Diabatic surface

The Landau-Zener transition probability is derived from an approximation to the frill two-state impact-parameter treatment of the collision. The single passage probability for a transition between the diabatic surfaces H, (/ ) and R AR) which cross at is the Landau-Zener transition probability... 

McDouall J J W, Robb M A and Bernard F 1986 An efficient algorithm for the approximate location of transition structures in a diabatic surface formalism Chem. Phys. Lett. 129 595... 

M Marchi, IN Gehlen, D Chandler, M Newton. Diabatic surfaces and the pathway for primary electron transfer in a photosynthetic reaction center. 1 Am Chem Soc 115 4178-4190, 1993. 

Let us consider the possible relations of LS and HS potential energy surfaces as shown schematically in Fig. 9. As long as the zero-order or diabatic surfaces are considered, the eleetrons remain localized on the particular spin state, no eleetron transfer being possible. In order that a conversion between the LS and HS state takes place, electronic coupling of the states is required. This coupling effectively removes the degeneracy at the interseetion of the zero-order surfaces... 

Figure 7. The PES of the X2B2S and A -Bi, states of the butatriene radical cation, (a) Diabatic surfaces, (b) Adiabatic surfaces. The surfaces are obtained as eigenfucations of the vibronic coupling model Hamiltonain that fitted to reproduce quantum chemical calculations. The coordinates are shown in Figure lc. See Section III. D for further details.

Figure 5. Energy diagram for charge separation resolved into reactant-like and product-like diabatic surfaces. The two diabatic curves do not intersect, but interact, to give an avoided crossing, whose energy gap is twice the electronic coupling, Vei, for the interaction. Also depicted is the Marcus-Hush classical rate expression for nonadiabatic ET.

The Landau-Zener expression is calculated in a time-dependent semiclassical manner from the diabatic surfaces (those depicted in Fig. 1) exactly because these surfaces, which describe the failure to react, are the appropriate zeroth order description for the long-range electron transfer case. As can be seen, in the very weak coupling limit (small A) the k l factor and hence the electron transfer rate constant become proportional to the absolute square of A ... 

The two diabatic surfaces and wave functions are allowed to couple by way of a Hamiltonian matrix element denoted / ... 

Figure 12 Plots of the energy surfaces appropriate to the D-B-A (left) and D -B-A (right) species as functions of the reaction coordinate along which the diabatic surfaces cross and the adiabatic surfaces undergo an avoided crossing (as shown) (appears as Figure 10.2 in ref. 12).

The adiabatic MOVE ground state potential surface is significantly lower in energy than the diabatic surfaces. The computed barrier for the proton transfer is 1.2 kcal/mol at the MOVE(3)/3-21G level, which may be compared with the... 

Diabatic surfaces connect electronic states having similar electron configurations. In other words the one-electron functions from which the are constructed change little as the nuclear coordinate of interest is changed. 

Suppose Va and V/, are diabatic surfaces which cross at some configuration and let cj/2 be the matrix element of the electronic Hamiltonian between the two diabatic states. In other words, the adiabatic curves are the eigenvalues of the potential energy matrix. 

Fig. 1. The autocorrelation function C(t) = (U (O)l I (i) is shown for a wavepacket initially prepared on the upper diabatic surface [7]. Panels (a) and (b) C(t) for the four core modes calculated by the standard MCTDH method for the model Hamiltonian Hy of Eq. (9), shown on different scales in the two panels. Panel (c) G-MCTDH calculation (bold line) as compared with standard MCTDH calculation (dotted line) for the composite system with four core modes (combined into two 2-dimensional particles

Let a crossing of diabatic surfaces of potential energy occur in a certain point R0. Taking into account only the linear expansion term of the difference between the energies of the diabatic states near the crossing point (the Landau-Zener model)... 

In Fig. 22, the lower of the each of the two diabatic surfaces in shown. The free energy as a function of AF. at fixed z is close to parabolic for each surface (due to the approximately gaussian sampling of AE), and the curvature and... 

The terms p and ep are similar to diabatic surfaces (35,6A, 65). We have introduced them starting directly from the Born-Oppenheimer approximation. 

Fig. 2 The model of coupled potential energy surfaces used to explain the vibronic spectral features in Re dioxo complexes. Solid and dashed lines represent adiabatic and diabatic surfaces, respectively. The lowest adiabatic surface corresponds to the electronic ground state used to calculate the luminescence spectra. The crystal field energies for all three Ai states are given along the vertical dashed line...

To our knowledge, the first PES suitable for dynamical studies of the title reaction was proposed in 1976 by Murrell and Sorbie [58] from spectroscopic data, but the first dynamical studies have been carried out in 1980 by Schinke and Lester in a PES fitted from ab initio data [32]. To better reproduce the experimental rate constant, those authors propose two different potential energy surfaces named SLl and SL3. Subsequently, Murrell, Carter, Mills and Guest have published a double-valued PES [57] to correctly account for the different crossings between the diabatic surfaces and Murrell and Carter proposed a simpler single-valued PES that approximates it [59] this last one is known as MC PES. 

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