Adiabatic potential energy

Finally, in brief, we demonstrate the influence of the upper adiabatic electronic state(s) on the ground state due to the presence of a Cl between two or more than two adiabatic potential energy surfaces. Considering the HLH phase, we present the extended BO equations for a quasi-JT model and for an A -1- B2 type reactive system, that is, the geometric phase (GP) effect has been inhoduced either by including a vector potential in the system Hamiltonian or... 

The two adiabatic potential energy surfaces that we will use in the present calculations, are called a reactive double-slit model (RDSM) [59] where the first surface is the lower and the second is the upper surface, respectively,... 

Figure 6. Diabatic and corresponding adiabatic potential energy along a relevant reaction coordinate for normal electron transfer...

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

Now, we examine the effect of vibronic interactions on the two adiabatic potential energy surfaces of nonlinear molecules that belong to a degenerate electronic state, so-called static Jahn-Teller effect. 

GP effect, with the shifts being equal to +0.0807, —0.0709, and —0.0273 eV for the Ai, A2, and E symmetries, respectively. Clearly, such shifts are larger than those obtained in the calculations for the lower adiabatic potential energy surface, namely, +0.0104, —0.0194, and —0.0043 eV (in the above order). 

Figure 11. Perspective view [60] of a relaxed triangular plot [68] for the two DMBE adiabatic potential energy surfaces of H3 using hyperspherical coordinates.

In such a case the last choice is to take the direction of the eigenvector of the only one nonzero eigenvalue of the rank one Hessian matrix of the difference between the two adiabatic potential energies [51]. In the vicinity of conical intersection, the topology of the potential energy surface can be described by the diadiabatic Hamiltonian in the form... 

On the other hand, one can use Eq. (1) to calculate the Hessiam matrix of the difference between the two adiabatic potential energy surfaces, AV R). Up to an irrelevant scalar factor, the result reads... 

Figure 5. Adiabatic potential energy surfaces of the DIM model potential showing conical intersection at the C21/ symmetry. Taken from Ref [51],...

Figure 21. Family of reactive trajectories in the ground adiabatic potential energy surface determined by Eq. (13). Crosses indicate the caustics. Taken from Ref. [29].

Figure 61. Adiabatic potential energy curves for the atomic hydrogen transmission through the five-membered ring in the case of center approach. Taken from Ref. [47].

The angular-dependent adiabatic potential energy curves of these complexes obtained by averaging over the intermolecular distance coordinate at each orientation and the corresponding probability distributions for the bound intermolecular vibrational levels calculated by McCoy and co-workers provide valuable insights into the geometries of the complexes associated with the observed transitions. The He - - IC1(X, v" = 0) and He + 1C1(B, v = 3) adiabatic potentials are shown in Fig. 3 [39]. The abscissa represents the angle, 9,... 

Figure 2.4 Adiabatic potential energy E q) for various values of A at equilibrium. The solvent coordinate q has been normalized so that the initial state corresponds to = 0 and the final state to = 1. The reorganization energy was taken as A = 1 eV.

From the given Hamiltonian, adiabatic potential energy surfaces for the reaction can be calculated numerically [Santos and Schmickler 2007a, b, c Santos and Schmickler 2006] they depend on the solvent coordinate q and the bond distance r, measured with respect to its equilibrium value. A typical example is shown in Fig. 2.16a (Plate 2.4) it refers to a reduction reaction at the equilibrium potential in the absence of a J-band (A = 0). The stable molecule correspond to the valley centered at g = 0, r = 0, and the two separated ions correspond to the trough seen for larger r and centered at q = 2. The two regions are separated by an activation barrier, which the system has to overcome. 

Song L, Gao J (2008) On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory. J Phys Chem A ASAP... 

Figure 5-3. Active site and calculated PES properties for the reactions studied, with the transferring hydrogen labelled as Hp (a) hydride transfer in LADH, (b) proton transfer in MADH and (c) hydrogen atom transfer in SLO-1. (i) potential energy, (ii) vibrationally adiabatic potential energy, (iii) RTE at 300K and (iv) total reaction path curvature. Reproduced with permission from reference [81]. Copyright Elsevier 2002...

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