Ab initio embedded cluster study of optical second-harmonic generation below the gap of a NiO„001... surface

An embedded cluster approach was applied to study the electronic excitations on the NiO~001! surface. Using a quantum chemical calculation, a small (NiO5) 82 cluster was embedded in a set of point charges to model the NiO~001! surface. Starting from the unrestricted Hartree-Fock level of theory, we calculate the ground-state properties to provide some insight into electronic structure and excitation. We estimate the excitation energies and oscillator strengths using the single excitation configuration-interaction ~CIS! technique. Our results show that the CIS method is reasonably accurate for estimating the low-lying d-d excitations below the gap. We then demonstrate the electron correlation effects on the d-d transitions at several levels of ab initio correlated theory @CID ~with all double substitutions!, CISD ~with all single and double substitutions!, ~quadratic! QCISD, and ~with all single, double, and triple substitutions! QCISD (T)]. The electron correlation tends to decrease the magnitude of d-electron excitation energies. Using the many-body wave functions and energies resulting from CID and QCISD(T) calculations, we compute the second harmonic generation ~SHG! tensor for the NiO~001! surface. In contrast to bulk NiO, where the SHG response is forbidden within the electric-dipole approximation because of the inversion symmetry, the C4v symmetry of the surface leads to five nonzero tensor elements. From that, the intensity of the nonlinear optical response as a function of photon energy at different polarizations of the incident and outgoing photons is obtained. This quantity can be directly measured in experiment, and we suggest possible conditions in order to detect it.