☆ 4.8 Review

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

CHEMICAL REVIEWS (2023)

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Article Chemistry, Physical

Development of nonlocal kinetic-energy density functional for the hybrid QM/MM interaction

Hideaki Takahashi

Summary: This work focuses on the development of a nonlocal kinetic-energy functional based on the response function for molecular systems, which enables the use of orbital-free density-functional theory (OF-DFT) in the hybrid QM/MM method. It differs from previous functionals that rely on the homogeneous electron gas as a reference for the response function. Benchmark tests on a QM water molecule in a dimer system and in a condensed environment show that our approach can adequately reproduce the energetics and polarization density of the QM solute under the influence of the MM environment. This suggests the potential ability of the kinetic-energy functional based on response functions for molecular reference systems.

JOURNAL OF CHEMICAL PHYSICS (2023)

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Article Chemistry, Multidisciplinary

The subsystem quantum chemistry program Serenity

Niklas Niemeyer et al.

Summary: SERENITY is an open-source quantum chemistry software that focuses on quantum-mechanical multilevel and embedding approaches. This study provides an overview of the developments in SERENITY since its original publication in 2018, including efficient electronic-structure methods for ground and excited states. SERENITY's modular structure allows for combination with density-functional theory-based embedding through various practical realizations and variants of subsystem DFT.

WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE (2023)

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Article Chemistry, Physical

A non-decomposable approximation on the complete density function space for the non-additive kinetic potential

Elias Polak et al.

Summary: A new approximation method for the non-decomposable non-additive kinetic energy potential is developed, which covers the function space for exponentially decaying densities and eliminates artificial charge leaks caused by artificial shallow wells.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Article Chemistry, Physical

Solvation Free Energies in Subsystem Density Functional Theory

Moritz Bensberg et al.

Summary: The accurate description of solvent effects is crucial for many chemical processes. In this study, we propose a hybrid approach based on subsystem density functional theory and continuum solvation schemes for the explicit quantum mechanical description of solute-solvent and solvent-solvent interactions. Our model incorporates consistent subsystem decomposition for transferability and demonstrates good scalability for increasing numbers of subsystems. By comparing the resulting free energies to experimental data, we show that our hybrid model accurately reproduces reaction barriers and energies.

JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2022)

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Article Chemistry, Physical

Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning

Kevin Ryczko et al.

Summary: In this study, voxel deep neural networks were used to predict energy densities and functional derivatives in electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. The researchers demonstrated that the ground-state electron density of a graphene lattice can be directly found via minimization without the need for a projection scheme, using a voxel deep neural network trained with the Thomas-Fermi model. Additionally, they were able to predict the kinetic energy of a graphene lattice with chemical accuracy after training from only two Kohn-Sham density functional theory calculations. The researchers also identified a sampling issue in Kohn-Sham density functional theory calculations and proposed future work to address this problem.

JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2022)

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Article Chemistry, Physical

Density functional theory of water with the machine-learned DM21 functional

Etienne Palos et al.

Summary: Recent research has shown that the deep-learned DM21 functional can overcome the delocalization error of traditional DFAs, but its ability to accurately predict the energetics of water clusters varies significantly with cluster size. Additionally, the size-dependent functional-driven errors identified in the analysis of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength when used in simulations of liquid water.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Article Chemistry, Multidisciplinary

Laser-Driven Petahertz Electron Ratchet Nanobubbles

Luke Bhan et al.

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NANO LETTERS (2022)

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Nonlocal pseudopotential energy density functional for orbital-free density functional theory

Qiang Xu et al.

Summary: The authors present a novel protocol that allows for the application of nonlocal pseudopotentials to orbital-free density functional theory (OF-DFT). They have developed a theoretical scheme that defies the traditional belief and enables the direct use of nonlocal pseudopotentials in OF-DFT.

NATURE COMMUNICATIONS (2022)

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Article Materials Science, Multidisciplinary

Deep dive into machine learning density functional theory for materials science and chemistry

L. Fiedler et al.

Summary: With the growth of computational resources, machine learning has gained traction in electronic structure simulations, offering the potential to reduce resource requirements and accelerate materials discovery and chemical reaction pathway research.

