Editorial: Advances in Density Functional Theory and Beyond for Computational Chemistry

Abstract

Editorial on the Research Topic Advances in Density Functional Theory and Beyond for Computational Chemistry The rapid development of modern computational chemistry has led to a growing need to understand the microscopic mechanisms determining the properties of molecular and solid materials at an atomic level. The interactions between atoms and electrons are governed by the laws of quantum mechanics; hence, accurate and efficient computational methods for solving the quantum-mechanical equations are needed. The Kohn-Sham density functional theory (DFT) Hohenberg and Kohn (1964), Kohn and Sham (1965) marks a decisive breakthrough in these efforts, and in the past few decades DFT has made an unparalleled impact on a variety of interesting and challenging problems in computational chemistry. The real forte of DFT is its favourable price and performance ratio as compared with electron-correlated wave-function-based methods, such as the Møller–Plesset perturbation theory Binkley and Pople (1975) or coupled cluster theory Čížek (1966). Thus, large-scale molecular and solid systems can be studied by DFT with sufficient accuracy, thereby expanding the predictive power inherent in electronic structure theory. As a result, DFT is now by far the most widely used electronic structure method. Although 50 years have passed since the formulation of the Kohn-Sham DFT, many open questions remain, including the mathematical issues in solving the Kohn-Sham equations, the developments of more accurate and efficient density functionals, and applying the DFT calculations to solve more scientific problems. This research topic focuses on covering recent advances within the framework of DFT. Computational chemistry methods have become increasingly important in recent years, as manifested by their rapidly extending applications in a large number of diverse fields, such as computations of molecular structures and properties, the design of pharmaceutical drugs and novel materials, etc. In part as a result of this general trend, the size of the systems which can be computationally studied has also increased, generating even further needs for large-scale applications. This is because larger molecular systems show interesting phenomena and have important implications in modern biochemistry, biotechnology, and nanotechnology. Thus, it is of great importance to apply and further develop computational methods which provide physically sound models for large molecules at a reasonable computational cost. A representative approach is the linear scaling technique Goedecker (1999), which owns a computational cost that scales linearly $\mathcal{O}\left(N\right)$ with the size of the system. The linear-scaling DFT is an area of active research in computational chemistry, with the performances improve steadily over the years, especially on parallel high-performance machines. Historically, linear-scaling implementations were restricted to basic ground state energy and electron density calculations, but this has also improved in recent years with geometry optimizations and molecular dynamics (MD) becoming available. Moreover, recent developments of machine learning algorithms enable the large-scale MD simulations with ab initio accuracy, and has been applied to a variety of applications Jia et al. (2020). This research topic aims to report the state-of-the-art computational methods in several of the important questions related to the family of linear scaling methods. A deep understanding of the excitations in molecules and solids are of fundamentally importance in many technological applications. There is already a rich set of theoretical and simulation methods for excited-state calculations, such as the GW plus Bethe-Salpeter equation Hedin (1965), time-dependent density functional theory (TDDFT) Runge and Gross (1984) and many-body coupled cluster (CC) theory Čížek (1966). Unfortunately, these post-Hartree-Fock and excited state methods for electronic excitations are all subject to computational bottlenecks, which are far more severe than those affecting the standard calculations of the ground-state energy, not only because of the system size, but also because the large number of excited states that need to be considered. A major difficulty for treating excited complex systems arises from the different nature of the various competing excited electronic states. For example, the localized neutral and delocalized charge transfer excitons, as a result of the relatively large length scale. Therefore, this research topic also aims to cover developments of novel electronic structure algorithms and scalable computational methods for excited states of complex systems. The past several decades have witnessed tremendous strides in the capabilities of computational chemistry simulations, driven in large part by the extensive parallelism offered by powerful computer clusters and scalable programming methods on high performance computing (HPC) Hu et al. (2021), Kowalski et al. (2021). However, such massively parallel simulations increasingly require more advanced algorithms to achieve satisfactory performance across the vastly diverse ecosystem of modern heterogeneous computer systems. The design of efficient parallel codes proves to be difficult: the diversity of involved data structures and algorithms, as well as the frequently occurring inherent sequential control propose enormous challenges to efficiently use of a large number of processors. This research topic also focuses on the developments of more effective computational methods by use of high performance parallel computing. This editorial sums up the contents of our Research Topic “Advances in Density Functional Theory and Beyond for Computational...