  Effects that are not captured by the generalized-gradient density-functional
theory play a prominent effect on the structural binding, and on the electronic
and optical properties of reduced-dimensional and weakly-bound materials. Here,
we report the exfoliation energy of selenium and tellurium atomic chains with
non-empirical van der Waals corrections, and their electronic and optical
properties with the GW and Bethe-Salpeter formalisms. The exfoliation energy is
found to be within 0.547 to 0.719 eV/u.c. for the selenium atomic chain, and
0.737 to 0.926 eV/u.c. for the tellurium atomic chain (u.c. stands for unit
cell), depending on the approximation for the van der Waals interaction and the
numerical tool chosen. The GW electronic bandgap turned out to be 5.22--5.47
(4.44--4.59) eV for the Se (Te) atomic chains, with the lowest bound obtained
with the Godby-Needs (GB), and the upper bound to the Hybertsen-Louie (HL)
plasmon-pole models (PPMs). The binding energy of the ground-state excitonic
state ranges between 2.69 to 2.72 eV for selenium chains within the HL and GB
PPM, respectively, and turned out to be 2.35 eV for tellurium chains with both
approximations. The ground state excitonic wave function is localized within 50
\AA{} along the axis for both types of atomic chains, and its energy lies
within the visible spectrum: blue [2.50(GN)--2.78(HL) eV] for selenium, and
yellow--green [2.09(GN)--2.28(HL) eV] for tellurium, which could be useful for
LED applications in the visible spectrum.