PHYSICAL REVIEW MATERIALS (2022)

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Development of Kinetic Energy Density Functional Using Response Function Defined on the Energy Coordinate (Jul, 10.1002/qua.26969, 2022)

Hideaki Takahashi

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2022)

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Article Chemistry, Physical

Is the non-additive kinetic potential always equal to the difference of effective potentials from inverting the Kohn-Sham equation?

Tomasz Adam Wesolowski

Summary: This paper examines the frequently used relation in the literature regarding the non-additive kinetic potential. It investigates whether the assumption behind this relation holds for certain density pairs. The results show that the assumption is not applicable for these density pairs, implying that the method of constructing the non-additive kinetic potential is not suitable for such cases.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Review Chemistry, Physical

Orbital-free methods for plasmonics: Linear response

Fabio Della Sala

Summary: Plasmonic systems, such as metal nanoparticles, have wide applications but classical electrodynamics models are not suitable when characteristic sizes are small. Methods based on the Time-Dependent Density Functional Theory (TD-DFT) are used to describe quantum effects, but they are computationally prohibitive for large plasmonic systems. Orbital-free (OF) methods can scale linearly with system size and accurately describe collective excitations in plasmonic systems without system-tuned parameters.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Article Chemistry, Physical

N-representability of the target density in Frozen-Density Embedding Theory based methods: Numerical significance and its relation to electronic polarization

Niccolo Ricardi et al.

Summary: The accuracy of observable derived from multi-scale simulations in Frozen-Density Embedding Theory (FDET) is influenced by two inseparable factors: (i) the approximation for the ExcTnad[rho A,rho B] component of the FDET energy functional and (ii) the choice of density rho(B)(r) for solving the FDET eigenvalue equation. This study proposes a method to estimate the relative significance of these two factors and provides numerical examples to illustrate. It is found that the violation of the non-negativity condition is the main source of error in FDET energy when rho(B) is the density of the isolated environment, and the error can be reduced by explicitly considering the electronic polarization of the environment.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Article Chemistry, Physical

Density Embedding Method for Nanoscale Molecule-Metal Interfaces

Xuecheng Shao et al.

Summary: In this work, the standard Kohn-Sham DFT theory is extended to realistically sized molecule-metal interfaces, introducing a multiscale subsystem DFT method that accurately reproduces the binding energy difference of molecules adsorbed on metal surfaces. The method is robust for Born-Oppenheimer molecular dynamics simulations and allows for large system sizes thanks to a parallelization scheme that avoids memory accumulation.

JOURNAL OF PHYSICAL CHEMISTRY LETTERS (2022)

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Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Kanun Pokharel et al.

Summary: This study designs a deep neural network using machine learning techniques to replicate strongly constrained and appropriately normed functional by only using electron density and local derivative information. The experimental results demonstrate that this machine learning approach shows good performance and transferability in molecular and periodic systems.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Subsystem density-functional theory: A reliable tool for spin-density based properties

Patrick Eschenbach et al.

Summary: Subsystem density-functional theory is an efficient method for calculating properties of large open-shell radical systems. It is computationally less costly and avoids the problem of electron overdelocalization. This method has seen rapid development in recent years and has become an important tool for describing open-shell properties.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Efficient Implementation of Density Functional Theory Based Embedding for Molecular and Periodic Systems Using Gaussian Basis Functions

Manas Sharma et al.

Summary: A practical and effective implementation of density functional theory based embedding is reported, which allows us to treat both periodic and aperiodic systems on an equal footing.

JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2022)

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Article Chemistry, Physical

Neural network-based pseudopotential: development of a transferable local pseudopotential

Jeheon Woo et al.

Summary: In this research, a novel approach based on a deep neural network was proposed to generate transferable LPPs. The neural network-based LPPs showed better transferability and performance in both atomic and bulk calculations compared to other types of LPPs.

