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We present ab initio calculations of frequency-dependent linear and nonlinear optical responses based on real-time time-dependent density functional theory for arbitrary photonic molecules. This approach is based on an extension of an approach previously implemented for a linear response using the electronic structure program SIESTA. Instead of calculating excited quantum states, which can be a bottleneck in frequency-space calculations, the response of large molecular systems to time-varying electric fields is calculated in real time. This method is based on the finite field approach generalized to the dynamic case. To speed the nonlinear calculations, our approach uses Gaussian enveloped quasimonochromatic external fields. We thereby obtain the frequency-dependent second harmonic generation beta(-2omega;omega,omega), the dc nonlinear rectification beta(0;-omega,omega), and the electro-optic effect beta(-omega;omega,0). The method is applied to nanoscale photonic nonlinear optical molecules, including p-nitroaniline and the FTC chromophore, i.e., 2-[3-Cyano-4-(2-{5-[2-(4-diethylamino-phenyl)-vinyl]-thiophen-2-yl}-vinyl)-5,5-dimethyl-5H-furan-2-ylidene]-malononitrile, and yields results in good agreement with experiment.

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Calculations of the hyperpolarizability are typically much more difficult to converge with basis set size than the linear polarizability. In order to understand these convergence issues and hence obtain accurate ab initio values, we compare calculations of the static hyperpolarizability of the gas-phase chloroform molecule (CHCl 3 ) using three different kinds of basis sets: Gaussian-type orbitals, numerical basis sets, and real-space grids. Although all of these methods can yield similar results, surprisingly large, diffuse basis sets are needed to achieve convergence to comparable values.These results are interpreted in terms of local polarizability and hyperpolarizability densities. We find that the hyperpolarizability is very sensitive to the molecular structure, and we also assess the significance of vibrational contributions and frequency dispersion.

For the past three decades, a full understanding of the electro-optic (EO) effect in amorphous organic media has remained elusive. Calculating a bulk material property from fundamental molecular properties, intermolecular electrostatic forces, and field-induced net acentric dipolar order has proven to be very challenging. Moreover, there has been a gap between ab initio quantum-mechanical (QM) predictions of molecular properties and their experimental verification at the level of bulk materials and devices. This report unifies QM-based estimates of molecular properties with the statistical mechanical interpretation of the order in solid phases of electric-field-poled, amorphous, organic dipolar chromophore-containing materials. By combining interdependent statistical and quantum mechanical methods, bulk material EO properties are predicted. Dipolar order in bulk, amorphous phases of EO materials can be understood in terms of simple coarse-grained force field models when the dielectric properties of the media are taken into account. Parameters used in the statistical mechanical modeling are not adjusted from the QM-based values, yet the agreement with the experimentally determined electro-optic coefficient is excellent.

Many-body effects such as local fields and the core-hole interaction can be significant in x-ray absorption spectra even several hundred eV above an absorption edge. The treatment of these effects requires theories beyond the independent-particle approximation, e.g., the Bethe-Saltpeter equation ͑BSE͒ or the time-dependent density-functional theory ͑TDDFT͒. However the BSE is usually limited to low energies, while the TDDFT often ignores the nonlocality of the core-hole interaction. Here we present a combined approach for the calculations of the x-ray spectra that include both of these effects, together with inelastic losses and self-energy shifts over a wide energy range. The approach is illustrated for a few materials, including metals and oxides.

Real-time, time-dependent density functional theory (RT-TDDFT) is used for the evaluation of the frequency dependence of the polarizability and hyperpolarizability of molecules intended for application in electrooptic devices. These first-principles computational methods are powerful but costly. Significantly easier calculations based on a simplified version of second-order time-dependent perturbation theory, the "two-state model" (TSM), are here used to provide another estimate of the frequency dependence. Furthermore, the TSM calculations can be done in the presence of a dielectric reaction field (the polarizable continuum model method) to provide estimates of the solvent dependent properties in addition to the frequency-dependent properties. Here we use RT-TDDFT to assess the accuracy of the frequency dependence of the TS, and a ground-state finite field calculation to assess the effect of additional states on the static hyperpolarizability. Both frequency and dielectric responses are important for evaluation of the suitability of molecules in nonlinear optical applications. † Part of the "Larry Dalton Festschrift".

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