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A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Rotational–vibrational spectroscopy is a branch of molecular spectroscopy that is concerned with infrared and Raman spectra of molecules in the gas phase.Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational (or ro-vibrational) transitions.
As the moment of inertia is higher when a vibration is excited, the rotational constants (B) decrease. Consequently, the rotation frequencies in each vibration state are different from each other. This can give rise to "satellite" lines in the rotational spectrum. An example is provided by cyanodiacetylene, H−C≡C−C≡C−C≡N. [16]
A diatomic molecule has one molecular vibration mode: the two atoms oscillate back and forth with the chemical bond between them acting as a spring. A molecule with N atoms has more complicated modes of molecular vibration, with 3N − 5 vibrational modes for a linear molecule and 3N − 6 modes for a nonlinear molecule. [4]
In physics and chemistry, a molecule (or other group of atoms) can undergo libration if it is subject to external forces or constraints that restrict its orientation. For example, in liquid water, any given water molecule is attracted to neighboring molecules, so that it has a preferred orientation and cannot freely rotate. (Of course, over ...
Example of a linear molecule. N atoms in a molecule have 3N degrees of freedom which constitute translations, rotations, and vibrations.For non-linear molecules, there are 3 degrees of freedom for translational (motion along the x, y, and z directions) and 3 degrees of freedom for rotational motion (rotations in R x, R y, and R z directions) for each atom.
Symmetric transversal vibrations with frequency ω s 2 = 2 k 2 M m A m B {\displaystyle \omega _{s2}={\sqrt {\frac {2k_{2}M}{m_{A}m_{B}}}}} In the previous formulas, M is the total mass of the molecule, m A and m B are the masses of the elements A and B, k 1 and k 2 are the spring constants of the molecule along its axis and perpendicular to it.
They make it possible to approximately separate rotation from vibration. Although the rotational and vibrational motions of the nuclei in a molecule cannot be fully separated, the Eckart conditions minimize the coupling close to a reference (usually equilibrium) configuration. The Eckart conditions are explained by Louck and Galbraith. [2]