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 Concept Videos

Dimensional Analysis01:23

Dimensional Analysis

Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
Dimensional Analysis02:19

Dimensional Analysis

The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
Dimensional Analysis03:40

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
Dimensional Analysis01:27

Dimensional Analysis

Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

You might also read

Related Articles

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

Sort by
Same author

Origins of Reactivity in SAM-Utilizing Ribozyme SAMURI-Catalyzed RNA Alkylation.

Journal of the American Chemical Society·2026
Same author

The scientific legacy of Martin Karplus from the perspective of his collaborators.

Biophysical journal·2026
Same author

Automated Force Field Developer and Optimizer Platform: Torsion Reparameterization.

Journal of chemical information and modeling·2026
Same author

A Relative Binding Free Energy Framework for Structurally Dissimilar Molecules.

Journal of chemical information and modeling·2026
Same author

SAMTI: Sampling Adaptive Thermodynamic Integration for Alchemical Free Energy Calculations.

The journal of physical chemistry. B·2025
Same author

DPA-2: a large atomic model as a multi-task learner.

npj computational materials·2025

Related Experiment Video

Updated: Jun 1, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Density-functional expansion methods: generalization of the auxiliary basis.

Timothy J Giese1, Darrin M York

  • 1BioMaPS Institute and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854-8087, USA.

The Journal of Chemical Physics
|May 24, 2011
PubMed
Summary

This study advances density-functional expansion methods by incorporating higher-order density and spin density terms. The new approach improves computational efficiency and accuracy in electronic structure calculations.

More Related Videos

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
07:16

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion

Published on: October 20, 2023

Related Experiment Videos

Last Updated: Jun 1, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
07:16

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion

Published on: October 20, 2023

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Materials Science

Background:

  • Density-functional theory (DFT) is a cornerstone of modern electronic structure calculations.
  • Accurate treatment of electron density response is crucial for understanding molecular properties and reactions.
  • Existing methods face challenges in efficiently handling higher-order terms in density expansions.

Purpose of the Study:

  • To extend density-functional expansion methods to include second and higher-order terms for response and spin densities.
  • To develop a computationally efficient and accurate approach for electronic structure calculations.
  • To improve the representation of density response in theoretical models.

Main Methods:

  • Formulation of density-functional expansion methods incorporating arbitrary single-center auxiliary basis sets.
  • Representation of two-center atomic orbital products using auxiliary functions and a local constrained variational procedure.
  • Pre-tabulation and spline fitting of mapping coefficients as a function of internuclear separation for efficient lookup.
  • Implementation of a linear-scaling algorithm by treating auxiliary density as a point-multipole expansion.

Main Results:

  • Demonstrated significant improvement in the representation of density response compared to models without auxiliary bases.
  • Explored the impact of angular and radial completeness on the accuracy of the method.
  • Parametrized and compared various auxiliary basis sets, including one analogous to the self-consistent-charge density-functional tight-binding model.

Conclusions:

  • The developed method offers a computationally efficient and accurate way to treat higher-order density response terms.
  • The use of auxiliary basis sets and spline-fitted coefficients enhances the performance of density-functional expansion methods.
  • This work provides a foundation for more sophisticated electronic structure calculations with improved accuracy and scalability.