Static and dynamic hyperpolarizability tensors of aluminum metal clusters, Al4M4 ( M=Li , Na, and K)

Static and dynamic hyperpolarizability calculations have been performed to explore the nonlinear optical properties of aluminum metal clusters ${\mathrm{Al}}_{4}{M}_{4}$ ($M=\mathrm{Li}$, Na, and K). An analytical approach combined with a finite difference technique has been used to evaluate the response properties within the framework of time-dependent density functional theory. Components of the first and second order hyperpolarizability tensors are estimated in the vicinity of excitation frequencies with substantial oscillator strength. At specific frequencies, large values of first and second order hyperpolarizability tensors reveal the importance of these materials as cluster with very large optical nonlinearity. The analysis of gross populations of molecular orbitals with the most significant symmetrized fragment orbitals indicate that except for ${\mathrm{Al}}_{4}{\mathrm{K}}_{4}$ [two-dimensional (2D) and (3D)] and ${\mathrm{Al}}_{4}{\mathrm{Li}}_{4}$ (3D) there exists excitations other than charge transfer interaction which can also lead to high nonlinear optical coefficients.