Accurate electric multipole moment, static polarizability and hyperpolarizability derivatives for N2

Abstract

We report accurate values of the electric moments, static polarizabilities, hyperpolarizabilities and their respective derivatives for N2. Our values have been extracted from finite-field Møller–Pleset perturbation theory and coupled cluster calculations performed with carefully designed basis sets. A large [15s12p9d7f] basis set consisting of 290 CGTF is expected to provide reference self-consistent-field values of near-Hartree–Fock quality for all properties. The Hartree–Fock limit for the mean hyperpolarizability is estimated at γ̄=715±4e4a04Eh−3 at the experimental bond length Re=2.074 32a0. Accurate estimates of the electron correlation effects were obtained with a [10s7p6d4f] basis set. Our best values are Θ=−1.1258ea02 for the quadrupole and Φ=−6.75ea04 for the hexadecapole moment, ᾱ=11.7709 and Δα=4.6074e2a02Eh−1 for the mean and the anisotropy of the dipole polarizability, C̄=41.63e2a04Eh−1 for the mean quadrupole polarizability and γ̄=927e4a04Eh−3 for the dipole hyperpolarizability. The latter value is quite close to Shelton’s experimental estimate of 917±5e4a04Eh−3 [D. P. Shelton, Phys. Rev. A 42, 2578 (1990)]. The R dependence of all properties has been calculated with a [7s5p4d2f] basis set. At the CCSD(T) level of theory the dipole polarizability varies around Re as ᾱ(R)/e2a02Eh−1=11.8483+6.1758(R−Re)+0.9191(R−Re)2−0.8212(R−Re)3−0.0006(R−Re)4, Δα(R)/e2a02Eh−1=4.6032+7.0301(R−Re)+1.9340(R−Re)2−0.5708(R−Re)3+0.1949(R−Re)4. For the Cartesian components and the mean of γαβγδ, (dγzzzz/dR)e=1398, (dγxxxx/dR)e=867, (dγxxzz/dR)e=317, and (dγ̄/dR)e=994e4a03Eh−3. For the quadrupole polarizability Cαβ,γδ, we report (dCzz,zz/dR)e=19.20, (dCxz,xz/dR)e=16.55, (dCxx,xx/dR)e=10.20, and (dC̄/dR)e=23.31e2a03Eh−1. At the MP2 level of theory the components of the dipole–octopole polarizability (Eα,βγδ) and the mean dipole–dipole–octopole hyperpolarizability B̄ we have obtained (dEz,zzz/dR)e=36.71, (dEx,xxx/dR)e=−12.94e2a03Eh−1, and (dB̄/dR)e=−108e3a03Eh−2. In comparison with some other 14-electron systems, N2 appears to be less (hyper)polarizable than most, as near the Hartree–Fock limit we observe ᾱ(N2)<ᾱ(CO)<ᾱ(HCN)<ᾱ(BF)<ᾱ(HCCH) and γ̄(N2)<γ̄(CO)<γ̄(HCN)<γ̄(HCCH)<γ̄(BF).