Repository based adaptive umbrella sampling

To determine free energy surfaces along chosen reaction coordinates is an important and challenging task in simulating complex systems. In this thesis we develop two techniques to enhance sampling: one is mass scaling; another is repository based adaptive umbrella sampling (RBAUS).;Scaling the atomic mass can enhance the sampling efficiency. By making the atomic masses more equal, the reduction of the frequencies of fastest motions will allow a lengthening of the time step. Our results showed that increasing the hydrogen mass to 10 amu would allow a time step of 3 fs in ab initio QM/MM BO-MD simulations and lead to little change in the simulated free energy profiles and structural properties in comparison with corresponding simulations using 1 fs time step and the normal mass.;More importantly, we developed RBAUS method and two further extensions. In this new adaptive sampling approach, a sampling repository is periodically updated based on the latest simulation data, and the accumulated knowledge and sampling history are then employed to determine whether and how to update the biasing umbrella potential for subsequent simulations. In comparison with other adaptive methods, a unique and attractive feature of the RBAUS approach is that the frequency for updating the biasing potential depends on the sampling history and is adaptively determined on the fly, which makes it possible to smoothly bridge non-equilibrium and quasi-equilibrium simulations. By introducing sampling entropy and concentration theorem into the biasing potential updating scheme, the second version of RBAUS has the significantly improved adaptivity, robustness and applicability. In the third version of RBAUS, the biasing potential updating is based on the Bayesian inference, which better describes the biasing potential.;The RBAUS methods are first tested by simulations on two simple systems: a double well model system with a variety of barriers and the dissociation of a NaCl molecule in water. Their efficiency and applicability are further illustrated in ab initio QM/MM MD simulations of a methyl-transfer reaction in aqueous solution and determining two dimensional free energy surfaces of alanine dipeptide in gas phase and in water.