Force fields relative speed

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

The reliability of molecular mechanics calculations hinges entirely on the validity and range of applicability of the force field. The parameterisation of these functions (the force field) represents the chemistry of the species involved. Many force fields have been developed and the one used in any application usually depends on the molecular mechanics package being used. The force field itself can be validated against experimental and ab initio results. Because of the relative speed of molecular mechanics calculations, it is possible to consider routine calculations of a large number of atoms, certainly tens of thousands, which makes the method amenable to calculations on polymers. To remove surface effects, calculations of bulk properties are normally carried out employing 3D periodic boundaries. In this way it is possible to perform calculations on both amorphous and crystalline systems. 

Because of their utility for very large systems, where their relative speed proves advantageous, force fields present several specific issues with respect to practical geometry optimization that merit discussion. Most of these issues revolve around the scaling behavior... 

Because of their utility for very large systems, where their relative speed proves advantageous, force fields present several specific issues with respect to practical geometry optimization that merit discussion. Most of these issues revolve around the scaling behavior that the speed of a force-field calculation exhibits with respect to increasing system size. Although we raise the issues here in the context of geometry optimization, they are equally important in force-field simulations, which are discussed in more detail in the next chapter. 

The Bom-Oppenheimer theorem is a goexi starting point. The theorem basically. stales that electrons move in a stationary field of nuclei and therefore, the electron and nuclear motions can be considered separately. This approximation is valid in most cases of interest to medicinal chemists. since on the lime. scale of electron motion, the nuclei do not move. The difference in speed is a consequence of the differences in mass of the electron and the particles within the nucleus. It is analogous to speedboats circling a heavy aircraft carrier. On the lime scale of the speedboats, during a brief snapshot of time, the aircraft carrier is molion-lc.ss relative to the lighter craft. The.se facts, summari /cd in the Bom-Oppenheimer theorem, enable successful use of the various mathematical mcxlcls used in quantum mechanics and force field-based melhcxls. 

The third type of approach introduces a concept of electrical roughness which gives rise to a sinusoidally distributed force field. The force field excites the asperities of rubber during the relative motion. No static coefficient is predicted by the theories. Although Rieger has predicted that a maximum value of friction occurs at a definite speed, there is no indication of the order of magnitude. 

The gravitational force in a centrifuge is dependent on two quantities the speed of rotation and the distance from the centre of rotation. Equation 4.12 expresses the relative centrifugal force (RCF) (in units of g - the Earth s gravitational field) in terms of these two parameters. 

In general, the retention of the stationary phase in the coil rotated in the unit gravity field entirely relies on relatively weak Archimedean screw force. In this situation, application of a high flow rate of the mobile phase would cause a depletion of the stationary phase from the column. This problem can be solved by the utilization of synchronous planetary centrifuges, free of rotary seals, which enable one to increase the rotational speed and, consequently, enhance the Archimedean screw force. The seal-free principle can be applied to various types of synchronous planetary motion. In all cases, the holder revolves around the centrifuge axis and simultaneously rotates about its own axis at the same angular velocity w. 

We conclude this discussion by alerting the reader to the concept of the dynamic contact angle (and line), which appears in the literature of flows governed by surface tension (Dussan V. 1979). In a flow field where the contact line moves, it is necessary to know the contact angle as a boundary condition for determining the meniscus shape. If this angle is a function of the speed of the contact line relative to the solid surface, then the force balance inherent in... 

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