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

Calculations of Electric Potential I01:15

Calculations of Electric Potential I

2.6K
Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of...
2.6K
Calculations of Electric Potential II01:27

Calculations of Electric Potential II

2.3K
An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
2.3K
Calculation of Volume of Solids by Integration01:27

Calculation of Volume of Solids by Integration

128
Volume calculation often begins with simple geometric solids. For example, the volume of a rectangular box is obtained by multiplying the area of its base by its height. This straightforward approach relies on the fact that the cross-sectional area of the box remains constant throughout its length. Many real-world objects, however, do not have uniform cross-sections, and their volumes cannot be determined using elementary geometric formulas.To address this limitation, the Slicing Method...
128
The Nucleosome Core Particle02:10

The Nucleosome Core Particle

14.6K
Nucleosomes are the DNA-histone complex, where the DNA strand is wound around the histone core. The histone core is an octamer containing two copies of H2A, H2B, H3, and H4 histone proteins.
The paradox
Nucleosomes, paradoxically, perform two opposite functions simultaneously. On the one hand, their main responsibility is to protect the delicate DNA strands from physical damage and help achieve a higher compaction ratio. While on the other hand, they must allow polymerase enzymes to access DNA...
14.6K
Velocity and Position by Integral Method01:13

Velocity and Position by Integral Method

8.4K
If acceleration as a function of time is known, then velocity and position functions can be derived using integral calculus. For constant acceleration, the integral equations refer to the first and second kinematic equations for velocity and position functions, respectively.
Consider an example to calculate the velocity and position from the acceleration function. A motorboat is traveling at a constant velocity of 5.0 m/s when it starts to decelerate to arrive at the dock. Its acceleration is...
8.4K
Calculating Standard Free Energy Changes02:49

Calculating Standard Free Energy Changes

25.7K
The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
25.7K

You might also read

Related Articles

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

Sort by
Same author

NN-xTB: density functional accuracy at semi empirical speed with neural network extended tight binding.

Nature communications·2026
Same author

Double-Hybrid, but Not Double-Cost: GPU-Accelerated DHDFT for the COMPAS-3 Data Set of Polybenzenoid Hydrocarbons.

Journal of chemical theory and computation·2026
Same author

Molecular Properties in Quantum-Classical Auxiliary-Field Quantum Monte Carlo: Correlated Sampling with Application to Accurate Nuclear Forces.

Journal of chemical theory and computation·2025
Same author

Efficient Algorithms for GPU Accelerated Evaluation of the DFT Exchange-Correlation Functional.

Journal of chemical theory and computation·2025
Same author

High-Performance, High-Angular-Momentum J Engine on Graphics Processing Units.

Journal of chemical theory and computation·2025
Same author

Acceleration of Self-Consistent Field Calculations Using Basis Set Projection and Many-Body Expansion as Initial Guess Methods.

Journal of chemical theory and computation·2025
Same journal

Photoinduced Charge-Transfer Suppresses Triplet Formation Efficiency in Thiocoumarins: Evidence from Ultrafast Spectroscopy and Theoretical Calculations.

The journal of physical chemistry. A·2026
Same journal

Porphyrin Aggregation Revisited: From the Four-Orbital Gouterman Model to an Eight-Orbital Framework in Porphin H-Dimers.

The journal of physical chemistry. A·2026
Same journal

Unraveling the Electronic Origin of Selectivity in Ambimodal Transition States with Valence Bond Theory.

The journal of physical chemistry. A·2026
Same journal

Mechanism and Kinetics of the Initial Oxidative Ring-Opening of Corannulene Radicals under Combustion Conditions.

The journal of physical chemistry. A·2026
Same journal

High-Resolution Absorption Spectroscopy of ND<sub>3</sub> between 59,000 and 93,000 cm<sup>-1</sup>.

The journal of physical chemistry. A·2026
Same journal

Twisted-Driven Photoionization of Aligned Chiral Molecules: Signatures of Circular and Helical Dichroism.

The journal of physical chemistry. A·2026
See all related articles

Related Experiment Video

Updated: Feb 14, 2026

An Efficient In Vitro Transposition Method by a Transcriptionally Regulated Sleeping Beauty System Packaged into an Integration Defective Lentiviral Vector
10:13

An Efficient In Vitro Transposition Method by a Transcriptionally Regulated Sleeping Beauty System Packaged into an Integration Defective Lentiviral Vector

Published on: January 12, 2018

9.5K

Efficient Method for Calculating Effective Core Potential Integrals.

Simon C McKenzie1, Evgeny Epifanovsky2, Giuseppe M J Barca1

  • 1Research School of Chemistry , Australian National University , Canberra , Australian Capital Territory 2601 , Australia.

The Journal of Physical Chemistry. A
|February 22, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a faster method for calculating effective core potential (ECP) integrals, crucial for quantum chemistry. The new algorithm improves computational efficiency for electronic structure calculations.

More Related Videos

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

6.9K
Sediment Core Extrusion Method at Millimeter Resolution Using a Calibrated, Threaded-rod
06:06

Sediment Core Extrusion Method at Millimeter Resolution Using a Calibrated, Threaded-rod

Published on: August 17, 2016

11.8K

Related Experiment Videos

Last Updated: Feb 14, 2026

An Efficient In Vitro Transposition Method by a Transcriptionally Regulated Sleeping Beauty System Packaged into an Integration Defective Lentiviral Vector
10:13

An Efficient In Vitro Transposition Method by a Transcriptionally Regulated Sleeping Beauty System Packaged into an Integration Defective Lentiviral Vector

Published on: January 12, 2018

9.5K
Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

6.9K
Sediment Core Extrusion Method at Millimeter Resolution Using a Calibrated, Threaded-rod
06:06

Sediment Core Extrusion Method at Millimeter Resolution Using a Calibrated, Threaded-rod

Published on: August 17, 2016

11.8K

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Effective core potential (ECP) integrals are challenging one-electron integrals in quantum chemistry.
  • The complexity arises from projection operators, involving radial terms like r⁰, r⁻¹, and r⁻².

Purpose of the Study:

  • To develop a more efficient algorithm for calculating ECP integrals.
  • To improve the speed of quantum chemical computations involving ECPs.

Main Methods:

  • Derived new recurrence relations and upper bounds for ECP integrals using analytic expressions for r⁰ terms.
  • Developed a reconstruction method to replace r⁻¹ and r⁻² terms with r⁰ terms, minimizing errors.

Main Results:

  • The new method provides accurate ECP integral calculations with chemically insignificant errors for r⁻¹ and r⁻² terms.
  • The algorithm demonstrates significant speed improvements compared to previous implementations in Q-Chem, GAMESS, and Dalton.

Conclusions:

  • The developed algorithm offers a faster and efficient approach to ECP integral calculations.
  • This advancement is expected to accelerate electronic structure calculations in computational chemistry.