Electric quadrupole and hexadecapole moment, dipole polarizability and hyperpolarizability of the copper tetramer (Cu4) from pseudopotential calculations and a comparison with all-electron ab initio results

We have obtained the electric quadrupole and hexadecapole moment, dipole polarizability and hyperpolarizability of copper tetramer from finite-field ab initio and density functional theory (DFT) calculations performed with a systematic sequence of basis sets built upon the Stevens/Basch/Krauss effective core potential triple-split basis set CEP-121G. Our present ab initio values show significant discrepancies with previous all-electron results [G. Maroulis, A. Haskopoulos, J. Comput. Theor. Nanosci. 6 (2009) 418]. Representative calculations yield self-consistent field (SCF) values (second-order Møller–Plesset results in parentheses) for (hyper)polarizability invariants: mean polarizability α ¯ = 187.41 ( 147.04 ) and anisotropy Δα = 158.95 (128.09) e 2 a 0 2 E h - 1 , mean hyperpolarizability 10 - 3 × γ ¯ = 551.7 ( 123.5 ) e 4 a 0 4 E h - 3 . Analogous all-electron results are α ¯ = 196.23 ( 161.24 ) and anisotropy Δα = 165.71 (138.68) e 2 a 0 2 E h - 1 , mean hyperpolarizability 10 - 3 × γ ¯ = 631 ( 271 ) e 4 a 0 4 E h - 3 .