Four-electron system

Figure 1. Jacobi vectors for a three-nuclei, four-electron system. The nuclei are Pi, P2, P3, and the electrons are ei, 02, 63, 64,...

The H4 system is the prototype for many four-elecbon reactions [34]. The basic tetrahedral sfructure of the conical intersection is preserved in all four-electron systems. It arises from the fact that the four electrons are contributed by four different atoms. Obviously, the tefrahedron is in general not a perfect one. This result was found computationally for many systems (see, e.g., [37]). Robb and co-workers [38] showed that the structure shown (a tetraradicaloid conical intersection) was found for many different photochemical transformations. Having the form of a tetrahedron, the conical intersection can exist in two enantiomeric structures. However, this feature is important only when chiral reactions are discussed. 

Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

Preuss, H., Z.Naturforsch. 10a, 165, "Die elektrostatische Metho-de und das kombinierte Naherungsverfahren." Extension of Hurley s method (1954) to four-electron systems. 

Yoshizumi, H., and Itoh, T., J. Chem. Phys. 23, 412, "Applications of the alternant molecular orbital method to six and four electron systems."... 

Two other systems that have been studied as possible aromatic or antiaromatic four-electron systems are the cyclopropenyl anion (59) and the cyclopentadienyl cation (60). In these cases also the evidence supports, antiaromaticity, not aromaticity. With respect to 59, HMO theory predicts that an unconjugated 61 (i.e., a single canonical form) is more stable than a conjugated 59, so that 61 would... 

Experimental evidence for the six electron systems has been described in Sect. 2.1.4. Skancke reproduced the relative stabihty of the cross conjugated systems relative to the linear isomers by calculating the trimethylenemethane and buta-l,4-diyl dianions [27] and their dilithio salts [28]. For the four electron systems butadiene is more stable than trimethylenemethane. Experimental examination of the relative stabihties of two electron systems using the trimethylenemethane and buta-14-diyl dications needs to overcome the intrinsic instabihties of dications dissatisfying the octet rule. 

Bicyclo-[3,l,0]hex-2-ene (BCE), phase-change rule, large four-electron systems, 459... 

In the simple four-electron systems, a route for cis-trans isomerisation of a diene is made available by the photochemical reaction usually being a disrotatory ring closure and the thermal reaction being a conrotatory ring opening ... 

In an early application to butadiene [16], and later to the ground and excited states of benzene [17], Berry analyzed MO-based wavefunctions using valence bond concepts, simply by considering the overlaps with nonorthogonal VB structures. Somewhat closer than this to a CASVB type of approach, are the procedures employed by Linnett and coworkers, in which small Cl wavefunctions were transformed (exactly) to nonorthogonal representations [18-20]. The main limitation in their case was on the size of systems that may be treated (the authors considered no more than four-electron systems), both because this non-linear transformation must exist, and because it must be possible to obtain it with reasonable effort. 

Even for a relatively small system, obtaining the Q, R) conditions is computationally challenging [25]. For example, using the 2-matrix to describe the beryllium atom in a minimal basis would require the (2,10) conditions for a four-electron system. In this case, the Slater hull is a polyhedron with on the order of ten billion facets. Only small R is interesting for computational applications. 

Four H atoms in a rectangular geometry of >2 symmetry. The rectangle is characterized by two distances, RA and RB. We map out a region of the ground state energy for this four-electron system as a function of the two distances. 

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