Density-functional theory for systems with noncollinear spin: orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer

A new class of orbital-dependent exchange-correlation (xc) potentials for applications in noncollinear spin-density-functional theory is developed. Starting from the optimized effective potential (OEP) formalism for the exact exchange potential - generalized to the noncollinear case - correlation effects are added via a self-consistent procedure inspired by the Singwi-Tosi-Land-Sjolander (STLS) method. The orbital-dependent xc potentials are applied to the Hubbard dimer in uniform and noncollinear magnetic fields and compared to exact diagonalization and to the Bethe-ansatz local spin-density approximation. The STLS gives the overall best performance for total energies, densities and magnetizations, particularly in the weakly to moderately correlated regime.Comment: Manuscript: 13 pages with 10 figures. Supplemental material: 12 page

(Spin-)density-functional theory for open-shell systems: exact magnetization density functional for the half-filled Hubbard trimer

According to the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, however, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. Here, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional.Comment: 10 pages, 7 figure

The particle-hole map: a computational tool to visualize electronic excitations

We introduce the particle-hole map (PHM), a visualization tool to analyze electronic excitations in molecules in the time or frequency domain, to be used in conjunction with time-dependent density-functional theory (TDDFT) or other ab initio methods. The purpose of the PHM is to give detailed insight into electronic excitation processes which is not obtainable from local visualization methods such as transition densities, density differences, or natural transition orbitals. The PHM is defined as a nonlocal function of two spatial variables and provides information about the origins, destinations, and connections of charge fluctuations during an excitation process; it is particularly valuable to analyze charge-transfer excitonic processes. In contrast with the transition density matrix, the PHM has a statistical interpretation involving joint probabilities of individual states and their transitions, it satisfies several sum rules and exact conditions, and it is easier to read and interpret. We discuss and illustrate the properties of the PHM and give several examples and applications to excitations in one-dimensional model systems, in a hydrogen chain, and in a benzothiadiazole based molecule.Comment: 33 pages, 13 figure

Three- to two-dimensional crossover in time-dependent density-functional theory

Quasi-two-dimensional (2D) systems, such as an electron gas confined in a quantum well, are important model systems for many-body theories. Earlier studies of the crossover from 3D to 2D in ground-state density-functional theory showed that local and semilocal exchange-correlation functionals which are based on the 3D electron gas are appropriate for wide quantum wells, but eventually break down as the 2D limit is approached. We now consider the dynamical case and study the performance of various linear-response exchange kernels in time-dependent density-functional theory. We compare approximate local, semilocal and orbital-dependent exchange kernels, and analyze their performance for inter- and intrasubband plasmons as the quantum wells approach the 2D limit. 3D (semi)local exchange functionals are found to fail for quantum well widths comparable to the 2D Wigner-Seitz radius, which implies in practice that 3D local exchange remains valid in the quasi-2D dynamical regime for typical quantum well parameters, except for very low densities.Comment: 13 pages, 9 figure

Direct calculation of exciton binding energies with time-dependent density-functional theory

Excitons are electron-hole pairs appearing below the band gap in insulators and semiconductors. They are vital to photovoltaics, but are hard to obtain with time-dependent density-functional theory (TDDFT), since most standard exchange-correlation (xc) functionals lack the proper long-range behavior. Furthermore, optical spectra of bulk solids calculated with TDDFT often lack the required resolution to distinguish discrete, weakly bound excitons from the continuum. We adapt the Casida equation formalism for molecular excitations to periodic solids, which allows us to obtain exciton binding energies directly. We calculate exciton binding energies for both small- and large-gap semiconductors and insulators, study the recently proposed bootstrap xc kernel [S. Sharma et al., Phys. Rev. Lett. 107, 186401 (2011)], and extend the formalism to triplet excitons

A brief compendium of time-dependent density-functional theory

Time-dependent density-functional theory (TDDFT) is a formally exact approach to the time-dependent electronic many-body problem which is widely used for calculating excitation energies. We present a survey of the fundamental framework, practical aspects, and applications of TDDFT. This paper is mainly intended for non-experts (students or researchers in other areas) who would like to learn about the present state of TDDFT without going too deeply into formal details.Comment: 33 pages, 18 figures; updated version, including additional reference

Assessment of long-range-corrected exchange-correlation kernels for solids: accurate exciton binding energies via an empirically scaled Bootstrap kernel

In time-dependent density-functional theory, a family of exchange-correlation kernels, known as long-range-corrected (LRC) kernels, have shown promise in the calculation of excitonic effects in solids. We perform a systematic assessment of existing static LRC kernels (empirical LRC, Bootstrap, and jellium-with-a-gap model) for a range of semiconductors and insulators, focusing on optical spectra and exciton binding energies. We find that no LRC kernel is capable of simultaneously producing good optical spectra and quantitatively accurate exciton binding energies for both semiconductors and insulators. We propose a simple and universal, empirically scaled Bootstrap kernel which yields accurate exciton binding energies for all materials under consideration, with low computational cost

Application of object-oriented programming in a time-dependent density-functional theory calculation of exciton binding energies

This paper discusses the benefits of object-oriented programming to scientific computing, using our recent calculations of exciton binding energies with time-dependent density-functional theory (arXiv: 1302.6972) as a case study. We find that an object-oriented approach greatly facilitates the development, the debugging, and the future extension of the code by promoting code reusing. We show that parallelism is added easily in our code in a object-oriented fashion with ScaLAPACK, Boost::MPI and OpenMP.Comment: 3 figure

Optical properties of CsCu2_2X3_3 (X=Cl, Br and I): A comparative study between hybrid time-dependent density-functional theory and the Bethe-Salpeter equation

The cesium copper halides CsCu$_2$X$_3$ (X=Cl, Br and I) are a class of all-inorganic perovskites with interesting and potentially useful optical properties, characterized by distinct excitonic features. We present a computational study of the optical absorption spectra of CsCu$_2$X$_3$, comparing time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation (BSE), using $GW$ quasiparticle band structures as input. The TDDFT calculations are carried out using several types of global hybrid exchange-correlation functionals. It is found that an admixture of nonlocal exchange determined by the dielectric constant produces optical spectra in excellent agreement with the BSE. Thus, hybrid TDDFT emerges as a promising first-principles approach for excitonic effects in solids

Direct extraction of excitation energies from ensemble density-functional theory

A very specific ensemble of ground and excited states is shown to yield an exact formula for any excitation energy as a simple correction to the energy difference between orbitals of the Kohn-Sham ground state. This alternative scheme avoids either the need to calculate many unoccupied levels as in time-dependent density functional theory (TDDFT) or the need for many self-consistent ensemble calculations. The symmetry-eigenstate Hartree-exchange (SEHX) approximation yields results comparable to standard TDDFT for atoms. With this formalism, SEHX yields approximate double-excitations, which are missed by adiabatic TDDFT.Comment: 6 pages, 2 figure