Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Nov 9, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

2.7K

Fast periodic Gaussian density fitting by range separation.

Hong-Zhou Ye1, Timothy C Berkelbach1

  • 1Department of Chemistry, Columbia University, New York, New York 10027, USA.

The Journal of Chemical Physics
|April 9, 2021
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

Gauss's Law01:07

Gauss's Law

8.7K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
8.7K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

226
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
226
Chromatographic Resolution01:15

Chromatographic Resolution

1.4K
In chromatography, a solute moves through a chromatographic column and tends to spread, forming a Gaussian-shaped band. The longer the solute spends in the column, the broader the band becomes. The broadening can lead to overlaps within the column, affecting separation effectiveness.
The effectiveness of separation can be evaluated by determining the level of separation between two neighboring peaks in a chromatogram, which represents the individual components of a sample.
In chromatography,...
1.4K
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

2.0K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
2.0K
Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

4.4K
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
4.4K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

181
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
181

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Tight distance-dependent estimators for screening two-center and three-center short-range Coulomb integrals over Gaussian basis functions.

The Journal of chemical physics·2021
Same author

Improving MP2 bandgaps with low-scaling approximations to EOM-CCSD.

The Journal of chemical physics·2021
Same author

Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches.

The Journal of chemical physics·2021
Same author

Vibrational heat-bath configuration interaction.

The Journal of chemical physics·2021
Same author

Full-frequency GW without frequency.

The Journal of chemical physics·2021
Same author

Bootstrap embedding with an unrestricted mean-field bath.

The Journal of chemical physics·2020
Same journal

The influence of chirality on the macroscopic behavior of multiferroic smectic phases.

The Journal of chemical physics·2026
Same journal

Polaron transformed canonically consistent quantum master equation.

The Journal of chemical physics·2026
Same journal

The x-ray absorption spectrum of the propargyl radical C3H3●.

The Journal of chemical physics·2026
Same journal

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. I. Conformer- and isomer-resolved infrared spectra.

The Journal of chemical physics·2026
Same journal

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. II. Isomer-resolved unimolecular dynamics.

The Journal of chemical physics·2026
Same journal

Quantum state-to-state dynamics studies of the C(3P) + OH(X2Π) → CO(a3Π) + H(2S) reaction based on a new HCO(12A″) potential energy surface.

The Journal of chemical physics·2026
See all related articles

We developed range-separated Gaussian density fitting (RSGDF) for efficient periodic calculations. This method significantly speeds up computations for solids while maintaining high accuracy.

Area of Science:

  • Computational chemistry
  • Materials science
  • Quantum mechanics

Background:

  • Periodic Gaussian density fitting (GDF) is crucial for accurate electronic structure calculations.
  • Existing GDF methods can be computationally intensive, especially for large systems or dense k-point meshes.

Purpose of the Study:

  • To introduce an efficient and accurate implementation of periodic Gaussian density fitting.
  • To improve the computational scaling of GDF for periodic systems.

Main Methods:

  • Range-separation of the Coulomb kernel into short-range (real space) and long-range (reciprocal space) components.
  • Implementation of algorithmic optimizations for evaluating three-center integrals.
  • Development of range-separated Gaussian density fitting (RSGDF).

More Related Videos

Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems
09:57

Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems

Published on: February 10, 2020

7.4K
Contrast-Matching Detergent in Small-Angle Neutron Scattering Experiments for Membrane Protein Structural Analysis and Ab Initio Modeling
10:27

Contrast-Matching Detergent in Small-Angle Neutron Scattering Experiments for Membrane Protein Structural Analysis and Ab Initio Modeling

Published on: October 21, 2018

12.7K

Related Experiment Videos

Last Updated: Nov 9, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

2.7K
Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems
09:57

Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems

Published on: February 10, 2020

7.4K
Contrast-Matching Detergent in Small-Angle Neutron Scattering Experiments for Membrane Protein Structural Analysis and Ab Initio Modeling
10:27

Contrast-Matching Detergent in Small-Angle Neutron Scattering Experiments for Membrane Protein Structural Analysis and Ab Initio Modeling

Published on: October 21, 2018

12.7K

Main Results:

  • RSGDF demonstrates sublinear to linear scaling with the number of k-points for common mesh sizes.
  • Achieved approximately ten-fold speedups compared to previous GDF methods for 3D solids.
  • Introduced minimal precision loss, with errors around 10^-5 E_h in Hartree-Fock energy.

Conclusions:

  • RSGDF offers a significant computational advantage for periodic electronic structure calculations.
  • The method provides a balance between computational efficiency and accuracy.
  • Precision can be systematically improved by adjusting auxiliary basis set size with minimal overhead.