on comparatively short propagation times. These features are of interest in particular for studying light-harvesting systems. For demonstration purposes, we study the Q band excitations of bacteriochlorophyll a (BChl a) and calculate coupling strengths between two BChl a's to check the validity of the dipole-dipole and pure Coulomb coupling mechanisms. For further illustration, we investigate the paradigm test system Na4 and the coupling between two Na2 dimers.