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Finite Difference Approximation

  X-PLOR makes use of a third-order finite difference approximation in dt (Brünger, Brooks, and Karplus 1984). First, the initial coordinates are subjected to the SHAKE method. Then the system gets the initial velocities . Next, the program prints the energy of the initial coordinates. A two-step method is used to obtain the coordinates :

IF SHAKE constraints are present, the SHAKE method is applied to with respect to .

Iteration from step n to step n+1 causes . The algorithm computes the forces . The algorithm then computes

If required, the SHAKE method is applied to with as the reference set. Finally, the velocities at this step are computed:

(The velocities do not enter the equations to compute the trajectory .) In case of zero friction coefficients , this algorithm reduces to the three-step Verlet method (Verlet 1967).  

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