RATTLE, algorithm

Miyamoto S, Kollman P (1992) SETTLE an analytical version of the SHAKE and RATTLE algorithms for rigid water models. J Comput Chem 13 952-962... 

Version of the SHAKE and RATTLE Algorithm for Rigid Water Models. 

These equations may be solved using a SHAKE or RATTLE algorithm [84, 201]. However, we will present an alternative which is both conceptually simpler and easier to implement. 

To investigate the effect of an external electric field on the photodynamics, a single point charge of magnitude -1-0.25 qe was placed 3 A from one of the carbon atoms (Fig. 4). Both the ethylene molecule s center of mass and the position of the point charge were held fixed using the RATTLE algorithm [62] to constrain their positions relative to one another. 

In an MD simulation, the eonstraints are treated in succession during one cycle of the iteration and the process is repeated until all constraints have converged to the desired aecuracy. An improvement of the SHAKE algorithm is the RATTLE algorithm, which was proposed by Andersen [19]. In RATTLE, the veloeity-Verlet algorithm is employed to integrate the dynamical equations. 

For most of the results presented here, the MD simulations used a multiple time step seeond-order sympleetie integrator (RESPA) [61] to solve the equations of motion. In some earlier simulations [59], the bond length was kept eonstant using the RATTLE algorithm [62]. For the polyolefins, the simulations were run using a 1.00 or 1.25 fs timestep while for PDMS [63], the timestep was 0.4 fs. Bonded interae-tions were updated every time step while angle, torsion, and improper forees were updated every two time steps and non-bonded Lennard-Jones and Coulomb forees every four time steps. For the polyolefins, N is the number of CHx sites per ehain. Details of system size and equilibration time ean be found in the original papers [59,60, 63, 64]. 

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

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

Our discussion so far has considered the use of SHAKE with the Verlet algorithm Versions have also been derived for other integration schemes, such as the leap-froj algorithm, the predictor-corrector methods and the velocity Verlet algorithm. In the cast of the velocity Verlet algorithm, the method has been named RATTLE [Anderson 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. 

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

To integrate these equations of motion [173,174] one can use a velocity verlet algorithm [117] propagating similarly the nuclei positions and the electronic degrees of freedom Cj(G). The orthonormality conditions can be taken into account by the SHAKE and RATTLE method [173, 175, 176]. Constant ionic temperature can also be imposed through the use of thermostats [169,170,173,177]. 

The global error of RATTLE is of 0(8 ), which is the same as for the SHAKE algorithm. An error analysis of RATTLE is given by Andersen. ... 

Lynch and Pettitt (36) employed a pure Nose thermostat and RATTLE-like algorithm for bond constraint, as well as a single fraction particle. Our approach (40) used quaternions (41) to allow separate Nose-Hoover thermostats for translational and rotational modes. We found that the system s tendency to freeze in metastable states could be overcome by introduction of multiple fractional particles (four were used). Curve (b) of Fig. 3 is an extreme example of runaway insertions at high chemical potential as compared to curve (a) where the actual chemical potential of water resulted in a stable density virtually undistin-guishable from the experimental one. 

Andersen HC (1983) Rattle - a velocity version of the shake algorithm for molecular-dynamics calculations. J Comput Phys 52(1) 24—34... 

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