Principal inertial axis

Prior to solvation, the solute is oriented according to its inertial axes such that the box size needed to accommodate it is minimized (minimizing the number of water molecules). The principal inertial axis is oriented along the viewer s Z axis, for example. Then water molecules are eliminated if any of the three atoms are closer to a solute atom than the contact distance you specify. 

The(2/ + l)-fold degeneracy ofan energy level with rotational quantum number J can be partially lifted by placing the molecule in a static electric field. This so-called Stark effect can be utilized to measure the magiutudes of the dipole moment components, fit, Mo in die principal inertial axis system of the molecule. For this purpose, Stark electrodes can be mounted outside the microwave cavity to generate a... 

To calculate the rotational energy due to the Hamiltonian in Eq. (7), we write Q and X in the principal inertial axis system with the direction cosine transformation,, leading to... 

For convenience in application we have obtained both atom and bond values. In the atom approach we have assumed that an atom in a particular bonding situation (particular hybridization) will always contribute the same amount to the molecular susceptibility. This contribution consists of the three principal components as shown in Table 8 under atom susceptibilities. To evaluate the molecular susceptibility, the atom or bond values in Table 8, which are principal values, are rotated into the principal inertial axis system (a, b, and c) of the molecule. The atom and bond susceptibilities were determined by least squares fitting the experimental molecular susceptibility components of the 14 common nonstrained, nonaromatic molecules shown in Table 7. 

Pitfalls still remain in determining the geometry of molecules and crystals, even for relatively simple systems. Pairs of interatomic distances that are not well separated cause problems in diffraction techniques, and atoms near a principal inertial axis are difficult to locate by spectroscopic measurements. On the other hand, quantitative structure determinations on large molecules have made major strides in recent years, and further progress can be expected. It is hoped that NMR, Raman, and infrared spectroscopy will prove valuable in complementing the information derived from x-ray diffraction. 

Table II.3. Diagonal values of molecular susceptibilities referred to the principal inertial axis system in units of 10 S erg/(G2 mole). In each case the first reference is for the susceptibilities, the second for the structure. The local values Xaa(loc), Xbb(loc), Jfcc(ioc) have been calculated according to Eq. (11.12), using the known structure and the atom susceptibilities listed in Table II.2...

Table 4 Atom coordinates in the principal inertial axis system and substitution (r ) structure for the diketo tautomer of uracil. Distances are given in A and angles in degrees... 

Angle between the a principal inertial axis and the N-Cl bond. 

The coordinate system is now drawn such that the origin is at the center of mass of the molecule. In order to describe the rotational motion of a nonlinear molecule, three angular coordinates are needed resulting in three moments of inertia. The position of each atom is now expressed in a coordinate system whereby the center of mass of the molecule is at the origin and each atom is along the axes labeled by convention as a, b, and c. This coordinate system is called the principal inertial axis system. The three moments of inertia that result from the principal inertial axis system are called the principal moments of inertia. 

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