Orbital deformation

Keywords Orbital mixing. Orbital amplitude. Orbital phase. Orbital polarization. Orbital deformation, Regioselectivity, Stereoselectivity, n Facial selectivity... 

Inagaki, Fujimoto and Fukui demonstrated that ir-facial selectivity in the Diels-Alder reaction of 5-acetoxy- and 5-chloro-l,3-cyclopentadienes, 1 and 2, can be explained in terms of deformation of a frontier molecular orbital FMO [2], The orbital mixing rule was proposed to predict the nonequivalent orbital deformation due to asymmetric perturbation of the substituent orbital (Chapter Orbital Mixing Rules by Inagaki in this volume). 

For the unperturbed orbit, dy//dt = 0 and d0/dt = ojo, which implies the relation 0= o)o t+ y/) for a weak perturbation, where 0 is the phase of W. It follows, therefore, that whenever the orbital deformation due to the diffusion coupling is negligible, the Ginzburg-Landau equation is contracted to... 

Recently, a first-principles calculation of the entire multiplet structure of ruby has been carried out by Duan et al and the pressure dependence of the multiplet structure of ruby has been well reproduced. They predicted an anomalous local relaxation which could explain the observed frequency shifts. However, their calculation was based on the analytic multiplet approach using the atomic Racah parameters and the matrix elements were calculated in the octahedral approximation. Although the effect of the covalency was taken into account by multiplying the orbital deformation parameters on the electron-electron repulsion integrals, these parameters were adjusted to the optical spectra of ruby under zero pressure for the quantitative analysis of the pressure dependence of the multiplet structure. Moreover, it would be difficult for their approach to predict the intensity of the optical spectra, since the optical spectra of ruby are dominated by the electric-dipole transitions arising... 

Magnusson, E. (1986). Atomic orbital deformation in bond formation energy effects. Chem. Phys. Lett. 131,224-229. 

Rosen [1931] presented the next significant modification to the wavefunction. Wang s basic treatment was further complicated by the inclusion of a polarization factor orbitals deformed along the molecular axis replaced the original spherically symmetric ones. These orbitals have the form... 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

Since the first bracket on the right-hand side is a constant and the second is an integer, it is evident that, for any particular /, some leeway must exist in the value of the ratio rj/G for the equality to be satisfied. Here too, the presence of screw helicity must affect either / , or G, or both. In view of the fairly small variations of G allowed if the hybridization of the C atoms is to remain sp, and since the deformation of the C orbitals decreases as the radius of the cylindrical sheets increases, the distance between successive cylinders must decrease and probably tend towards a value characteristic of turbostratic graphite. 

The natural orbitals %2v and %3p are, in contrast to the hydrogenlike functions, localized within approximately the same region around the nucleus as the Is orbital. This means that the polarization caused by the long-range interaction is associated mainly with an angular deformation of the electronic cloud on each atom. If %2p and %3p are expanded in the standard hydrogen-like functions, an appreciable contribution will again come from the continuum. 

Now many physical properties depend mainly on the behaviour of the electron in the outer part of its orbit. As an example we may mention the mole refraction or polarizability of an atom, which arises from deformation of the orbit in an external field. This deformation is greatest where the ratio of external field strength to atomic field strength is greatest that is, in the outer part of the orbit. Let us consider such a property which for hydrogen-like atoms is found to vary with nrZ t. Then a screening constant for this property would be such that... 

The wave functions for the two inner-core spherons can, of course, be described as the symmetric and antisymmetric combinations of l.t and Ip-functions. The Nilsson (19) treatment of neutron and proton orbitals in deformed nuclei is completely compatible with the foregoing discussion, which provides a structural interpretation of it. 

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