Combining Local Range Separation and Local Hybrids: A Step in the Quest for Obtaining Good Energies and Eigenvalues from One Functional.

Some of the most successful exchange-correlation approximations in density functional theory are "hybrids", i.e., they rely on combining semilocal density functionals with exact nonlocal Fock exchange. In recent years, two classes of hybrid functionals have emerged as particularly promising: range-separated hybrids on the one hand, and local hybrids on the other hand. These functionals offer the hope to overcome a long-standing "observable dilemma", i.e., the fact that density functionals typically yield either a good description of binding energies, as obtained, e.g., in global and local hybrids, or physically interpretable eigenvalues, as obtained, e.g., in optimally tuned range-separated hybrids. Obtaining both of these characteristics from one and the same functional with the same set of parameters has been a long-standing challenge. We here discuss combining the concepts of local range separation and local hybrids as part of a constraint-guided quest for functionals that overcome the observable dilemma.

Predicting fundamental gaps accurately from density functional theory with non-empirical local range separation.

We present an exchange-correlation approximation in which the Coulomb interaction is split into long- and short-range components and the range separation is determined by a non-empirical density functional. The functional respects important constraints, such as the homogeneous and slowly varying density limits, leads to the correct long-range potential, and eliminates one-electron self-interaction. Our approach is designed for spectroscopic purposes and closely approximates the piecewise linearity of the energy as a function of the particle number. The functional's accuracy for predicting the fundamental gap in generalized Kohn-Sham theory is demonstrated for a large number of systems, including organic semiconductors with a notoriously difficult electronic structure.

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.

Understanding Primary Charge Separation in the Heliobacterial Reaction Center.

The homodimeric reaction center of heliobacteria retains features of the ancestral reaction center and can thus provide insights into the evolution of photosynthesis. Primary charge separation is expected to proceed in a two-step mechanism along either of the two reaction center branches. We reveal the first charge-separation step from first-principles calculations based on time-dependent density functional theory with an optimally tuned range-separated hybrid and ab initio Born-Oppenheimer molecular dynamics: the electron is most likely localized on the electron transfer cofactor 3 (EC3, OH-chlorophyll a), and the hole on the adjacent EC2. Including substantial parts of the surrounding protein environment into the calculations shows that a distinct structural mechanism is decisive for the relative energetic positioning of the electronic excitations: specific charged amino acids in the vicinity of EC3 lower the energy of charge-transfer excitations and thus facilitate efficient charge separation. These results are discussed considering recent experimental insights.

Hybrid functionals with local range separation: Accurate atomization energies and reaction barrier heights.

Range-separated hybrid approximations to the exchange-correlation density functional mix exact and semi-local exchange in a position-dependent manner. In their conventional form, the range separation is controlled by a constant parameter. Turning this constant into a density functional leads to a locally space-dependent range-separation function and thus a more powerful and flexible range-separation approach. In this work, we explore the self-consistent implementation of a local range-separated hybrid, taking into account a one-electron self-interaction correction and the behavior under uniform density scaling. We discuss different forms of the local range-separation function that depend on the electron density, its gradient, and the kinetic energy density. For test sets of atomization energies, reaction barrier heights, and total energies of atoms, we demonstrate that our best model is a clear improvement over common global range-separated hybrid functionals and can compete with density functionals that contain multiple empirical parameters. Promising results for equilibrium bond lengths, harmonic vibrational frequencies, and vertical ionization potentials further underline the potential and flexibility of our approach.

Investigating Primary Charge Separation in the Reaction Center of Heliobacterium modesticaldum.

We compute the primary charge separation step in the homodimeric reaction center (RC) of Heliobacterium modesticaldum from first principles. Using time-dependent density functional theory with the optimally tuned range-separated hybrid functional ωPBE, we calculate the excitations of a system comprising the special pair, the adjacent accessory bacteriochlorophylls, and the most relevant parts of the surrounding protein environment. The structure of the excitation spectrum can be rationalized from coupling of the individual bacteriochlorophyll pigments similar to molecular J- and H-aggregates. We find excited states corresponding to forward-charge transfer along the individual branches of the RC of H. modesticaldum. In the spectrum, these are located at an energy between the coupled Qy and Qx transitions. With ab initio Born-Oppenheimer molecular dynamics simulations, we reveal the influence of thermal vibrations on the excited states. The results show that the energy gap between the coupled Qy and the forward-charge transfer excitations is ∼0.4 eV, which we consider to conflict with the concept of a direct transfer mechanism. Our calculations, however, reveal a certain spectral overlap of the forward-charge transfer and the coupled Qx excitations. The reliability and robustness of the results are demonstrated by several numerical tests.

Superadiabatic Forces via the Acceleration Gradient in Quantum Many-Body Dynamics.

We apply the formally exact quantum power functional framework (J. Chem. Phys. 2015, 143, 174108) to a one-dimensional Hooke's helium model atom. The physical dynamics are described on the one-body level beyond the density-based adiabatic approximation. We show that gradients of both the microscopic velocity and acceleration field are required to correctly describe the effects due to interparticle interactions. We validate the proposed analytical forms of the superadiabatic force and transport contributions by comparison to one-body data from exact numerical solution of the Schrödinger equation. Superadiabatic contributions beyond the adiabatic approximation are important in the dynamics and they include effective dissipation.