PHYSICAL CHEMISTRY CHEMICAL PHYSICS (2022)

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Performance Enhancement of APW+lo Calculations by Simplest Separation of Concerns

Long Zhang et al.

Summary: This study interfaces the Exciting-Plus DFT code with the SIRIUS software package to optimize the LAPW/APW+lo algorithms and improve performance. Significant performance enhancement is achieved through task parallelism without changing the source code and user interface.

COMPUTATION (2022)

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Article Chemistry, Physical

Is the non-additive kinetic potential always equal to the difference of effective potentials from inverting the Kohn-Sham equation?

Tomasz Adam Wesolowski

Summary: This passage examines a relation commonly used in literature regarding the non-additive kinetic potential, pointing out that the assumption it is based on may not hold in certain scenarios, rendering the inversion process of densities not applicable to the Kohn-Sham equation.

JOURNAL OF CHEMICAL PHYSICS (2022)

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Article Chemistry, Physical

Analytical shell models for light atoms

Kati Finzel

Summary: This study presents a parameter-free analytical representation for the Pauli potential, which exhibits two separate minima for atoms from Li to C. These minima correspond to structured and unstructured electron densities, with only the unstructured solution found for atoms from N to Ne. The proposed ansatz allows for energetic minima reflecting both the fermionic nature of electrons and Boson-like characteristics.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2021)

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Review Chemistry, Multidisciplinary

DFTpy: An efficient and object-oriented platform for orbital-freeDFTsimulations

Xuecheng Shao et al.

Summary: In silico materials design face challenges due to the computational complexities of Kohn-Sham DFT, but new-generation kinetic energy density functionals have enabled successful applications of orbital-free DFT in various semiconductor and finite systems. DFTpy, an open-source software written in Python 3, implements OFDFT and outsources computationally expensive operations to third-party modules, offering easy implementation of new features for fast simulations.

WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE (2021)

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eQE 2.0: Subsystem DFT beyond GGA functionals

Wenhui Mi et al.

Summary: sDFT, utilizing nonlocal nonadditive kinetic energy and exchange-correlation functionals, can significantly reduce the computational cost of large-scale electronic structure calculations, but its accuracy is somewhat limited in certain systems. eQE 2.0 dramatically improves the accuracy of sDFT simulations by introducing new tools and functionalities, delivering excellent interaction energies compared to traditional methods.

COMPUTER PHYSICS COMMUNICATIONS (2021)

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Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method

Matthew S. Ryley et al.

Summary: This study presents a Gaussian-basis implementation of orbital-free density-functional theory using the trust-region image method for optimization, achieving tight convergence of particle-number constraint and chemical potential. By optimizing density and chemical potential simultaneously, a significant reduction in the number of required iterations for convergence is achieved. The implementation allows for handling of semilocal kinetic-energy functionals in all-electron calculations, facilitating comparison with other quantum-chemical methods and Kohn-Sham density-functional theory.

JOURNAL OF PHYSICAL CHEMISTRY A (2021)

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Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics

Li Li et al.

Summary: Incorporating prior knowledge into machine learning models for physics is crucial for improving generalization performance. Solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides implicit regularization, enhancing predictive capabilities effectively.

PHYSICAL REVIEW LETTERS (2021)

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Learning Electron Densities in the Condensed Phase

Alan M. Lewis et al.

Summary: A local machine-learning method is introduced for predicting electron densities in periodic systems, achieving high accuracy in density functional calculations.

JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2021)

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Bhupalee Kalita et al.

Summary: Density functional theory (DFT) calculations are widely used in scientific research, with machine learning (ML) offering new possibilities for improving the accuracy and usefulness of these calculations. ML has the potential to propose or enhance approximations for DFT, but challenges such as generalization remain to be addressed for implementing ML-designed functionals in standard codes.

ACCOUNTS OF CHEMICAL RESEARCH (2021)

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Extended Lagrangian Born-Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models

Anders M. N. Niklasson

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JOURNAL OF CHEMICAL PHYSICS (2021)

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Hector I. Francisco et al.

