Exchange potential from the common energy denominator approximation for the Kohn–Sham Green’s function: Application to (hyper)polarizabilities of molecular chains.

An approximate Kohn–Sham (KS) exchange potential v[sub xσ][sup CEDA] is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green’s function, which preserves the essential structure of the density response function. v[sub xσ][sup CEDA] is an explicit functional of the occupied KS orbitals, which has the Slater v[sub Sσ] and response v[sub respσ][sup CEDA] potentials as its components. The latter exhibits the characteristic step structure with “diagonal” contributions from the orbital densities |ψ[sub iσ]|[sup 2], as well as “off-diagonal” ones from the occupied–occupied orbital products ψ[sub iσ]ψ[sub j(≠1)σ][sup *]. Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger–Li–Iafrate (KLI), exact exchange (EXX), and Hartree–Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical “closure approximations” to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies &Vegr;[sub iσ] are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX–&Vegr;[sub iσ] values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans’ theorem. However, the additional off-diagonal orbital structure of v[sub xσ][sup CEDA] appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H[sub n] over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons... [ABSTRACT FROM AUTHOR]