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The borders of hydrogen bonds

The problem of what interactions should be considered 'hydrogen bonds' is as old as the field of hydrogen bond research. In the 1920s when the field was in its infancy, liberal views held sway and borders were open. In the late 1930s, rigid and exclusive hydrogen bond definitions became the order of the day and remained practically unchanged (though not unchallenged) for about 50 years. Typical definitions held that in a hydrogen bond X-H···A, X and A must be 'very electro-negative atoms' and that H···A or even X···A must be significantly shorter than the sum of the van der Waals radii. In the 1980s and 90s, conflicts with experimental data reached such a level that stringent criteria were increasingly ignored by researchers. A modern and useful definition of a hydrogen bond has not yet been found. In an informal meeting arranged by Roland Boese in Essen on September 19, 2000, the current state of this matter was explored to determine where borderlines should be drawn between interactions that are of the 'hydrogen bond type' and interactions that are clearly not hydrogen bonds. (Participants included R. Boese, G.R. Desiraju, A. Gehrke, R. Goddard, S. Harder, M. Kirchner, C. Lehmann, M. Mazik, T. Steiner, R. Sustmann.)

It was agreed that as a primary requirement, a hydrogen bond must involve a hydrogen atom, however trivial this might sound. The question of whether the term 'hydrogen bond' should be applied only to interactions formed by protic X-H groups (where H carries a positive partial charge relative to X), or be extended to include interactions involving hydridic X-H groups of opposite polarity, is more controversial. In fact, structural and functional features of Xδ+-Hδ-···Aδ+ interactions (e.g. agostic interactions, diboranes, 'inverse hydrogen bonds', etc.) in many significant ways parallel 'normal' Xδ-Hδ+···Aδ-. hydrogen bonds. Nevertheless, the electronic nature of the interactions are different, being formally three center.four electron in one case, and three center.two electron in the other. This difference makes it possible to define a borderline on a chemical basis and term as a proper 'hydrogen bond' only the four-electron interaction.

[hydrogen bond] Figure 1: Example of a hydrogen bond type that does not fit early hydrogen bond  definitions: typical N-H···Ph interaction in a protein (from T. Steiner, G. Koellner, J. Mol. Biol., 305, 2001, 535).
However, the use of the three center.four-electron condition as a stringent criterion is inappropriate because it would exclude such acceptors as the π-faces of benzene rings (see Figure 1). In fact, it is only required that the acceptor is a sterically accessible concentration of negative charge.

A hydrogen bond is a complex interaction composed of electrostatic, covalent and van der Waals forces that can be further divided (e.g. electrostatics into monopole, dipole and multipole contributions with different distance and angular characteristics, and van der Waals forces into attractive dispersion and exchange repulsion terms). In different kinds of hydrogen bonds, these constituents have different weights. In 'normal' hydrogen bonds, for example, electrostatics are dominant, while very strong hydrogen bonds can be dominated by covalent interactions and weak hydrogen bonds have electrostatic and van der Waals contributions of similar weight. In some cases, continuous transition to 'pure' interaction types is observed as in the transition to covalency that occurs with strong hydrogen bonds. Symmetric hydrogen bonds (X-H-X with two equal X-H distances) can be characterized as two half covalent bonds. It is more difficult to evaluate a transition to purely ionic (i.e. non-directional) electrostatics that occurs if the partners carry large charges but only small dipole or quadrupole moments. Here, a liberal view was favored that concedes a certain hydrogen bond nature to an X-H···A interaction if some positive directionality can be detected, i.e. discernible favoring of linear over bent X-H··· angles.

Most difficult to define is the transition to pure van der Waals forces. If donor or/and acceptor are only weak dipoles, such as in typical C-H···A or X-H···Hal-C interactions, positive directionality was again accepted as the primary criterion for the definition of a hydrogen bond. If the distance fall-off of the electrostatic component is fast, a dividing line can only be drawn subjectively. A possible borderline that can be drawn between dipole-quadrupole and quadrupole-quadrupole interactions was discussed.

It is currently fashionable to assign hydrogen bond character to a given contact by locating 'bond-critical points' in electron density distributions. After intense discussion, the group concluded that the existence of a bond critical point is a necessary though not a sufficient criterion for hydrogen bonding. It appears that a simple definition of the hydrogen bond is not possible. The complexity of the phenomenon, the large number of different contributing factors and the gradual transition to other types of interactions, does not permit the definition of clear borderlines. Once the openness of borders is acknowledged, a more general view of hydrogen bonding becomes possible. It is noteworthy that throughout the discussion, the 'van der Waals cutoff '-criterion was not mentioned. This criterion, which ruled the field for decades, is now completely abandoned - clearly a sign that the field has evolved.

Thomas Steiner, Freie U. Berlin