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Structure of Amines01:19

Structure of Amines

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The hybridized nitrogen atom in amines possesses a lone pair of electrons and is bound to three substituents with a bond angle of around 108°, which is less than the tetrahedral angle of 109.5°. However, the C–N–H bond angle is slightly larger at 112°, with a carbon–nitrogen bond length of 147 pm. This carbon–nitrogen bond length of of amines is longer than the carbon–oxygen bond of alcohols (143 pm) but shorter than alkanes’...
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In proton NMR spectroscopy, primary amines and secondary amines showcase their N–H protons as a broad signal in the chemical shift range between δ 0.5 and 5 ppm. The exact position in this range depends on several factors, including sample concentration, hydrogen bonding, and the type of solvent used. Since amine protons undergo fast proton exchange in solution, the protons are labile and therefore do not participate in any splitting with adjacent protons. Thus, the observed peak is...
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Alkylation is one of the methods used to prepare amines. Direct alkylation of ammonia or a primary amine with an alkyl halide gives polyalkylated amines along with a quaternary ammonium salt through successive SN2 reactions. This process of making the quaternary salt through the direct alkylation method is called exhaustive alkylation.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
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Tunneling Quantum Dynamics in Ammonia.

Ciann-Dong Yang1, Shiang-Yi Han2

  • 1Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 701, Taiwan.

International Journal of Molecular Sciences
|August 7, 2021
PubMed
Summary
This summary is machine-generated.

Quantum tunneling in ammonia molecules is explained using quantum Hamilton mechanics and quantum trajectories, offering a deterministic view beyond probability. This approach reveals underlying mechanisms for nitrogen atom tunneling and vibration periods.

Keywords:
ammoniaquantum Hamilton mechanicsquantum molecular dynamicsquantum trajectorytunneling dynamics

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Area of Science:

  • Quantum Mechanics
  • Physical Chemistry
  • Computational Chemistry

Background:

  • Ammonia (NH3) serves as a classic two-state quantum system.
  • Quantum tunneling is typically described using probabilistic quantum mechanics.
  • The tunneling phenomenon in ammonia involves the inversion of the nitrogen atom.

Purpose of the Study:

  • To explain ammonia tunneling using trajectory-based quantum dynamics.
  • To describe the tunneling phenomenon from a deterministic quantum mechanical perspective.
  • To analyze the vibrations of the nitrogen atom via quantum trajectories.

Main Methods:

  • Application of quantum Hamilton mechanics to describe tunneling.
  • Solving Hamilton's equations of motion to obtain quantum trajectories.
  • Analysis of nitrogen atom vibrations using computed quantum trajectories.

Main Results:

  • Quantum trajectories provide a deterministic description of nitrogen atom tunneling.
  • The study reveals underlying mechanisms for tunneling in ammonia.
  • Computed vibration periods from quantum trajectories show good agreement with experimental data.

Conclusions:

  • Trajectory-based quantum dynamics offers a mechanistic understanding of ammonia tunneling.
  • Quantum Hamilton mechanics provides a deterministic framework for analyzing molecular tunneling.
  • This approach enhances the understanding of quantum phenomena in molecular systems.