Density functional methods, nonlinear optics

Kama and A. T. Yeates, Eds., American Chemical Society, Washington, DC, 1996, pp. 164-173. A Combined Hartree-Fock and Local-Density-Functional Method to Calculate Linear and Nonlinear Optical Properties of Molecules. 

Ah initio methods are applicable to the widest variety of property calculations. Many typical organic molecules can now be modeled with ah initio methods, such as Flartree-Fock, density functional theory, and Moller Plesset perturbation theory. Organic molecule calculations are made easier by the fact that most organic molecules have singlet spin ground states. Organics are the systems for which sophisticated properties, such as NMR chemical shifts and nonlinear optical properties, can be calculated most accurately. 

Microscopy methods based on nonlinear optical phenomena that provide chemical information are a recent development. Infrared snm-frequency microscopy has been demonstrated for LB films of arachidic acid, allowing for surface-specific imaging of the lateral distribution of a selected vibrational mode, the asymmetric methyl stretch [60]. The method is sensitive to the snrface distribntion of the functional gronp as well as to lateral variations in the gronp environmental and conformation. Second-harmonic generation (SHG) microscopy has also been demonstrated for both spread monolayers and LB films of dye molecules [61,62]. The method images the molecular density and orientation field with optical resolution, and local qnantitative information can be extracted. 

In the previous Maxwelhan description of X-ray diffraction, the electron number density n(r, t) was considered to be a known function of r,t. In reality, this density is modulated by the laser excitation and is not known a priori. However, it can be determined using methods of statistical mechanics of nonlinear optical processes, similar to those used in time-resolved optical spectroscopy [4]. The laser-generated electric field can be expressed as E(r, t) = Eoo(0 exp(/(qQr ot)), where flo is the optical frequency and q the corresponding wavevector. The calculation can be sketched as follows. 

Monodisperse spherical colloids and most of the applications derived from these materials are still in an early stage of technical development. Many issues still need to be addressed before these materials can reach their potential in industrial applications. For example, the diversity of materials must be greatly expanded to include every major class of functional materials. At the moment, only silica and a few organic polymers (e.g., polystyrene and polymethylmethacrylate) can be prepared as truly monodispersed spherical colloids. These materials, unfortunately, do not exhibit any particularly interesting optical, nonlinear optical or electro-optical functionality. In this regard, it is necessary to develop new methods to either dope currently existing spherical colloids with functional components or to directly deal with the synthesis of other functional materials. Second, formation of complex crystal structures other than closely packed lattices has been met with limited success. As a major limitation to the self-assembly procedures described in this chapter, all of them seem to lack the ability to form 3D lattices with arbitrary structures. Recent demonstrations based on optical trapping method may provide a potential solution to this problem, albeit this approach seems to be too slow to be useful in practice.181-184 Third, the density of defects in the crystalline lattices of spherical colloids must be well-characterized and kept below... 

During the last 10-20 years, a large number of efficient theoretical methods for the calculation of linear and nonlinear optical properties have been developed— this development includes semi-empirical, highly correlated ab initio, and density functional theory methods. Many of these approaches will be reviewed in later chapters of this book, and applications will be given that illustrate the merits and limitations of theoretical studies of linear and nonlinear optical processes. It will become clear that theoretical studies today can provide valuable information in Are search for materials with specific nonlinear optical properties. First, there is the possibility to screen classes of materials based on cost and time effective calculations rather then labor intensive synthesis and characterization work. Second, there is Are possibility to obtain a microscopic understanding for the performance of the material—one can investigate the role of individual transition channels, dipole moments, etc., and perform systematic model Improvements by inclusion of the environment, relativistic effects, etc. 

The most commonly used model for understanding the relationship between the hyperpolarizability P and molecular structure is the two-state model (Oudar and Chemla, 1977). This model provides only a rough description but it allows a qualitative understanding of the nonlinear optical properties of molecules. For push-pull compounds with electron donors and acceptors, the P value depends mainly on the intramolecular polarization, the oscillator strength, and the excited state of the material (Allis and Spencer, 2001). There are three different possibilities for a refinement of the two-state model semi-empirical, ab initio and density functional theory methods (Li et al., 1992 Kanis et al., 1994 Kurtz and Dudis, 1998). 

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