Linear response at the 4-component relativistic density-functional level: application to the frequency-dependent dipole polarizability of Hg, AuH and PtH2

Abstract

Abstract We report the implementation and application of linear response density-functional theory (DFT) based on the 4-component relativistic Dirac–Coulomb Hamiltonian. The theory is cast in the language of second quantization and is based on the quasienergy formalism (Floquet theory), replacing the initial state dependence of the Runge–Gross theorem by periodic boundary conditions. Contradictions in causality and symmetry of the time arguments are thereby avoided and the exchange-correlation potential and kernel can be expressed as functional derivatives of the quasienergy. We critically review the derivation of the quasienergy analogues of the Hohenberg–Kohn theorem and the Kohn–Sham formalism and discuss the nature of the quasienergy exchange-correlation functional. Structure is imposed on the response equations in terms of Hermiticity and time-reversal symmetry. It is observed that functionals of spin and current densities, corresponding to time-antisymmetric operators, contribute to frequency-dependent and not static electric properties. Physically, this follows from the fact that only a time-dependent electric field creates a magnetic field. It is furthermore observed that hybrid functionals enhance spin polarization since only exact exchange contributes to anti-Hermitian trial vectors. We apply 4-component relativistic linear response DFT to the calculation of the frequency-dependent polarizability of the isoelectronic series Hg, AuH and PtH2. Unlike for the molecules, the effect of electron correlation on the polarizability of the mercury atom is very large, about 25%. We observe a remarkable performance of the local-density approximation (LDA) functional in reproducing the experimental frequency-dependent polarizability of this atom, clearly superior to that of the BLYP and B3LYP functionals. This allows us to extract Cauchy moments (S(−4) = 382.82 and S(−6) = 6090.89 a.u.) that we believe are superior to experiment since we go to higher order in the Cauchy moment expansion.