Electron Donation in the Water–Water Hydrogen Bond

Hydrogen bonding is central to aqueous systems, from small water clusters and microsolvated ions to bulk water, and solvated biomolecules. Despite numerous experimental and theoretical studies, the physical nature of hydrogen bonding is still debated. One issue is the extent of intermolecular charge transfer (CT) in hydrogen bonding. Natural bond orbital (NBO) analysis and natural energy decomposition analysis suggest that CT is predominant because, if CT is neglected, NBO analysis shows no binding at the water-dimer equilibrium geometry. However, other earlier decomposition methods estimated that CT contributes only around 20% of the overall binding energy. This question has practical significance for aqueous molecular dynamics simulations, where models based on purely electrostatic potentials, such as Coulomb plus Lennard-Jones with perhaps polarizability, seem to be very successful in reproducing many structural and thermodynamic properties of water. Is such good agreement soundly based or fortuitous? Recent X-ray absorption and X-ray Raman scattering experiments have challenged the accepted locally tetrahedral structure of liquid water. The failure of classical molecular dynamics simulations to reproduce the “chain and ring” local structure inferred from these experiments has generated questions about the reliability of existing water potentials. 12] This fact, combined with the CT character of the hydrogen bonding suggested by NBO analysis, has led to proposals to incorporate CT effects into empirical water potentials. However, the “chain and ring” interpretation of the X-ray experiments is highly controversial and has been challenged on many fronts. Herein, we rationalize the success of empirical electrostatic potentials by clarifying intermolecular CT effects in the simplest water cluster, the water dimer. We have used our recently developed energy-decomposition analysis (EDA) and charge-transfer analysis (CTA) based on absolutely localized molecular orbitals (ALMOs), which are ideal for separating CT from frozen density and polarization interactions. In ALMO EDA, the frozen density (FRZ) term is calculated as the interaction energy of the unrelaxed electron densities on the molecules. The polarization (POL) term is due to the deformation (or polarization) of the electron clouds of the molecules in the field of each other. Quantum mechanically, it is described as the energy lowering due to the intramolecular relaxation of each molecule s ALMOs in the field of the other molecule. CT is calculated as the energy lowering due to the intermolecular relaxation of the molecular orbitals corrected for the basis set superposition error (BSSE). Like related earlier methods, the ALMO atomic-tomolecular orbital transformation is constrained to be blockdiagonal in terms of the molecular fragments (prohibiting CT). Unlike those earlier methods, ALMO EDA and CTA treat the optimization of the ALMO s in a variationally optimal way. CT effects (energy lowering due to electron transfer from occupied orbitals on one molecule to virtual orbitals of another molecule, and then any further repolarization or higher-order relaxation) are corrections to the optimal polarized reference system, and cannot be over or underestimated. The ALMO charge transfer scale, DQ, provides a measure of the distortion of the electronic clouds upon formation of an intermolecular bond and is such that all CT terms, that is, forward-donation, back-donation, and higher order relaxation, have well defined energetic effects. The water dimer geometry with Cs symmetry was optimized at the MP2/aug-cc-pVQZ level. All calculations were [a] Dr. R. Z. Khaliullin Department of Chemistry, University of California Berkeley Berkeley, CA 94720 (USA) Fax: (+1)510-643-1255 E-mail : rustam@khaliullin.com [b] Prof. A. T. Bell Department of Chemical Engineering, University of California Berkeley Berkeley, CA 94720 (USA) [c] Prof. M. Head-Gordon Department of Chemistry, University of California Berkeley Berkeley, CA 94720 (USA) Fax: (+1)510-643-1255 E-mail : mhg@bastille.cchem.berkeley.edu Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.200802107.