  Electronic properties of molecular conductors exhibiting antiferromagnetic
(AFM) spin order and charge order (CO) owing to electron correlation are
studied using first-principles density functional theory calculations. We
investigate two systems, a quasi-two-dimensional Mott insulator
$\beta^\prime$-(BEDT-TTF)$_{2}$ICl$_{2}$ with an AFM ground state, and several
members of quasi-one-dimensional (TMTTF)$_2$$X$ showing CO. The stabilities of
the AFM and CO states are compared between the use of a standard
exchange-correlation functional based on the generalized gradient approximation
and that of a range-separated hybrid functional; we find that the latter
describes these states better. For $\beta^\prime$-(BEDT-TTF)$_{2}$ICl$_{2}$,
the AFM order is much stabilized with a wider band gap. For (TMTTF)$_2$$X$,
only by using the hybrid functional, the AFM insulating state is realized and
the CO states coexisting with AFM order are stable under structural
optimization, whose stability among different \textit{X} shows the tendency
consistent with experiments.
