Rotation kinetic energy

The rotational kinetic energy operator for a rigid polyatomic molecule is shown in Appendix G to be... 

Again, the rotational kinetic energy, which is the full rotational Hamiltonian, can be written in terms of the total rotational angular momentum operator J2 and the component of angular momentum along the axis with the unique principal moment of inertia ... 

Rotational Kinetic Energy. Rotational kinetic energy of a rotating body is equal to 1/2 ICO. Its SI unit is J. 

AT is the change in kinetic energy, made up of a change in linear kinetic energy and rotational kinetic energy. 

The molar heat capacities of gases composed of molecules (as distinct from atoms) are Higher than those of monatomic gases because the molecules can store energy as rotational kinetic energy as well as translational kinetic energy. We saw in Section 6.7 that the rotational motion of linear molecules contributes another RT to the molar internal energy ... 

The shared memory OpenMP library is used for parallelization within each node. The evaluation of the action of potential energy, rotational kinetic energy, and T2 kinetic energy are local to each node. These local calculations are performed with the help of a task farm. Each thread dynamically obtains a triple (/2, il, ir) of radial indices and performs evaluation of first the kinetic energy and then the potential energy contribution to hps local( , i2, il, ir) for all rotational indices. 

Translational kinetic energy and rotational kinetic energy... 

The vibration-rotation interaction term makes the Hamiltonian for nuclear motion of a polyatomic molecule difficult to deal with. Frequently, this term is small compared to the other terms. We shall make the initial approximation of omitting Tvib rot. The rotational kinetic energy TTOt involves the moments of inertia of the molecule, which in turn depend on the instantaneous nuclear configuration. However, the vibrational motions are much faster than the rotational motions, so that we can make the approximation of calculating the moments of inertia averaged over the vibrational motions. 

The subscript G indicates that this is an approximate and an as yet unverified result based on the Gaussian approximation. Similarly, the normalized rotational kinetic energy autocorrelation function where... 

These higher-order correlation functions play a large role in determining many physical properties of polyatomic systems. For example, the vibrational relaxation can, in some cases, be expressed in terms of the rotational kinetic energy autocorrelation function.27... 

As described by Schweizer and Chandler [123] and also by Myers and Mar-kel [124], the effective potential for the vibration-rotation centrifugal coupling is the rotational kinetic energy which is given by... 

This is a very important result because the first term describes the vibrational kinetic energy of the nuclei, whilst the second and third terms represent the rotational kinetic energy. The transformation is straightforward provided one takes proper note of the non-commutation of the operator products which arise. 

The Hamiltonian which represents the rotational kinetic energy of an asymmetric top with three unequal moments of inertia is... 

The operator which describes the rotational kinetic energy in Hund s case (b) notation is... 

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