Four-state system electrons

Ammonia is a two-state system [16], in which the two base states lie at a minimum energy. They are connected by the inversion reaction with a small baiiier. The process proceeds upon the spin re-pairing of four electrons (Fig. 15) and has a very low barrier. The system is analogous to the tetrahedral carbon one... 

A dye molecule has one or more absorption bands in the visible region of the electromagnetic spectrum (approximately 350-700 nm). After absorbing photons, the electronically excited molecules transfer to a more stable (triplet) state, which eventually emits photons (fluoresces) at a longer wavelength (composing three-level system.) The delay allows an inverted population to build up. Sometimes there are more than three levels. For example, the europium complex (Figure 18.15) has a four-level system. 

The novel four-center two-electron delocalized o-bishomoaromatic species 593, 594,599,601a, and 603 are representatives of a new class of 2jt-aromatic pericyclic systems. These may be considered as the transition state of the Woodward-Hoffmann allowed cycloaddition of ethylene to ethylene dication or dimerization of two ethylene radical cations985 (Figure 3.25, 604). Delocalization takes place among the orbitals in the plane of the conjugated system, which is in sharp contrast to cyclobutadiene dication 605 having a conventional p-type delocalized electron structure (Figure 3.25). 

Fig. 8.3. Singlet states of the four-electron, four-site system for the strongly-coupled NUHH (A(0) defines the gap in ISB)...

So far we carried out only a very preliminary study of the excited states [62] for four typical 7r-electron systems CBT, benzene, hexatriene and naphthalene. In all cases we found that the PPP-VB method can successfully describe the low lying excited states using only a small subset of VB structures. For states of a predominantly covalent character, the same OEAO basis as for the ground state can be used. However, for higher lying states with significant ionic character, a re-optimized OEAO basis is preferable. 

The most basic PCET system can be represented by a four-state VB model with electronic VB states defined as... 

A corresponding example in a simple molecular system would be the multielectron excitation of Li2 la la 2a S+, where three or four of the electrons in the subshells could be excited to relatively low-lying states labeled... 

Figure 17.2 The four-state PCET reaction in a solvent coordinate system. The four states are abbreviated with labels according to the initial and final states of the electron (i and f, respectively), and the initial and final states of the proton (a and b, respectively). The coordinates Zj and Zp refer to the collective solvent coordinates that are coupled to ETand PT, respectively. A concerted PCET reaction can...

Obviously, the electronic energies E (R) for n 0 corresponds in a similar manner to potential surfaces for electronically excited states. Each PES usually exhibits considerable structure for a polyatomic system and will provide useful pictures with reactant and product valleys, local minima corresponding to stable species, and transition states serving as gateways for the system to travel from one valley to another. However, for the number of nuclear degrees of freedom beyond six, i.e. for more than four-atom systems it becomes extremely cumbersome to produce the PES s and quite complicated to visuahze the topology. Furthermore, when more than one PES is needed, which is not unusual, there is a need for nonadiabatic coupling terms, which also may need interpolation in order to provide useful information. 

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