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IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

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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.
According to Hooke's law, the vibrational frequency is directly proportional to...
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IR Spectroscopy: Molecular Vibration Overview01:24

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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.
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...
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IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

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Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single...
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IR Spectrum Peak Broadening: Hydrogen Bonding01:23

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The vibrational frequency of a bond is directly proportional to its bond strength. As a result, stronger bonds vibrate at higher frequencies, while weaker bonds vibrate at lower frequencies. The stretching vibration of the strong O–H bond in alcohols and phenols (very dilute solution or gas phase) appears as a sharp peak at 3600–3650 cm−1.
However, the extent of hydrogen bonding influences the observed stretching frequency and band broadening. Intermolecular or intramolecular...
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Spin–Spin Coupling Constant: Overview01:08

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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.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must...
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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Basis Set Extrapolation of Vibrational Frequencies.

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  • 1Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark.

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|March 21, 2023
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Three methods for extrapolating harmonic vibrational frequencies to the complete basis set limit were studied. For most molecules, results were similar, but loosely bound complexes showed unpredictable behavior with extrapolated Hessians.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry

Background:

  • Accurate prediction of molecular properties is crucial in chemistry.
  • Harmonic vibrational frequencies are key molecular properties.
  • Basis set extrapolation aims to approximate results at the complete basis set limit.

Purpose of the Study:

  • To compare three distinct methods for extrapolating harmonic vibrational frequencies to the complete basis set limit.
  • To assess the reliability of these extrapolation methods for different types of molecular systems.

Main Methods:

  • Direct extrapolation of harmonic vibrational frequencies.
  • Frequency calculation using extrapolated Hessians.
  • Frequency calculation using Hessians from extrapolated energy surfaces.

Main Results:

  • All three extrapolation methods produced similar results for regular molecules.
  • Extrapolation using Hessians led to unpredictable vibrational frequencies for loosely bound complexes.
  • No significant improvement in accuracy was observed compared to the underlying non-extrapolated results.

Conclusions:

  • The choice of extrapolation method can significantly impact results for loosely bound systems.
  • Basis set extrapolation for harmonic vibrational frequencies does not inherently improve accuracy over the initial calculations.