There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The hydrogen bond is the most important of all directional intermolecular interactions. It is operative in determining molecular conformation, molecular aggregation, and the function of a vast number of chemical systems ranging from inorganic to biological. Research into hydrogen bonds experienced a stagnant period in the 1980s, but re-opened around 1990, and has been in rapid development since then. In terms of modern concepts, the hydrogen bond is understood as a very broad phenomenon, and it is accepted that there are open borders to other effects. There are dozens of different types of X-H.A hydrogen bonds that occur commonly in the condensed phases, and in addition there are innumerable less common ones. Dissociation energies span more than two orders of magnitude (about 0.2-40 kcal mol(-1)). Within this range, the nature of the interaction is not constant, but its electrostatic, covalent, and dispersion contributions vary in their relative weights. The hydrogen bond has broad transition regions that merge continuously with the covalent bond, the van der Waals interaction, the ionic interaction, and also the cation-pi interaction. All hydrogen bonds can be considered as incipient proton transfer reactions, and for strong hydrogen bonds, this reaction can be in a very advanced state. In this review, a coherent survey is given on all these matters.

The hydrogen bond in the solid state.

Ferroelectric Metal–Organic Frameworks

Hydrogen bonding is an important interaction playing a key role in chemical, physical, and biochemical processes. One can mention numerous examples such as the role of hydrogen bonding in enzymatic catalysis, arrangement of molecules in crystals, crystal engineering, proton transfer reactions, and also its important role in life processes. Hence, its nature is often the subject of investigations and polemics. One of the first definitions of hydrogen bonding was formulated by Pauling who stated that “under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms, instead of only one, so that it may be considered to be acting as a bond between them. This is called the hydrogen bond”. Pauling also pointed out that the hydrogen atom is situated only between the most electronegative atoms and it usually interacts much stronger with one of them. The latter interaction is a typical covalent bond (A-H). The interaction between hydrogen and another electronegative atom is much weaker and mostly electrostatic in nature; it is a nonbonding interaction (H 3 3 3B). This system is often designated as AH 3 3 3B where the B-center (acceptor of proton) should possess at least one lone electron pair; A-H is called the protondonating bond. Pauling stated that sometimes the H 3 3 3B interaction possesses characteristics of the covalent bond. The [FHF] ion is an example where the proton is inserted between two negative fluorine ions, accurately in the middle of the F 3 3 3 F distance. Hence, both H 3 3 3 F interactions are equivalent. This is in line with an early conclusion of Lewis that “an atom of hydrogen may at times be attached to two electron pairs of two different atoms” and with the statement of Latimer and Rodebush that “the hydrogen nucleus held by two octets constitutes a weak bond”. The latter statements correspond to recent studies on proton bound homodimers, that is, systems where the proton is inserted between two closed-shell moieties and where it often interacts equivalently with both of them. Chan and co-workers analyzed recently what factors determine whether the protonbound homodimer has a symmetric or an asymmetric hydrogen bond. In the other study, it is discussed what conditions should be fulfilled for the proton situated accurately in the midpoint of the donor-acceptor distance. The high level calculations up to CCSD(T)/6-311þþ(3df,3pd)//CCSD/6-311þþ(3df,3pd) were performed on the [FHF] ion and systems with O-H 3 3 3O or N-H 3 3 3N hydrogen bonds. The latter study is supported by the experimental X-ray and neutron diffraction data because there are numerous crystal structures with short O-H 3 3 3O hydrogen bonds and the proton situated in the central position or nearly so. Also recently, homogeneous and heterogeneous short and strong hydrogen bonds (SSHBs) as well as the proton bound homodimers were analyzed theoretically at MP2/aug-ccpVDZ þ diffuse(2s,2p) level. Among various topics, the matter was raised if hydrogen bonding is an electrostatic or covalent interaction. The following question arises: what does the covalency of hydrogen bonding mean? The decomposition of the interaction energy is useful to analyze hydrogen bonding and particularly to answer the latter question. One of the first decomposition schemes introduced is one of Morokuma and Kitaura, where the interaction energy is calculated within the Hartree-Fock one-electron approximation and it is decomposed into the following components: the exchange energy, EEX (arising from repulsive forces), and the other components, which might be a result of attractive forces: the polarization energy, EPL, the charge transfer energy, ECT, and the electrostatic energy, EES. If a method is applied where the correlation of electrons is taken into account, then the correlation energy may be included. One of the most important attractive components of the correlation energy is the dispersive energy. Different H-bonded systems were analyzed early by Umeyama and Morokuma who stated that: “The energy components are strongly distance dependent. At a relatively small separation, ES, CT, and PL can all be important attractive components, competing against a large EX repulsion. At larger distances for the same complex the short-range attractions CT and PL are usually unimportant and ES is the only important attraction.” One can see that the “covalency of interaction”may be connected with short H 3 3 3B distances where terms other than the electrostatic attractive one are important.

