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

Kinematic Equations - II01:17

Kinematic Equations - II

9.2K
The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
9.2K
Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

1.2K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
1.2K
Kinematic Equations - III01:18

Kinematic Equations - III

7.4K
The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
7.4K
Kinematic Equations - I01:26

Kinematic Equations - I

10.2K
When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
10.2K
Moment-of-Momentum Equation01:09

Moment-of-Momentum Equation

78
The moment-of-momentum equation is a critical tool for analyzing the torque produced by the rotating blades of a wind turbine. This equation is derived by applying Newton's second law to a fluid particle, which states that the rate of change of linear momentum is equal to the external force acting on the particle.
78
Equation of Motion: Rotation About a Fixed Axis01:18

Equation of Motion: Rotation About a Fixed Axis

195
Consider a flywheel, having an uneven mass distribution, rotating steadily around a fixed axis. As this rotation occurs, the center of mass of the flywheel traces a circular path. Understanding the acceleration of this center of mass requires observing both its tangential and normal components.
The tangential component is dependent on the direction of the angular acceleration of the flywheel. The tangential component of the acceleration propels the flywheel along its path. On the other hand,...
195

You might also read

Related Articles

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

Sort by
Same author

Metastable excited states of iodide-alkyl halide cluster anions: Insights from photodetachment spectroscopy and non-Hermitian quantum chemistry.

The Journal of chemical physics·2026
Same author

The Anionic States of Ubiquinone Characterized by Second-Order Approximate Coupled-Cluster Theory.

Journal of computational chemistry·2026
Same author

A Fresh Look at Signatures of <i>s</i>-Wave Scattering: Symmetry and the Breakdown of the Born-Oppenheimer Approximation.

The journal of physical chemistry. A·2026
Same author

Density Functional Theory with Complex Absorbing Potentials: A Fast and Accurate Way of Modeling Metastable Anions.

The journal of physical chemistry letters·2026
Same author

Computation of Partial Auger Decay Widths from Complex-Valued Equation-of-Motion Coupled-Cluster Energies.

The journal of physical chemistry. A·2026
Same author

Complex-energy second-order approximate coupled-cluster methods for electronic resonances.

The Journal of chemical physics·2025

Related Experiment Video

Updated: May 20, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.1K

Complex-Variable Equation-of-Motion Coupled-Cluster Singles and Doubles Theory with the Resolution-of-the-Identity

Simen Camps1, Cansu Utku1, Joel Creutzberg1

  • 1Department of Chemistry, KU Leuven, 3001 Leuven, Belgium.

The Journal of Physical Chemistry. A
|May 15, 2025
PubMed
Summary

This study introduces a computationally efficient complex-variable equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method with resolution-of-the-identity (RI) approximation for studying electronic resonances in molecules like N2 and CO.

More Related Videos

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

2.3K
Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
08:51

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

9.0K

Related Experiment Videos

Last Updated: May 20, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.1K
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

2.3K
Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
08:51

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

9.0K

Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Computational Chemistry

Background:

  • Electronic resonances are crucial for understanding molecular properties and reactions.
  • Accurate theoretical methods are needed to study these short-lived states.
  • Previous methods faced limitations in computational cost and accuracy.

Purpose of the Study:

  • To implement and validate a complex-variable equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) method using the resolution-of-the-identity (RI) approximation.
  • To investigate its performance for various electronic resonances in N2 and CO molecules.
  • To assess the impact of the RI approximation on the accuracy of resonance properties.

Main Methods:

  • Implementation of complex-variable equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory.
  • Application of the resolution-of-the-identity (RI) approximation to reduce memory requirements.
  • Utilizing complex basis functions (CBFs) and complex absorbing potential (CAP) methods.
  • Testing on temporary anions, Stark resonances, autoionizing Rydberg states, and core-ionized states of N2 and CO.

Main Results:

  • The RI-approximated EOM-CCSD method significantly reduces memory requirements compared to canonical EOM-CCSD.
  • RI error is generally smaller than basis set error for most resonance types.
  • The RI approximation can lead to qualitatively incorrect decay widths when they approach the RI error magnitude.
  • For states requiring larger auxiliary basis sets (autoionizing, core-ionized), RI error in decay width increases tenfold.

Conclusions:

  • The developed RI-approximated EOM-CCSD method offers a computationally feasible approach for studying electronic resonances.
  • Care must be taken when using the RI approximation for resonances with small decay widths.
  • The choice of auxiliary basis set is critical for accurate RI calculations of decay widths, especially for autoionizing and core-ionized states.