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Related Concept Videos

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

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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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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...
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The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect indicates a “loss” in mass of 4.0331 amu – 4.0026 amu = 0.0305 amu. The loss in mass accompanying the formation of an atom from protons, neutrons, and electrons is due to the conversion of that mass into energy that is evolved as the atom forms. The nuclear binding energy is the energy produced when the atoms’ nucleons...
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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
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Efficient Method for the Computation of Frozen-Core Nuclear Gradients within the Random Phase Approximation.

Viktoria Drontschenko1, Daniel Graf1, Henryk Laqua1

  • 1Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), 81377 Munich, Germany.

Journal of Chemical Theory and Computation
|November 4, 2022
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Summary
This summary is machine-generated.

This study presents an efficient method for calculating analytical frozen-core gradients in random phase approximation. The approach significantly speeds up computations with minimal error for molecular geometries.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • The frozen-core approximation simplifies electronic structure calculations by excluding core electrons.
  • Evaluating the response of active electron density is crucial but challenging.
  • Standard Kohn-Sham density response is also a key component.

Purpose of the Study:

  • To develop an efficient method for evaluating analytical frozen-core gradients within the random phase approximation (RPA).
  • To address the computational difficulties associated with the frozen-core approximation in density response calculations.
  • To extend the methodology to other electron correlation methods.

Main Methods:

  • Development of a procedure to efficiently evaluate the response of active electron density under the frozen-core approximation.
  • Integration with the response of the standard Kohn-Sham density.
  • Utilizing Cholesky decomposed densities to reintroduce occupied index in time-determining steps.

Main Results:

  • Achieved speedups of 20-30% using the frozen-core approximation with Cholesky decomposed densities.
  • Observed computational efficiency comparable to molecular orbital formulations.
  • Demonstrated that errors introduced by the frozen-core approximation are negligible for molecular geometries.

Conclusions:

  • The presented method offers an efficient way to compute analytical frozen-core gradients in RPA.
  • The approach is generalizable to various electron correlation methods.
  • The frozen-core approximation is reliable for geometry calculations in terms of accuracy.