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Related Concept Videos

Conformations of Cyclohexane02:11

Conformations of Cyclohexane

Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal tetrahedral value,...
¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

¹H NMR of Conformationally Flexible Molecules: Temporal Resolution

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

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

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.
Newman Projections02:06

Newman Projections

Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.
Chair Conformation of Cyclohexane02:02

Chair Conformation of Cyclohexane

The chair conformation is the most stable form of cyclohexane due to the absence of angle and torsional strain. The absence of angle strain is a result of cyclohexane’s bond angle being very close to the ideal tetrahedral bond angle of 109.5° in its chair conformer. Similarly, the torsional strain is also absent owing to the perfectly staggered arrangement of bonds.
The hydrogen atoms linked to carbons are arranged in two different axial and equatorial orientations to achieve this staggered...
MO Theory and Covalent Bonding02:40

MO Theory and Covalent Bonding

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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DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
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DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

Hamiltonian formalism for semiflexible molecules in Cartesian coordinates.

G R Kneller1

  • 1Centre de Biophysique Moléculaire, CNRS, Rue Charles Sadron, 45071 Orléans, France. kneller@cnrs-orleans.fr

The Journal of Chemical Physics
|September 27, 2006
PubMed
Summary

This study details Hamiltonian dynamics for semiflexible molecules using constrained inverse matrices. Mass-weighted coordinates ensure unbiased sampling and define effective masses for thermal velocity averages.

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Area of Science:

  • Computational chemistry
  • Molecular dynamics
  • Statistical mechanics

Background:

  • Understanding molecular dynamics and thermal averages is crucial for chemical simulations.
  • Semiflexible molecules present unique challenges due to their complex motion.
  • Existing methods may introduce biases in constrained simulations.

Purpose of the Study:

  • To develop a robust framework for Hamiltonian dynamics of semiflexible molecules in Cartesian coordinates.
  • To derive explicit expressions for constrained Hamiltonians and related quantities.
  • To introduce unbiased sampling methods and define effective masses.

Main Methods:

  • Application of constrained inverse matrices (Bott and Duffin).
  • Derivation of explicit formulas for constrained Hamiltonian and equations of motion.
  • Utilizing mass-weighted coordinates for sampling.
  • Generalization of Sachs-Teller recoil masses.

Main Results:

  • Explicit expressions for constrained Hamiltonian, equations of motion, and momentum partition function.
  • Fixman-type corrections for constrained configurational averages.
  • Demonstration of nonbiased sampling using mass-weighted Cartesian coordinates.
  • Definition and calculation of effective masses for thermal velocity averages.

Conclusions:

  • The developed formalism accurately describes Hamiltonian dynamics and thermal averages for semiflexible molecules.
  • Mass-weighted coordinates provide an unbiased approach for constrained simulations.
  • The calculated effective masses generalize Sachs-Teller masses to partially rigid molecules, offering insights into molecular behavior.