<p class="rtecenter"><br /> <a href="http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jpccck/2011/jpccck.2011.115.issue-29/jp2027737/production/images/medium/jp-2011-027737_0005.gif" rel="lightbox[center]"><img alt="" src="http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jpccck/2011/jpccck.2011.115.issue-29/jp2027737/production/images/medium/jp-2011-027737_0005.gif" /></a></p> <p>The line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry have been applied for symmetry analysis of double-wall boron nitride and titania nanotubes (DW BN and TiO2 NTs) formed by rolling up the stoichiometric two-periodic (2D) slabs of hexagonal structure with the same or opposite orientation of translation and chiral vectors. We have considered the two sets of commensurate DW BN and TiO2 NTs with either armchair- or zigzag-type chiralities, i.e., (n1,n1)@(n2,n2) or (n1,0)@(n2,0), respectively. To establish the equilibrium interwall distances corresponding to the minima of energy, we have varied chiral indices n1 and n2 of the constituent single-wall (SW) nanotubes. To analyze the structural and electronic properties of hexagonal DW NTs, we have performed ab initio LCAO calculations using the hybrid Hartree&ndash;Fock/Kohn&ndash;Sham exchange-correlation functional PBE0 as implemented in CRYSTAL-09 code. The inversely stacked structure of zigzag-type DW BN NT, characterized by arrangement of positively and negatively charged rings in each atomic cross section (consisting of either B or N atoms, respectively), has been found to be energetically more preferable as compared to the straightly stacked structure containing nanotube rings consisting of the same type of atoms in cross sections, i.e., B(N) and B(N). In armchair-type DW BN NTs, each atomic ring contains the whole number of B&ndash;N bonds, which reduces the electrostatic interaction between both walls. On the other hand, main contribution to interwall bonding in DW TiO2 NTs is provided by interaction between the nearest oxygen and titanium ions of neighboring shells. The interaction between the walls results in a decrease of band gaps for double-wall NTs as compared to those for SW NTs, which is substantially larger for TiO2.</p>