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Related Concept Videos

Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Conformations of Cyclohexane02:11

Conformations of Cyclohexane

Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal tetrahedral value,...
Symmetric Member in Bending01:07

Symmetric Member in Bending

In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
Upward Impending Motion01:21

Upward Impending Motion

A square-threaded screw jack is a mechanical device widely used for lifting heavy loads or applying considerable force. Its operation is based on converting the force applied at its handle into a torsional moment, causing the upward impending motion of the screw. This movement is accomplished by overcoming the static friction between the threads of the screw and the jack.
To better comprehend how a screw jack functions, consider the completely unraveled thread as a block in contact with the...
Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
Chair Conformation of Cyclohexane02:02

Chair Conformation of Cyclohexane

The chair conformation is the most stable form of cyclohexane due to the absence of angle and torsional strain. The absence of angle strain is a result of cyclohexane’s bond angle being very close to the ideal tetrahedral bond angle of 109.5° in its chair conformer. Similarly, the torsional strain is also absent owing to the perfectly staggered arrangement of bonds.
The hydrogen atoms linked to carbons are arranged in two different axial and equatorial orientations to achieve this staggered...

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Theoretical Calculation and Experimental Verification for Dislocation Reduction in Germanium Epitaxial Layers with Semicylindrical Voids on Silicon
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The entropic barrier around the conical intersection seam.

Johannes C B Dietschreit1, Sebastian Mai1, Leticia González1

  • 1Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria.

The Journal of Chemical Physics
|June 23, 2026
PubMed
Summary

Mixed quantum-classical simulations capture nonadiabatic transitions without sampling exact conical intersections (CIs). Classical nuclear motion is statistically constrained, preventing trajectories from reaching the CI seam due to diverging free energy.

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Area of Science:

  • Chemical Physics
  • Quantum Chemistry
  • Computational Chemistry

Background:

  • Conical intersections (CIs) are crucial for nonadiabatic transitions in molecular systems.
  • Mixed quantum-classical (MQC) methods are widely used to simulate these processes.
  • A key challenge is understanding why MQC simulations succeed despite rarely sampling exact electronic degeneracies at CIs.

Purpose of the Study:

  • To investigate the statistical-mechanical reasons behind MQC simulations not sampling exact conical intersections.
  • To explain how MQC methods accurately describe nonadiabatic dynamics without reaching CI geometries.

Main Methods:

  • Derivation of free energy along the adiabatic energy gap using a linear vibronic coupling model.
  • Analytical demonstration of free energy divergence near the CI seam.
  • Molecular dynamics simulations of the methaniminium cation on the S1 surface.

Main Results:

  • Classical nuclear motion is subject to a statistical-mechanical constraint that prevents sampling exact degeneracies.
  • The free energy along the adiabatic energy gap diverges as the gap approaches zero.
  • Simulated trajectories approached regions with small gaps but never reached the CI seam.

Conclusions:

  • MQC simulations successfully capture nonadiabatic behavior due to a fundamental statistical-mechanical constraint on classical nuclear motion.
  • Classical trajectories can effectively sense the presence of CIs without needing to visit them.
  • This clarifies the validity and success of MQC approaches in describing photochemical processes.