A new algorithm to compute long time molecular dynamics trajectories is presented. The technique is based on the stochastic path integral of Onsager and Machlup. Trajectories of fixed length of time are computed by path optimization between two end points. Modes of motion with periods shorter than the discrete time step are automatically filtered out, making the trajectories stable for almost an arbitrary time step. Several numerical examples are provided, including motions on the Mueller potential and a conformational transition in alanine dipeptide. Paths similar to the usual molecular dynamics trajectories are obtained, employing time steps 100 times larger than those used in straightforward molecular dynamics.

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A novel method to compute long-time molecular dynamics trajectories is employed to study the folding kinetics of C peptide. The computational method makes it possible to use a time step larger by orders of magnitude compared to widely used molecular dynamics integrators. Rather than solving the trajectory in small time steps, the whole trajectory is optimized. The algorithm filters high-frequency modes that are modeled as Gaussian noise. The assumption of "Gaussian noise" is tested numerically in two cases and found to be adequate. In all, 31 trajectories of C peptide that folds into a helix in explicit solvent (TIP3P water molecules) are computed. The time step is 500 ps. The folding pathways and the early formation of structure are discussed. Comparisons to a 2-ns trajectory calculated with the usual molecular dynamics approach and to available experimental data are made.

A molecular dynamics study of macromolecules in good solvents: Comparison with dielectric spectroscopy experiments Molecular dynamics simulations are used to study solvation and solvation dynamics of a classic charge in a series of ethers of increasing molecular weights, CH 3 ͑CH 2 OCH 2 ͒ n H with nϭ1, 2, and 4. Equilibrium structures of the solvated species, ion mobility, linear response solvation functions, and nonequilibrium solvation are studied and compared with the corresponding results for a simple ͑Stockmayer͒ fluid. For a typical positive ion, Na ϩ , solvation in these systems is found to belong to the nonlinear response regime; the nonlinear behavior is associated with the specific binding of the cation to the negative oxygen sites. Solvation dynamics in the timescale studied ͑tϽ0.5 ns͒ is found to be essentially bimodal, with a short component similar in duration and magnitude to that found in simpler solvents. However, except for the simplest system studied ͑ethyl methyl ether͒ the short time component is not Gaussian ͑i.e., its Gaussian part is limited to insignificantly short times͒ and cannot be interpreted as inertial free streaming of solvent molecules in the potential field of the solute. Instead we suggest that it originates from damped solvent vibrations about solvent inherent structures. The character of the solvent motions that drive the solvation process changes as the molecular size increases: From overall molecular rotations in the monoether, to intramolecular segmental motions in the larger solvents. It is suggested that solvation dynamics ͑studied, e.g., by laser induced fluorescence͒ can be used as a probe for the dynamics of such segmental motions in polymer electrolytes.

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