Variational Principles in Conformation Dynamics - FU Berlin, FB MI

IV.3. Application of the Roothan-Hall method 4110.990.98Estimated λ3, large Roothan−HallEstimated λ3, large MSMEstimated λ3, small Roothan HallEstimated λ3, small MSM1210Third eigenvalue λ30.970.960.95Implied time scale t38640.940.930.920 50 100 150Time lag τEstimated t3, large Roothan−Hall2Estimated t3, large MSMEstimated t3, small Roothan HallEstimated t3, small MSM00 50 100 150Time lag τ(a)(b)0.80.60.4Estimated φ3, Roothan−HallEstimated φ3, MSM10.980.96Estimated λ4, large Roothan−HallEstimated λ4, large MSMEstimated λ4, small Roothan HallEstimated λ4, small MSMφ3(ψ)0.20−0.2Fourth eigenvalue λ40.940.92−0.40.9−0.60.88−0.8−4 −3 −2 −1 0 1 2 3 4ψ(c)0.860 50 100 150Time lag τ(d)760.80.6Estimated φ4, Roothan−HallEstimated φ4, MSM50.4Implied time scale t4432Estimated t4, large Roothan−Hall1Estimated t4, large MSMEstimated t4, small Roothan HallEstimated t4, small MSM00 50 100 150Time lag τ(e)φ4(ψ)0.20−0.2−0.4−0.6−4 −3 −2 −1 0 1 2 3 4ψ(f)Figure IV.6.: Continuation of Figure IV.5. (a) Third eigenvalue λ 3 . (b) Third implied timescale t 3 . (c) Projection of third eigenfunction φ 3 . (d) Fourth eigenvalue λ 4 .(e) Fourth implied time scale t 4 .(f)Projectionoffourtheigenfunctionφ 4 .