Electrostatics of ionic and moleсular ideal crystals
Abstract
Short review and some new results on nonlinear optical and polarization characteristics of ionic and molecular crystals are presented. The Bloembergen-Armstrong formula for the first nonlinear susceptibility (NS) of a molecular crystal in terms of constituting molecules hyperpolarizabilities (HP) is generalized to an arbitrary order of nonlinearity and expressed in the same terms as the original one. The HP dispersion is accounted. The graphic technique is employed. NS is expressed through HP of all orders not exceeding that of NS. The diagrams are built of root trees graphs. Each tree corresponds to a term of NS expansion which is a product of HP with frequency-arguments and ranks determined by the peculiarities of the corresponding tree. The integer coefficient at the product is also defined by the tree structure.
The methods of the Lorentz tensor and Madelung potential are described in detail for molecular and ion crystals of various types. This approach is based on expansions over McDonald function of increasing arguments. The examples of calculations of both quantities in various ionic and molecular crystals and their layers are given. The obtained values of electric field gradient, refraction index, electric permittivity in bulk, surface and lone layers, and found linear interrilations between ionic local potentials and their formal charges etc. are used for comparison with the experiment and description of other specific properties of crystals.
The Lorentz formula of the phenomenological reaction field theory is derived from the microscopic time-dependent Hartree-Fock HP equations for conjugated hydrocarbons. The Madelung polarization potential is included in an approximate form of oscillator potential with the Lorentz tensor as the force constants matrix. The Hartree-Fock equations for the optical polarizability (PL) with this Madelung correction are solved without further approximations. The solution can be put in the form of the Lorentz interrelation between the PL of molecule in crystal and the free molecule PL.
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