There has been dramatic progress in recent years both in the calculation and interpretation of various x-ray spectroscopies. However, current theoretical calculations often use a number of simplified models to account for many-body effects, in lieu of first principles calculations. In an effort to overcome these limitations we describe in this article a number of recent advances in theory and in theoretical codes which offer the prospect of parameter free calculations that include the dominant many-body effects. These advances are based on ab initio calculations of the dielectric and vibrational response of a system. Calculations of the dielectric function over a broad spectrum yield system dependent self-energies and mean-free paths, as well as intrinsic losses due to multielectron excitations. Calculations of the dynamical matrix yield vibrational damping in terms of multiple-scattering Debye-Waller factors. Our ab initio methods for determining these many-body effects have led to new, improved, and broadly applicable x-ray and electron spectroscopy codes.

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.