  We report benchmark results for one-dimensional (1D) atomic and molecular
systems interacting via the Coulomb operator $|x|^{-1}$. Using various
wavefunction-type approaches, such as Hartree-Fock theory, second- and
third-order M{\o}ller-Plesset perturbation theory and explicitly correlated
calculations, we study the ground state of atoms with up to ten electrons as
well as small diatomic and triatomic molecules containing up to two electrons.
A detailed analysis of the 1D helium-like ions is given and the expression of
the high-density correlation energy is reported. We report the total energies,
ionization energies, electron affinities and other interesting properties of
the many-electron 1D atoms and, based on these results, we construct the 1D
analog of Mendeleev's periodic table. We find that the 1D periodic table
contains only two groups: the alkali metals and the noble gases. We also
calculate the dissociation curves of various 1D diatomics and study the
chemical bond in H$_2^+$, HeH$^{2+}$, He$_2^{3+}$, H$_2$, HeH$^+$ and
He$_2^{2+}$. We find that, unlike their 3D counterparts, 1D molecules are
primarily bound by one-electron bonds. Finally, we study the chemistry of
H$_3^+$ and we discuss the stability of the 1D polymer resulting from an
infinite chain of hydrogen atoms.
