Challenges in Large Scale Quantum Mechanical Calculations

Abstract

During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.

accepted for publication by WIREs Computational Molecular Science

References in corpus (47)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Linear-scaling ab-initio calculations for large and complex systems
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Daubechies wavelets as a basis set for density functional pseudopotential calculations
• Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network
• Total energy global optimizations using non orthogonal localized orbitals
• Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
• Efficient solution of Poisson's equation with free boundary conditions
• Generalization of the density-matrix method to a non-orthogonal basis
• Accurate and efficient linear scaling DFT calculations with universal applicability
• Efficient implementation of the nonequilibrium Green function method for electronic transport calculations
• Exponential decay properties of Wannier functions and related quantities
• The Decay Properties of the Finite Temperature Density Matrix in Metals
• Daubechies Wavelets for Linear Scaling Density Functional Theory
• Calculations on millions of atoms with DFT: Linear scaling shows its potential
• Norm-conserving pseudopotentials with chemical accuracy compared to all-electron calculations
• A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments
• Efficient and accurate three dimensional Poisson solver for surface problems
• Short to long-range charge-transfer excitations in the zincbacteriochlorin-bacteriochlorin complex: a Bethe-Salpeter study
• Linear scaling Krylov subspace method for large scale {\it ab initio} electronic structure calculations of metals
• Accurate ionic forces and geometry optimisation in linear scaling density-functional theory with local orbitals
• Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion
• Minimal parameter implicit solvent model for ab initio electronic structure calculations
• Electrostatic considerations affecting the calculated HOMO-LUMO gap in protein molecules
• Ab-initio molecular dynamics simulation of liquid water by Quantum Monte Carlo
• Linear-scaling time-dependent density-functional theory in the linear response formalism
• Kinetic Energy Density Study of Some Representative Semilocal Kinetic Energy Functionals
• Calculating optical absorption spectra for large systems using linear-scaling density-functional theory
• Electronic Structure of Large-Scale Graphene Nanoflakes
• Difficulties in applying pure Kohn-Sham density functional theory electronic structure methods to protein molecules
• Embedded-Cluster Calculations in a Numeric Atomic Orbital Density-Functional Theory Framework
• Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions
• Critical analysis of fragment-orbital DFT schemes for the calculation of electronic coupling values
• Renormalization of myoglobin-ligand binding energetics by quantum many-body effects
• Linear-scaling time-dependent density-functional theory (TDDFT) beyond the Tamm-Dancoff approximation: obtaining efficiency and accuracy with in situ optimised local orbitals
• Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond
• Novel structural features of CDK inhibition revealed by an ab initio computational method combined with dynamic simulations
• Augmented orbital minimization method for linear scaling electronic structure calculations
• Random close packing in protein cores
• Efficient Calculations with Multisite Local Orbitals in the large-scale DFT Code CONQUEST
• Linear-scaling DFT+U with full local orbital optimization
• SIESTA-PEXSI: Massively parallel method for efficient and accurate \textit{ab initio} materials simulation without matrix diagonalization
• Fragment Approach to Constrained Density Functional Theory Calculations using Daubechies Wavelets
• Supercell convergence of charge-transfer energies in pentacene molecular crystals from constrained DFT
• Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory

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• The MRChem multiresolution analysis code for molecular electronic structure calculations: performance and scaling properties
• Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis
• Elastocaloric Effect in Graphene Kirigami
• Large-scale DFT methods for calculations of materials with complex structures
• Pseudo-Fragment Approach for Extended Systems Derived from Linear-Scaling DFT
• Self-Supervised Generative Models for Crystal Structures
• A General Algorithm to Calculate the Inverse Principal $p$-th Root of Symmetric Positive Definite Matrices
• Complexity Reduction in Density Functional Theory: Locality in Space and Energy
• Accurate Prediction of Free Solvation Energy of Organic Molecules via Graph Attention Network and Message Passing Neural Network from Pairwise Atomistic Interactions
• Multiscale Approach to Fluid-Solid Interfaces: An overview of methodologies coupling fluid mechanics to molecular dynamics and quantum theory
• Positivity Preserving Density Matrix Minimization at Finite Temperatures via Square Root
• Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling
• On the Efficient Evaluation of the Exchange Correlation Potential on Graphics Processing Unit Clusters
• Learning electron densities in the condensed phase
• Exchange-Correlation Functionals in 2D Materials: Applications, Challenges, and Limitations