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

• Published in: The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Molecules, spectroscopy, kinetics, environment, & general theory, 2003-08, Vol.107 (33), p.6495-6499
• Main Author: Maroulis, George
• Format: Article
• Language: English
• ISSN: 1089-5639; 1520-5215
• DOI: 10.1021/jp0352128

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/e 2 a 0 2 E h -1). For the Cartesian components and the mean of the hyperpolarizability (10-3γαβγδ/e 4 a 0 4 E h -3) we obtain γ zzzz = 309, γ xxxx = 209, γ xxzz = 87, and γ̄ = 244. Electron correlation lowers ᾱ but increases considerably Δα. The effect on the hyperpolarizability is enormous, as the longitudinal component γ zzzz is drastically reduced, while γ xxxx and γ xxzz are nearly halved. At the CCSD(T) level of theory with a [7s6p6d2f] basis set we obtain ᾱ = 93.82, Δα = 67.09 and γ zzzz = 18, γ xxxx = 101, γ xxzz = 35, and γ̄ = 86. The dipole polarizability varies as [ᾱ(R) − ᾱ(R e)]/e 2 a 0 2 E h -1 = 28.09(R − R e) + 4.69(R − R e)2 − 0.52(R − R e)3 − 0.36(R − R e)4 and [Δα(R) − Δα(R e)]/e 2 a 0 2 E h -1 = 49.58(R − R e) + 11.92(R − R e)2 − 1.94(R − R e)3 −1.32(R − R e)4 around the experimental bond length R e = 2.2197 Å. B3LYP density functional theory calculations with a [8s7p7d5f] basis set yield ᾱ = 77.62, Δα = 44.73e 2 a 0 2 E h -1, and γ̄ = (95.9 × 103)e 4 a 0 4 E h -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 R e, 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.