New algorithms for sampling and exploring multidimensional free energy surfaces(FES) are developed. The first algorithm, unified free energy dynamics (UFED), is based on temperature acceleration molecular dynamics(TAMD) and driven adiabatic free energy dynamics(d-AFED). Mean force as an unbiased quantity in these biased enhanced sampling algorithms is discussed and a way to reconstruct a FES from the mean force is provided. A biasing potential constituted by Gaussians are used and an asymptotic analysis of d-AFED with biasing potential is discussed to prove the convergence. Examples like alanine dipeptide in vacuum and aqueous solution, met-enkephalin in vacuum, and alanine tripeptide in vacuum are provided to illustrate this algorithm.
The second part discuss the leading errors in TAMD/d-AFED with perturbation analysis. The first order error of TAMD with Brownian dynamics is discussed by averaging procedure. An application of this analysis, which prove that this error will be finite when the harmonic coupling constant approaching infinity, is discussed. The limit equation of d-AFED with Langevin thermostat is discussed in the cases of different friction coefficients of slow variables. The perturbation analysis of Langevin equation shows that the leading error is related to the mechanical power from the slow variables to physical degrees of freedom. However, the error of mean force is the second order error and does not directly related to this power. Numerical examples have been provided to illustrate the analysis of Langevin equations.
The third part discuss a non-sampling way to explore a high dimensional FES(HDFES). First a method that can explore index-1 saddles, named as gentlest ascent dynamics (GAD), has been extended to FES. Then stochastic approximation has been introduced as a way of optimization on a FES. With iteratively searching for minima and saddles, this optimization based strategy can perform a global search on a HDFES. Various post-analysis tools are introduced to pin down the exact locations of minima and saddles (landmarks). Alanine tripeptide and met-enkephalin are successful examples to illustrate the algorithm. Together with modern enhanced sampling algorithms, this method can determine the most important states and transitions on a HDFES. At last, we show some preliminary theoretical development that applies this method to molecular crystal polymorph search.
|Advisor:||Tuckerman, Mark E.|
|Commitee:||Kirshenbaum, Kent, Turner, Daniel B., Zhang, John, Zhang, Yingkai|
|School:||New York University|
|School Location:||United States -- New York|
|Source:||DAI-B 77/07(E), Dissertation Abstracts International|
|Keywords:||Collective variable, Enhanced sampling, Free energy surface, Langevin equation, Machine learning, Multiscale problem|
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