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When Infrared (IR) radiation passes through a covalently bonded molecule, the bonds transition from lower to higher vibrational levels. The fundamental vibrational motions that result in infrared absorption can be classified as stretching or bending vibrations.
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A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
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At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
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A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
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Concordant Mode Approach for Molecular Vibrations.

Mitchell E Lahm1, Nathaniel L Kitzmiller1, Henry F Mull1

  • 1Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602 United States.

Journal of the American Chemical Society
|December 15, 2022
PubMed
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The Concordant Mode Approach (CMA) offers a new hierarchy for quantum chemical computations, enabling faster calculations of harmonic vibrational frequencies for larger systems. This method significantly speeds up computations while maintaining high accuracy.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Spectroscopy

Background:

  • Accurate calculation of harmonic vibrational frequencies is crucial for understanding molecular properties and reaction mechanisms.
  • Current computational methods face limitations in system size and computational cost for high-level theories.

Purpose of the Study:

  • To introduce the Concordant Mode Approach (CMA) as a novel computational hierarchy.
  • To enable efficient and accurate computation of harmonic vibrational frequencies for larger systems.

Main Methods:

  • CMA utilizes transferrable internal-coordinate normal modes from a lower level of theory (B) as a basis for higher-level theory (A).
  • This approach scales linearly with system size, allowing for significant CPU time speedups.
  • Validated against CCSD(T)/cc-pVTZ (Level A) using CCSD(T)/cc-pVDZ and B3LYP/6-31G(2df,p) (Level B).

Main Results:

  • CMA achieved nearly order-of-magnitude speedups in CPU time.
  • The diagonal CMA-0A(nc) scheme showed remarkable accuracy with mean absolute deviations (MADs) of 0.2 cm⁻¹.
  • Standard deviations for frequency residuals were less than 0.5 cm⁻¹.
  • Zero-point vibrational energies (ZPVEs) exhibited negligible errors (~0.3 cm⁻¹).

Conclusions:

  • CMA provides a computationally efficient and highly accurate method for determining harmonic vibrational frequencies.
  • The approach significantly expands the feasibility of high-level quantum chemical computations for larger molecular systems.
  • CMA represents a significant advancement in computational spectroscopy and quantum chemistry.