Single-layered chrysotile nanotubes: A quantum mechanical ab initio simulation

Chrysotile single-layered nanotubes, obtained by wrapping the Mg(3)Si(2)O(5)(OH)(4) lizardite monolayer along the (n,-n) hexagonal lattice vector, are simulated at the ab initio level by using an all electron 6-31G( *) basis set and the B3LYP functional for n varying from 14 to 24 (the nanotube radius R referred to the oxygen connecting the Mg and Si layers increases from 20 to 35 A). Because of the full exploitation of the helical symmetry, recently implemented in the CRYSTAL code, the computational cost for the full self-consistent field (SCF) and gradient calculation increases only by a factor of 2 and 1.2, respectively, when passing from the lizardite monolayer [18 atoms and 236 AOs (atomic orbitals) in the unit cell] to the (24, -24) tube (864 atoms and 11,328 AOs). The total energy of the tubes is always larger than that of the lizardite monolayer; the difference DeltaE decreases very rapidly with n; for the largest tube here considered (n=24) DeltaE is as small as 2.7 kJ/mol per formula unit (f.u.); extrapolating to larger n values, at about R=50 A, DeltaE becomes smaller than 1 kJ mol f.u. Very large energy gains are observed for small n values during optimization after rolling, mainly due to the rotation of the SiO(4) tetrahedra that are in the inner part of the cylinder ("normal rolling"); such a rigid rotation accounts for about 85% of the overall relaxation energy. "Inverse rolling" tubes (SiO(4) on the external wall of the tube) are shown to be less stable than the corresponding "normal" tubes.