Step size, molecular dynamics

An interesting approach has recently been chosen in the MBO(N)D program ([Moldyn 1997]). Structural elements of different size varying from individual peptide planes up to protein domains can be defined to be rigid. During an atomistic molecular dynamics simulation, all fast motion orthogonal to the lowest normal modes is removed. This allows use of ca. 20 times longer time steps than in standard simulations. 

In this paper, we discuss semi-implicit/implicit integration methods for highly oscillatory Hamiltonian systems. Such systems arise, for example, in molecular dynamics [1] and in the finite dimensional truncation of Hamiltonian partial differential equations. Classical discretization methods, such as the Verlet method [19], require step-sizes k smaller than the period e of the fast oscillations. Then these methods find pointwise accurate approximate solutions. But the time-step restriction implies an enormous computational burden. Furthermore, in many cases the high-frequency responses are of little or no interest. Consequently, various researchers have considered the use of scini-implicit/implicit methods, e.g. [6, 11, 9, 16, 18, 12, 13, 8, 17, 3]. 

The standard discretization for the equations (9) in molecular dynamics is the (explicit) Verlet method. Stability considerations imply that the Verlet method must be applied with a step-size restriction k < e = j2jK,. Various methods have been suggested to avoid this step-size barrier. The most popular is to replace the stiff spring by a holonomic constraint, as in (4). For our first model problem, this leads to the equations d... 

Abstract. The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes - analogously to classical molecular dynamics - symplectic integration schemes the methods of choice for long-term simulations. This has already been demonstrated by the symplectic PICKABACK method [19]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK. 

Here we suggest a different approach that propagates the system using multiple step-sizes, i.e., few steps with step-size At are taken in the slow classical part whereas many smaller steps with step-size 5t are taken in the highly oscillatory quantum subsystem (see, for example, [19, 4] for symplectic multiple-time-stepping methods in the context of classical molecular dynamics). Therefore, we consider a splitting of the Hamiltonian H = Hi +H2 in the following way ... 

In many molecular dynamics simulations, equilibration is a separate step that precedes data collection. Equilibration is generally necessary to avoid introducing artifacts during the heating step and to ensure that the trajectory is actually simulating equilibrium properties. The period required for equilibration depends on the property of interest and the molecular system. It may take about 100 ps for the system to approach equilibrium, but some properties are fairly stable after 10-20 ps. Suggested times range from 5 ps to nearly 100 ps for medium-sized proteins. 

Fig. 6.10. Comparison of overlap sampling and FEP calculation results for the free energy change along the mutation of an adenosine in aqueous solution (between A = 0.05 and 0.45) in a molecular dynamics simulation. The results represent the average behavior of 14 independent runs. (MD time step.) The sampling interval is 0.75 ps. The upper half of the plot presents the standard deviation of the mean (with gives statistical error) for AA as a function of sample size N the lower half of the plot gives the estimate of A A - for comparison of the accuracy, the correct value of AA is indicated by the bold horizontal line...

The BIOGRAF program was run on a Micro VAX II conmuter equipped with an Evans and Sutherland PS390 graphics terminal. The size of coal structures evaluated, and the duration of molecular dynamics runs, were limited by the available computing speed of this system (a 5000-step, 10-ps molecular dynamics run for a 1040-atom structure, with about 75,000 van der Waals interactions per step, required about 100 hours of computation). 

The need for computer simulations introduces some constraints in the description of solvent-solvent interactions. A simulation performed with due care requires millions of moves in the Monte Carlo method or an equivalent number of time steps of elementary trajectories in Molecular Dynamics, and each move or step requires a new calculation of the solvent-solvent interactions. Considerations of computer time are necessary, because methodological efforts on the calculation of solvation energies are motivated by the need to have reliable information on this property for a very large number of molecules of different sizes, and the application of methods cannot be limited to a few benchmark examples. There are essentially two different strategies. 

Select the Molecular dynamics menu to open the dialog box. Specify Time, Temperature, and Step size for Heating cycle, Equilibrium period, and Cooling cycle. 

Raman intensities were calculated by differentiation of the molecular polarizability with respect to nuclear coordinates. It is often sufficient or desirable to calculate only Raman intensities for selected modes instead of for all 3N - 6 vibrational modes of a large molecule, which can be achieved if the normal modes of the molecule are already known. Therefore, a frequency analysis was performed using numerical differentiation of analytical gradients with respect to Cartesian nuclear coordinates in the first step. This yields vibrational frequencies and normal modes. Then, we used displacements along selected mass-weighted normal coordinates Q/t, for which (static and/or dynamic) polarizabilities are calculated. With a step size SQk,... 

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