Adiabatic free energy

Figure 10. Classical adiabatic free energy curve (solid line) forthe Fe /Fe electron transfer at the water/Pt(lll) interface calculated using the Anderson-Newns Hamiltonian and the molecular dynamics umbrella sampling method. Also shown by the dashed line is the parabolic fit of the data. (Reprinted from Ref. 14.)...

Figure 14. Adiabatic free energy curves for the precursor and successor complexes with respect to A j values of the reaction coordinate A . (Reprinted from Ref 64.)...

The adiabatic free energy curve can be calculated by umbrella sampling using the adiabatic Hamiltonian Hgj as discussed earlier. If the coupling r is constant (independent of nuclear positions), then it is possible to show that the adiabatic free energy curve can be obtained from the diabatic free energy curve according to... 

Figure 13. Adiabatic free energy curves for the electron transfer reaction Fe + e" for...

Fig. 9.16. Adiabatic free energy curves for the electron-transfer reaction for Fe +e-Fe2+ for an overpotential q and electronic coupling coefficient, r. (Reprinted from I. Benjamin and D. A. Rose, J. Chem. Phys. 100 3545, 1994 with permission of the American Institute of Physics.)...

Figure 12 The CT adiabatic free energy surfaces in the normal CT region. The labels and indicate two adiabatically split absorption transitions corresponding to two minima of the lower surface with the coordinates Yj and Y Ae = 0.7, AFl = 0, AEnlyJ = 0.2. The gap AEmin is the minimum splitting between the upper and lower CT surfaces (Eq. [149]).

Figure 15 Adiabatic free energy surfaces F (Y ) in the present model (solid lines, Eqs. [105] and [106]) and in the Marcus-Hush formulation (long-dashed lines, Eqs. [41] and [119]) for self-exchange CT with AF = APf = 0, X = = 1 eV, AE12 = 0.2 eV,...

Equation [139] is exact for a two-state solute, but differs from the traditionally used connection between the transition dipole and the emission intensity by the factor Vo/Vav." The commonly used combination miiVo/Vav appears as a result of neglect of the frequency dependence of the transition dipole mi2(v) entering Eq. [129]. It can be associated with the condensed-phase transition dipole in the two-state approximation." Exact solution for a two-state solute makes the transition dipole between the adiabatic free energy surfaces inversely proportional to the energy gap between them. This dependence, however, is eliminated when the emission intensity is integrated with the factor... 

Figure 5. Plot of the adiabatic free-energy surfaces against the reaction coordinate for an electron transfer reaction with AG" = 0 and //ab/- varying from 0 to 0.5.

This equation satisfies the relationship Ag = HX2(l — Q)/Q, where Ag is the adiabatic free-energy barrier of Equation (31). Now, when 9 1 we have A[Pg.291]

Equilibrium Statistical Mechanics, Non-Hamiltonian Molecular Dynamics, and Novel Applications from Resonance-Free Timesteps to Adiabatic Free Energy Dynamics... 

Free Energies via Adiabatic Free Energy Dynamics.180... 

The organization of this document is as follows The basis of all of these methods, equilibrium statistical mechanics, will be reviewed in Sect. 2. Section 3 will discuss the use of non-Hamiltonian systems to generate important ensembles. Novel non-Hamiltonian method, such as variable transformation techniques and adiabatic free energy dynamics will be discussed in Sect. 4. Finally, some conclusions and remarks will be provided in Sect. 5. 

L. Rosso, J. B. Abrams, and M. E. Tuckerman (2005) Mapping the backbone dihedral free-energy surfaces in small peptides in solution using adiabatic free-energy dynamics. J. Phys. Chem. B 109, p. 4162... 

J. B. Abrams, M. E. Tuckerman, and G. J. Martyna, Equilibrium statistical mechanics, non-hamiltonian molecular dynamics, and novel applications from resonance-free timesteps to adiabatic free energy dynamic. Lect. Notes in Phys. 703, pp. 139-192... 

J. VandeVondele and U. Rothlisberger (2002) Canonical Adiabatic Free Energy Sampling (CAFES) A Novel Method for the Exploration of Free Energy Surfaces. J. Phys. Chem. B 106, p. 203... 

Fig. 32. Adiabatic free energy curves as a function of reaction coordinate for selected overpotential / (in V) and electronic coupling constant F (in eV). Data are taken with permission from the work of Rose and Benjamin [197].

Rose and Benjamin [197] calculated the adiabatic free energy curves for several choices of overpotential rj and electronic coupling parameter T (Fig. 32) from... 

Figure 21. Adibatic solvent activation free-energy curves for the Fe /Fe electron transfer reaction with a platinum electrode at 300 K calculated obtained using the model of Ref. 50, path-integral quantum transition-state theory, and umbrella sampling. The solid line depicts the quantum adiabatic free-energy curve, while the dashed line depicts the curve in the classical limit. In both cases, the left-hand well corresponds to the Fe stable state, while the right-hand well is the Fe " stable state.

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