Summary: A new density functional for total kinetic energy has been developed by introducing an enhancement factor that leads to correct behavior in various limits. This functional offers a reasonable description of atomic and molecular kinetic energies when combined with Hartree-Fock densities. Additionally, a new enhancement factor for Pauli kinetic energy is proposed to improve kinetic energy density behavior.

JOURNAL OF CHEMICAL PHYSICS (2021)

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Artificial neural networks for the kinetic energy functional of non-interacting fermions

S. Alireza Ghasemi et al.

Summary: A new approach to finding the fermionic non-interacting kinetic energy functional with chemical accuracy using machine learning techniques is presented, demonstrating performance for three model systems and accurately reproducing ground state electron density and total energy with an error of less than 5 mHa. This method opens up a new avenue for advancing orbital-free density functional theory through machine learning.

JOURNAL OF CHEMICAL PHYSICS (2021)

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Random Structure Searching with Orbital-Free Density Functional Theory

William C. Witt et al.

Summary: Using orbital-free density functional theory for structure searching, low-energy crystal structures of Li, Na, Mg, and Al at zero pressure were successfully mapped, identifying different ground state and low-energy structures.

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Highly accurate machine learning model for kinetic energy density functional

Mohammed Alghadeer et al.

Summary: A highly accurate predictive model was developed using Machine Learning to estimate one-dimensional kinetic energy density functionals, showing better accuracy than standard KEDF. The statistical training approach suggested the reliability of the model for large-scale orbital free density functional theory calculations.

PHYSICS LETTERS A (2021)

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Artificial intelligence sees split electrons

John R. Perdew

SCIENCE (2021)

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Pushing the frontiers of density functionals by solving the fractional electron problem

James Kirkpatrick et al.

Summary: Density functional theory has long been plagued by systematic errors in approximations, but a new neural network-based functional, DM21, shows promise in accurately describing complex systems and outperforming traditional functionals in benchmarks. By relying on data and constraints, DM21 represents a viable pathway toward the exact universal functional.

SCIENCE (2021)

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Laplacian-Level Quantum Hydrodynamic Theory for Plasmonics

Henrikh M. Baghramyan et al.

Summary: This article introduces a more general QHT method for accurately calculating the absorption spectra of metallic nanoparticles, avoiding the influence of spurious resonances, and proposes a novel Laplacian-level KE functional for describing the optical properties of NPs of different sizes.

PHYSICAL REVIEW X (2021)

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Machine Learning of Analytical Electron Density in Large Molecules Through Message-Passing

Bruno Cuevas-Zuviria et al.

Summary: The study demonstrates the successful application of machine learning to reproduce electron density in molecules with a low absolute error rate. The methodology was also adapted to describe electron density in large biomolecules and obtain atomic charges, interaction energies, and DFT energies. This research highlights electron density learning as a promising avenue with numerous potential applications.

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GGA-Level Subsystem DFT Achieves Sub-kcal/mol Accuracy Intermolecular Interactions by Mimicking Nonlocal Functionals

Xuecheng Shao et al.

Summary: The key feature of nonlocal kinetic energy functionals is their ability to reduce to specific functionals in regions of high density and low-density/high reduced density gradient. A new GGA nonadditive kinetic energy functional successfully simulates and reproduces the interaction energies of weakly interacting dimers, with a mean absolute deviation well below 1 kcal/mol.

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Efficient DFT Solver for Nanoscale Simulations and Beyond

Xuecheng Shao et al.

Summary: OE-SCF is an orbital-free DFT solver that extends the applicability of DFT to beyond nanoscale system sizes with high accuracy and fast convergence. It enables large-scale ab initio simulations of silicon-based materials at a low computational cost, and opens up the possibility of adopting more accurate functionals in practical applications.

