Ground adiabatic potential sheet

The shapes of the adiabatic potential sheets are governed by eight parameters - V, v1, ih. A1, A2, t, coBi, coAi. In order to elucidate the conditions that favor the photochromic effect, first we shall try to discuss the values of the above-mentioned parameters. For the usually accepted value of k = 105 dyn cm-1 the frequencies o Bi and coAl are estimated as 340 and 400 cm-1, respectively. The energy gaps A2 and Ai can be approximately identified with those between the HOMO and the split components of LUMO in the MS2 state. These values are calculated in paper [ 17] by the DFT method and prove to be equal to A2 = 21185 cm-1 and A = 15850 cm-1. 

The vibronic coupling parameter V was roughly evaluated under the assumption that Vi = v2 = 0, t = 0. If the energy 

It should be mentioned that the coordinates Ql and g3 (see Table 1) of the ground and second excited minima nearly coincide with those estimated for V = 9.83hwBi with the aid of equation (10) in the case of rq = v2 = 0. At the same time, the coordinate Q2 of the first excited minimum is close to zero. From this it follows that the minima of the sheet u2(q = 0, Q) [equations (9) and (10)] convert into the minima GS and MSI at the points Ql and (ft given in the table, whereas the minimum of the sheet iq (q = 0, Q) turns into the first excited minimum MS2 at the point Q2, when the values rq. v2. and t are non-vanishing. Such a minima conversion justifies to an extent the evaluation of the starting value of the parameter 

V with the aid of equation (10) and the experimental value of the activation energy for the MS2-state. However, the inclusion in the model of the interaction with the full-symmetric vibration Aj (Fig. 1) and of the electron transfer processes brings to a lower value of the barrier height between the ground (GS) and first excited minima (MS2) as compared with experimental data (see Fig. 3). The changes in Fe-N and Fe-0 bonds have been also estimated. The calculated and experimental values of the lengthening are comparable. For instance, the difference between the Fe-O bond length in the GS and MS2 states was obtained to be equal to 0.4 A, while the experimental value [10] is 0.7 A. 

1 -energy gap between the first excited and ground minima, ft  

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Table 1. Angles (degrees) for the ground, first and second excited minima of the lower adiabatic potential sheet in the case of V = 9.8ha>Bi, t = 5.5ha>Bv v2 = 6.2hcoBl, iq = 1.5hcoBl, ft = 15850 cm-1, ft = 21185 cm-1, uBl = 340 cm-1, coAl = 400 cm-1...

Fig. 5. Energy gaps (a) between the ground and excited minima of the lower adiabatic potential sheet Ui(q,Q) and angles ft (b) characterizing the configuration of the Fe-(NO) fragment in these minima as functions of the vibronic parameter V with t = 5.5hcoBl, v2 = 6.2ho)Bl, Vi = 1.5h(oBl, Deltas = 15850 cm-1, A2 = 21185 cm-1 coBi = 340 cm-1 coAl = 400 cm"1.

Table 1 Angles degrees) for the ground, first and second excited minima of the lower adiabatic potential sheet (the parameters are the same as in Fig. 41)...

In dealing with the MO-LCAO wave function no additional assumptions concerning the vibronic matrix elements are necessary. The evaluation of the total molecular energy exactly copies the lower sheet of the adiabatic potential. This is a consequence of the well-known fact that the Hartree-Fock equations are equivalent to the statement of the Brillouin theorem the matrix elements of the electronic Hamiltonian between the ground-state and... 

In case of the quadratic vibronic interactions are taken into account three minima appear on the lowest sheet of the adiabatic potential. The tunneling between them leads to a complicated local dynamics that in its turn significantly influences the cooperative problem interaction. If the lowest ground state is a vibronic doublet and the first excited state is a vibronic singlet well separated from the higher energy levels, Thomas and Muller [12] had shown that the Hamiltonian of the CITE system can be described as... 

Fig. 1. Three-dimensional perspective plot of the adiabatic potential energy surfaces of the double-sheeted ground electronic state of H3 in the (R,r) plane for 7 = tt/2, corresponding to the C 2v arrangements of the three nuclei. The contour line diagram is included in the base of the plot. The spacing between the successive contour lines is 0.3 eV. The potential energies are obtained from the DMBE PES and the lower (y ) and the upper (V ) adiabatic sheets are shown by the thin and thick solid curves, respectively. The conical intersection of the two surfaces should not be realized as an isolated point as apparently revealed by the perspective plot, rather, it represents a seam of intersections occurring for R = which is more clearly indicated by the...

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