Mode of motion

P. Dauber-Osguthorpe and D. J. Osguthorpe. Partitioning the motion in molecular dynamics simulations into characteristic modes of motion. J. Comp. Chem., 14 1259-1271, 1993. 

Dauber-Osguthorpe P and D J Osguthorpe 1993. Partitioning the Motion in Molecular Dynamii Simulations into Characteristic Modes of Motion. Journal of Computational Chemistry 14 1259-127... 

The four steric energy sums in Eq. (4-13) corresponding to sketching, bending, and torsional modes of motion and van der Waals inhamolecultu interaction appear to be about the smallest number one can use in an accurate MM geomehy minimization. 

We shall treat coupling of modes of motion in some detail because there are fundamental mechanical and mathematical topics involved that will be useful to us in both MM and quantum mechanical calculations. In the tieatment of coupled haiinonic oscillators, matrix diagonalization and normal coordinates are encountered in a simple form. 

Figure 5-2 Synchronous and Antisynchronous Modes of Motion in a Bound, Two-Mass Harmonic Oscillator.

Two degrees of freedom lead to two modes of motion. These two modes of motion, synchronous and antisynchronous, are the normal modes of motion for this system. If only synchronous motion is excited, the antisynchronous mode will never contribute to the motion. The same is true for the pure antisynchronous mode (Fig. 5-2b) there will never be a synchronous conPibution. Under these conditions, but only under these conditions, energy does not pass from one mass to the other. 

If the masses are displaced in an arbiPary way or arbiPary initial velocities are given to them, the motion is asynchronous, a complex mixture of synchronous and antisynchronous motion. But the point here is that even this complex motion can be broken down into two normal modes. In this example, the synchronous mode of motion has a lower frequency than the antisynchronous mode. This is generally Pue in systems with many modes of motion, the mode of motion with the highest symmePy has the lowest frequency. 

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

Mode of Motion. Nicotine, anabasine, and imidocloprid affect the ganglia of the insect central nervous system, faciUtating transsynaptic conduction at low concentrations and blocking conduction at higher levels. The extent of ionisation of the nicotinoids plays an important role in both their penetration through the ionic barrier of the nerve sheath to the site of action and in their interaction with the site of action, which is befleved to be the acetylcholine receptor protein. There is a marked similarity in dimensions between acetylcholine and the nicotinium ion. 

Mode of Motion. The cyclodienes, like lindane and toxaphene, affect the nerve axon produciag hyperactivity, convulsions, prostration, and death. The biochemical lesion is the competitive inhibition of the y-aminobutyric acid (GABA) neurotransmitter binding site of the nerve axon. Spray workers with lengthy exposure to dieldrin have suffered from prolonged and repeated central nervous system disturbances produciag epileptiform coavulsioas. Similar disturbances occurred ia workers heavily exposed to chlordecoae. 

M. Richmond in M. Salton and G. D. Shockman, eds., j5-Eactam A.ntihiotics (Mode of Motion, Nein Developments, and Euture Prospects), Academic Press, New York, 1981, pp. 261-274. 

Keystoning is an undesirable mode of motion that can arise with quadrilateral or hexahedral elements. These modes have no volume change and no shear. For example, the top of the element elongates and the bottom contracts in the appropriate ratio to give no volume change as shown in Fig. 9.12. Additional stiffness must be added to damp out the keystone modes [33]. 

Normal mode analysis exists as one of the two main simulation techniques used to probe the large-scale internal dynamics of biological molecules. It has a direct connection to the experimental techniques of infrared and Raman spectroscopy, and the process of comparing these experimental results with the results of normal mode analysis continues. However, these experimental techniques are not yet able to access directly the lowest frequency modes of motion that are thought to relate to the functional motions in proteins or other large biological molecules. It is these modes, with frequencies of the order of 1 cm , that mainly concern this chapter. 

When the number of degrees of freedom becomes greater than two, no critical new parameters enter into the problem. The dynamics of all machines can be understood by following the mles and guidelines established in the one and two degree(s)-of-freedom equations. There are as many natural frequencies and modes of motion as there are degrees of freedom. 

A linear molecule, such as any diatomic molecule, carbon dioxide, and ethyne (acetylene, HC=CH), can rotate about two axes perpendicular to the line of atoms, and so it has two rotational modes of motion. Its average rotational energy is therefore 2 X jkT = kT, and the contribution to the molar internal energy is NA times this value ... 

A nonlinear molecule, such as water, methane, or benzene, can rotate about any of three perpendicular axes, and so it has three rotational modes of motion. The average rotational energy of such a molecule is therefore 3 X jkT = ]kT. The contribution of rotation to the molar internal energy of a gas of nonlinear molecules is therefore... 

This approximation is valid if the modes of motion are completely independent-an assumption that is often made. The ratio in equation 6.5-17 can therefore be written as a product of ratios ... 

Figure 8.10 Transverse acoustic and optic modes of motion in a one-dimensional diatomic chain at the same wavelength.

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