Perturbation theory nonlinear optical properties

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. 

In this chapter we have introduced the basic elements of the theory of nonlinear optical properties. Emphasis has been laid on the basic physical processes involved and how these processes are reflected in the basic formulas derived from time-dependent perturbation theory. We have also briefly outlined the strategies for developing efficient computational methods for the calculation of linear and nonlinear optical properties. A brief discussion of the contributions to the nonlinear optical properties arising from the nuclear motions, as well as the connection between the... 

There are two major ways to view tlie vibrational contribution to molecular linear and nonlinear optical properties, i.e. to (hyper)polarizabilities. One of these is from the time-dependent sum-over-states (SOS) perturbation theory (PT) perspective. In the usual SOS-PT expressions [15], based on the adiabatic approximation, the intermediate vibronic states K, k> are of two types. Either the electronic wavefunction... 

Care must be taken in using the expressions above for obtaining nonlinear optical properties, because the values obtained may not be the same as those obtained from Eq. [4]. The results will be equivalent only if the Hellmann-Feyn-man theorem is satisfied. For the case of the exact wavefunction or any fully variational approximation, the Hellmann-Feynman theorem equates derivatives of the energy to expectation values of derivatives of the Hamiltonian for a given parameter. If we consider the parameter to be the external electric field, F, then this gives dE/dP = dH/d ) = (p,). For nonvariational methods, such as perturbation theory or coupled cluster methods, additional terms must be considered. 

The most recognizable expressions for obtaining nonlinear optical properties are the expressions derived from time-dependent perturbation theory. This procedure is straightforward and has been described in detail. " The following equations show the expressions for a, P, and 7 ... 

For nonlinear (magneto-) optical properties, calculations of an accuracy close to that of modern gas phase experiments require - similar to what has also been found for other properties like structures [79, 109], reaction enthalpies [79, 110, 111], vibrational frequencies [112, 113], NMR chemical shifts [114], etc. - at least an approximate inclusion of connected triple excitations in the wavefunction. This has been known for years now from calculations of static hyperpolarizabilities with the CCSD(T) approximation [9-13]. CCSD(T) accounts rather efficiently for connected triples through a perturbative correction on top of CCSD. For the reasons pointed out in Section 2.1 CCSD(T) is, as a two-step approach, not suitable for the calculation of frequency-dependent properties. Therefore, the CC3 model has been proposed [56, 58] as an alternative to CCSD(T) especially designed for use in connection with response theory. CC3 is an approximation to CCSDT - alike CCSDT-la and related methods - where the triples equations are truncated such that the scaling of the computational efforts with system size is reduced to as for CCSD(T),... 

In this chapter we review some of the developments that have been made over the past fifteen years with regard to the calculation of vibrational contributions to linear and nonlinear (NLO) optical properties. Despite a number of advances it is important to recognize that more are needed since there is still no fully satisfactory general treatment for either resonant or non-resonant NLO processes in polyatomic molecules. Two major intertwining approaches to practical computations that include electrical and mechanical anharmonicity have emerged. The older approach is from the viewpoint of ordinary sum-over-states perturbation theory and it is presented in Section 1. The other approach, discussed in Section 2, is from what may be called the nuclear relaxation/curvature point of view. Even though there is 101... 

Liquid crystals are generally characterized by the strong correlation between molecules, which respond cooperatively to external perturbations. That strong molecular reorientation (or director reorientation) can be easily induced by a static electric or magnetic field is a well-known phenomenon. The same effect induced by optical fields was, however, only studied recently. " Unusually large nonlinear optical effects based on the optical-field-induced molecular reorientation have been observed in nematic liquid-crystal films under the illumination of one or more cw laser beams. In these cases, both the static and dynamical properties of this field-induced molecular motion are found to obey the Ericksen-Leslie continuum theory, which describe the collective molecular reorientation by the rotation of a director (average molecular orientation). 

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