Electrostatics, Charge Transfer, and the Nature of the Halide–Water Hydrogen Bond

Abstract

Binary halide-water complexes X − (H2O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful chargetransfer component from the induction energy. As is known, the X − (H2O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C2v-symmetric saddle point, with a tunneling barrier height that is < 2 kcal/mol except in the case of F − (H2O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (< 2 kcal/mol except for X = F), and thus considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X − (H2O) and provides a driving force for the formation of quasi-linear X• • • H-O hydrogen bonds. Charge-transfer energies correlate well with measured O-H vibrational redshifts for both halidewater complexes as well as OH − (H2O) and NO − 2 (H2O), providing some indication of a general mechanism.

Interaction Energy Analysis of Monovalent Inorganic Anions in Bulk Water Versus Air/Water Interface

“…Because the SCF procedure is variational, lifting of this constraint necessarily lowers the energy (to that of the fully-relaxed SCF solution), and this energy lowering is taken to define E CT . The CT energy thus obtained is then subtracted from the induction energy to obtain the CT-free polarization energy, E pol = E ind − E CT [64,[66][67][68]. CT energies defined in this way are very nearly converged already in double-ζ basis sets [64].…”

“…CT energies defined in this way are very nearly converged already in double-ζ basis sets [64]. This approach has previously been used to demonstrate that E CT furnishes a driving force for formation of quasi-linear hydrogen bonds in binary halide-water complexes [52,68]. Implementation of the charge-constrained SCF procedure requires a method to count electrons, and Becke's multicenter partition scheme [69] is commonly used for this purpose [65].…”

“…Alternatively, and specifically for the purpose of defining a CT-free reference state in order to effect the partition suggested in Eq. ( 6), a counting procedure based on fragment-based Hirshfeld (FBH) weighting has also been suggested [66,68]. In the latter approach, the number of electrons contained in fragment A is defined as…”

“…In the Becke definition, the size and shape of the Voronoi cell that contains the iodide anion is sensitive to the instantaneous values of all iodide-water distances in the first solvation shell, whereas the FBH definition uses a spherically-symmetric charge density for the isolated anion in order to define the charge constraint; the latter definition is less sensitive to fluctuations in the atomic coordinates. (Note that FBH definition certainly remains sensitive to the presence of hydrogen bonds [52,68].) CT energies for snapshots of I − (aq) in bulk water, computed using a charge-constrained SCF procedure with the charge constraint defined either using fragment-based Hirshfeld (FBH) weights (scale at left), or else Becke's multicenter partitioning procedure (scale at right).…”

“…However, the original implementation of the charge-constrained SCF procedure in the Q-Chem program did not include these corrections [73], for reasons that are unclear because the same algorithm with these size adjustments was implemented in the NWChem program, by the same authors at around the same time [74]. Atomic size corrections were later added to Q-Chem's version of Becke partition for the purpose of SAPT-based CT analysis [68]. Absent these corrections, the Voronoi cell boundaries are placed at midpoints of the internuclear vectors, which affords unreasonable results in cases where neighboring atoms have very different size.…”