Coupling description

SEMICLASSICAL CLOSE-COUPLING DESCRIPTION OF ELECTRON TRANSFER IN MULTICHARGED ION-ATOM COLLISIONS... 

Semiclassical close-coupling description of electron transfer in multi-charged ion-atom collisions 121... 

B.L. Christensen-Dalsgaard, Combined hyperspherical and close-coupling description of two-electron wave functions Application to e-H elastic-scattering phase shifts, Phys. Rev. A 29 (1984) 2242. 

The spin-coupled description of the rt-electron systems in the heteroaromatic molecules furan, pyrrole, thiophen and thiazole is also based on localized but non-orthogonal orbitals. The spin-coupled orbitals for pyrrole are shown in Fig. 5. There is one orbital localized on each carbon atom and one on the heteroatom ([Pg.50]

S. C. Wright, D. L. Cooper, J. Gerratt, M. Raimondi, J. Phys. Chem. 96, 7943 (1992). Spin-Coupled Description of Cyclobutadiene and 2,4-Dimethylenecyclo-butane-l,3-diyl Antipairs. 

Analysis of the total spin function reveals that the spins associated with the pairs (v /2,V /4), (v3,V6) and (v / V /6) remain essentially singlet coupled throughout the course of the reaction, with no evidence for any aromatic structure along the IRC. As such, the spin-coupled description corresponds to a mechanism that involves the simultaneous relocation of three orbital pairs, as might be represented by the following simplistic scheme ... 

During the Diels-Alder reaction [1] and in the electrocyclization of cis-1,3,5-hexatriene [2], bonds break and form in a homolytic fashion, with orbitals remaining associated with the same centres throughout the reaction. For such systems, there is a major recoupling of the electron spins. This last takes place most rapidly at or near the transition state. The resonance pattern, taken together with other characteristics, is reminiscent of the spin-coupled description... 

D.L. Cooper, J. Gerratt and M. Raimondi,The spin-coupled description of aromatic, antiaromatic and nonaromatic systems, in Pauling s legacy Modem modelling of the chemical bond, Vol. 6, ed. Z. B. Maksic and W. J. Orville-Thomas (Elsevier, Amsterdam, 1999). 

In the previous, fixed-input determination of the IT bond indices this discontinuity in the transition from the decoupled to the coupled descriptions of the molecular fragments prevents an interpretation of the former as the limiting case of the latter, when all external communications of the subsystem in question become infinitely small. In other words, the fixed-and flexible-input approaches generate the mutually exclusive sets of bond indices, which cannot describe this transition in a continuous ("causal") fashion. As we have demonstrated in the decoupled approach of the preceding section, only the overall input normalization equal to the number of the decoupled orbital subsystems gives rise to the full agreement with the accepted chemical intuition. 

The spin-coupled description of aromatic, antiaromatic and nonaromatic systems... 

In the spin-coupled description of a molecule such as SF6, the sulfur atom contributes six equivalent, nonorthogonal sp -like hybrids which delocalize onto the fluorine atoms. Each of these two-centre orbitals overlaps with a distorted F(2p) function and the perfect-pairing spin function dominates. Of course, using only 3s, 3px, 3p and 3pz atomic orbitals, we can at most form four linearly independent hybrid orbitals localized on sulfur, with a maximum occupancy of 8 electrons, as in the octet rule. However, the six sulfur+fluorine hybrids which emerge in the spin-coupled description are not linearly dependent, precisely because each of them contains a significant amount of F(2p) character. It is thus clear that the polar nature of the bonding is crucial. 

The mode of bonding which emerges from spin-coupled descriptions on various of 1,3-dipoles and related molecules [22-24] turns out to be closely analogous to the one that we have since established for second-row atoms. Calculations have... 

Spin-coupled descriptions analogous to that for CH2N2 have been found to apply to all of the 1,3-dipoles that we have studied, as well as to related systems such as NNO. It is indeed tempting to represent the latter with the structural formula N=N=0, but it must be clearly understood that the singly occupied orbitals involved in a given bond are not strictly localised on individual atoms. 

The molecules PF5 jCH,), (ra=l-3) all adopt trigonal bipyramidal structures, with a preference for the methyl substituents to occupy equatorial positions. We have found [29] that the spin-coupled description of the P—F bonds in these systems resemble closely that for the parent molecule, PF5. The two spin-coupled orbitals that describe a typical P—CH3 bond are shown in Figure 5. The closer match of electronegativities results in a phosphorus-based spx-like hybrid that exhibits less delocalization onto the methyl group, and in some delocalization of the methyl-based sp -like hybrid back onto phosphorus. These bonds are clearly much less polar than the P—F bonds, as we would have anticipated. 

Our own geometry optimizations confirmed the preference for equatorial methyl groups, but we could discern no significant difference in the spin-coupled description of axial and equatorial P—CH3 bonds. This seems to suggest, at least for these systems, that the geometric preference is more closely linked to steric factors than to details of the bonding. 

Figure 4.6 Cyclic voltammogram of the Fe(CN)64 (1m KN03) couple. Descriptions of...

---