Polarisation energy

The first term consists of both the kinetic energy of the electrons and the complete Coulomb energy, the second is the vibrational kinetic energy, the third is the rotational kinetic energy, the fourth is the mass polarisation energy involving the total linear momentum of the electrons P = Pi > the fifth and sixth are the parts of the electronic... 

In order to obtain energetic corrections, the contribution of the bonds around nucleus A to the polarisation energy has to be calculated. The total energy can be approximated by... 

Another remark is connected with the method of the estimation of polarisation energy. Our curves were drawn in the assumption that I-A 3 ev, but last experimental data shows that I-A is more close to 4 ev. In this case the curve would not have a minimum and would be zero. But it turns... 

The term Vpoi in Eq. (1) is a polarisation contribution which includes the many-body non-additive effects. It has been demonstrated (dementi and Corongiu, 1983) that the many-body corrections are necessary for an accurate quantitative prediction of the system properties. These effects are included by ascribing to each molecule a dipole moment and a bond polarizability, according to the classical model (Bottcher, 1973). Within this scheme the polarisation energy can be expressed as ... 

Peh(t) = Polarisation energy of the lattice due to the electron-hole pair at the distance r,... 

The energies Eg and Eh differ from the energies of the ionised molecules in the gas phase by the polarisation energies Pg and Ph- Due to the high polarisabUity of the molecules, these polarisation energies are not small (see also Chap. 2). The electronic polarisation energy Pj, of the positive polarons is the difference between the ionisation energy Ig of the free molecule and Ic of the crystal ... 

Fig. 8.6 The energy diagram of an organic semiconductor, a The energy levels of the neutral isolated molecules. Sq Is the electronic ground state, S], S2. .. S are the electronic singlet excited states, Iq is the molecular ionisation energy, Aq the electron affinity of the isolated molecule, b The energy bands of the ionised states of the ideal crystal. /, is the energy of holes, VB = valence band = transport level of the holes Eg = is the energy of the conduction electrons, CB = conduction band = transport level of the electrons. P/, and Pg are the mean polarisation energies of the holes...

All these states are localised. The origin of the energy scale lies at the centre of the DOS. ff is the width of the distribution. The distribution itself is based on the stochastic variation of the polarisation energies (cf Sect. 8.3). This energy distribution is also termed diagonal disorder. 

Typical application (as demonstrated in chapter) Characterisation of quenching, spectral shifts, polarisation, energy transfer, excited state reactions... 

For the smallest ion in question (Li) after it has lost part of its hydration water will add on fixation more polarisation energy than the greater Na and K ions. Thus for an ionised group more polarisable than water the order of decreasing affinity will be Li > Na ) K. And as the reversal of charge concentrations can be considered as an inverse measure of cation affinity we must expect that the reversal of charge concentrations increase in the order Li <( Na < K. 

Considering now the same cations in the case that the polarisability of the ionised group is less than that of water, then the polarisation energy of the water molecules (cation hydration) will oppose the Coulomb energy. Now the Li ion, with smallest radius and therefore the most hydrated of the three will be fixed most difficultly on the ionised group. It will have the greatest tendency to rest in the perfect hydrated state free in the medium. 

Let E denote the lattice energy, that is, the energy needed to dissociate 1 Mol. of the lattice into gaseous ions. Then EjN is this energy referred to one ion pair of the lattice it is connected with the energy E needed to produce a Mol. of Schottky lattice defects, and the corresponding polarisation energy, J poi, released around the vacant sites, by In... 

Interactions between induced quadrupoles also contribute to the polarisation energy. 

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