Ammm:Adaptive umbrella sampling

Multicanonical ensemble

Background of adaptive umbrella sampling

• Review of umbrella sampling (more details please refer to Yue's page)

    http://water.bme.utexas.edu/wiki/index.php/ABS:Umbrella_sampling_and_WHAM

    Umbrella sampling attempts to overcome the sampling problem by modifying the Hamiltonian so that

    the unfavorable states are sampled sufficiently. The modification can be written as a perturbation.

• The trial and error method for umbrella sampling

Theory of adaptive umbrella sampling

• Definitions

• The outline of the algorithm:

The potential energy as the variable for adaptive umbrella sampling

[[Image:Multidimensional Adaptive Umbrella Sampling Applications to Main Chain and Side Chain Peptide Conformationsjcc 97.pdf |600px]

  The potential energy, in contrast to the commonly used umbrella potentials,

  is of particular interest for complex systems because it does not depend on

  assumptions about the geometry nor on a knowledge of the important

  conformations and transition states that are involved in the equilibration.

• Range of Sampling:

• Extrapolation of the Umbrella Potential:

Application:Threonine Dipeptide

• System setup
  • adaptive umbrella sampling runs were performed at 303 K.
  • T-min was set equal to 280 K, while T-max was set equal to 2000 K.
  • V-min ~ V-max set as -50 to 100 kcal/mol.
  • 200 bins.
  • The umbrella potential was represented as a linear combination of 40 trigonometric functions

• Results