Quantum calculations, nonlinear optics

Jensen, L. and Duijnen P. Th. van, The Discrete Solvent Reaction Field model A Quantum me-chanics/Molecular mechanics model for calculating nonlinear optical properties of molecules in the condensed phase., in Atoms, molecules and clusters in electric fields. Theoretical approaches to the calculation of electric polarizability, G. Maroulis, Editor. 2006, Imperial College Press London, p. 1-43. 

Both the classical and quantum approaches ultimately lead to a model in which the polarizability is related to the ease with which the electrons can be displaced within a potential well. The quantum mechanical picture presents a more quantitative description of the potential well surface, but because of the number of electrons involved in nonlinear optical materials, theoreticians often use semi-empirical calculations with approximations so that quantitative agreement with experiment is not easily achieved. 

The calculation of the electric properties of individual molecules as found in an infinitely dilute gas has for long been of great interest to quantum chemists. This curiosity has been spurred in recent decades by the increasing importance of the communications industry in the world and the parallel need for materials having specific properties for electronic, optical, and other devices. In particular, the nonlinear-optical quantities, defined at the microscopic level as hyperpolarizabilities and at the macroscopic level as nonlinear susceptibilities, have played a... 

With few exceptions, a useful nonlinear optical material will be in the solid phase for example, a single crystal or a poled polymer embedded in a film. Ironically, the quantum chemical calculations of nonlinear optical properties have for the most part been concerned with a single microscopic species. Much has been learned in this way about appropriate molecular construction, but the ultimate goal must be to investigate the nonlinear optical (NLO) properties in the solid phase. 

In the past two decades, a significant effort has been made towards development of reliable computational techniques for calculations of nonlinear optical properties of molecules. This has been reflected in many methods for calculations of first-(jS) and second-order (y) hyperpolarizabilities implemented in widely available quantum-chemical packages. However, the purely resonant properties, like two-and three-photon absorptivities have been coded in only a few of them. Also the inclusion of the influence of environment on NLO properties made a significant step forward in comparisons of theoretical and experimental data for large organic systems. 

The phase distribution function (143) allows for calculations of the phase variances for the individual modes as well as the phase correlations between the two modes by performing simple integrations over the phase variables Qa and 0/,. Detailed discussion of the phase properties of the fields can be found in Ref. 16, and we will not repeat it here. The material presented in this section has been chosen as to illustrate how quantum noise, which is an indispensable ingredient of quantum description of optical fields, can be incorporated into the theory of nonlinear optical phenomena, in particular the phenomenon of second-harmonic generation. 

As to the content of Volume 25, the Editors thank the authors for their contributions, which give an interesting picture of part of the current state of the art of the quantum theory of matter From nonlinear-optical calculations, over a study of ion motion in molecular channels, a treatment of molecular integrals over Gaussian basis functions, and an investigation of soliton dynamics in franr-polyacetylene, to applications of quantum molecular similarity measures. 

The coefficients W determine the probabilities of third-order nonlinear optical processes in an unbounded crystal. An analogous expression can be derived for the coefficients determining the probabilities of fourth-order nonlinear optical processes. As already mentioned the derivation for multilevel molecules is rather complicated and has not yet been obtained. However, the simplicity of the final result, that is the simplicity of the nonlinear Hamiltonian, determines the simplicity of the calculations of nonlinear processes. Note also that a similar polariton approach can be applied for consideration of nonlinear processes in low-dimensional nanostructures (chains, quantum wells). For such structures just resonances of the pumping radiation with polaritons of low-dimensional structure and not with excitons will determine the resonances in the absorption of light as well as resonances in nonlinear processes. 

B. Kirtman, Int. J. Quantum Chem., 43, 147 (1992). Nonlinear Optical Properties of Conjugated Polyenes from Ab Initio Finite Oligomer Calculations. 

The quantum chemical calculations of optical and nonlinear optic molecular parameters are an important step in designing new materials. However, adequate description of molecular optical parameters presents a challenge for contemporary quantum chemistry. The main problem in such calculations is the necessity of accounting for a significant part of the electron correlation effects. In the last decade the density functional theory (DFT) has been used for (hyperjpolarizability calculations (see for instance [45]). It allows the consideration of systems with extended sizes. However, the DFT calculations are known to produce significant errors in the evaluation of the optical properties of a -conjugated systems [8, 26, 83]. 

Kirtman, B. 1992. Nonlinear optical properties of conjugated polymers from ab initio finite oligomer calculations. International Journal of Quantum Chemistry 43 (1) 147. 

P -Values can be measured by several techniques, including electric field induced second harmonic generation and solvatochromic measurements of absorption and fluorescence Moreover, quantum mechanical calculations can be used to estimate these nonlinearities For a more detailed description of the physical backgrounds of nonlinear optics we like to refer to excellent reviews and books< ° >. 

The effect of quantum confinement in semiconductors is supported by rigorous theoretical calculations by Brus [27]. The linear and resonant nonlinear optical properties will... 

Organic compounds with delocalized 7r-electron systems are leading candidates for nonlinear optical (NLO) materials, and interest in these materials has grown tremendously in the past decade [108-118]. Reliable structure-property relationships—where property here refers to first-order (linear) polarizability a, second-order polarizability and third-order polarizability y—are required for the rational design of optimized materials for photonic devices such as electro-optic modulators and all-optical switches. Here also, quantum-chemical calculations can contribute a great deal to the establishment of such relationships. In this section, we illustrate their usefulness in the description of the NLO response of donor-acceptor substituted polymethines, which are representative of an important class of organic NLO chromophores. We also show how much the nonlinear optical response depends on the interconnection between the geometric and electronic structures, as was the case of the properties discussed in the previous sections [ 119]. 

Bulk and molecular nonlinear optical properties have been measured by laser optical techniques such as second and third harmonic generation (SHG, THG), electric field-induced second harmonic generation (EFISH), and degenerate four-wave mixing (DFWM). Molecular NLO responses can also be calculated by quantum-mechanical (ab initio and semiempirical) methods, and suitable computing programs are being developed. 

Of particular significance with regard to relating the nonlinear susceptibilities to the microscopic nature of materials is the application of the Phillips-Van Vechten (PV) quantum dielectric theory of solids (Chapter 1, this volume) by Levine " to the calculation of the Miller delta. He has successfully computed the Miller delta and nonlinear optical susceptibility d for a large variety of nonlinear optical materials, including those in whieh d electrons play a role in the bonding. 

The linear and nonlinear optical properties of C60-triphenylamine (TPhA) hybrids are reported. The synthesized materials were prepared following the 1,3-dipolar cycloaddition of azomethine ylides onto the skeleton of Cgo forming the TPhA-based monoadduct, equatorial bis-adduct and dumbell Ceo- It was proved that in all considered cases, Ceo serves as an acceptor while triphenylamine unit acts as a donor. It was found that the total second-order hyperpolarizability of C60-TphA-C60 system is several times larger than that of TPhA-C60. The results of experimental measurements are supported by quantum-chemical calculations. 

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