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Rotational energies are quantized. For a diatomic molecule like CO or HCl, or a linear polyatomic molecule like OCS in its ground vibrational state, the allowed rotational energies in the rigid rotor approximation are = = (+) = (+). J is the quantum number for total rotational angular momentum and takes all integer values starting at zero, i.e., =,,, …, = is the rotational constant, and is ...
The rotational spectrum (power spectral density vs. rotational frequency) of polar molecules can be measured in absorption or emission by microwave spectroscopy [1] or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy.
The characteristic rotational temperature (θ R or θ rot) is commonly used in statistical thermodynamics to simplify the expression of the rotational partition function and the rotational contribution to molecular thermodynamic properties.
The rotational constant of the ground vibrational state B′′ and centrifugal distortion constant, D′′ can be found by least-squares fitting this difference as a function of J. The constant B ′′ is used to determine the internuclear distance in the ground state as in pure rotational spectroscopy .
In chemistry, rotamers are chemical species that differ from one another primarily due to rotations about one or more single bonds. Various arrangements of atoms in a molecule that differ by rotation about single bonds can also be referred to as different conformations. Conformers/rotamers differ little in their energies, so they are almost ...
The Langevin equation can be generalized to rotational dynamics of molecules, Brownian particles, etc. A standard (according to NIST [ 5 ] ) way to do it is to leverage a quaternion -based description of the stochastic rotational motion.
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.
When a rotational transition occurs, there is a change in the value of rotational quantum number J. Selection rules for rotational transition are, when Λ = 0 , Δ J = ±1 and when Λ ≠ 0 , Δ J = 0, ±1 as absorbed or emitted photon can make equal and opposite change in total nuclear angular momentum and total electronic angular momentum ...