Session A02: Developments of DFT from Quantum to Statistical Mechanics (I)

Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations

The delocalization error of common density functional approximations leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC–DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra. (ref: Chen Li,1 Xiao Zheng, Neil Qiang Su, and Weitao Yang, “Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations”, DOI: 10.1093/nsr/nwx111)   

Directly Patching Exchange-Correlation Energy in Density Functional Theory

Kohn-Sham density functional theory is widely used nowadays for large-scale material simulations, however its accuracy is limited by the accuracy of the exchange-correlation (XC) functionals. We will discuss our effort on developing the exchange-correlation energy patching (XCEP) method in which for each atom (called central atom) we select its nearby atoms as its buffer atoms. The central atom and its buffer atoms form the cluster. The rest atoms form the environment. The system’s electron density is then partitioned among the cluster and environment using the finite-temperature density functional embedding theory developed recently in our group. The obtained cluster is a small KS system, whose XC energy density can be computed using a high-level XC functional. The system’s XC energy is constructed by patching these high-level, local XC energy densities over the entire system in an atom-by-atom manner. The performance of XCEP is investigated by patching the random phase approximation correlation energy in some one-dimensional systems, and by patching the exact exchange energy in molecules. We show that by increasing the clusters’ sizes the XCEP results converge to the benchmarks.   

How Derivative Discontinuities in the Energy Yield Interatomic Steps in the Exact Kohn-Sham Potential of Density-Functional Theory

Accurate density-functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features in this regard are the spatially uniform shift in the potential, as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form, e.g., between the atoms of stretched molecules. Although both aforementioned concepts are well-known, the exact relationship between them remained unclear. In this talk, we establish this relationship and introduce a new concept: the charge-transfer derivative discontinuity, Δ^CT. By numerically solving the many-electron Schrödinger equation, we extract the exact Kohn-Sham potential and directly observe its features, particularly the spatial interatomic steps. For the first time, spatial steps are observed in the exact xc potential of a three-dimensional full configuration-interaction (FCI) calculation of a molecule.   

Temperature and the strong-interaction limit of density functional theory

The strictly correlated electron approach to density functional theory, first proposed by Seidl and coworkers [1-4], offers a unique perspective on finite-temperature density functional theory and one of its application areas, simulations in the warm dense matter regime. Recent work relating tied coordinate-temperature-interaction scaling to the strong-interaction limit of density functional theory is presented via formal and numerical results. Strategies for analyzing the competition between strong interaction and temperature in complicated physical systems will be discussed.

[1] M. Seidl, Phys. Rev. A 60, 4387 (1999).
[2] M. Seidl, J. P. Perdew, and M. Levy, Phys. Rev. A 59, 51 (1999).
[3] M. Seidl, P. Gori-Giorgi, and A. Savin, Phys. Rev. A 75, 042511 (2007).
[4] P. Gori-Giorgi, G. Vignale, and M. Seidl, J. Chem. Theory Comput. 5, 743 (2009).   

Comparison of electronic properties of atoms with d orbitals using coupled-cluster singles and doubles (CCSD) and self-energy functional theory

We examine the electronic correlation effects of isolated atoms containing d orbitals by using calculations based on the CCSD and the self-energy functional theories. The self-energy functional theory[1] was proposed originally for analyzing models of correlated systems. We adopt it for realistic description of the atoms by employing exact diagonalization of their second-quantized Hamiltonians. We calculate the single-particle Green's functions[2] to clarify how the many-body nature of the atoms affects on the spectral functions. We also discuss the differences in the spectra between both methods.

[1] M. Potthoff, Eur. Phys. J. B 36, 335 (2003); M. Potthoff, M. Aichhorn, and C. Dahnken, Phys. Rev. Lett. 91, 206402 (2003);
[2] K. Bhaskaran-Nair, K. Kowalski, and W. A. Shelton, J. Chem. Phys. 144, 144101 (2016) and references therein.   

