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

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Gradient and Del Operator01:14

Gradient and Del Operator

In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

You might also read

Related Articles

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

Sort by
Same author

Wound, Pressure Ulcer, and Burn Guidelines (2023)-6: Guidelines for the Management of Burns, Third Edition.

The Journal of dermatology·2026
Same author

Molecular docking, MM/GBSA, FEP/MD, and DFT/MM MD studies on predicting binding affinity of carbonic anhydrase II inhibitors.

Physical chemistry chemical physics : PCCP·2026
Same author

Hermansky-Pudlak Syndrome Type 3 Complicated by Schizophrenia and Crohn's-Like Colitis.

The Journal of dermatology·2026
Same author

Updated Analysis of Albinism in Japan: 290 Families With Novel Pathological Variants.

Pigment cell & melanoma research·2025
Same author

Complete response to nivolumab in a patient with HPV-associated squamous cell carcinoma of the anus: the predictive value of tumour-infiltrating CD8+PD-1+ T cells.

European journal of dermatology : EJD·2025
Same author

Deep intronic variant in TYR causes OCA1A in Japanese families through pseudoexon activation.

Journal of dermatological science·2025

Related Experiment Video

Updated: May 17, 2026

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
06:34

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

Published on: September 2, 2016

Analytical gradients for density functional calculations with approximate spin projection.

Toru Saito1, Walter Thiel

  • 1Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany.

The Journal of Physical Chemistry. A
|October 24, 2012
PubMed
Summary

This study introduces analytical gradients for broken-symmetry DFT (BS-UDFT) calculations, improving geometry optimization for open-shell systems. The new method (AGAP-opt) is more precise and efficient than previous approaches, handling spin contamination effectively.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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

Published on: May 27, 2020

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

Related Experiment Videos

Last Updated: May 17, 2026

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging
06:34

In Situ Monitoring of Diffusion of Guest Molecules in Porous Media Using Electron Paramagnetic Resonance Imaging

Published on: September 2, 2016

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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

Published on: May 27, 2020

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

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Density Functional Theory (DFT) is crucial for molecular modeling.
  • Unrestricted DFT (UDFT) is used for open-shell systems but can suffer from spin contamination.
  • Geometry optimization is essential for determining molecular structures.

Purpose of the Study:

  • To derive and implement analytical gradients for BS-UDFT calculations.
  • To improve the efficiency and robustness of geometry optimizations for open-shell systems.
  • To demonstrate the effectiveness of removing spin contamination during optimization.

Main Methods:

  • Development of analytical gradients for BS-UDFT.
  • Implementation of Yamaguchi's approximate spin projection method for spin contamination removal.
  • Geometry optimization using analytical gradients (AGAP-opt) and numerical gradients (NAP-opt).

Main Results:

  • AGAP-opt provides results consistent with NAP-opt but is more precise, efficient, and robust.
  • The method enables full geometry optimizations for large open-shell systems.
  • Demonstrated effectiveness on organic diradicals and a binuclear vanadium(II) complex, handling significant spin contamination.

Conclusions:

  • Analytical gradients significantly enhance BS-UDFT geometry optimizations.
  • AGAP-opt is a superior alternative to NAP-opt for open-shell systems.
  • The method is capable of handling complex systems with pronounced spin contamination, such as transition metal complexes.