# Quantum Mechanics and Density Functional Theory Model Driven by Machine Learning

## Introduction

AISI electronic structure team is committed to developing AI-assisted electronic structure enhancement algorithms represented by Periodic Density Functional Theory calculation software. ABACUS，Density Functional Theory software, is developed by Professor He Lixin, Researcher Ren Xinguo and Researcher Chen Mohan.

ABACUS is a domestic open-source Density Functional Theory software with independent intellectual property rights. It can use Plane-Wave basis vector and Numerical Atomic Orbital basis vector for simulation calculation.Numerical atomic orbital basis vector have obvious efficiency advantage for large-scale systems.

## Achievements

### Periodic Density Functional Theory calculation software ABACUS

Compared with other popular DFT software, ABACUS has a remarkable feature that it supports Plane-wave (PW) and Numerical Atomic Orbitals at the same time. The program innovatively uses the Spillage Function to construct the Numerical Atom Orbit, which effectively improves the calculation accuracy and portability, and shows high accuracy and efficiency in the simulation of large complex systems.

ABACUS adopted the open source cooperative development method according to LGPL protocol and joined the DeepModeling community. At present, the participating developers are mainly from University of Science and Technology of China, Peking University, Institute of Physics CAS and other units, and more developers are expected to join.

### Development and Application of Machine Learning Driven Functional Model DeePKS for Periodic Systems

Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for high-level QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training a ML potential has remained computationally challenging due to their high cost.

We demonstrate that this issue can be largely alleviated with Deep Kohn-Sham (DeePKS), a ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely-matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model, and then use the DeePKS model to label a much larger amount of configurations to train a ML potential.This scheme for periodic systems is implemented in a DFT package ABACUS, which is open-source and ready for use in various applications.

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