Influence of the long-range exchange effect on dynamic polarizability

The long-range interaction in density functional theory ( DFT) is corrected using a partition technique of the two-electron operator when applied in the equation of motion ( EOM) on the. first-order density matrix. While the correction produces a minor effect on the static polarizabilities of small molecules, it improves the overestimated Cauchy coefficients of small molecules by the DFT without the correction. The same technique is applied to compute the polarizabilities of long chain molecules, a long standing problem of DFT. The overestimations by the DFT without the correction are remarkably improved for hydrogen chains and polyacetylene. Finally, the method is applied to compute the dynamic polarizabilities of C(4)H(6) and C(12)H(14). The frequency dependencies obtained by the DFT with the long-range correction ( LRC) are different from that obtained by the DFT without LRC and similar to that obtained by the HF. The adiabatic approximation taken in the TDDFT of the. first-order density matrix without LRC causes complete neglect of the interaction among anti-symmetric modes in the EOM, which plays an important role in the near-resonance situation and provides an incorrect frequency dependence.