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Diabatic energy difference

Hence, it appears desirable to readjust the parameters used for Demkov s model. Suitable parameters to approximate HF results are introduced in Table 1 as set II. The nondiagonal matrix element H,2 is treated in accordance with Eq. (18c). Moreover, the parameter Aa is set equal to the diabatic energy difference at the coupling radius as justified explicitly in Section 3.4. This diabatic energy difference is obtained from the related asymptotic value Ae using the reduction factor z from Table 2. It may readily be verified that with the modified model parameters the radial... [Pg.436]

It is noted that for low velocities the sharing probability is not influenced by the slope of the diabatic potential curves. From Eq. (32) follows the same expression, but the factor 1 - cos is missing in the exponent. This factor determines the diabatic energy difference in the coupling region, since A//(l c) = Ae(l - cos 6), as may readily be deduced from Eq. (15). Thus, in the low-velocity range the treatments by Nikitin and Demkov are identical provided that in Demkov s formula the diabatic energy difference AH Rc) is inserted instead of the asymptotic value Ae 2- Thus, the modified value for Ae is justified in Table 1. [Pg.441]

The situation is different when the diabatic potential curves cross as assumed in the Landau-Zener model. In this case the diabatic energy difference vanishes and it loses significance as a model parameter. Then, the expression (33) should be interpreted differently. As noted in Section 3.2, the Landau-Zener model implies 6 1 so that 1 - cos d [sin 0]/2 = 2[Hi2(Rc)/ Ae]. Here, it is useful to introduce the derivative of the diabatic energy difference F = dAH/dR, which may be regarded as the force holding the system in the diabatic state. Likewise, the interaction Hu pushes ... [Pg.441]

Once the diabatic energy difference AH(Rc) is known, Nikitin s model may be utilized as well. When As is set to be equal to the asymptotic value Ae 2, the Nikitin angle 6 is obtained from... [Pg.456]

The Quasi-variational method (Method II) An alternative approach, which we recommend, consists of optimizing each diabatic state separately, in an independent calculation. Consequently, the resulting orbitals of the diabatic states are different from those of the adiabatic states, and each diabatic state possesses its best possible set of orbitals. The diabatic energies are obviously lower compared with those obtained by the previous method, and are therefore quasi-variational. The diabatic energies of the covalent and ionic structures of F2, calculated with Methods I and II in the L-BOVB framework, are shown in Table 10.4. It is seen that the ionic structures have much lower energies in the quasi-variational procedure, and as such, the procedure can serve a basis for deriving quantities such as resonance energies (see below). [Pg.283]

The diabatic solvent reorganization energy is defined by the nuclear response function Xn and by the diabatic field difference... [Pg.164]

The matrix element can be inferred from the deviations of observed properties from those expected of the reacting system in the diabatic limit. The size of those deviations tends to increase as a function of the fraction of an electron that is delocalized between donor and acceptor, where is the vertical energy difference between the diabatic reactants and products states H -p/E = app is the coefficient for mixing and V p. [Pg.1181]

Thus, for a given diabatic state, z is the free energy difference between the minimum energy point and the point corresponding to the minimum energy of the other state. The effective z value for the two-state system can be taken as the arithmetic mean of z, and z/ [47] (i.e., one-half of the Stokes shift for the optical ET process). [Pg.92]

Figure 1. An example of a pair of adiabatic potentials with an avoided crossing at Q= Qc where the energy separation is 27. As the energy difference between them becomes much larger than 7, each of them approaches one of the diabatic potentials Vr(Q) and Vp Q) of Figure 2. Figure 1. An example of a pair of adiabatic potentials with an avoided crossing at Q= Qc where the energy separation is 27. As the energy difference between them becomes much larger than 7, each of them approaches one of the diabatic potentials Vr(Q) and Vp Q) of Figure 2.
In this definition, Q has energy dimensions, giving the energy difference between the diabatic potentials for the reactant and the product states, while Q in Eqs. 17 and 18 was defined to be dimensionless. Inserting Eqs. 38 and 39 into Eq. 40, we get... [Pg.155]

In the atomic collision, the v value has been determined extrinsically by the initial relative velocity of the two atoms. In the present problem of electron transfer between donor and acceptor, v takes various values, arising from the thermal fluctuations of atoms along the reaction coordinate. On a trajectory Q t) along the reaction coordinate in the semiclassical picture, the value of v is given by the time derivative Q(t) since Q was defined as the energy difference between the diabatic potentials for the reactant and the product state (Eq. 40). Since fluctuations in Q(t) are statistically independent of those in Q(t), the average value of v is the same at any value of Q(t). [Pg.163]

From Eq. 3b the vertical difference between the diabatic energies at the equilibrium configuration (adiabatic minimum) of the reactants for AG° = 0 is given by... [Pg.1253]

There is thus an inverse relationship between the ratio of the adiabatic and diabatic dipole-moment changes and the ratio of the corresponding free-energy differences within the two-state model. [Pg.1265]

Before we continue in the discussion of the significance of our analysis, it is useful to consider related results of Nam et al.87 These workers used a QM/MM MO approach, which does not provide a diabatic energy gap or the corresponding C(t)-Instead, they evaluated the force autocorrelation, C(t)F, which is a valid but somewhat less direct measure of the solvation dynamics than C(t). It was found that C(t)F relaxes more slowly in water than in DhlA. Furthermore, the C(t)F of the enzyme also showed some oscillations. The finding that C(t) can be somewhat different in the enzyme and in water is not new and has been reported by Villa and Warshel.4 Unfortunately, the study of Nam et al.87 did not provide a separate analysis for the solute and solvent coordinate. Such an analysis is quite challenging when one uses standard QM/MM studies. [Pg.296]


See other pages where Diabatic energy difference is mentioned: [Pg.119]    [Pg.425]    [Pg.428]    [Pg.436]    [Pg.446]    [Pg.455]    [Pg.456]    [Pg.461]    [Pg.360]    [Pg.119]    [Pg.425]    [Pg.428]    [Pg.436]    [Pg.446]    [Pg.455]    [Pg.456]    [Pg.461]    [Pg.360]    [Pg.353]    [Pg.355]    [Pg.433]    [Pg.274]    [Pg.179]    [Pg.201]    [Pg.189]    [Pg.54]    [Pg.372]    [Pg.201]    [Pg.124]    [Pg.255]    [Pg.283]    [Pg.219]    [Pg.440]    [Pg.1184]    [Pg.138]    [Pg.321]    [Pg.1248]    [Pg.1254]    [Pg.358]    [Pg.41]    [Pg.223]    [Pg.184]    [Pg.355]    [Pg.519]    [Pg.88]   
See also in sourсe #XX -- [ Pg.441 , Pg.461 ]




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