Rotational energy of molecules

Nielsen, H. H. (1959), The Vibration-Rotation Energies of Molecules and their Spectra in the Infra-red, in Handb. Physik, S. Flugge (ed.), Vol. 37, part 1, Springer, Berlin. 

H. H. Nielsen, The vibration-rotation energies of molecules and their spectra in the infra-red, in Handbuch der Physik, part XXXVII/1, Springer-Verlag, Berlin, 1959, p. 173-313. 

First, however, the behaviour in respect of rotational energies of molecules other than hydrogen must be dealt with. 

The rotational energy of a rigid molecule is given by 7(7 + l)h /S-n- IkT, where 7 is the quantum number and 7 is the moment of inertia, but if the energy level spacing is small compared to kT, integration can replace summation in the evaluation of Q t, which becomes... 

Fig. 3-11 shows that, foi watei, entropy and heat capacity ai e summations in which two terms dominate, the translational energy of motion of molecules treated as ideal gas paiticles. and rotational, energy of spin about axes having nonzero rnorncuts of inertia terms (see Prublerris). 

Before considering the special case of rotation about bonds in polymers it is useful to consider such rotations in simple molecules. Although reference is often made to the free rotation about a single bond, in fact rotational energies of the order of 2kcal/mole are required to overcome certain energy barriers in such simple hydrocarbons as ethane. During rotation of one part of a molecule about... 

Rotational Energy Levels The rotational energy of a molecule depends upon the molecular geometry. For a linear molecule that behaves as a rigid rotator,3... 

A nonlinear molecule, such as water, methane, or benzene, can rotate about any of three perpendicular axes, and so it has three rotational modes of motion. The average rotational energy of such a molecule is therefore 3 X jkT = ]kT. The contribution of rotation to the molar internal energy of a gas of nonlinear molecules is therefore... 

The isotope effects of reactions of HD + ions with He, Ne, Ar, and Kr over an energy range from 3 to 20 e.v. are discussed. The results are interpreted in terms of a stripping model for ion-molecule reactions. The technique of wave vector analysis, which has been successful in nuclear stripping reactions, is used. The method is primarily classical, but it incorporates the vibrational and rotational properties of molecule-ions which may be important. Preliminary calculations indicate that this model is relatively insensitive to the vibrational factors of the molecule-ion but depends strongly on rotational parameters. 

Here, ej f are the vibration-rotation energies of the initial (anion) and final (neutral) states, and E denotes the kinetic energy carried away by the ejected electron (e.g., the initial state corresponds to an anion and the final state to a neutral molecule plus an ejected electron). The density of translational energy states of the ejected electron is p(E) = 4 nneL (2meE) /h. We have used the short-hand notation involving P P/p to symbolize the multidimensional derivative operators that arise in the non BO couplings as discussed above ... 

Vibrational spectroscopy measures and evaluates the characteristic energy transitions between vibrational or vibrational-rotational states of molecules and crystals. The measurements provide information about nature, amount and interactions of the molecules present in the probed substances. Different methods and measurement principles have been developed to record this vibrational information, amongst which IR and Raman spectroscopy are the most prominent. The following focuses on these two techniques, the corresponding instrumentation and selected applications. 

Most of what we know about the structure of atoms and molecules has been obtained by studying the interaction of electromagnetic radiation with matter. Line spectra reveal the existence of shells of different energy where electrons are held in atoms. From the study of molecules by means of infrared spectroscopy we obtain information about vibrational and rotational states of molecules. The types of bonds present, the geometry of the molecule, and even bond lengths may be determined in specific cases. The spectroscopic technique known as photoelectron spectroscopy (PES) has been of enormous importance in determining how electrons are bound in molecules. This technique provides direct information on the energies of molecular orbitals in molecules. 

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