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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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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...
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Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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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.
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

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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...
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Directionality of Nuclear Transport01:42

Directionality of Nuclear Transport

3.8K
Ras-related nuclear protein or Ran is a small G protein that cycles between its GTP and GDP bound states. Ran specific regulators, a Ran GTPase Activating Protein or RanGAP present in the cytosol and a Ran guanine nucleotide exchange factor or RanGEF present inside the nucleus regulate GTP/GDP exchange. A high concentration of GTP inside the cells, in addition to this asymmetric distribution of  Ran-specific regulators, leads to a higher RanGTP concentration inside the nucleus. This...
3.8K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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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...
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Updated: Apr 22, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Analytical Nuclear Gradients for State-Averaged Configuration Interaction Singles Variants: Application to Conical

Takashi Tsuchimochi1,2

  • 1College of Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548, Japan.

Journal of Chemical Theory and Computation
|April 21, 2026
PubMed
Summary
This summary is machine-generated.

State-averaged orbital-optimized configuration interaction singles (SACIS) and its spin-projected extension (SAECIS) accurately predict conical intersection geometries. These methods offer reliable excited-state descriptions at a low computational cost.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate prediction of molecular geometries and reaction pathways is crucial in chemistry.
  • Minimum-energy conical intersections (MECXs) play a vital role in understanding photochemical reactions and excited-state dynamics.
  • Existing methods often struggle to accurately describe conical intersections, especially within cost-effective computational frameworks.

Purpose of the Study:

  • To derive analytical nuclear gradients for state-averaged orbital-optimized configuration interaction singles (SACIS) and its spin-projected extension (SAECIS).
  • To enable efficient geometry optimization and MECX searches using these low-cost methods.
  • To assess the accuracy and reliability of SACIS and SAECIS for describing conical intersections.

Main Methods:

  • Development of analytical nuclear gradients using a Lagrangian approach.
  • Explicit removal of null-space contributions in coupled-perturbed equations for numerical stability.
  • Application of SACIS and SAECIS to twisted-pyramidalized ethylene and benchmark calculations on 12 MECXs.

Main Results:

  • SACIS and SAECIS qualitatively reproduce correct conical intersection topology, outperforming conventional CIS and ECIS.
  • Benchmark calculations show mean RMSDs below 0.1 Å compared to high-level references for both methods.
  • SACIS effectively incorporates static correlation via variational orbital relaxation, mitigating ground-state Hartree-Fock orbital bias.
  • Spin projection was found to be nonessential for the qualitative description of these intersections.

Conclusions:

  • SACIS and SAECIS provide qualitatively reliable conical intersection descriptions at mean-field computational cost.
  • SACIS offers a better cost-performance balance for general applications due to its comparable accuracy and lower computational overhead.
  • SAECIS may be advantageous for systems involving higher excited states with significant double-excitation character.