Hydrogen bonds: relation between lengths and electron densities at bond critical points

Abstract. The electron densities for a number of molecules with either inter- or intra-molecular hydrogen bonds are analyzed using the theory of atoms in molecules. The levels of theory used include second order Møller Plesset and density functional methods. The molecules investigated ranges from small molecules/ions to an alanine octa-peptide. The hydrogen bond length, BL, varies from 1.15 to 3.01 Å and ρb, the electron density at the bond critical point, spans the interval 0.0033 to 0.168 (au). We find that the data may be represented by the relation $\rho_{b} = A \exp (-B\times {\it BL}$), where A and B are empirical constants. The relation is compared to a similar relation derived from solid state experiments. Since the ρb values are related to the bond strengths, this general relationship may useful for hydrogen bond studies.

[1]  E. Molins,et al.  About the evaluation of the local kinetic, potential and total energy densities in closed-shell interactions , 2001 .

[2]  B. Dittrich,et al.  Intra- and intermolecular topological properties of amino acids: a comparative study of experimental and theoretical results. , 2002, Journal of the American Chemical Society.

[3]  G. Madsen,et al.  Topological Analysis of the Charge Density in Short Intramolecular O−H···O Hydrogen Bonds. Very Low Temperature X-ray and Neutron Diffraction Study of Benzoylacetone , 1998 .

[4]  I. Csizmadia,et al.  Strong and symmetric hydrogen bonding in the hydrogen di-superoxide anion , 2000 .

[5]  J. Elguero,et al.  Comparison of models to correlate electron density at the bond critical point and bond distance , 2000 .

[6]  I. Csizmadia,et al.  Structural changes of hydrogen bonded hexagonal trimers upon ionization , 1999 .

[7]  P Coppens,et al.  Chemical applications of X-ray charge-density analysis. , 2001, Chemical reviews.

[8]  S. Larsen,et al.  Charge Density Study of Naphthalene Based on X-ray Diffraction Data at Four Different Temperatures and Theoretical Calculations , 2004 .

[9]  I. Csizmadia,et al.  Structural changes of triplet states of hydrogen bonded hexagonal dimers upon ionization and electron capture , 1999 .

[10]  A. Rashin,et al.  alpha- and 3(10)-helix interconversion: a quantum-chemical study on polyalanine systems in the gas phase and in aqueous solvent. , 2001, Journal of the American Chemical Society.

[11]  R. Bader,et al.  A Bond Path: A Universal Indicator of Bonded Interactions , 1998 .

[12]  J. Platts,et al.  Directionality of Hydrogen Bonds to Sulfur and Oxygen , 1996 .

[13]  B. Iversen,et al.  Interanionic O−H⋅⋅⋅O Interactions: The Charge Density Point of View , 2000 .

[14]  Chick C. Wilson,et al.  From weak interactions to covalent bonds: a continuum in the complexes of 1,8-bis(dimethylamino)naphthalene. , 2003, Journal of the American Chemical Society.

[15]  M. Messerschmidt,et al.  Atomic volumes and charges in a system with a strong hydrogen bond: L-tryptophan formic acid. , 2004, Acta crystallographica. Section B, Structural science.

[16]  C. Lecomte,et al.  Topological analysis of the electron density in hydrogen bonds. , 1999, Acta crystallographica. Section B, Structural science.

[17]  I. Csizmadia,et al.  Binding properties of carbohydrate sulfamates based on ab initio 6–31 + G∗∗ calculations on N-methyl and N-ethyl sulfamate anions , 1996 .

[18]  T. Tang,et al.  Binding properties of carbohydrate O-sulfate esters based on ab initio 6-31 +G** calculations on methyl and ethyl sulfate anions , 1993 .

[19]  E. Molins,et al.  From weak to strong interactions: A comprehensive analysis of the topological and energetic properties of the electron density distribution involving X–H⋯F–Y systems , 2002 .

[20]  R. Bader,et al.  Description of conjugation and hyperconjugation in terms of electron distributions , 1983 .

[21]  R. J. Boyd,et al.  Coming to Grips with N−H···N Bonds. 2. Homocorrelations between Parameters Deriving from the Electron Density at the Bond Critical Point1 , 2003 .

[22]  Y. Abramov.  On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution , 1997 .

[23]  Uwe Koch,et al.  CHARACTERIZATION OF C-H-O HYDROGEN-BONDS ON THE BASIS OF THE CHARGE-DENSITY , 1995 .

[24]  R. Bader.  Atoms in molecules : a quantum theory , 1990 .