Is the Hyperpolarizability of Cu2 Negative? A Study of Basis Set and Electron Correlation Effects

Abstract

The dipole (hyper)polarizability of the copper dimer has been obtained from conventional ab initio and density functional theory calculations. A very large (23s16p12d6f) basis set consisting of 346 Gaussian-type functions is thought to provide reference results of near-Hartree−Fock quality for all properties. We obtain ᾱ = 102.54 and Δα = 41.89 for the mean and the anisotropy of the dipole polarizability (ααβ/e2a02Eh-1). For the Cartesian components and the mean of the hyperpolarizability (10-3γαβγδ/e4a04Eh-3) we obtain γzzzz = 309, γxxxx = 209, γxxzz = 87, and γ̄ = 244. Electron correlation lowers ᾱ but increases considerably Δα. The effect on the hyperpolarizability is enormous, as the longitudinal component γzzzz is drastically reduced, while γxxxx and γxxzz are nearly halved. At the CCSD(T) level of theory with a [7s6p6d2f] basis set we obtain ᾱ = 93.82, Δα = 67.09 and γzzzz = 18, γxxxx = 101, γxxzz = 35, and γ̄ = 86. The dipole polarizability varies as [ᾱ(R) − ᾱ(Re)]/e2a02Eh-1 = 28.09(R − Re) + 4.69(R − Re)2 − 0.52(R − Re)3 − 0.36(R − Re)4 and [Δα(R) − Δα(Re)]/e2a02Eh-1 = 49.58(R − Re) + 11.92(R − Re)2 − 1.94(R − Re)3 −1.32(R − Re)4 around the experimental bond length Re = 2.2197 Å. B3LYP density functional theory calculations with a [8s7p7d5f] basis set yield ᾱ = 77.62, Δα = 44.73e2a02Eh-1, and γ̄ = (95.9 × 103)e4a04Eh-3. These values differ from the conventional ab initio results. The present investigation shows that the longitudinal component and the mean of the hyperpolarizability are positive around Re, in conflict with previous findings. The extension of (hyper)polarizability calculations to higher copper clusters is highly nontrivial and will require the development of new computational strategies.