1549380323-Statistical Mechanics Theory and Molecular Simulation

344 Free energy calculations the equilibrium value of the harmonic restraining potential is chosen to be a set of intermediate p ...

Umbrella sampling 345 histogram obtained from each molecular dynamics or Monte Carlo simulation. Then, the biased distribution i ...

346 Free energy calculations that the sampling is of equal quality for each simulation. Note that this does not necessarily mean ...

Wang–Landau sampling 347 simulation in the window. Because we have assumed a specific form forthe distribution, we can calculate ...

348 Free energy calculations toh(s)→h(s) +α, whereα= lnf. This is equivalent to scalingg(s)→fg(s). As the simulation proceeds,g( ...

Adiabatic dynamics 349 In order to exploit eqn. (8.10.3) for the development of a free energy method, it is useful to express bo ...

350 Free energy calculations p ̇η 2 = ∑^3 N α=n p^2 α 2 m′α −(3N−n)kT. (8.10.6) In practice, it is recommended that a a more rob ...

Adiabatic dynamics 351 time-scale integrators of Section 3.11, we write this operator usingthe Trotter theorem as exp ( iL 2 ∆t ...

352 Free energy calculations the reaction coordinates which, for finiteM, leads to a sum of force terms at different times ∆t/M. ...

Adiabatic dynamics 353 SinceZY(q 1 ,...,qn) is the potential of mean force for the reaction coordinates, thefree energy hypersur ...

354 Free energy calculations A(x) =D 0 ( x^2 −a^2 ) 2 − λ^2 2 k x^2. (8.10.22) The bare double well has minima atx=±aand a barri ...

Metadynamics 355 atoms in an arbitrary dihedral angle be denotedrk+1,...,rk+4. The transformation can be carried out in the foll ...

356 Free energy calculations is subsequently filled in, and so forth until the entire landscape is “flat.” When this state is ac ...

Metadynamics 357 is a time interval. The purpose of this bias potential is to add Gaussians of heightW and width ∆sat intervalsτ ...

358 Free energy calculations H= ∑n α=1 p^2 α 2 mα + ∑N i=1 p^2 i 2 mi +U(r 1 ,...,rN) + ∑n α=1 1 2 k(sα−fα(r))^2 (8.11.9) for sa ...

Committor distribution 359 free energy dynamics method by allowing a wider range of collective variables to be used, and emerges ...

360 Free energy calculations a true transition state, thenpB(r) = 1/2. Inherent in the definition of the committor is the assump ...

Problems 361 configuration, average the 1s and 0s, and record the average value asp(k). 5) Repeat for all of the configurations ...

362 Free energy calculations fromx=−atox= 0, i.e., the value ofyremains fixed in each ensemble member during this process. The w ...

Problems 363 ∗8.12. Develop a weighted histogram procedure to obtain the free energy derivative dA/dqiat a set of integration po ...