We developed a technique to decrease memory requirements when solving the integral equations of three-dimensional (3D) molecular theory of solvation, a.k.a. 3D reference interaction site model (3D-RISM), using the modified direct inversion in the iterative subspace (MDIIS) numerical method of generalized minimal residual type. The latter provides robust convergence, in particular, for charged systems and electrolyte solutions with strong associative effects for which damped iterations do not converge. The MDIIS solver (typically, with 2 × 10 iterative vectors of argument and residual for fast convergence) treats the solute excluded volume (core), while handling the solvation shells in the 3D box with two vectors coupled with MDIIS iteratively and incorporating the electrostatic asymptotics outside the box analytically. For solvated systems from small to large macromolecules and solid-liquid interfaces, this results in 6- to 16-fold memory reduction and corresponding CPU load decrease in MDIIS. We illustrated the new technique on solvated systems of chemical and biomolecular relevance with different dimensionality, both in ambient water and aqueous electrolyte solution, by solving the 3D-RISM equations with the Kovalenko-Hirata (KH) closure, and the hypernetted chain (HNC) closure where convergent. This core-shell-asymptotics technique coupling MDIIS for the excluded volume core with iteration of the solvation shells converges as efficiently as MDIIS for the whole 3D box and yields the solvation structure and thermodynamics without loss of accuracy. Although being of benefit for solutes of any size, this memory reduction becomes critical in 3D-RISM calculations for large solvated systems, such as macromolecules in solution with ions, ligands, and other cofactors.

While graphene is a semi-metal, a recently synthesized hydrogenated graphene called graphane is an insulator. We have probed the transformation of graphene upon hydrogenation to graphane within the framework of density functional theory. By analysing the electronic structure for 18 different hydrogen concentrations, we bring out some novel features of this transition. Our results show that the hydrogenation favours clustered configurations leading to the formation of compact islands. The analysis of the charge density and electron localization function (ELF) indicates that, as hydrogen coverage increases, the semi-metal turns into a metal, showing a delocalized charge density, then transforms into an insulator. The metallic phase is spatially inhomogeneous in the sense it contains islands of insulating regions formed by hydrogenated carbon atoms and metallic channels formed by contiguous bare carbon atoms. It turns out that it is possible to pattern the graphene sheet to tune the electronic structure. For example, removal of hydrogen atoms along the diagonal of the unit cell, yielding an armchair pattern at the edge, gives rise to a bandgap of 1.4 eV. We also show that a weak ferromagnetic state exists even for a large hydrogen coverage whenever there is a sublattice imbalance in the presence of an odd number of hydrogen atoms.

Hydrogenation has proven to be an effective tool to open the bandgap of graphene. In the present density functional study we demonstrate that single-side-hydrogenated graphene is a semiconductor with an indirect bandgap of 1.89 eV, in between the gapless graphene and wide bandgap graphane. We show that its electronic structure and lattice characteristics are substantially different from those of graphene, graphone, or graphane. The lattice parameter and C-C bond length are found to be lengthened by 15% of those of graphene. Our binding energy analysis confirms that such a single sided hydrogenation leads to thermodynamically stable material.