Principal axis of inertia

As discussed in Section II. A, the adiabatic electronic wave functions, a and / 1,ad depend on the nuclear coordinates R> only through the subset (which in the triatomic case consists of a nuclear coordinate hyperradius p and a set of two internal hyperangles this permits one to relate the 6D vector W(1)ad(Rx) to another one w(1 ad(q J that is 3D. For a triatomic system, let aIX = (a1 -. blk, crx) be the Euler angles that rotate the space-fixed Cartesian frame into the body-fixed principal axis of inertia frame IX, and let be the 6D gradient vector in this rotated frame. The relation between the space-fixed VRi and is given by... 

The rotational degree of freedom about the smaller principal axis of inertia in CH3 is treated in the RBU model. The corresponding rotational distributions of CH3 can therefore be calculated for the X - - CH4 —> HX T CH3 reactions. The results obtained show that the rotational distribution of CH3 is rather cold for the X + CH4 reactions out of the vibrational ground-state of CH4. This is consistent with... 

The theoretical expressions for the molecular tensor quantities introduced above are as follows (principal-axis-of-inertia system throughout) ... 

If the oscillating dipole moment of a normal vibration has a component along the principal axis of inertia A, then the... 

The negative coefficient in this expansion is contrary to that obtained by Tanaka and Yamakawa using the Zimm-Hearst theory. Minato and Hatano have evaluated the effect of excluded volume on the three separate principal components (along the principal axis of inertia) of a polymer chain. Solc has shown that the shape of a random flight chain is far from spherical, in fact the ratio of the lengths of the principal axes is, on average, in the ratio... 

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