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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.
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¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR01:15

¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR

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The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
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¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

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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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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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MO Theory and Covalent Bonding02:40

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The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
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Vibrational Analysis of Constrained Molecular Systems.

Ankur K Gupta1, Krishnan Raghavachari1

  • 1Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States.

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Summary

This study introduces a new vibrational spectroscopy method to accurately analyze flexible biomolecules. It uses constraint projection to maintain native conformations, enabling precise structural determination.

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Area of Science:

  • Molecular spectroscopy
  • Computational chemistry
  • Biophysics

Background:

  • Vibrational spectroscopy (IR, Raman, VCD) is crucial for molecular structure and composition analysis.
  • Full molecular optimization can alter native conformations of large biomolecules like polypeptides.
  • Existing methods struggle with vibrational analysis of conformationally constrained geometries.

Purpose of the Study:

  • To develop a robust method for calculating theoretical vibrational spectra of conformationally flexible biomolecules.
  • To address the challenge of analyzing non-stationary points arising from dihedral angle constraints.
  • To provide a mathematical framework for accurate vibrational analysis under constraints.

Main Methods:

  • Imposing dihedral angle constraints during molecular geometry optimization.
  • Reformulating vibrational analysis to treat constrained geometries as subspace minima.
  • Projecting the force constant matrix onto a space orthogonal to constrained coordinates.

Main Results:

  • A novel method for computing vibrational spectra of constrained molecular geometries.
  • Demonstrated applicability to flexible biomolecules, exemplified by enkephalin.
  • Yields 3N - 6 - m nonzero frequencies, reflecting constraint incorporation.

Conclusions:

  • The developed method accurately computes vibrational spectra for conformationally flexible molecules under constraints.
  • This approach enhances the structural and compositional analysis of complex biomolecules.
  • Offers a comprehensive mathematical framework for constrained vibrational spectroscopy.