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The main protease (Mpro) of SARS-CoV-2 is central to viral maturation and is a promising drug target, but little is known about structural aspects of how it binds to its...

The BigDFT project started in 2005 with the aim of testing the advantages of using a Daubechies wavelet basis set for Kohn-Sham density functional theory with pseudopotentials. This project led to the creation of the BigDFT code, which employs a computational approach with optimal features for exibility, performance and precision of the results. In particular, the employed formalism has enabled the implementation of an algorithm able to tackle DFT calculations of large systems, up to many thousands of atoms, with a computational eort which scales linearly with the number of atoms. In this work we recall some of the features that have been made possible by the peculiar properties of Daubechies wavelets. In particular, we focus our attention on the usage of DFT for large-scale systems. We show how the localised description of the KS problem, emerging from the features of the basis set, are helpful in providing a simplied description of large-scale electronic structure calculations. We provide some examples on how such simplied description can be employed, and we consider, among the case-studies, the SARS-CoV-2 main protease.

The high cost of computing the Hartree-Fock exchange energy has resulted in a limited use of hybrid density functionals in solid-state and condensed phase calculations. Approximate methods based on the use of localized orbitals have been proposed as a way to reduce this computational cost. In particular, Boys orbitals (or maximally localized Wannier functions in solids) were recently used in plane wave, first-principles molecular dynamics simulations of water. Recently, the recursive subspace bisection (RSB) method was used to compute orbitals localized in regular rectangular domains of varying shape and size, leading to efficient calculations of the Hartree-Fock exchange energy in the plane-wave, pseudopotential framework. In this paper, we use the RSB decomposition to analyze orbital localization properties in inhomogeneous systems (e.g., solid/liquid interfaces) in which localized orbitals have widely varying extent. This analysis reveals that some orbitals cannot be significantly localized and thus cannot be truncated without incurring a substantial error in computed physical properties, while other orbitals can be well localized to small domains. We take advantage of the ability to systematically reduce the error in RSB calculations through a single parameter to study the effect of orbital truncation. We present the errors in PBE0 ground state energies, ionic forces, band gaps, and relative energy differences between configurations for a variety of systems, including a tungsten oxide/water interface, a silicon/water interface, liquid water, and bulk molybdenum. We show that the RSB approach can adapt to such diverse configurations by localizing orbitals in different domains while preserving a 2-norm upper bound on the truncation error. The resulting approach allows for efficient hybrid DFT simulations of inhomogeneous systems in which the localization properties of orbitals vary during the course of the simulation.

First-principles molecular dynamics (FPMD) simulations based on density functional theory are becoming increasingly popular for the description of liquids. In view of the high computational cost of these simulations, the choice of an appropriate equilibration protocol is critical. We assess two methods of estimation of equilibration times using a large dataset of first-principles molecular dynamics simulations of water. The Gelman-Rubin potential scale reduction factor [A. Gelman and D. B. Rubin, Stat. Sci. 7, 457 (1992)] and the marginal standard error rule heuristic proposed by White [Simulation 69, 323 (1997)] are evaluated on a set of 32 independent 64-molecule simulations of 58 ps each, amounting to a combined cumulative time of 1.85 ns. The availability of multiple independent simulations also allows for an estimation of the variance of averaged quantities, both within MD runs and between runs. We analyze atomic trajectories, focusing on correlations of the Kohn-Sham energy, pair correlation functions, number of hydrogen bonds, and diffusion coefficient. The observed variability across samples provides a measure of the uncertainty associated with these quantities, thus facilitating meaningful comparisons of different approximations used in the simulations. We find that the computed diffusion coefficient and average number of hydrogen bonds are affected by a significant uncertainty in spite of the large size of the dataset used. A comparison with classical simulations using the TIP4P/2005 model confirms that the variability of the diffusivity is also observed after long equilibration times. Complete atomic trajectories and simulation output files are available online for further analysis.

With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in the size of system treated comes an increase in complexity, making it challenging to analyze such large systems and determine the cause of emergent properties. To address this issue, in this paper we present a systematic complexity reduction methodology which can break down large systems into their constituent fragments, and quantify inter-fragment interactions. The methodology proposed here requires no a priori information or user interaction, allowing a single workflow to be automatically applied to any system of interest. We apply this approach to a variety of different systems, and show how it allows for the derivation of new system descriptors, the design of QM/MM partitioning schemes, and the novel application of graph metrics to molecules and materials.

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with