Figure 1

Axial optical absorption spectra for the molecular ${\mathrm{H}}_2$ chain $A$ (Peierls distorted, left-hand frame) and chain $B$ (nearly equally spaced H atoms, right-hand frame). While the present $f_{\mathrm{xc}}$ kernel yields an excellent agreement with the many-body calculations in both cases, ALDA works only in the small gap case when the exciton is not localized. The excitonic wave functions [22] corresponding to the main absorption peak are also shown by fixing the hole in the middle of the central hydrogen molecular bond. A delocalized exciton wave function in chain $B$ is connected with a successful description of the spectra by the ALDA (see text).Reuse & Permissions

Figure 2

Axial polarizability per monomer of the molecular ${\mathrm{H}}_2$ chains. TDDFT calculations within the ALDA, $f_{\mathrm{xc}}$, and $f_{\mathrm{xc}}^{\mathrm{SIC}}$ (see text) are compared with coupled cluster CCSD(T) [5] and CDFT [10] results. The real-space excitonic wave functions of selected chains, with the hole placed in the middle of the central hydrogen molecule bond, are also shown.Reuse & Permissions

Figure 3

Calculated axial polarizability of the finite trans-polyacetylene chain with alternating C–C distances of 1.339 and 1.451 Å. We also show the result of HF [23], MP2 [4], and ALDA calculations. In the insets we report the absorption spectrum of the infinite chain (left inset) and dependence of the excitonic energy ($E_{\mathrm{exc}}$) as a function of the number of monomers ($N$). In contrast to the ALDA, the experimental absorption at 1.7 eV [24] is perfectly reproduced by either the BS or the present TDDFT calculations. At difference with the ALDA, the axial polarizability calculated with the present $f_{\mathrm{xc}}$ correctly saturates at 15 monomers, in excellent agreement with the MP2 results. At the same time, the excitonic energy saturates towards the infinite chain experimental peak position. Bottom: Excitonic wave functions corresponding to the most intense and bright peak of the infinite and 15 monomers long chains, respectively. It is significant to note that in both cases the exciton extends over the same number of neighbors.Reuse & Permissions