Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Newtonian Fluid: Problem Solving

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...

Gaussian Elimination: Problem Solving

Gaussian Elimination: Problem Solving

Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

Kinematic Equations: Problem Solving

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...

Maxwell-Boltzmann Distribution: Problem Solving

Maxwell-Boltzmann Distribution: Problem Solving

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

Euler Equations of Motion

Euler Equations of Motion

Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...

You might also read

Related Articles

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

Sort by

Same author

Influence of food groups on plasma total homocysteine for specific MTHFR C677T genotypes in Chinese population.

Molecular nutrition & food research·2016

Same author

NIR Light Propulsive Janus-like Nanohybrids for Enhanced Photothermal Tumor Therapy.

Small (Weinheim an der Bergstrasse, Germany)·2016

Same author

Smart Hydrogels with Inhomogeneous Structures Assembled Using Nanoclay-Cross-Linked Hydrogel Subunits as Building Blocks.

ACS applied materials & interfaces·2016

Same author

Synergy between von Hippel-Lindau and P53 contributes to chemosensitivity of clear cell renal cell carcinoma.

Molecular medicine reports·2016

Same author

Aerobic Degradation of Sulfadiazine by Arthrobacter spp.: Kinetics, Pathways, and Genomic Characterization.

Environmental science & technology·2016

Same author

Downregulation of ClC-3 in dorsal root ganglia neurons contributes to mechanical hypersensitivity following peripheral nerve injury.

Neuropharmacology·2016

Same journal

Core-shell structured nanomaterials in dual-modal magnetic resonance imaging guided antitumor effect via combined treatment.

Frontiers in chemistry·2026

Same journal

Photo-responsive nanozymes: from photocatalytic mechanisms to precision therapy.

Frontiers in chemistry·2026

Same journal

From theoretical energy to practical utilization: interfacial stability, transport kinetics, and cell-level design in high-energy lithium-metal batteries.

Frontiers in chemistry·2026

Same journal

Zinc-vacancy defects in ZnO nanorods induced visible-light activity of photoelectrochemical glucose sensing: experimental and DFT+U analysis.

Frontiers in chemistry·2026

Same journal

Integrating multi-isotope calibration and infrared-assisted digestion for robust and sustainable multielemental determination in agroalimentary matrices by ICP-MS.

Frontiers in chemistry·2026

Same journal

Simultaneous phosphorus recovery as vivianite crystallization and hydrogen generation from acidified oil wastewater by Fe-C micro-electrolysis.

Frontiers in chemistry·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Nov 24, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Solving Coupled Cluster Equations by the Newton Krylov Method.

Chao Yang¹, Jiri Brabec², Libor Veis²

¹Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, United States.

Frontiers in Chemistry

|December 28, 2020

Summary

This summary is machine-generated.

We present a Newton Krylov method for solving coupled cluster equations, enhancing computational efficiency. This approach utilizes iterative methods for faster convergence in quantum chemistry calculations.

Keywords:

DIIS Newton-Krylov method couple cluster approximation nonlinear solver precondition

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Related Experiment Videos

Last Updated: Nov 24, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Spatial Separation of Molecular Conformers and Clusters

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

Area of Science:

Computational Chemistry
Quantum Mechanics
Numerical Analysis

Background:

Coupled cluster (CC) equations are fundamental in quantum chemistry for accurate electronic structure calculations.
Solving these nonlinear equations efficiently is crucial for enabling larger and more complex molecular systems.
Existing methods, like direct inversion of iterative subspace (DIIS), have limitations in convergence and stability.

Purpose of the Study:

To introduce and evaluate a novel Newton Krylov method for solving coupled cluster equations.
To assess the computational cost and convergence properties of this new approach.
To compare its performance against established methods like DIIS.

Main Methods:

Implementation of the Newton Krylov method to iteratively solve the coupled cluster amplitude equations.
Utilizing Krylov subspace methods (e.g., Generalized Minimum Residual - GMRES) for Newton corrections.
Employing finite difference approximations for Jacobian-vector multiplications, requiring additional residual evaluations.
Investigating pre-conditioning techniques and regularization for accelerated and stable convergence.

Main Results:

The Newton Krylov method provides an alternative approach to solving coupled cluster equations.
The computational cost is influenced by the interplay of inner Krylov and outer Newton iterations.
Analysis of termination criteria for inner iterations and the impact of pre-conditioners and regularization on convergence speed and stability.
Numerical examples demonstrate comparisons with DIIS methods.

Conclusions:

The Newton Krylov method offers a viable and potentially more efficient alternative for solving coupled cluster equations.
Careful selection of termination criteria, pre-conditioners, and regularization techniques can optimize performance.
Further studies are warranted to fully establish its advantages over existing methods across a broader range of chemical problems.