Calculation of nonlinear properties

Most theoretical discussions for molecules concentrate on calculations of second-order nonlinear optical properties. These results can be used equally well for the design of either molecules or molecular fragments. The latter are intended for inclusion in polymers as either a solid solution or side-chains. These are discussed in detail in section 4.3, together with systems in which a crystalline phase is dispersed in a polymer matrix. In molecularly dispersed systems the incorporation and orientation of an active species in a polymer obviates the need for a non-centrosymmetric crystal structure but does require the imposition of a polar state on the polymer (e.g. with an applied electric field). Thus molecular species that as crystals are not useful as second-order nlo materials (because they adopt a centrosymmetric structure) may be applicable in a polymeric system. Though it has received less attention in the past, considerable effort has recently been devoted to theoretical studies of 

Most calculations have focused on determining the nonlinear coefficients for second-harmonic generation. By anology with the formalism for discussed above, the relevant polarization can be written as 

Since the establishment of necessary basis for accurate computation, simpler approaches with appropriate parameterization have been developed. In particular, parameterization of the PPP-SCF-CI (Pariser, Parr, Pople-self-consistent-field-configuration interaction) method has enabled /8-values (of sufficient accuracy to provide a basis for molecular design) to be obtained with much less powerful computers. Routines are now available for microcomputers that run in reasonable time with adequate accuracy [20]. 

An alternative methodology within the sum-over-states (SOS) approach has been proposed to enable the important states and excitation processes to be evaluated. When a convergent SOS is obtained, a quality factor for the nth-order nonlinearity 

At an elementary level, the relevant factors can be determined by considering the result for the simple model of a linear molecule for which only the ground and first excited states are important. Such a simple two-level model can be used to adequately describe the basis of the second-order nonlinearity [22]. In this case the molecular nonlinearity can be written as 

---