**1. Methods related to Random Phase Approximation and GW**

**1.1. Development of model kernels for the ground-state correlation energy within the Random Phase Approximation**

In order to remedy some of the shortcomings of the random phase approximation (RPA) within adiabatic connection fluctuation-dissipation (ACFD) density functional theory, we introduce a short-ranged, exchange-like kernel (NEO kernel) that is one-electron self-correlation free and exact for two-electron systems in the high-density limit. We have implemented RPA renormalized perturbation theory with the kernel for extended systems, and demonstrate its capability to describe the dominant correlation effects with a low-order expansion in both metallic and nonmetallic systems. We are currently testing our approximation on various materials problems, from structural phase transitions to interlayer binding energies.

**1.2. Development of vertex correction for GW**

We explore employing a modified dielectric function in the screened Coulomb interaction. The vertex is responsible for the many-body effects that are missing from the RPA screening. Most efforts utilize the three-point vertex function or ALDA. Modeling the vertex can combine the positive features of these. We explore the impact of various model vertices on the band gaps.

**2. Self-Interaction Corrected Linear Response for Accurate Charge Transfer Excitations**

The photoelectric efficiency of organoelectronic devices is strongly dependent on the charge separation process at the donor-acceptor interface. The charge transfer (CT) process itself is what creates the exciton, a crucial ingredient of photovoltaic devices.

An accurate theoretical treatment of the CT process has always raised difficulties. Time-dependent density functional theory (TDDFT) offers an efficient procedure to compute optical properties for large systems, but fails to yield accurate CT excitation energies. TDDFT inherits the self-interaction error (SIE) from ground-state DFT. Due to the SIE and the derivative discontinuity, the CT excitation energies remain too low within TDDFT. Self-interaction corrections (SIC’s) have been known for a long time within ground-state DFT. Some of these SIC schemes are accurate enough to describe stretched systems. A significant requirement of SIC is the localization of the orbitals, as required by size-consistency. But the localization procedure can make SIC computationally infeasible for large systems. In 2014, Pederson and collaborators recommended a computationally much more attractive version of the earlier Perdew-Zunger (PZ) SIC. This SIC utilizes Fermi orbitals, greatly restricting the number of possible unitary transformations of the occupied Kohn-Sham orbitals. The result of this specific construction of the localized orbitals is a computationally feasible SIC for the ground state energy.

This project is a straightforward continuation of the Fermi orbital PZ-SIC to a self-consistent version with a model potential from a simplified OEP scheme. The next step extends the SIC to TDDFT with a one-electron self-interaction free model kernel to treat exchange-correlation effects. The proposed method will be extensively tested and applied to various CT problems such as polymer-fullerene donor-acceptor systems.

**3. Applications of the recently developed SCAN meta-GGA density functional**

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The recently developed SCAN meta-GGA functional displays intermediate range weak interactions. This kind of interaction can be relevant in materials such as layered transition–metal dichalcogenates, organic semiconductors and molecular crystals. Our applications focus on energetics where weak interactions can be relevant, and situations where an improvement in the band gap can be expected from SCAN’s potential as a differential operator.

**4. Strain, bending, doping, and substrate effects in two dimensional materials for enhancing photocatalysis**

* Interplay between bending and defects*

We recently found that for 2D materials, using first-principles calculations, the carrier type and carrier concentration can be tuned by external mechanical bending – a unique attribute of 2D material. We are using SCAN meta-GGA functional to systematically study how bending interplays with defects and doping, and their consequences on the electronic, optical, and catalytic properties of 2D materials. By this study, we aim to design new transformative techniques for controlling the properties of interest (especially conductivity) in 2D materials.

Negative Poisson’s Ratio (NGR): NGR is unusual for materials. Such materials have the potential for use as components of microelectromechanical systems We are using our new developed SCAN functional to design and discover new and stable Negative Poisson’s Ratio (NGR) 2D materials.

Moiré Pattern in 2D:

Moiré are often an artifact of images formed when two identical layers are overlaid while displaced or rotated a small amount from one another. They are often found in the STM images of 2D materials (e.g., graphene, MoS2). However, it is yet unclear whether and how Moiré Patterns control other material properties of interests (e.g., electronic structure and optical properties). The objective of this research is to discover the relationship between the electric structure and Moiré patterns in selective 2D materials, which can be used to design new functional 2D materials. Instead of using a few-thousand-atom supercell that is often adopted to study this Moiré pattern effect, we will be developing a new supercell model that contains only a few hundred atoms.

The newly developed SCAN+rVV10 density functional will be used in this work. This study will be done in collaboration with Prof. Maria Iavarone’s group working on STM experiment.

The effects of curvature, substrate, and defects on the catalytic performance of MoS2:

MoS2 is a promising electro-catalytic material for hydrogen evolution, whose performance is proportional to the density of active reaction sites. Two types of active sites have been proposed previously. One is the edge site. The other is the sulfur vacancy defect. In this study, we will be exploring two issues: (i) new active sites in the basal plane of defected MoS2 with various curvatures, (ii) the coupling effects between curvature, substrate and sulfur vacancy. The goal of this study to significantly improve the hydrogen evolution performance of MoS2. This work will be done in collaboration with Linyou Cao’s group.

**5. Beyond RPA approximations for van der Waals interactions in materials**

Many-body correlation effects are essential for the accurate description of interfaces, and adsorption processes. Approximations beyond RPA such as pp-RPA and ISTLS have this effect, and are also one-electron self-interaction free. These methods, however, show a very slow scaling with the number of electrons. We are interested in algorithms which can make these approximations applicable for materials.