Density functional theory of molecular solids: Local versus periodic effects in the two-dimensional infinite hydrogen-bonded sheet of formamide

The performance of an ab initio computational scheme for molecular crystals based on density functional theory (DFT) was investigated by computing several structural and energetic properties of hydrogen bonded infinite chains and of two-dimensional infinite periodic networks of formamide. The applied DFT potentials covered a wide range in quality, starting with a simple local exchange (X) without correlation (C), and then gradually introducing C and gradient corrections for both X and C. At the same time, five atomic basis sets of systematically increasing size, in the range of DZ to TZ(2df,2pd) were used to construct the Bloch-type crystal orbitals, to optimize the structures, and to extrapolate different physical quantities to the limit of a hypothetical infinite basis set. Infinite lattice sums were computed by the multipole expansion technique, and basis set superposition errors were (partly) eliminated by the counterpoise method. To be able to assess the accuracy of the theoretical models, the formamide monomer and two different dimers were also investigated using the same methods. Detailed comparisons were made for all models also with recent results obtained by using different orders of many-body perturbation theory. Structural optimizations for the dimers and the infinite crystal demonstrated the importance of gradient terms both for exchange and correlation. For the most successful DFT functional, containing the Becke exchange and the Lee-Yang-Parr correlation term, the lengths of the hydrogen bonds, R(HB), were reduced by 0.16-0.19 Angstrom (depending on the basis set) as compared with dimers, due to cooperative interactions in the crystalline environment. The binding energies were increased typically by 60-70%. The theoretical model explained why the R(HB) values for open-chain dimers become shorter in the crystal than those obtained for the cyclic ones (as opposed to free dimers), correctly predicted changes of bong lengths in going from the monomer to the crystal, and provided N-H ... O bond distances and lattice constants reasonably close to experiments.