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

Convergent Evolution01:54

Convergent Evolution

33.0K
Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.
33.0K
Region of Convergence01:17

Region of Convergence

955
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
955
pH Scale02:41

pH Scale

80.0K
Hydronium and hydroxide ions are present both in pure water and in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion product of water (Kw). The concentrations of these ions in a solution are often critical determinants of the solution’s properties and the chemical behaviors of its other solutes. Two different solutions can differ in their hydronium or hydroxide ion concentrations by a million, billion, or even trillion times. A common means of...
80.0K
Convergence of Fourier Series01:21

Convergence of Fourier Series

427
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
427
Space Trusses01:25

Space Trusses

1.3K
A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.
At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape...
1.3K
State Space Representation01:27

State Space Representation

593
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
593

You might also read

Related Articles

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

Sort by
Same author

Rational donor placement into a native exciton manifold: cavity-anchored dyes drive sub-picosecond energy transfer in light-harvesting complex 2.

Physical chemistry chemical physics : PCCP·2026
Same author

Molecular Crystals With Reversible Chromic Three-State Crystal-to-Crystal Transformation via the Dynamic Motion of Negatively Curved π-Frameworks.

Chemistry (Weinheim an der Bergstrasse, Germany)·2026
Same author

Hydrogen Atom Transfer Barriers by High-Valent Iron(IV)-Oxo Complexes: A DFT and Multireference Ab Initio Study.

Inorganic chemistry·2026
Same author

A copper-dependent redox-based hydrogen peroxide perception in plants.

Nature communications·2026
Same author

Ca<sup>2+</sup>-Driven Protein Compaction Tunes NIR Absorption in the Thermophilic Purple Bacterial LH1.

The journal of physical chemistry letters·2026
Same author

High-quality quantum chemical data for spin state determination in transition-metal complexes.

Physical chemistry chemical physics : PCCP·2026
Same journal

A data-driven modeling study on the accurate identification of Doppler-free saturated absorption spectra in diatomic tellurium (130Te2).

The Journal of chemical physics·2026
Same journal

Anharmonic phonons via quantum thermal bath simulations.

The Journal of chemical physics·2026
Same journal

Quantum simulation of alignment dependent differential cross sections in co-propagating molecular beams at cold collision energies.

The Journal of chemical physics·2026
Same journal

Non-additive ion effects on the coil-globule equilibrium of a generic polymer in aqueous salt solutions.

The Journal of chemical physics·2026
Same journal

Insights into the unexpected small reduction of the temperature of maximum density of water by lithium chloride addition.

The Journal of chemical physics·2026
Same journal

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm-1 states of ethylene.

The Journal of chemical physics·2026
See all related articles

Related Experiment Video

Updated: Feb 8, 2026

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
07:28

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

Published on: January 21, 2017

7.3K

Large-scale relativistic complete active space self-consistent field with robust convergence.

Ryan D Reynolds1, Takeshi Yanai2, Toru Shiozaki1

  • 1Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA.

The Journal of Chemical Physics
|July 9, 2018
PubMed
Summary
This summary is machine-generated.

We developed a more stable and efficient density fitting algorithm for relativistic complete active space self-consistent field (CASSCF) calculations. This new method accelerates convergence and handles complex interactions, including external magnetic fields.

More Related Videos

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

14.2K
A Robust Method for the Large-Scale Production of Spheroids for High-Content Screening and Analysis Applications
06:40

A Robust Method for the Large-Scale Production of Spheroids for High-Content Screening and Analysis Applications

Published on: December 28, 2021

4.0K

Related Experiment Videos

Last Updated: Feb 8, 2026

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity
07:28

Psychophysically-anchored, Robust Thresholding in Studying Pain-related Lateralization of Oscillatory Prestimulus Activity

Published on: January 21, 2017

7.3K
Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

14.2K
A Robust Method for the Large-Scale Production of Spheroids for High-Content Screening and Analysis Applications
06:40

A Robust Method for the Large-Scale Production of Spheroids for High-Content Screening and Analysis Applications

Published on: December 28, 2021

4.0K

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Relativistic Quantum Mechanics

Background:

  • Relativistic quantum chemistry methods are crucial for accurately describing heavy elements.
  • Complete Active Space Self-Consistent Field (CASSCF) is a key method for electron correlation.
  • Previous algorithms for relativistic CASSCF faced stability challenges.

Purpose of the Study:

  • To develop a significantly more stable and efficient algorithm for relativistic CASSCF calculations.
  • To improve the computational performance of relativistic CASSCF by employing density fitting.
  • To extend the applicability of relativistic CASSCF to systems with Gaunt and Breit interactions and external magnetic fields.

Main Methods:

  • Implementation of a novel density fitting algorithm for relativistic CASSCF.
  • Utilizing a second-order orbital update scheme with an iterative augmented Hessian procedure.
  • Direct contraction of the density-fitted orbital Hessian to trial vectors for efficiency.
  • Employing approximate orbital Hessians computed with the Dirac-Coulomb Hamiltonian for Gaunt and Breit interactions.
  • Using gauge-including atomic orbitals for molecular integrals in external magnetic fields.

Main Results:

  • The new algorithm demonstrates significantly improved stability compared to previous methods.
  • Each microiteration is computationally less demanding than a Dirac-Hartree-Fock iteration.
  • Macroiterations exhibit quadratic convergence, leading to faster overall convergence.
  • Efficient performance is achieved for CASSCF calculations including Gaunt and full Breit interactions.
  • The algorithm is successfully applied to systems under external magnetic fields.

Conclusions:

  • The developed density fitting algorithm offers a more stable and efficient approach to relativistic CASSCF.
  • This advancement facilitates accurate electronic structure calculations for heavy elements and complex systems.
  • The method's ability to handle magnetic fields and advanced interactions broadens its applicability in computational chemistry.