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We revisit the derivation of the expressions for the calculation of second-harmonic generation spectra and show the equivalence of different approaches proposed in the literature. A method is suggested to include excitonic effects in the calculation. Numerical tests are performed for the linear and nonlinear optical response of bulk GaAs. Excitonic effects are found to give rise to a redistribution of oscillator strength, thus improving the agreement with experiment. A. Time-dependent perturbation theoryWithin the interaction picture, the time evolution operator is given bywith the external perturbation Hamiltonian in minimum coupling convention PHYSICAL REVIEW B 71, 195209 ͑2005͒

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The optical spectrum of water is not well understood. For example, the main absorption peak shifts upwards by 1.3 eV upon condensation, which is contrary to the behavior expected from aggregation-induced broadening of molecular levels. We investigate theoretically the effects of electron-electron and electron-hole correlations, finding that condensation leads to delocalization of the exciton onto nearby hydrogen-bonded molecules. This reduces its binding energy and has a dramatic impact on the line shape. The calculated spectrum is in excellent agreement with experiment.

We calculate the surface optical properties of the passivated Si(110) surface using a real-space multigrid technique and ab initio pseudopotentials. Rather than from the usual eigenvalue representation, the macroscopic polarizability is obtained from the solution of an initial-value problem, which allows inclusion of excitonic and local-field effects in addition to the electronic self-energy in the surface calculations. It is shown that the electron-hole attraction is largely responsible for the peculiar line shape of the surface reflectance anisotropy.