Molecular angular velocity

The Euler equations of motion relate the time derivative of the molecular angular velocity coj, expressed in the body-fixed (principal) axis system, to the torques given above ... 

The procedure Split selects the internal displacement coordinates, q, and momenta, tt, (describing vibrations), the coordinates, r, and velocities, v, of the centers of molecular masses, angular velocities, a>, and directional unit vectors, e, of the molecules from the initial Cartesian coordinates, q, and from momenta, p. Thus, the staring values for algorithm loop are prepared. Step 1 Vibration... 

In a centrifugal field the energy per mole at a distance r from the axis is M(cor2)/2. M is molecular weight and go angular velocity. The ratio of partial pressures for two isotopomers (primed and unprimed) at the wall, rw, and on the axis, ro, yields the elementary separation factor. 

Here M is molecular weight, R is the gas constant, T is the absolute temperature in degrees Kelvin, V is the partial specific volume of the solute, p is the density of solution, w is the angular velocity, r is the distance from the center of rotation, and c is the concentration measured at r. Under... 

Here /m is the molar chemical potential of species i, angular velocity (radians/second) of the rotor, and Mi is the molecular weight of associating species i. From this relation it can be shown that (14)... 

V, C.M. velocity of tagged molecule 2 angular velocity about molecular C.M. 

In order to determine specific phase regions of a molecular ensemble, we express the full energy of a linear molecule as a function of a polar coordinate 0 and of two angular velocities ... 

One of the practical applications of the optical polarization of molecular angular momenta is the investigation of the stereochemical forces in the process of molecule-atom collisions. The most complete information on the dependence of atom-molecule interaction potential on the orientation of the molecule with respect to the relative collision velocity can be obtained by the method of molecular beams, and often in conjunction with inhomogeneous magnetic and electric fields which orient the molecules. Such investigations are undoubtedly very complex, and their realization rather costly. To convince oneself of it one might just peruse the Proceedings of the First Workshop on Dynamic Stereochemistry in Jerusalem in 1986 [66] see also [67, 341],... 

At smaller distances the orbital momentum is always strongly coupled to the molecular axis n, and the spin s follows the rotation if the frequency of the fine-structure splitting between A 2ni/2 and A 2n3/2 components is appreciably higher than the angular velocity of n. 

The angular velocity and angular momentum acfs themselves are important to any dynamical theory of molecular liquids but are very difficult to extract directly from spectral data. The only reliable method available seems to be spin-rotation nuclear magnetic relaxation. (An approximate method is via Fourier transformation of far-infrared spectra.) The simulated torque-on acfs in this case become considerably more oscillatory, and, which is important, the envelope of its decay becomes longer-lived as the field strength increases. This is dealt with analytically in Section III. In this case, computer simulation is particularly useful because it may be used to complement the analytical theory in its search for the forest among the trees. Results such as these for autocorrelation functions therefore supplement our... 

The nature of the excitation has a profound influence on the subsequent relaxation of molecular Uquid systems, as the molecular dynamics simulations show. This influence can be exerted at field-on equiUbrium and in decay transients (the deexdtation effect). GrigoUni has shown that the effect of high-intensity excitation is to slow the time decay of the envelope of such oscillatory functions as the angular velocity autocorrelation function. The effect of high-intensity pulses is the same as that of ultrafast (subpicosecond laser) pulses. The computer simulation by Abbot and Oxtoby shows that... 

Figure 6. (a) 2-Gilorobutane at 50 K, 6x6 site-site potential, angular velocity autocorrelation functions. Crosshatdiing indicates computer noise difference between R and S enantiomers. (—) Racemic mixture, (b) As for (a), under the influence of a strong field E, producing a torque — 63 XE in each molecule of the molecular dynamics sample. (1) (—) Racemic mixture (2) (—) R enantiomer. Ordinate Normalized correlation function abscissa time, ps. 

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