Polarizability, core

Attempts to account for this bending have emphasized two physical effects, (1) d-orbital participation,18 and (2) core polarization,19 but no clear theoretical consensus has been achieved. The calculated bending in BaH2, for example, is found to disappear with removal of either d-orbitals or a polarizable-core, suggesting that both aspects are operative. The adequacy of the core-polarization rationale was questioned, and an alternative rationalization based on differences in atomic softness between metal and ligand was proposed by Szentpaly and Schwerdtfeger.20... 

The sum in W runs over all polarizable cores (k=Na, Ar) a% is the dipole polarizability of core X, namely 0.9947 ao and 11.08 ao for sodium and argon respectively fx is the electrostatic field at center X, produced by the ion [Na ] and the single valence electron at relative distance r of core k. The electronic field is truncated by a stepwise cut-off function Fx, in order to avoid integral divergencies ... 

The basic idea behind the pseudopotential method is to treat the valence electron as moving in a potential from a fixed ion core. Chemically this is very reasonable and it is only if one is interested in very accurate investigation of spectroscopic data of elements with highly polarizable cores (typically alkali metals) that this approach fails7. 

Bhatia and Drachman have also made important progress in applying the asymptotic expansion methods to the Rydberg states of lithium [27-29]. The calculations in this case are more difficult because the polarizable core now consists of the nucleus and two Is electrons, and so its multipole moments cannot be calculated analytically. 

A reasonable assumption for any chemist is that molecules are made up of fixed cores (the nucleus and the inner electrons) and of chemically active valence electrons moving in the field of these fixed cores (frozen-core approximation). Obviously for accurate investigations in spectroscopy this assumption would fail, for example for alkali or alkaline-rich elements on the left of the periodic table, which possess highly polarizable cores. In the following only fixed atomic cores will be considered. 

On the other hand, core polarization is easily treated by a fairly simple model due to Mayer and Mayer which reduces the I dependence of the energies of high-1 states to a few parameters. The essence of the model is that the electric field of the electron at the ionic core distorts the polarizable core leading to an energy shift. Explicitly the energy level is given by... 

In this model the molecular tilt is determined by induction interaction between the off-center dipole and the polarizable core of the neighboring molecules. After averaging over the rotation around the molecular long axes the corresponding interaction potential reads [79] ... 

Only for systems with easily polarizable cores, such as those containing the alkali and alkaline-earth atoms, are core correlation effects routinely included because of their sizable effect. This necessity was first demonstrated in the classic study on the first and second row hydrides by Meyer and Rosmus, where they showed that the core-valence electron correlation terms could affect the bond length as strongly as the valence shell correlation, but that the core effect decreased... 

Another approach which has proven effective for including inner-shell effects is the core polarization potential (CPP) method introduced by Muller, Flesh, and Meyer. The method can be employed in both all-electron and pseudopotential calculation. It is based on the classical description of the interaction of a polarizable core with the field generated by the valence electrons and other cores ... 

The nonlinear optical response of thermotropic hquid crystals and similar organic materials is due mainly to the delocalization of the rr-electron wave functions of the so-called polarizable core of a liquid crystal. The polarizable core usually consists of more than one benzene ring cormected by a variety of linkages or bonds. 

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