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.

[1]  Gregory K. Schenter,et al.  Natural Energy Decomposition Analysis: The Linear Response Electrical Self Energy , 1996 .

[2]  Y. Mo,et al.  Energy decomposition analysis of intermolecular interactions using a block-localized wave function approach , 2000 .

[3]  Rustam Z. Khaliullin,et al.  An efficient self-consistent field method for large systems of weakly interacting components. , 2006, The Journal of chemical physics.

[4]  Margaret E. Johnson,et al.  Tetrahedral structure or chains for liquid water. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Robert S. Mulliken,et al.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies , 1955 .

[6]  Eric D. Glendening,et al.  Natural energy decomposition analysis: An energy partitioning procedure for molecular interactions with application to weak hydrogen bonding, strong ionic, and moderate donor–acceptor interactions , 1994 .

[7]  Mario Raimondi,et al.  Modification of the Roothaan equations to exclude BSSE from molecular interaction calculations , 1996 .

[8]  Jean-Philip Piquemal,et al.  A CSOV study of the difference between HF and DFT intermolecular interaction energy values: The importance of the charge transfer contribution , 2005, J. Comput. Chem..

[9]  F. Weinhold,et al.  Natural population analysis , 1985 .

[10]  Rustam Z. Khaliullin,et al.  Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals. , 2007, The journal of physical chemistry. A.

[11]  Paul S. Bagus,et al.  A new analysis of charge transfer and polarization for ligand–metal bonding: Model studies of Al4CO and Al4NH3 , 1984 .

[12]  Myron W. Evans,et al.  Water in Biology, Chemistry and Physics: Experimental Overviews and Computational Methodologies , 1996 .

[13]  Hermann Stoll,et al.  On the use of local basis sets for localized molecular orbitals , 1980 .

[14]  Giulia Galli,et al.  X-ray absorption spectra of water from first principles calculations. , 2006, Physical review letters.

[15]  P. Wernet,et al.  The Structure of the First Coordination Shell in Liquid Water , 2004, Science.

[16]  Bertrand Guillot,et al.  A reappraisal of what we have learnt during three decades of computer simulations on water , 2002 .

[17]  E. D. Isaacs,et al.  Covalency of the Hydrogen Bond in Ice: A Direct X-Ray Measurement , 1999 .

[18]  Consequences of chain networks on thermodynamic, dielectric and structural properties for liquid water. , 2007, Physical chemistry chemical physics : PCCP.

[19]  Eric D Glendening,et al.  Natural energy decomposition analysis: extension to density functional methods and analysis of cooperative effects in water clusters. , 2005, The journal of physical chemistry. A.

[20]  Kazuo Kitaura,et al.  A new energy decomposition scheme for molecular interactions within the Hartree‐Fock approximation , 1976 .

[21]  Richard J. Saykally,et al.  Energetics of Hydrogen Bond Network Rearrangements in Liquid Water , 2004, Science.

[22]  R. C. Cohen,et al.  Probing the local structure of liquid water by X-ray absorption spectroscopy. , 2006, The journal of physical chemistry. B.

[23]  Francesc Illas,et al.  Decomposition of the chemisorption bond by constrained variations: Order of the variations and construction of the variational spaces , 1992 .

[24]  Bin Chen,et al.  Structural correlations and motifs in liquid water at selected temperatures: ab initio and empirical model predictions. , 2006, The journal of physical chemistry. B.

[25]  R. Car,et al.  Ab initio molecular dynamics with maximally localized Wannier functions , 2003 .

[26]  Mark S. Gordon,et al.  Energy Decomposition Analyses for Many-Body Interaction and Applications to Water Complexes , 1996 .

[27]  A. K. Soper.  An asymmetric model for water structure , 2005 .

[28]  Gang Zhang,et al.  Comparison of DFT methods for molecular orbital eigenvalue calculations. , 2007, The journal of physical chemistry. A.

[29]  Rustam Z. Khaliullin,et al.  Analysis of charge transfer effects in molecular complexes based on absolutely localized molecular orbitals. , 2008, The Journal of chemical physics.

[30]  Ernest R. Davidson,et al.  Is the Hydrogen Bond in Water Dimer and Ice Covalent , 2000 .

[31]  Gautam R. Desiraju,et al.  The Weak Hydrogen Bond: In Structural Chemistry and Biology , 1999 .

[32]  William H. Fink,et al.  Frozen fragment reduced variational space analysis of hydrogen bonding interactions. Application to the water dimer , 1987 .

[33]  Osamu Takahashi,et al.  Basis set superposition error free self-consistent field method for molecular interaction in multi-component systems : Projection operator formalism , 2001 .

[34]  P. Löwdin.  On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals , 1950 .

[35]  Shawn T. Brown,et al.  Advances in methods and algorithms in a modern quantum chemistry program package. , 2006, Physical chemistry chemical physics : PCCP.