Moment inertia

Moment of Inertia. Moment of inertia, I, is a property of the mass distribution of a body around an axis (I = Smr ). Its SI unit is kg-m. ... 

AB and ABC are the products of the principal moments of inertia. Moments of inertia are calculated from bond angles and bond lengths. Many values are given by Landolt-Bornsteiu. is Avogadro s number, and M is the molecular weight of the molecule. Stuper et al. give a computerized method for prediction of the radius of gyration. 

Tragheits-kraft, /. force of inertia, -mittel-punkt, m. center of inertia, -moment, w. moment of inertia,... 

Lewis. G. N. 1. 248. 264, 265 line integrals 605-8 linear molecules electronic energy levels 506 fundamental frequencies 645 inertia, moments of 643 vibrational energy levels 504 Linhart. G.A. 481-3 liquid crystals 4... 

Discussion of selection rules must be modified for NH2D (ND2H) because they are asymmetric top molecules The convention for inertia moments in asymmetric, tops is/ [Pg.83]

Since the first quantum mechanical calculation of phenol performed in 1967 using the CNDO/2 method" , the phenol geometry was considered at a variety of computational levels "" ranging from the HE to the MP2 method of molecular orbital theory and density functional theory (DFT) employed with several basis sets, mainly of the split valence type as, e.g. 6-31G(d,p) and 6-31- -G(d,p). These computational results are summarized in Tables 1-3 and Figure 4. It seems noteworthy that the semi-empirical geometries listed in Table 1 are rather close to the experimental observations. Also, to complete the theoretical picture of the phenol molecule, its theoretical inertia moments calculated at the B3LYP/6-31- -G(d,p) level are equal to 320.14639, 692.63671 and 1012.78307 a.u. 

The computation of rotational constants Be from the inertia moments I corresponding to the interatomic distances in both types of comple.xes illustrates the situation clearly the cyanide and isocyanide isomers have rotational constants separated by about 0.6 GHz, and this shift upwards for the isocyanide species may be useful for their spectroscopic investigation, as already done for the pair of isomers MgNC and MgCN. Corresponding dipole moments are indicated in this connection. It should be added that the present values are consistent with the experimental parameter B = 4.358596 GHz assigned to a related complex FeCO [34]. 

These directions are determined by diagonalization of the inertia moment matrix (cf.. Appendix K available at booksite.elsevier.com/978-0-444-59436-5). 

To describe this effect we should write Eq. (9.21) for the director motion, i.e., the balance of torques. However, up to now, nobody has observed any effect related to the inertia of the director. Such effects would result in oscillatory character of the director relaxation. The inertial term for the director in a unit volume can be estimated as a sum of the inertia moments of the molecules in this volume. Let... 

Here symmetry number of a molecule, / is the inertia moment respective to a rotation axis. Denoting I as we will obtain for the degree of a freedom (assuming that... 

The frequency of the deformational vibrations of the reaction center C...H...C lies in the range of 100-400 cm" [94]. For the reaction center C-H...0 this center is probably shifted to the higher frequency kinetically nonactive range. This is associated with the fact that lies in the range of 1000-1600 cm" and that of C-H in 400-1000 cm. Hence the contribution of the vibrational sums should not differ from 1. However one cannot rule out the probability of the vibration sum of the reaction center for bigger cycles to reach values by 5-10% higher than those for the small cycles. Even in this case the trend in the calculations remains the same. Upon increasing the inertia moment of cycloalkanes as shown above, the vibration frequency should also increase since it is inverse to its square root. For example, if we accept that v =200 cm for C, then for Cj it will be 120 cm. In this case the vibration term will be increased 3.5-fold. 

Finally, the nonuniform angle of twist with respect to x shear center axis has to satisfy the following quasi-static (torsional and warping inertia moments are ignored) boundary value problem (Sapountzakis and Mokos, 2003)... 

The three principal moments of inertia characterize the mass distribution in the analyzed molecule. The maximum and minimum values of the inertia moments, Im and allow the calculation of eccentricity (Arteca 1991), which is a measure of the deviation from the spherical shape. 

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