Electronic molecular nonlinear optical determination

Recently there has been a great deal of interest in nonlinear phenomena, both from a fundamental point of view, and for the development of new nonlinear optical and optoelectronic devices. Even in the optical case, the nonlinearity is usually engendered by a solid or molecular medium whose properties are typically determined by nonlinear response of an interacting many-electron system. To be able to predict these response properties we need an efficient description of exchange and correlation phenomena in many-electron systems which are not necessarily near to equilibrium. The objective of this chapter is to develop the basic formalism of time-dependent nonlinear response within density functional theory, i.e., the calculation of the higher-order terms of the functional Taylor expansion Eq. (143). In the following this will be done explicitly for the second- and third-order terms... 

When the external electric field is time-dependent, there is no well-defined energy of the molecular system in accordance with Eq. (100), and the wave function response can thus not be retrieved from a variational condition on the energy as in the analytic derivative approach described above. Instead the response parameters have to be determined from the time-dependent Schrodinger equation, a procedure which was illustrated in Section 3 for the exact state case. In approximate state theories, however, our wave function space only partially spans the 7V-electron Hilbert space, and the response functions that correspond to an approximate state wave function will clearly be separate from those of the exact state wave function. This fact is disregarded in the sum-over-states approach, and, apart from the computational aspect of slowly converging SOS expressions, it is of little concern when highly accurate wave function models are used. But for less flexible wave function models, the correct response functions should be used in the calculation of nonlinear optical properties. 

On the basis of the molecular orbital energies, all the non-carbon clusters considered seem to be better electron donors and better electron acceptors than Ceo- They also possess lower electronically excited states and therefore should display enhanced nonlinear optical properties. Interestingly, the energy gap, which plays a direct role in the determination of the metallic behavior of the system, changes negligibly when one considers the HF level data for the semiconducting Si and Ge or the metal Sn type clusters. 

In the second part of this work we review our theoretical and experimental works to obtain enhanced two-photon cross-sections by using the super-linear response of centrosymmetric monomers that are coherently coupled. In this alternative approach, the nonlinear material consists of an assembly of nonsubstituted /r-electron systems that are coupled by dipole-dipole interactions. The monomer two-photon term is a pure transition dipole term ( UQ,jU,2). Typical materials can be molecular aggregates, nanocrystals, oligomers, and dendrimers. The dipole-dipole interactions determine the size dependency of optical properties, and in particular of two-photon cross-sections. 

The intramolecular charge transfer through zr-electron conjugation gives large optical nonlinearities in the molecular level, whereas the centro-symmetry of the crystal structure determines the macroscopic second order nonlinearity... 

As we can see from this simple but general consideration of a multilevel molecule, nonlinear electronic polarizations occur naturally in all materials illuminated by an optical field. The differences among the nonlinear responses of different materials are due to differences in their electronic properties (wave functions, dipole moments, energy levels, etc.) which are determined by their basic Hamiltonian Hq. For Uquid crystals in their ordered phases, an extra factor we need to take into account are molecular correlations. 

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