What is the covalency of hydrogen bonding

Low-toxic bismuth-based perovskites are prepared for the possible replacement of lead perovskite in solar cells. The perovskites have a hexagonal crystalline phase and light absorption in the visible region. A power conversion efficiency of over 1% is obtained for a solar cell with Cs3 Bi2 I9 perovskite, and it is concluded that bismuth perovskites have very promising properties for further development in solar cells.

Bismuth Based Hybrid Perovskites A3Bi2 I9 (A: Methylammonium or Cesium) for Solar Cell Application.

Among many various kinds of molecular interactions, the H-bond has a special position. The term is ubiquitous in the world that surrounds us, but also it is often applied in different ways. The H-bond is of great importance in natural sciences. This relates particularly to biological aspects, such as molecular recognition that could be a basis for the creation of life,1-4 formation of higher order structures of peptides and nucleic acids,5 and biochemical processes, particularly the enzymes catalyzed.6,7 One can say that the H-bond plays a double role in biological systems: on one hand, as a relatively strong directional interaction, it leads to relatively stable supramolecular structures, and on the other hand, because of dynamic features of the proton, it is an active site for initiation of chemical reactions. H-bonds are the source of specific properties of associated liquids, with water being the most popular among them.8 Water as a medium in which life was most probably created is saturated by H-bonds with highly mobile protons in between, even in the solid state.9 In many crystal lattices of organic compounds, the H-bonds are a decisive factor governing packing.10 In designing new interesting crystal structures, which is the subject of fast developing crystal engineer* To whom correspondence should be addressed. E-mail: slagra@ uni.lodz.pl or slagra@ccmsi.us. Fax: +48-42-6790447. 3513 Chem. Rev. 2005, 105, 3513−3560

Interrelation between H-bond and Pi-electron delocalization.

A review of the results of studies on the structure, phase transitions and physical properties of alkylammonium halogenoantimonates (III) and bismuthates (III) is presented. The crystals of these compounds are characterized by a variety of anionic structures and show a number of phase transitions including those to polar phases. We concentrate here mainly on dielectric and pyroelectric properties, spontaneous polarization and DSC studies. The mechanism of the phase transitions is discussed based on the results of X-ray, dielectric relaxation, PMR, IR and R spectra studies gathered so far. A particular role is played by a reorientational motion of the alkylammonium cations.

Phase transitions in alkylammonium halogenoantimonates and bismuthates

The crystals of (CH3NH3)3Bi2Br9 have been grown which at room temperature are isomorphous with Cs3Bi2Br9 and (CH3NH3)3Sb2Br9. The space group is P3m1, a = 0.807, c = 1.008 nm, V = 0.5685 nm3, Z = 1. The crystals reveal, when cooling, three phase transitions at 188 ± 0.5, 140 ± 1, and 101.5 ± 0.5 K. The high temperature phase (I) behaves as a plastic one with respect to a freedom of rotation of methylammonium cations. The two high temperature transitions I II and II III can be related, similarly to (CH3NH3)3Sb2Br9, to a freezing of reorientation of those cations. At 101.5 K a transition to the improper ferroelectric phase IV was discovered. The features of this phase are non-typical and the nature of the transition is unknown.

Lucjan Sobczyk

Papers

Interrelation between H-bond and Pi-electron delocalization.

Phase transitions in alkylammonium halogenoantimonates and bismuthates

Structure and phase transition in (CH3NH3)3Bi2Br9. A novel improper ferroelectrics

Proton transfer and correlations between the C-O, O-H, N-H and O⋯N bond lengths in amine phenolates

Dipole Moments of Hydrogen‐Bonded Complexes and Proton‐Transfer Effect