Diabatic potential energy

The potential matrix elements are then obtained by making Taylor expansions around 00, using suitable zero-order diabatic potential energy functions,... 

Figure 6. Diabatic potential energy surfaces for electron transfer reactions in the system AL/B.

Note that since the profile of the lower adiabatic potential energy surface for the proton depends on the coordinates of the medium molecules, the zeroth-order states and the diabatic potential energy surfaces depend also on the coordinates of the medium molecules. The double adiabatic approximation is essentially used here the electrons adiabatically follow the motion of all nuclei, while the proton zeroth-order states adiabatically follow the change of the positions of the medium molecules. 

When two electronic states are degenerate at a particular point in configuration space, the elements of the diabatic potential energy matrix can be modeled as a linear function of the coordinates in the following form ... 

Activationless ET processes (1, 4, 6, 9) are described by two diabatic potential energy surfaces crossing at the minimum of the initial surface. This limit is characterized by a rate which decreases with increasing temperature at high T (negative apparent activation energy)... 

Figure 1. Diabatic potential energy curves for Nal with an expanded view of the adiabatic potential curves, e, and Ej, near the diabatic curve crossing.

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

The diabatic potential-energy hypersurfaces U(Q [([).]) are of use to examine the energy reshuffling in neighborhoods of a crossing point Q, where U(Q [([)]]) = U(Q [(t)j>]). This may look like a conic intersection but it should not be confused with that the domain where this condition holds can be named a seam as it is common practice in the adiabatic scheme, see vol.127 of Faraday Discussions... 

Figure 2. To the left, quasi-diabatic potential energy surfaces in the B3LYP/cc-pvtz Dunning s basis set. AA represents a cis state (solid line) BB a trans state (solid line) AB is the excited diradical state spin singlet (dashed line) Triplet is the diradical state S=1 (dotted line). To the right, extrapolated diabatic potential energy surfaces for the same states. The angle used to plot energy entries is a = 2 0. All calculations were done with Gaussian 98 [23].

Not shown to the quasi-diabatic potential energy surfaces in Fig. (3) there is a adiabatic potential energy surface. This is distinguished by the maximum at the crossing point nil. The system has a saddle-point structure. In the regions about the cis and trans attractors there is no difference between them. Between 2%1 i... 

Once the diabatic potential energy surfaces relevant to describing a process, the integration of the sources of external potential (nuclear dynamics) can be done in real space using numerical integration methods. 

A rigorous electro-nuclear separability scheme has been examined. Therein, an equivalent positive charge background replaces the nuclear configuration space the coordinates of which form, in real space, the -space. Diabatic potential energy hypersurfaces for isomers of ethylene in -space were calculated by adapting standard quantum chemical packages. 

Figure 1 Left Enol-keto tautomerism in salicylaldimine (SA) and normal mode displacements for skeleton modes 1 4 and 1/30. Middle H/D diabatic potential energy curves Ua(Qu) for mode i/u (lowest states ground state, bolding and stretching fundamental, first bolding overtone arrows indicate laser excitation). Right two-dimensional (Qj4,Q3o) cuts through the adiabatic PES (obtained upon diagonalizing the field-free part of Eq. (1)) which has dominantly H/D stretching character but includes state and mode couplings (contours from 0 to 7400 cm-1).

Let us consider a typical situation as sketched in Figure 7.5. V and V2 represent the (diabatic) potential energy curves (or surfaces) of two... 

Klos J, Chalasinski G, Szczesniak MM, Werner H-J (2001) Ab initio calculations of adiabatic and diabatic potential energy surfaces of cl... HC1 Van der Waals complex. J Chem Phys 115 3085-3098... 

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