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...e '''Dunham expansion''' is an expression for the rotational-vibrational [[energy level]]s of a [[diatomic molecule]]: {{cite journal| last=Dunham|first=J. L.|title=The Energy Levels of a Rotating Vibrator|journal=Phys. Rev. |year=1932|volume=41|issue ...

...hod''' or '''Birge–Sponer plot''' is a way to calculate the [[dissociation energy]] of a molecule. This method takes its name from [[Raymond Thayer Birge]] a ...ciation; summing over all the differences up to this point gives the total energy required to dissociate the molecule, i.e. to promote it from the [[ground s ...

...which gives rise to a simple analytical approximation for the vibrational energy levels: ...</sub>, and <math>v_{\mathfrak D}</math> can be identified as an effective vibrational quantum number at dissociation. ...

For a lattice, the Helmholtz free energy ''F'' in the quasi-harmonic approximation is ...e temperature, ''V'' is the volume and ''S'' is the [[entropy]] due to the vibrational degrees of freedom. ...

{{Short description|Theory for simulation vibrational spectra}} Please also link to other QM & vibrational pages.|u=SpectroGuy|ns=118|decliner=Ldm1954|declinets=20250209225447|ts=202 ...

...onequilibrium plasmas where substantial fraction of energy input goes into vibrational excitation of molecules. The formulas are obtained by applying classical m 1. Translational-vibrational non equilibrium: <math> T>T_v </math> or <math> T<T_v </math>. ...

It is analogous to vibrational [[Raman scattering]], which is a widely used tool in optical spectroscopy, ...X-ray absorption, exactly as in Raman scattering in optics vibrational low-energy excitations can be observed by studying the spectrum of light scattered fro ...

...ations of [[Doppler cooling]], Doppler cooling being limited by the recoil energy of a photon given to an atom. This scheme can be performed in simple [[opti ...h>. The frequency difference <math>f_2-f_1</math> here matches exactly the energy difference between <math>|g_1\rangle</math> and <math>|g_2\rangle</math>. ...

...'' relates the rotational degrees of freedom to the rotational part of the energy. For molecules, under the assumption that total energy levels <math>E_j</math> can be partitioned into its contributions from diff ...

...hese are degrees of freedom that contribute in a quadratic function to the energy of the system. ...f-freedom|title = Physical chemistry - Does a diatomic gas have one or two vibrational degrees of freedom?}}</ref> ...

...escription|Study of simultaneous change in atoms' electronic and vibration energy}} ...are also accompanied by changes in [[rotational spectroscopy|rotational]] energy. ...

...st6=Wang|first6=Jiemin|last7=Wang|first7=Xiaohui|title=Covalency-Dependent Vibrational Dynamics in Two-Dimensional Titanium Carbides|journal=The Journal of Physic ...e of the overlap of the single atomic contributions to a specific range of vibrational frequencies.]] ...

...ique provides information beyond linear infrared spectra, by spreading the vibrational information along multiple axes, yielding a frequency correlation spectrum. ...g, [[anharmonicity|anharmonicities]], along with chemical dynamics such as energy transfer rates and molecular dynamics with femtosecond time resolution. 2DI ...

==Vibrational spectra== ...ly.<ref>{{cite web |author=Takehiko Shimanouchi |title=Tables of Molecular Vibrational Frequencies Consolidated |volume=I |date=1972 |id=NSRDS-NBS-39 |publisher=[ ...

...ecause it is free of any [[rotational energy|rotational]] or [[vibrational energy]].<ref>{{cite web|title=monatomic gas|url=http://www.britannica.com/science ...ins an [[Avogadro number]] (<math>N_\text{A}</math>) of atoms, so that the energy of one mole of atoms of a monatomic gas is <math> \frac{3}{2} k_\text{B} T ...

...hoton gas]], where the vibrations are not to individual oscillators but as vibrational modes of the ionic lattice. [[Debye model|Debye's model]] allowed to predic ...corresponding to a quadratic kinetic energy term and a quadratic potential energy term. By the [[equipartition theorem]], the average of each quadratic term ...

...both photons (<math>\omega_p-\omega_S</math>) resembles that of a specific vibrational (or rotational) transition (<math>\omega_\nu</math>) the occurrence of this [[File:SRS energy levels scheme.png|thumb|300px|Molecule's energy levels and the SRS transition]] ...

...tom or molecule when the collision energy is below the [[Ionization energy|energy]] required to ionize the reagents.<ref name=":0">{{Cite Q|Q51494633}}</ref> == Energy requirements == ...

...tes are becoming more widely used in the aerospace, marine, automotive and energy industry. This is due to the decreasing cost and superior strength to weigh ...e the quality of the weld to reducing any fiber disruption during welding. Energy directors that are triangular or semi-circle often achieve the highest stre ...

...o subsystem division. The DEA method predicts the flow of vibrational wave energy across complex structures in terms of (linear) transport equations. These e * The flow of energy is tracked across a mesh. Can be thought of as ray tracing using density of ...