Session L58: DFT and Beyond VII

Quasiparticle Energies and Excitation Energies from Ground State DFT Calculations

The perspectives of fractional charges and fractional spins provide a clear analysis of the errors of commonly used density functional approximations (DFAs). These errors, the delocalization and static correlation error, of popular DFAs lead to diversified problems in present-day density functional theory calculations. To achieve a universal elimination of these two errors, we developed a localized orbital scaling correction (LOSC) framework. The LOSC–DFAs lead to systematically improved results, including the dissociation of ionic species, single bonds, multiple bonds without breaking space or spin symmetry, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra. Comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function approach and LOSC shows that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This leads the development of the Quasiparticle Energy DFT (QE-DFT) approach to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the (N - 1)-electron systems. Results show good performance of QE-DFT for valence excitations with commonly used DFAs with or without LOSC, for Rydberg states only with the use of LOSC-DFA, and the accurate description of conical interactions. This highlights a new and simplest pathway to describe excited states.
  

Self-consistent first-principles method for extended Hubbard interactions

We present an efficient self-consistent first-principles computational approach that extends the density functional theory plus on-site interaction (DFT+U) method further to include inter-site Hubbard Coulomb interaction (V). The extended DFT+U +V method is suitable to calculate electronic structures of periodic systems with various interactions with disparate spatial ranges. It has been known that typical computational methods for DFT+U and DFT+U+V require additional set of computations to obtain U and (or) V. In this presentation, we suggest a scheme to compute the Hubbard parameters self-consistently and ab initio without additional computations for a set of parameters of U and V. A few examples of calculations of energy bands for semiconductors and insulators will also be presented.
  

Self-consistent DFT+U+V study of oxygen vacancies in SrTiO3

DFT calculations of defects in transition-metal oxides constitute a challenging task, often requiring advanced methods to ensure a reasonable description of the electronic structure and large supercells to mimic the dilute defect concentration. Several contradicting DFT results were reported for oxygen vacancies (V_O) in SrTiO₃ (STO) and were often related to the peculiar properties of STO, which is a d⁰ transition metal oxide with mixed ionic-covalent bonding. Here, for the first time, we apply the extended Hubbard DFT+U+V approach, including on-site (Ti-3d) as well as inter-site (Ti-3d and O-2p) electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently via density-functional perturbation theory. The negligible additional cost of DFT+U+V compared to standard DFT enables the treatment of large supercells, yet the obtained structural and electronic properties agree well with hybrid-functional calculations and experiments. As such, DFT+U+V results in a bandgap and crystal field splitting for STO in good agreement with experiments. In turn, the description of the electronic properties of V_O is improved, with formation energies much less dependent on the cell size compared to DFT+U and in excellent agreement with experiments.

  

Spectral function database for correlated materials using beyond-DFT methods

While DFT or DFT+U methods give quite accurate results for structural parameters in most materials, correct predictions of excited-state properties, even at a qualitative level, and other properties of correlated materials, usually require beyond-DFT methods. The existing materials databases, constructed in the spirit of the Materials Genome Initiative, are built almost exclusively by the DFT method and are thus very often making incorrect predictions for correlated materials. Various beyond DFT methods, such as meta-GGA, hybrid functionals, GW approximation, or dynamical mean-field theory have been developed to describe the electronic structure of correlated materials, but it is unclear how accurate these methods are when applied to a given strongly correlated solid. It is thus of pressing interest to compare their accuracy as applied to different categories of materials, and at the same time, to build the database of beyond-DFT calculations. We discuss a systematic study of these methods on a few training sets of correlated materials such as binary transition-metal oxides, Fe-pnictides & chalcogenides, and transition-metal dichalcogenides, and we compare theoretical predictions with experimental photoemission data, where available.   

Assessment of excited-state molecular geometries with optimally-tuned range-separated hybrid functionals

Computational modelling of photochemical processes (e.g., for photocatalysis) requires accurate descriptions of excited-state structural dynamics of the involved molecules. Often, the starting point of such investigations are geometries optimized for the lowest-lying excited state, as obtained in time-dependent density functional theory (TD-DFT) or high-level wave-function methods. While calculations based on TD-DFT are computationally very efficient, they often do not reach the accuracy of computationally more expensive wave-function methods[1]. However, the recently developed class of optimally-tuned range-separated hybrid (OT-RSH) functionals promises to reduce the gap in accuracy[2].
Here, we assess the precision of excited-state geometries obtained with TD-DFT and OT-RSH for a selection of organic molecules. Our focus lies on structural parameters (e.g., bond lengths, bond angles, etc.) of the lowest-excited singlet states, which we compare to high accuracy wave-function data from literature to benchmark our results.

[1] C. Azarias, J. Phys. Chem. A, 121, 32, 6122 (2017)
[2] L. Kronik et al., J. Chem. Theory Comput., 8, 5, 1515 (2012)
  

Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma

We show that using complex, spin-restricted orbitals in Kohn-Sham (KS) density functional theory allows one to access a new class of densities that is not accessible by either spin-restricted (RKS) or spin-unrestricted (UKS) orbitals [1]. We further show that the real part of a complex RKS (CRKS) density matrix can be nonidempotent when the imaginary part of the density matrix is not zero. Using CRKS orbitals shows significant improvements in the triplet-singlet gaps of a benchmark set, called TS12, for well-established, widely used density functionals. Moreover, it was shown that RKS and UKS yield qualitatively wrong charge densities and spin densities, respectively, leading to worse energetics. We demonstrate that representative modern density functionals show surprisingly no improvement even with a qualitatively more accurate density from CRKS orbitals. To this end, our work not only provides a way to escape the symmetry dilemma whenever there exists a CRKS solution, but also suggests a new route to design better approximate density functionals.
[1] J. Lee, L. W. Bertels, D. W. Small, M. Head-Gordon, Phys. Rev. Lett., 2019, 123, 113001.   

"Implementation of imaginary time dependent density functional theory to periodic and noncollinear systems"

Recently an alternative to the SCF method for calculating the DFT electronic ground state was proposed that evolves the DFT wave function in imaginary time [1]. One benefit of this new method is that the DFT wave function is guaranteed to lower its energy and eventually reach the ground state with a sufficiently small time step. This avoids the problems in SCF that hinder convergence such as charge sloshing, which can necessitate fractional level filling. We extend imaginary time dependent density functional theory to periodic systems using a modification of the DFT package Quantum ESPRESSO, with the option of noncollinear and DFT+U calculations. We discuss some of the technical aspects of this as well as example systems which converge with this modification but have difficulty with standard implementations of SCF.

[1] arXiv:1903.00766v2 [physics.comp-ph] (2019)   

PyProcar: A Python library for electronic structure pre/post-processing

We present PyProcar, a Python package providing graphical representations for electronic structure calculations including band structures and Fermi surfaces as a function of atomic and/or s, p, d, f – orbital projected wavefunctions. This is compatible with DFT codes which output band and projection information in the PROCAR format, as done by the VASP and ABINIT codes. PyProcar is particularly suitable for studying atomic effects into the band structure, Fermi surface and spin texture. Aside from spin, orbital and atom projected band structures and Fermi surfaces, PyProcar plots Fermi surfaces which map colors to properties such as the electron velocity, electron-phonon mean path and effective mass. Another existing feature refers to the band unfolding of supercell calculations into predefined unit cells. PyProcar can be conveniently used in either a stand-alone command line mode or a library mode easily accessible through the Python packaging index (pip) and performs tasks with simple commands.