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Orbital-free embedding applied to the calculation of induced dipole moments in CO2•••X (X=He, Ne, Ar, Kr, Xe, Hg) van der Waals complexes -: art. no. 174104

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Article Materials Science, Multidisciplinary

Structural and thermal behavior of compact core-shell nanoparticles:: Core instabilities and dynamic contributions to surface thermal stability -: art. no. 205420

A Aguado et al.

PHYSICAL REVIEW B (2005)

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Article Chemistry, Physical

Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding

J Neugebauer et al.

JOURNAL OF CHEMICAL PHYSICS (2005)

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Article Physics, Multidisciplinary

Cusp conditions for non-interacting kinetic energy density of the density functional theory

Z Jánosfalvi et al.

PHYSICS LETTERS A (2005)

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Nearsightedness of electronic matter

E Prodan et al.

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2005)

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Review Chemistry, Physical

Orbital- and state-dependent functionals in density-functional theory -: art. no. 062203

A Görling

JOURNAL OF CHEMICAL PHYSICS (2005)

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Letter Chemistry, Physical

Competing thermal activation mechanisms in the meltinglike transition of NaN (N=135-147) clusters

A Aguado

JOURNAL OF PHYSICAL CHEMISTRY B (2005)

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Article Physics, Multidisciplinary

Anomalous size dependence in the melting temperatures of free sodium clusters:: An explanation for the calorimetry experiments -: art. no. 233401

A Aguado et al.

PHYSICAL REVIEW LETTERS (2005)

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Differential equation for the ground-state density of artificial two-electron atoms with harmonic confinement

P Capuzzi et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2005)

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Nonlinear instability of density-independent orbital-free kinetic-energy functionals -: art. no. 214106

X Blanc et al.

JOURNAL OF CHEMICAL PHYSICS (2005)

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First principles local pseudopotential for silver: Towards orbital-free density-functional theory for transition metals

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JOURNAL OF CHEMICAL PHYSICS (2005)

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Review Materials Science, Multidisciplinary

Finite element methods in ab initio electronic structure calculations

JE Pask et al.

MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING (2005)

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Real-space formulation of the electrostatic potential and total energy of solids

JE Pask et al.

PHYSICAL REVIEW B (2005)

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The merits of the frozen-density embedding scheme to model solvatochromic shifts

J Neugebauer et al.

JOURNAL OF CHEMICAL PHYSICS (2005)

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Melting-like transition in a ternary alkali nanoalloy:: Li13Na30Cs12

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JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2005)

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Liquid-vapor interface in liquid binary alloys:: An ab initio molecular dynamics study -: art. no. 077801

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PHYSICAL REVIEW LETTERS (2005)

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Introducing ONETEP: Linear-scaling density functional simulations on parallel computers

CK Skylaris et al.

JOURNAL OF CHEMICAL PHYSICS (2005)

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Real-space grid implementation of the projector augmented wave method

JJ Mortensen et al.

PHYSICAL REVIEW B (2005)

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Molecular dynamics simulations of the meltinglike transition in Li13Na42 and Na13Cs42 clusters

A Aguado et al.

PHYSICAL REVIEW B (2005)

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First principles methods using CASTEP

SJ Clark et al.

ZEITSCHRIFT FUR KRISTALLOGRAPHIE (2005)

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Potential functionals:: Dual to density functionals and solution to the υ-representability problem -: art. no. 146404

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PHYSICAL REVIEW LETTERS (2004)

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Microscopic dynamics in the liquid Li-Na alloy:: An ab initio molecular dynamics study -: art. no. 031205

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PHYSICAL REVIEW E (2004)

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Surface structure of liquid Li and Na:: An ab initio molecular dynamics study -: art. no. 085501

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PHYSICAL REVIEW LETTERS (2004)

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Generalization of the Kohn-Sham equations with constrained electron density formalism and its time-dependent response theory formulation

ME Casida et al.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2004)

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Hydrogen-bonding-induced shifts of the excitation energies in nucleic acid bases: An interplay between electrostatic and electron density overlap effects

TA Wesolowski

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY (2004)

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Exact analytic total energy functional for Hooke's atom generated by local-scaling transformations

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2004)

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Thermal properties of impurity-doped clusters:: Orbital-free molecular dynamics simulations of the meltinglike transition in Li1Na54 and Cs1Na54

A Aguado et al.

