Electronic excitations from a linear-response range-separated hybrid scheme

Photoionization and core resonances from range-separated time-dependent density-functional theory for open-shell states: Example of the lithium atom

We consider the calculations of photoionization spectra and core resonances of open-shell systems using range-separated time-dependent density-functional theory. Specifically, we use the time-dependent range-separated hybrid (TDRSH) scheme, combining a long-range Hartree-Fock exchange potential and kernel with a short-range potential and kernel from a local density-functional approximation, and the time-dependent locally range-separated hybrid (TDLRSH) scheme, which uses a local range-separation parameter. To efficiently perform the calculations, we formulate a spin-unrestricted linear-response Sternheimer approach in a non-orthogonal B-spline basis set using appropriate frequency-dependent boundary conditions. We illustrate this approach on the Li atom, which suggests that TDRSH and TDLRSH are adequate simple methods for estimating the single-electron photoionization spectra of open-shell systems.

Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom

We explore the merits of linear-response range-separated time-dependent density-functional theory (TDDFT) for the calculation of photoionization spectra. We consider two variants of range-separated TDDFT, namely, the time-dependent range-separated hybrid (TDRSH) scheme, which uses a global range-separation parameter, and the time-dependent locally range-separated hybrid (TDLRSH), which uses a local range-separation parameter, and compare with standard time-dependent local-density approximation (TDLDA) and time-dependent Hartree-Fock (TDHF). We show how to calculate photoionization spectra with these methods using the Sternheimer approach formulated in a non-orthogonal B-spline basis set with appropriate frequency-dependent boundary conditions. We illustrate these methods on the photoionization spectrum of the Be atom, focusing, in particular, on the core resonances. Both the TDRSH and TDLRSH photoionization spectra are found to constitute a large improvement over the TDLDA photoionization spectrum and a more modest improvement over the TDHF photoionization spectrum.

A general range-separated double-hybrid density-functional theory

A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order Møller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.

Excited states using the simplified Tamm-Dancoff-Approach for range-separated hybrid density functionals: development and application

The recently introduced sTDA methodology [S. Grimme, J. Chem. Phys., 2013, 138, 244104] to compute excitation spectra of huge molecular systems is extended to range-separated hybrid (RSH) density functionals. The three empirical parameters of the method which describe a screened two-electron interaction are obtained for some common RSH functionals (ωB97 family, CAM-B3LYP, LC-BLYP) from a fit to theoretical SCS-CC2 reference vertical excitation energies for a set of small to medium-sized chromophores. The method is cross-validated on a set of inter- and intramolecular charge transfer states and a set composed of typical valence transitions. Overall small deviations from reference data of only about 0.2-0.4 eV are found with best performance for CAM-B3LYP and ωB97X-D3. To demonstrate versatility and robustness of the new methodology, applications (the UV/Vis spectrum of the pyridine polymer and the ECD spectrum of (P)-[11]helicene) and frequently used charge transfer examples are discussed. In one case, 11 000+ excited electronic states of a system containing 330 atoms were calculated. We show that the asymptotically correct sTDA-RSH combination yields results often superior to those based on global hybrids and that it opens up new possibilities for the computation of excited states in materials science and bio-molecular systems.

Excitation energies along a range-separated adiabatic connection

We present a study of the variation of total energies and excitation energies along a range-separated adiabatic connection. This connection links the non-interacting Kohn-Sham electronic system to the physical interacting system by progressively switching on the electron-electron interactions whilst simultaneously adjusting a one-electron effective potential so as to keep the ground-state density constant. The interactions are introduced in a range-dependent manner, first introducing predominantly long-range, and then all-range, interactions as the physical system is approached, as opposed to the conventional adiabatic connection where the interactions are introduced by globally scaling the standard Coulomb interaction. Reference data are reported for the He and Be atoms and the H2 molecule, obtained by calculating the short-range effective potential at the full configuration-interaction level using Lieb's Legendre-transform approach. As the strength of the electron-electron interactions increases, the excitation energies, calculated for the partially interacting systems along the adiabatic connection, offer increasingly accurate approximations to the exact excitation energies. Importantly, the excitation energies calculated at an intermediate point of the adiabatic connection are much better approximations to the exact excitation energies than are the corresponding Kohn-Sham excitation energies. This is particularly evident in situations involving strong static correlation effects and states with multiple excitation character, such as the dissociating H2 molecule. These results highlight the utility of long-range interacting reference systems as a starting point for the calculation of excitation energies and are of interest for developing and analyzing practical approximate range-separated density-functional methodologies.