Bond length constraints

The aim of applying bond length constraints in protein simulations is to save computer time.3i The leng th of the time step At in a MD simulation is limited by the highest frequency (v ,ax) in the system At Constrain- 

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These difficulties have led to a revival of work on internal coordinate approaches, and to date several such techniques have been reported based on methods of rigid-body dynamics [8,19,34-37] and the Lagrange-Hamilton formalism [38-42]. These methods often have little in common in their analytical formulations, but they all may be reasonably referred to as internal coordinate molecular dynamics (ICMD) to underline their main distinction from conventional MD They all consider molecular motion in the space of generalized internal coordinates rather than in the usual Cartesian coordinate space. Their main goal is to compute long-duration macromolecular trajectories with acceptable accuracy but at a lower cost than Cartesian coordinate MD with bond length constraints. This task mrned out to be more complicated than it seemed initially. 

The state splittings discussed above for rl are based on individual reactants which, aside from the bond length constraint (r1 ), are otherwise non-interacting. If we now consider the full initial and final states associated with the exchange reaction (Equations 2-7), we note that the relative energies of high-spin and low-spin states in the bimolecular transition-state complex may be affected by differences in initial and final state coupling, as represented by the electron-transfer matrix element, Hj f, discussed in the introduction. While for the "three-electron ... 

For instance, for a bond length constraint between the atoms i and j,... 

Enforcement of bond length constraints typically allows the time step to be increased by a factor of 2 or 3. Angles may also be frozen by adding a distance constraint on atoms that are 1,3 relative to each other. Angle bending, however, affects calculated properties more than bond stretching and fixing them may often introduce... 

As we can see from Fig. 2, the TB and REBO relaxations give similar results for the radial distribution function. The relaxation of the RMC models results in an intensity increase along with a decrease in width of the first peak. These results arises from the different bond length constraints used in RMC and the REBO or TB potential. In RMC, it is assumed that two atoms can have a minimum distance of approach of 1.2 A and that two atoms are considered bonded if the distance between them is less than 1.6 A. This definition is obtained from the... 

Geometrical constraints can also be considered as boundary conditions. A typical example is the use of bond-length constraints in simulations [34, 35, 36, 37, 38, 39], which represent a better approximation to the quantum-mechanical behavior of high-frequency oscillators (hv ksT) compared to the classical treatment [40]. Since they are satisfied exactly at every timepoint during a simulation, geometrical constraints represent hard boundary conditions. 

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