Charge displacement, second-order

A more widely used approach for organic molecules is based on second-order perturbation theory. Here the dipolar contribution to the field induced charge displacement is calculated by inclusion of the optical field as a perturbation to the Hamiltonian. Since the time dependence of the field is included here, dispersion effects can be accounted for. In this approach the effect of the external field is to mix excited state character into the ground state leading to charge displacement and polarization. The accuracy of this method depends on the parameterization of the Hamiltonian in the semi-empirical case, the extent to which contributions from various excited states are incorporated into the calculation, and the accuracy with which those excited states are described. This in turn depends on the nature of the basis set and the extent to which configuration interaction is employed. This method is generally referred to as the sum over states (SOS) method. 

Let us consider another, so-called, second-order effect of an external electric field E on a given molecule M2 This field influences the molecular charges, electTOTis, and nuclei, causing their displacements, and as a result, there appears the induced dipole moment d . ... 

Gradient coefficients > 0 and q > 0 the expansion coefficient an>0 for the second order phase transitions. Coefficient ai(T) = ar T — Tc), E is the transition temperature of a bulk material. Note, that the coefficient flu for displacement type ferroelectrics does not depend on T, while it is temperature dependent for order-disorder type ferroelectrics (see corresponding reference in [117]). Eq is the homogeneous external field, the term Ed (P3) represents depolarization field, that increases due to the polarization inhomogeneity in confined system. Linear operator Ed P3) essentially depends on the system shape and boundary conditions. Below we consider the case when depolarization field is completely screened by the ambient free charges outside the particle, while it is nonzero inside the particle due to inhomogeneous polarization distribution (i.e., nonzero divP 0) (see Fig. 4.35b). 

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