State trajectory

We counted the contribution of only those trajectories that have a positive momentum at the transition state. Trajectories with negative momentum at the transition state are moving from product to reactant. If any of those trajectories were deactivated as products, their contribution would need to be subtracted from the total. Why Because those trajectories are ones that originated from the product state, crossed the transition state twice, and were deactivated in the product state. In the TST approximation, only those trajectories that originate in the reactant well are deactivated as product and contribute to the reactive flux. We return to this point later in discussing dynamic corrections to TST. 

Fig. 8.5 State variable time response and state trajectory for Example 8.4. Solution...

The step response of the state variables, together with the state trajectory, is shown in Figure 8.6. 

The tracking or servomechanism problem is defined in section 9.1.1(e), and is directed at applying a control u(t) to drive a plant so that the state vector t) follows a desired state trajectory r(t) in some optimal manner. 

In forward-time, use the command vector vf/cT) and state vector xf/cT) to caicuiate Uopif/cT) in equation (9.55) and hence, using the piant state transition equation (9.56) caicuiate the state trajectories. 

Barrier potential, transition state trajectory, stochastically moving manifolds, 221-222... 

Colored noise, transition state trajectory, 208-209 Configuration interaction (Cl), ab initio... 

Damping effects, transition state trajectory deterministic driving, 209-213 stochastically moving manifolds, 215-222 De Broglie wavelength, two-pathway excitation, coherence spectroscopy 165-166 Decoherence, two-pathway excitation, coherence spectroscopy ... 

Dirac delta function, transition state trajectory, white noise, 203-207... 

Eigenvalues, transition state trajectory colored noise, 209... 

Escape actions, transition state trajectory, deterministically moving manifolds, 230-231... 

Friction interactions, multiparticle collision dynamics, single-particle friction and diffusion, 114—118 Friction kernel, transition state trajectory, colored noise, 209... 

Periodic boundary conditions, Monte Carlo heat flow simulation, nonequilibrium molecular dynamics, 79—81 Periodic-orbit dividing surface (PODS) geometric transition state theory, 196-201 transition state trajectory, 202-213 Perturbation theory, transition state trajectory, deterministically moving manifolds, 224-228... 

Solvent properties, transition state trajectory, future research issues, 232-233 Space inversion symmetry (P) ab initio calculations, 253—259 barium fluroide molecules, 256-259 ytterbium molecule, 254—256 electric dipole moment search, 241-242 nonconservation, 239—241 Spatial neighbor tables, Monte Carlo heat flow simulation, 68—70... 

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