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Related Concept Videos

Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

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. This...
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 Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
Atomic Nuclei: Magnetic Resonance01:05

Atomic Nuclei: Magnetic Resonance

The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
Nuclear Overhauser Enhancement (NOE)01:06

Nuclear Overhauser Enhancement (NOE)

Irradiation of a spin-active nucleus causes an increase or decrease in the signal intensity of neighboring nuclei that are not necessarily chemically bonded or involved in J-coupling. This phenomenon, called the nuclear Overhauser enhancement (NOE), results from through-space interactions between the nuclear spins. The NOE effect decreases with increasing internuclear distance and is generally not observed beyond 4 angstroms. In NOE, dipole-dipole interactions between neighboring spin-active...
Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...

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External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
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Analytic Nuclear Gradients Including Oriented External Electric Fields in a Molecule-Fixed Frame.

Duc Anh Lai1, Devin A Matthews1

  • 1Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States.

Journal of Chemical Theory and Computation
|July 3, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed new molecular reference frames to precisely control electric fields for flexible molecules. This innovation enhances computational modeling for electric-field-controlled chemistry applications.

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Area of Science:

  • Computational chemistry
  • Physical chemistry
  • Molecular modeling

Background:

  • Electric-field-assisted chemistry offers control over molecular structure and reactivity.
  • Flexible molecules pose challenges due to orientation changes affecting applied electric fields.
  • Existing methods struggle with defining fixed fields for dynamic molecular systems.

Purpose of the Study:

  • To introduce novel molecular reference frames for unambiguous electric field definition.
  • To develop analytic nuclear gradients for electric-field-assisted calculations.
  • To enable accurate computational studies of molecular behavior in oriented electric fields.

Main Methods:

  • Proposed principal axis and local reference frames for molecular orientation.
  • Derived and implemented analytic nuclear gradients for external electric fields.
  • Performed field-dependent geometry optimizations on cis- and trans-formanilide.

Main Results:

  • The new reference frames eliminate orientation ambiguities between fields and molecules.
  • Distinct structural responses were observed for cis- and trans-formanilide under electric fields.
  • The formalism accurately predicts field-induced structural changes.

Conclusions:

  • The proposed molecular reference frames provide a robust method for defining oriented electric fields.
  • Analytic gradients facilitate systematic investigations of molecular properties under electric fields.
  • This work advances computational design for electric-field-controlled chemical processes.