Inter- and intramolecular hydrogen bonds are important in both molecular and biological chemistry, because they contribute a large part of the interactions responsible for the conformations and functions of many compounds in those fields. Different approaches and methods have been employed to determine geometrical, topological, energetic and functional properties of hydrogen bonds. Besides spectroscopic methods, X-ray diffraction is an important tool for providing answers to structural questions regarding hydrogen bonds. Koch & Popelier (1995
) proposed eight criteria that establish the existence of hydrogen bonds. Geometric, energetic and IR spectroscopic properties were suggested by Jeffrey (1997
), thus allowing a classification of strong, medium and weak hydrogen bonds.
A sophisticated approach to analyze the topological properties of electron densities is provided by Bader’s Atoms in Molecules (AIM) theory (Bader, 1994
). The AIM theory allows the determination of BCPs and their properties, such as the electron density and its Laplacian, leading to the detection of hydrogen bonds in crystal structures as well as providing a quantitative characterization of the type and strengths of these bonds. Analyses according to the AIM theory (Bader, 1994
) of experimental electron densities of amino acids and peptides have been performed by Destro et al.
), Benabicha et al.
), Pichon-Pesme et al.
), Wagner & Luger (2001
), Flaig et al.
), Scheins et al.
), Mebs et al.
), Checinska et al.
), Rödel et al.
) and Kalinowski et al.
). Amino acids were studied on the basis of electron densities derived from quantum mechanical calculations by Matta & Bader (2000
) introduced a method which uses the densities at BCPs and their Laplacians for calculating the kinetic energy densities at the BCPs. Employment of the local virial theorem (Bader, 1994
) allows the calculation of the potential energy densities at the BCPs. These energy densities provide information on the character of the bond analyzed (Abramov, 1997
; Cremer & Kraka, 1984a
). Extensive studies of energy densities and topological properties at the BCPs of hydrogen bonds have been performed by Espinosa et al.
), Espinosa, Lecomte & Molins (1999
) and Espinosa, Souhassou et al.
Experimental charge densities are usually based on the multipole model (Hansen & Coppens, 1978
). Alternatively, they can be determined by the maximum entropy method (MEM; Sakata & Sato, 1990
; Hofmann, Kalinowski et al.
; Hofmann, Netzel & van Smaalen, 2007
; Netzel et al.
; Nishibori et al.
). MEM electron densities (
) have been successfully used to study disorder in crystal structures. The most prominent application has been the determination of the location of the metal atom in endohedral fullerenes (Takata et al.
). Earlier studies have stressed artifacts in MEM densities, which have magnitudes equal to the deformation densities of chemical bonds, and thus would prohibit the use of the MEM in charge-density studies (Jauch & Palmer, 1993
; Jauch, 1994
; de Vries et al.
; Takata & Sakata, 1996
; Roversi et al.
). These problems have been overcome by a combination of extensions to the MEM, including the use of a procrystal prior density (de Vries et al.
), the use of static weights in the
constraint (de Vries et al.
), the use of prior-derived
constraints (Palatinus & van Smaalen, 2005
) and the definition of a criterion of convergence for the MEM iterations, which is based on difference-Fourier maps (Hofmann, Netzel & van Smaalen, 2007
). The MEM has the potential to become the method of choice in accurate charge-density studies on proteins (Hofmann, Kalinowski et al.
; Nishibori et al.
), because the MEM (unlike multipole refinements) does not suffer from correlations between parameters.
The present work reports the analysis of MEM electron densities of several amino acids and peptides. The study includes the analysis of geometrical, topological and energetic properties of all 52 hydrogen bonds that have been identified in these compounds. The quantitative analysis is supplemented by a descriptive analysis of electron densities in the regions of the hydrogen bonds. Since the role of a promolecule (procrystal) has been discussed as being important for the extraction of information of bonding (Spackman, 1999
; Downs et al.
), the contribution of the prior density to properties of chemical bonds is discussed. The systematic dependence of properties of hydrogen bonds on the distance between the H atom and acceptor atom is supplemented by an analysis of the properties of covalent bonds with respect to the bond distance.