Variational Principles in Conformation Dynamics - FU Berlin, FB MI

40 IV. Application to molecules121080.90.80.70.6Estimated φ1, Roothan−HallEstimated φ1, samplingV(ψ)64φ1(ψ)0.50.40.320−4 −3 −2 −1 0 1 2 3 4ψ(a)0.20.10−4 −3 −2 −1 0 1 2 3 4ψ(b)10.99Estimated λ2, large Roothan−HallEstimated λ2, large MSMEstimated λ2, small Roothan HallEstimated λ2, small MSM181614Second eigenvalue λ20.980.970.96Implied time scale t2121080.950.940 50 100 150Time lag τ6Estimated t2, large Roothan−HallEstimated t2, large MSM4Estimated t2, small Roothan HallEstimated t2, small MSM20 50 100 150Time lag τ(c)(d)0.80.6Estimated φ2, Roothan−HallEstimated φ2, MSM0.40.2φ2(ψ)0−0.2−0.4−0.6−0.8−4 −3 −2 −1 0 1 2 3 4ψ(e)Figure IV.5.: Approximation results for system B. Every fifth step of a 30 million trajectorycorresponding to a sampling time step ∆t =10 −3 ps was used. We comparethe results obtained with the small and the large basis set to a 4 set and a100 set MSM discretization. The functions displayed were computed using thelarge basis sets. (a) Potential energy for the dihedral angle. (b) Projectionof first eigenfunction φ 1 ,comparedwithdirectestimatefromsampling. (c)Second eigenvalue λ 2 . (d) Second implied time scale t 2 . (e) Projection ofsecond eigenfunction φ 2 .