SHAKE algorithm

Andersen H C 1983 RATTLE a velocity version of the SHAKE algorithm for molecular dynamics calculations J. Comput. Phys. 52 24-34... 

For example, the SHAKE algorithm [17] freezes out particular motions, such as bond stretching, using holonomic constraints. One of the differences between SHAKE and the present approach is that in SHAKE we have to know in advance the identity of the fast modes. No such restriction is imposed in the present investigation. Another related algorithm is the Backward Euler approach [18], in which a Langevin equation is solved and the slow modes are constantly cooled down. However, the Backward Euler scheme employs an initial value solver of the differential equation and therefore the increase in step size is limited. 

H. C. Andersen. Rattle A velocity version of the Shake algorithm for molecular dynamics calculations. J. Comp. Phys., 52 24-34, 1983. 

The algorithm that is usually employed to account for the hydrogen positions is SHAKE [15,16] (and its variant RATTLE [17]). Stated in a simplistic way, the SHAKE algorithm assumes that the length of the X — H bond can be considered constant. Because in a numerical simulation there are always flucmations, this means that the deviation of the current length dt(t) of the Mi bond from its ideal (constant) bond length d° must be smaller than some tolerance value e. 

As an alternative, the SHAKE algorithm (21) is used if angle constraints are implemented or the LINCS algorithm otherwise fails. 

To achieve an evenly distributed thermal excitation, the nuclei were brought to a temperature of 300 K by applying a sequence of 30 sinusoidal pulses, each of which was chosen to raise the temperature by 10 K. Each of the excitation vectors was chosen to be orthogonal to the already excited modes. The warmed-up systems were equilibrated for the 10 000 timesteps. The time step of 7 au. was used. Constraints were maintained by SHAKE algorithm.36 A temperature of 300 K was controlled by a Nose thermostat.23,24 The fictitious kinetic energy of the electrons was controlled in a similar fashion by a Nose thermostat.52... 

W. Smith and T. R. Forester, Daresbury Laboratory Preprint DL/SC1/P874T Warrington, U.K., 1993. Parallel Macromolecular Simulations and the Replicated Data Strategy. II. The RD-SHAKE Algorithm. 

Separability theorem, 309 SHAKE algorithm, 385 SHAPES force field, 40 Simulated Annealing (SA), global optimization, 342 Simulation methods, 373 Supidfiidiil, iulcs, 3j6 Susceptibility, 237 Symbolic variables, for optimizations, 416 Symmetrical orthogonalization of basis sets, 314 Symmetry adapted functions, 75 Symmetry breaking, of wave functions, 76 ... 

H. C. Andersen, /. Comput. Phys., 52, 24 (1983). RATTLE A Velocity Version of the SHAKE Algorithm for Molecular Dynamics Calculations. 

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