Potential energy surfaces electronically adiabatic

Fig. 2 The molecular structure of I—III and the representation of the potential energy surfaces for adiabatic to nonadiabatic electron transfer reactions...

Fig. 1 Potential energy surfaces in adiabatic outer sphere electron transfer.

The position of the maximum value of Ead(v,r) depends on v because, although Eei(x) increases toward the potential barrier, iivib(v,x) decreases, and this second contribution to f ad(v,x) assumes increasing importance as v increases. Although the v = 0 adiabatic maximum is usually located at the electronic saddle point, the maxima for higher states of bond-stretching vibration may be displaced into the entrance and exit valley on the potential energy surface. Vibrationally adiabatic motion is then expected up to the first of these maxima (r-AB > r-Bc). Trajectory calculations support this expectation [39-44]. 

Fig. 10 Smith lifetimes for Ai and A2 rovibronic wavefunctions. The vertical arrows indicate the energies of the bound states on the upper electronic potential energy surface, with adiabatic corrections...

In the previous sections it has been implicitly assumed that the unimolecular reaction is electronically adiabatic and, thus, occurs on a single potential energy surface. Electronically excited states (i.e., multiple potential energy surfaces) for unimolecular reactions was discussed in chapter 3 and it is assumed that the reader has read and is familiar with this material (Nikitin, 1974 Hirst, 1985 Steinfeld et al., 1989). Transitions between electronic states are particularly important for the unimolecular decomposition of ions. For example, the following two dissociation paths ... 

Figure 1 Hush diagram for intervalence transfer within a class II mixed-valence ion. The dotted lines correspond to diabatic potential energy surfaces. The solid lines are adiabatic potential energy surfaces. Electron transfer can occur either optically (vertical transition with energy, Eop, equaling A) or thermally by moving along the lower adiabatic surface. In the diabatic limit, the barrier height for thermal electron...

Figure 4.1 shows a schematic of relative energy in theF( P) + H2(j = 0) reaction. Due to the spin-orbit interaction, the fluorine atom degenerate ground electronic state F( P) is split into two states the spin-orbit ground state F( P3/2> and the spin-orbit excited state F ( Pj/2), respectively. As shown in Fig. 4.1, on the three adiabatic potential energy surfaces, electronic states l A and l A"... 

In many instances tire adiabatic ET rate expression overestimates tire rate by a considerable amount. In some circumstances simply fonning tire tire activated state geometry in tire encounter complex does not lead to ET. This situation arises when tire donor and acceptor groups are very weakly coupled electronically, and tire reaction is said to be nonadiabatic. As tire geometry of tire system fluctuates, tire species do not move on tire lowest potential energy surface from reactants to products. That is, fluctuations into activated complex geometries can occur millions of times prior to a productive electron transfer event. 

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... 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

The adiabatic picture is the standard one in quantum chemistry for the reason that, not only is it mathematically well defined, but it is also that used in ab initio calculations, which solve the electronic Hamiltonian at a particular nuclear geometry. To see the effects of vibronic coupling on the potential energy surfaces one must move to what is called a diabatic representation [1,65,180, 181]. 

Let S be any simply connected surface in nuclear configuration space, bounded by a closed-loop L. Then, if 4>(r,R) changes sign when transported adiabatically round L, there must be at least one point on S at which (r, R) is discontinuous, implying that its potential energy surface intersects that of another electronic state. 

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. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

In the Bom-Oppenheimer picture the nuclei move on a potential energy surface (PES) which is a solution to the electronic Schrodinger equation. The PES is independent of the nuclear masses (i.e. it is the same for isotopic molecules), this is not the case when working in the adiabatic approximation since the diagonal correction (and mass polarization) depends on the nuclear masses. Solution of (3.16) for the nuclear wave function leads to energy levels for molecular vibrations (Section 13.1) and rotations, which in turn are the fundamentals for many forms of spectroscopy, such as IR, Raman, microwave etc. 

The adiabatic electronic potential energy surfaces (a function of both nuclear geometry and electric field) are obtained by solving the following electronic eigenvalue equation... 

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