Related papers: An Adaptive Multiscale Approach for Electronic Str…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
Quantum Monte Carlo methods are first-principle approaches that approximately solve the Schr\"odinger equation stochastically. As compared to traditional quantum chemistry methods, they offer important advantages such as the ability to…
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to…
[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schr\"odinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the…
The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially…
We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are…
Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements…
We develop a simple model of shape resonances in electron-molecule collisions that is based on the modified effective-range expansion and analytical solutions of the Schrodinger equation for the long-range part of the interaction potential.…
The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to…
We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element…
In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experiments that the method is efficient and reliable for atomic…
The electronic density of states (DOS) provides information regarding the distribution of electronic energy levels in a material, and can be used to approximate its optical and electronic properties and therefore guide computational…
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…