Algorithm leap-frog

The leap-frog algorithm uses the simplest central difference I or-m n la for a derivative... 

HyperChem employs the leap frog algorithm to integrate the equations of motion. This algorithm updates the positions of atoms and the velocities for the next time step by this calculation (equation 26). 

As described previously, the Leap-frog algorithm for molecular dynamics requires an initial configuration for the atoms and an initial set of velocity vectors. /2- These initial velocities can come... 

Modifications to the basic Verlet scheme have been proposed to tackle the above deficiencies, particularly to improve the velocity evaluation. One of these modifications is the leap-frog algorithm, so called for its half-step scheme Velocities are evaluated at the midpoint of the position evaluation and vice versa [12,13]. The algorithm can be written as... 

The main disadvantage of this algorithm is that it is computationally a little more expensive than the simpler Verlet or leap-frog algorithms (though the added accuracy often outweighs this slight overhead). 

The numerical aspect, and the lack of explicit velocities, in the Verlet algorithm can be remedied by the leap-frog algorithm. Performing expansions analogous to eqs. (16.28) and (16.29) with half a time step followed by subtraction gives... 

The above molecular dynamics equations are then solved using the the standard and robust leap-frog algorithm [29]. 

Eqs. (16.32) and (16.33) define the leap-frog algorithm, and it is seen that the positions i.e. only the positions and relative orientations of individual mnleriiles are, allowed to ... 

Langevin Methotls and the effect of T in momentum, space. Analovouslv to the leap-frog algorithm for the... 

MD simulations can also be used for the pmf calculations with umbrella sampling or the perturbation method. An effective procedure for implementing isothermal-isobaric conditions is to couple the system to a constant temperature and pressure bath. A leap-frog algorithm is then preferred for integrating Newton s equations. " In addition, the SHAKE procedure can be applied to constrain intramolecular degrees of freedom, This is often done to eliminate bond vibrations which permits use of a larger time step, about 1-2 fs. 

Computation was carried out using a leap-frog algorithm proposed by Fincham with a time step of 1 fs. The total run was 20 ns for the CH4 system and 14 ns for the Xe system. Temperature and pressure were kept constant at 298 K and 100 MPa, respectively, using a method proposed by Berendsen et al Details of the simulation method is given in Ref. 4. 

These equations are solved numerically using a leap-frog algorithm. The classical and quantum parts of the problem are solves simultaneously. Each provides information at each time step necessary to the other. The expansion coefficients give the final state populations for the product vibrational modes. 

The motion equations have been solved by the Verlet Leap-frog algorithm subject to periodic boundary conditions in a cubic simulation cell and a time step of 2 fs. The simulations have been performed in the NVT ensemble with the Nose-Hoover thermostat [62]. The SHAKE constraints scheme [65] was used. The spherical cutoff radius comprises 1.2 nm. The Ewald sum method was used to treat long-range electrostatic interactions. 

Several variations on the Verlet algorithm have been developed. The leap-frog algorithm [Hockney 1970] uses the following relationships ... 

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