Cooperative effects in hydrogen bonding: Fourth-order many-body perturbation theory studies of water oligomers and of an infinite water chain as a model for ice

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Abstract
As a step toward the first principles quantum mechanical modeling of the structural and electronic properties of ice, hydrogen-bonded periodic infinite chains of water molecules have been investigated by the ab initio crystal orbital method at the Hartree–Fock (HF) level and by including electron correlation up to the complete fourth order of Mo/ller–Plesset perturbation theory (MP4). The Bloch functions of the crystal have been expanded in a series of high quality atomic orbital basis sets complemented by extended sets of polarization functions, up to TZ(3d2f,3p2d). Basis set superposition errors have been (partly) eliminated by the counterpoise method and the infinite lattice sums have been computed using the multipole expansion technique. The systematically increasing size of the basis sets has allowed the extrapolation of structural and electronic indices of this ice model to the limit of an infinite atomic basis at both the HF and various correlated levels, respectively. For each theoretical model, detailed comparisons have been made with the corresponding physical properties of water monomers, dimers, and some larger linear oligomers. The results convincingly prove that hydrogen bonding in ice is a highly cooperative phenomenon, both from the structural and energetic points of view. The cohesive energy per hydrogen bond of the crystal is −5.30 kcal/mol at the HF level (with RHFO,O=2.88 Å) as compared with the dimer value of −3.60 kcal/mol (at the optimized distance of 3.03 Å). At the MP2 level of theory, the crystalline binding energy decreases to −6.60 kcal/mol and the lattice contracts to RMP2O,O=2.73 Å (compared with −4.50 kcal/mol at 2.88 Å for the dimer). The correlation corrections at third and fourth order slightly expand the crystal lattice (to RMP4O,O=2.75 Å) and reduce the cohesion by 0.15 kcal/mol. A decomposition of the intermolecular interactions according to different terms of MP4 theory suggests that the cohesive energy of ice results from a delicate balance between different repulsive and attractive terms in third and fourth order, which exhibit different long-range behaviors. The detailed study of the role of high-energy virtual energy bands in computing electron correlation effects in ice provides further insight into the important role that basis set flexibility plays in such investigations. The resulting cohesive energy of −6.83 kcal/mol at the MP4 level is in reasonable agreement with the experimental energy per hydrogen bond in ice I, −6.7 kcal/mol.