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Conjugate-gradient optimization method for orbital-free density functional calculations

H Jiang et al.

JOURNAL OF CHEMICAL PHYSICS (2004)

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Correction Chemistry, Physical

Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes (vol 119, pg 12129, 2003)

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First-principles prediction of icosahedral quantum dots for tetravalent semiconductors

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PHYSICAL REVIEW LETTERS (2004)

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Modified statistical treatment of kinetic energy in the Thomas-Fermi model

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Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes

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Small representative benchmarks for thermochemical calculations

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Testing the kinetic energy functional: Kinetic energy density as a density functional

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Collective ionic dynamics in the liquid Na-Cs alloy:: An ab initio molecular dynamics study -: art. no. 041204

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A direct optimization method for calculating density functionals and exchange-correlation potentials from electron densities

Q Wu et al.

JOURNAL OF CHEMICAL PHYSICS (2003)

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First-principles local pseudopotentials for group-IV elements

B Wang et al.

PHYSICAL REVIEW B (2003)

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Complete functional theory for the fermion density of independent particles subject to harmonic confinement in d dimensions for an arbitrary number of closed shells -: art. no. 054501

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Direct method for optimized effective potentials in density-functional theory

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PHYSICAL REVIEW LETTERS (2002)

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Link between the kinetic- and exchange-energy functionals in the generalized gradient approximation

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY (2002)

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An object-oriented scripting interface to a legacy electronic structure code

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COMPUTING IN SCIENCE & ENGINEERING (2002)

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Dynamical properties of liquid Al near melting:: An orbital-free molecular dynamics study -: art. no. 184201

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The SIESTA method for ab initio order-N materials simulation

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JOURNAL OF PHYSICS-CONDENSED MATTER (2002)

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Kinetic energy density functionals for non-periodic systems

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SOLID STATE COMMUNICATIONS (2002)

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Linear-scaling density-functional-theory calculations of electronic structure based on real-space grids: design, analysis, and scalability test of parallel algorithms

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COMPUTER PHYSICS COMMUNICATIONS (2001)

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Pseudopotentials for the calculation of dynamic properties of liquids

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JOURNAL OF PHYSICS-CONDENSED MATTER (2001)

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Orbital free ab initio molecular dynamics study of liquid Al near melting

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JOURNAL OF CHEMICAL PHYSICS (2001)

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Melting in large sodium clusters:: An orbital-free molecular dynamics study

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JOURNAL OF PHYSICAL CHEMISTRY B (2001)

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Finite-element methods in electronic-structure theory

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COMPUTER PHYSICS COMMUNICATIONS (2001)

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Orbital-free molecular dynamics study of melting in K20, K55, K92, K142, Rb55, and Cs55 clusters -: art. no. 115404

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PHYSICAL REVIEW B (2001)

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Thomas-Fermi-Dirac-von Weizsacker models in finite systems

GKL Chan et al.

JOURNAL OF CHEMICAL PHYSICS (2001)

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2001)

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Gaussian-3X (G3X) theory: Use of improved geometries, zero-point energies, and Hartree-Fock basis sets

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JOURNAL OF CHEMICAL PHYSICS (2001)

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Review Physics, Multidisciplinary

Real-space mesh techniques in density-functional theory

TL Beck

REVIEWS OF MODERN PHYSICS (2000)

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Linear-scaling parallel algorithms for the first principles treatment of metals

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COMPUTER PHYSICS COMMUNICATIONS (2000)

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Local kinetic-energy density of the Airy gas -: art. no. 052511

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PHYSICAL REVIEW A (2000)

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Assessment of Gaussian-3 and density functional theories for a larger experimental test set

LA Curtiss et al.

JOURNAL OF CHEMICAL PHYSICS (2000)

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The role of the kinetic energy density in approximations to the exchange energy

M Ernzerhof

JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM (2000)

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