Linear and nonlinear molecular propertie

C.B. Nielsen, O. Christiansen, K.V. Mikkelsen, J. Kongsted, Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties Applications to solvated water and formaldehyde, J. Chem. Phys. 126 (2007) 154112. 

We observe that these contributions to the response equations have the same structure as the response equations for the molecule in vacuum [83]. We note that the implementation of these modifications to the vacuum MCSCF response equations gives us the possibility of investigating linear and nonlinear molecular properties of molecular systems interacting with heterogeneous dielectric media. 

Except through the study of linear and nonlinear optical properties of molecular crystals, methods to determine the nature of / require evaluation of appropriate characteristics of... 

Several organometallic moieties serving as acceptors and donors have been evaluated. Molecular crystals of stilbenes have been shown to be unusually active in second harmonic generation. The linear and nonlinear optical properties of 3-methyl-4-methoxy-4 -nitro-stilbene (MMONS) single crystals will be presented. 

The pz orbitals have not been used so far. They are antisymmetric perpendicular to the (x,y)-plane and therefore orthogonal to the above combined sp and sp2 orbitals. pz orbitals from neighboring atoms combine independently to form molecular orbitals with their wavefunction delocalized over many atoms. The corresponding electrons are the 7T-electrons, which dictate to a large extend the linear and nonlinear optical properties. 

Recently, Pt-TEE molecular scaffolding yielded PTA oligomers with [Pt(PEt3)2] as spacer units [44]. Both the linear and nonlinear optical properties of these compounds revealed an... 

Moreover, if we recall Eq. (3), which we used as a starting point for defining linear and nonlinear optical properties, then it is seen that for time-independent perturbations, we may equally well choose an expansion of the molecular energy for tills purpose... 

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... 

The linear and nonlinear optic properties of organic materials, including a -conjugated molecular polymers, make it possible to develop numerous technological and industrial applications of these systems. The applications in the field... 

Linear and nonlinear optical properties of liquid crystals in their mesophases have been studied in several contexts, in both fundamental and application-oriented pursuits. In the context of nonlinear optical processes, they have recently received considerable renewed interests as a result of the newly discovered extraordinarily large optical nonlinearity due to the laser-induced molecular reorientation, and a renewed effort explicitly at the large thermal index effect in liquid crystals. In the last few years, several groups [2]-[10] have looked at the optical nonlinearity in the mesophases of liquid crystals and the associated nonlinear processes. A brief review of some of these nonlinear optical processes and the fundamental mechanisms in both the liquid crystal and the isotropic phases has recently appeared [1]. In this paper, therefore, we will concentrate only on optical wave mixing processes that are relevant to this Special Issue. 

The existence or nonexistence of mirror symmetry plays an important role in nature. The lack of mirror symmetry, called chirality, can be found in systems of all length scales, from elementary particles to macroscopic systems. Due to the collective behavior of the molecules in liquid crystals, molecular chirality has a particularly remarkable influence on the macroscopic physical properties of these systems. Probably, even the flrst observations of thermotropic liquid crystals by Planer (1861) and Reinitzer (1888) were due to the conspicuous selective reflection of the helical structure that occurs in chiral liquid crystals. Many physical properties of liquid crystals depend on chirality, e.g., certain linear and nonlinear optical properties, the occurrence of ferro-, ferri-, antiferro- and piezo-electric behavior, the electroclinic effect, and even the appearance of new phases. In addition, the majority of optical applications of liquid crystals is due to chiral structures, namely the ther-mochromic effect of cholesteric liquid crystals, the rotation of the plane of polarization in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals. 

An essential-state description has been employed to analyze the linear and nonlinear optical properties of octupolar systems in comparison with their dipolar analogs. This approach, which accounts for couplings of electrons to molecular vibrations as well as for solvent effects has shown that the TPA intensity per branch is amplified by a factor of 2 when going from dipolar to octupolar species, in agreement with TDDFT calculations of TPA intensities. 

The microscopic (hyper)polarizabilities are studied by means of the so-called theory of the response functions which is of importance for aU molecular and cluster entities (Roman et al. 2006). The most commonly used approach in studying the linear and nonlinear optical properties of clusters is the so-caUed semiclassical one. According to this approach a classical treatment is used to describe the response of the cluster to an external field (radiation) while the system itself is treated using the lows and techniques of quantum mechanics. This is done by using a Hamiltonian which combines both of the above treatments ... 

Figure 1 Ward graphs (at left) and ladder graphs (at right) for linear (S2.a), second-order nonlinear (S3.a, b), and third-order nonlinear (S4.a, b1, b2) elastic scattering processes. The broken horizontal lines in the ladder graphs represent virtual, nonstationary states of the molecular system. Reproduced with permission from Wagniere GH (1993) Linear and Nonlinear Optical Properties of Molecules. Basel Verlag Helvetica Chimica Acta.

Understanding the fundamental issues from the atomic or molecular scale to macroscopic morphology in such a complex system is challenging. Most analytical theories [11] are severely limited for such complex systems that exhibit linear and nonlinear response properties on different spatial and temporal scales. Computer simulations remain the primary choice to probe multiscale phenomena from microscopic characteristics of constituents to macroscopic observables in such complex systems. Most real systems [9] are still too complex to be fully addressed by computing and computer simulations alone. Coarse-grained descriptions are almost unavoidable in developing models for such nanocomposite systems. 

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

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