Test of theory for long time dynamics of floppy molecules in solution using Brownian dynamics simulation of octane

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Abstract
Tests are introduced of one basic approximation inherent in a recent theory for long time dynamics of flexible proteins and polymers in solution. The approximation in question concerns the neglect of memory functions, which for these systems involve a memory function matrix whose properties are not readily modeled without input from simulations. The memory function matrix affects the dynamics on all time scales, but our focus is on those portions influencing mainly the long time dynamics, which is not amenable to simulation for interesting complicated systems. Thus the tests are made on a simple, yet nontrivial system for which long time simulations are possible and provide the most stringent test of the parameter free theory. The test involves Brownian dynamics simulations of united atom models for single octane and pentadecane dynamics in a structureless solvent. The octane case, for instance, yields a 7×7 memory function matrix whose properties are more complex than those of the one‐dimensional Kramers model recently studied. More importantly, our computations determine those necessary ingredients of the memory function matrix for describing long time dynamics of flexible large molecules in solution. We compare the theoretical and simulation computations of the bond vector time autocorrelation functions. The leading approximation without memory functions fares remarkably well despite the frequent conformational transitions occurring during the Brownian dynamics trajectories. This approximation systematically leads to faster decay than the simulations due to the neglect of the long time frictional influence of the memory function matrix. We consider computations of these memory functions using both the Mori continued function formalism, and a generalization of the matrix methods introduced to treat the one‐dimensional Kramers model. A procedure is developed to obtain the long time influence of the memory function matrix. This procedure improves agreement between theory and simulation and displays good convergence towards the simulation results at the longer times (≳100 ps) for which we are interested.