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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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A mass spectrum is the graphical representation of the relative abundance of the charged fragments in an analyte plotted against their mass-to-charge ratio (m/z). The plot's x-axis represents the ratio of the mass of the charged fragment to the number of charges it carries. The y axis of the plot represents the relative abundance of each charged species. The relative abundance is calculated from the signal intensity of each charged species recorded at the detector. The most intense signal (the...
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Unlike ethane and propane that have only two major conformations, butane has more than two conformers. The staggered form of butane in which the bulky methyl groups on the two carbons are placed on opposite sides, that is, at a dihedral angle of 180°, is the lowest energy, most stable form — called the anti conformer. This conformation is stabilized due to the absence of steric repulsion between the largely spaced out methyl groups. The other two staggered conformations are...
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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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In an organic molecule, free rotation about the carbon-carbon single bond results in energetically different conformers of the molecule. Due to this rotation, called the internal rotation, ethane has two major conformations — staggered and eclipsed.
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A highly accurate ab initio potential energy surface for methane.

Alec Owens1, Sergei N Yurchenko1, Andrey Yachmenev1

  • 1Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom.

The Journal of Chemical Physics
|September 17, 2016
PubMed
Summary

A new potential energy surface (PES) for methane was created using advanced ab initio theory. This highly accurate PES precisely predicts vibrational energy levels, advancing molecular dynamics and spectroscopy research.

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Area of Science:

  • Quantum Chemistry
  • Molecular Spectroscopy
  • Computational Physics

Background:

  • Accurate potential energy surfaces (PES) are crucial for understanding molecular behavior.
  • Previous methane PES models had limitations in reproducing experimental spectroscopic data.

Purpose of the Study:

  • To develop a highly accurate nine-dimensional ab initio potential energy surface for methane.
  • To achieve sub-wavenumber accuracy for vibrational energy levels.

Main Methods:

  • Utilized explicitly correlated coupled cluster calculations with complete basis set extrapolation.
  • Incorporated higher-level additive energy corrections (core-valence correlation, relativistic effects, etc.).
  • Calculated equilibrium C-H bond length and pure rotational energies.

Main Results:

  • Achieved sub-wavenumber accuracy for most experimentally known vibrational energy levels.
  • Reproduced the four fundamental vibrational modes of (12)CH4 with a 0.70 cm(-1) root-mean-square error.
  • Computed equilibrium C-H bond length shows excellent agreement with previous studies.

Conclusions:

  • The developed ab initio PES is the most accurate to date for methane.
  • The surface provides a robust starting point for empirical refinement.
  • Minor systematic errors in rotational energies can be mitigated by adjusting equilibrium geometry.