Comprehensive study of coupled-cluster singles and doubles Green function (GFCCSD) on periodic systems

Coupled-cluster singles and doubles (CCSD) is known to reproduce electronic correlation with high accuracy. By employing the Green’s function developed within the CCSD scheme (GFCCSD), one is capable of obtaining physical quantities including energy spectrum [1]. No periodic system, however, has been treated by GFCCSD except for electron gas [2]. In this work, we have developed a code to calculate the one-particle Green’s functions of periodic systems through GFCCSD and applied it to several realistic materials. We have found that the spectral functions and the band structures well exhibit the effects of the electronic correlation. We have also examined the differences between the calculated and experimental results.

[1] M. Nooijen and J. G. Snijders, Int. J. Quantum Chem. Symp. 44(S26), 55 (1992). M. Nooijen and J. Snijders, Int. J. Quantum Chem. 48, 15 (1993).
[2] J. McClain, J. Lischner, T. Watson, D. A. Matthews, E. Ronca, S. G. Louie, T. C. Berkelbach and G. K. Chan, Phys. Rev. B 93, 235139 (2016).   

Classical DFT of Ions in the Electrical Double Layer and Nanofluidics

Compared to DFTs of short-range interactions (e.g., hard spheres), the long-range Coulombic interaction poses a special problem for developing classical density functional theory for ions and electrolytes. Over the last 25 years, significant progress has been made on more accurate DFTs for Coulombic systems. Recent progress in such DFTs will be reviewed. Applications of DFTs of electrolytes to the equilibrium electrical double layer (including 2D DFT calculations of a heterogeneous surface charge) and in the transport of ions in nanofluidic systems will be discussed.   

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.   

Orbital-free density functional theory with atom-centered density matrices

Orbital-free density functional theory (OFDFT) is one of the most computationally efficient methods for performing electronic structure calculations. OFDFT achieves its speed by treating the electron density as the sole quantity of interest, in contrast to Kohn-Sham density functional theory which incorporates single-particle wave functions. The lack of wave-function manipulations makes OFDFT suitable for the study of millions of atoms, provided it can be made sufficiently accurate.

This presentation will explore recent work that aims to improve the accuracy of OFDFT. The primary modification is the replacement of the density-only description of the system by a hybrid description that includes on-site density matrices. These local density matrices are defined only in spheres immediately surrounding nuclei, and the remainder of the system is described by the electron density alone. The extra information afforded by the hybrid description helps overcome the two primary limitations of conventional OFDFT: that it requires an explicit density functional for the non-interacting kinetic energy, and that it is frequently restricted to calculations involving only pseudopotentials.   

On the development of non-adiabatic functionals in real-time TDDFT

Time-Dependent Density Functional Theory (TDDFT) has made remarkable achievements in the description of excitation spectra and response properties. On the other hand, for the description of dynamical processes in the non-linear regime, the adiabatic approximation is widely used, with groundstate DFT functionals that depend only on the instantaneous density. In systems driven far from equilibrium, memory-dependence can dramatically affect the shape of the exact exchange-correlation potential, and as a result, adiabatic approximations give poor predictions of the dynamics.
Starting from an exact expression of this potential we derive a simple non-adiabatic and non-local approximation. We study this approximation for several numerically exactly-solvable model systems, for a range of physical situations: field-free dynamics of superposition states, laser-driven dynamics, and scattering.
  

The GW Self-Screening Error and its Correction Using a Local Density-Functional

In electronic structure theory, the self-screening error is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction W were used, causing each electron to artificially screen its own presence. In the GW approach to many-electron theory, the self-screening introduces error into the electron density, energy and ionization potential. We illustrate this self-screening error in a straightforward way for model systems using orbital-dependent potentials. We propose a simple, computationally inexpensive correction to any GW calculation (including fully self-consistent GW) to remove this error. Our correction is a spatially local potential, added to the self-energy, that depends on the local electron density, obtained via a series of one-dimensional one-electron finite training systems. We then test our correction for other one-dimensional systems where we have access to the exact many-electron density and energy, and show that our correction removes the unwanted effects of self-screening on the electron density and the ionization potential.