The shapes of protons in hydrogen bonds depend on the bond length.

Hydrogen bonds (HBs) are ubiquitous in nature and play an essential role in such diverse phenomena as biomolecular function, supramolecular recognition, and dissolution of minerals. The constituents of HBs are the proton donor and acceptor “heavy atoms”, such as oxygen or nitrogen, but most importantly the shared hydrogen atom (or proton) inbetween. Hydrogen, being the lightest element in the periodic table, is especially prone to quantum effects such as delocalization due to zero-point motion or tunneling. Such phenomena are no longer issues of purely theoretical interest in view of the growing evidence in biochemistry that so-called low-barrier hydrogen bonds (LBHBs) and even hydrogen tunneling may be crucial ingredients in numerous classes of enzymatic reactions. However, these subtle effects are difficult to study reliably and systematically in ill-defined situations such as are met in biomolecular environments, which are subject to disorder, confinement, and large-amplitude fluctuations. In contrast, crystalline H2O, ice, can be viewed as a realistic but well-defined system that exhibits, upon external compression, shortening of the donor–acceptor distance. This results in a cascade of structural (phase) transitions from molecular forms via a partially ionized regime to a fully dissociated phase, driven by proton tunneling and zero-point motion Using ab initio path integrals, we study essentially the square of the proton’s wavefunction as it varies upon shortening the average HB length. This measure of the protons’ “shape” is a quantity that can be determined directly by neutron Compton scattering experiments. Investigations of quantum effects on proton transfer were among the first nontrivial problems treated in the early days of quantum mechanics and have continued to be an issue of major activity ever since. In particular, it is well known that the potential felt by a proton as it moves between two fixed donor and acceptor heavy atoms, that is, the adiabatic protontransfer potential, is strongly dependent on the HB length. In the simplest example H5O2 + , that is, two water molecules with an excess proton inbetween, it is a symmetric doublewell potential with a high barrier at the center of the HB at large distances. The barrier decreases on shortening the HB before it vanishes below a critical distance. Thereby, the double-well potential is transformed into a single-well potential with the minimum right at the center of the HB. When quantum effects are taken into account, the proton can tunnel between the two equivalent minima, and this results in maximum proton densities close to the minima. However, if the barrier is sufficiently small, zero-point motion leads to a situation in which the adiabatic potential is still of double-well type, whereas the proton’s wavefunction is centered at the bond midpoint, which corresponds to a single-well “effective potential” (or potential of mean force). In this so-called LBHB regime, small changes in bond length can dramatically increase or decrease the localization properties of the proton within the HB. Interestingly, both tunneling and LBHB phenomena are currently discussed as being “utilized” in biomolecular machines such as enzymes. Here we investigate how changes in the donor–acceptor distance, or correspondingly in the HB length, affect the realspace shape of protons in HBs, or more precisely the diagonal part of the nuclear density matrix in three-dimensional space in the vicinity of the proton sites; note that this is related to the “atomic thermal motion parameters” or “Debye–Waller factors” if anisotropy is fully taken into account. In general such quantum effects are “exponential” in the sense that small changes in parameters can have dramatic consequences. This implies that biomolecular environments are somewhat ill defined if the aim is a systematic understanding of the basic phenomenon. A minimalistic model that is still complex and realistic enough to capture the essentials of these phenomena is ice at low temperatures. It is known that hydrostatic pressure results in shortening of the oxygen–oxygen distance dOO, which induces a cascade of phase transformations on converting the effective proton-transfer potential from the double-well to the single-well regime. 12–14] To study how the HBs change during this process, both thermal and quantum fluctuations of all degrees of freedom are taken into account by using the ab initio path integral technique, a fully quantum-mechanical extension of Car–Parrinello molecular dynamics; note that the “heavy atoms” should also be treated quantum-mechanically in view of previous findings. These simulations were performed with the CPMD code on ice samples consisting of 16 water molecules subject to periodic boundary conditions at a constant temperature of 25 K and thirteen different densities spanning HB lengths from dOO 2.85 to 2.17 @. The path integrals were discretized in imaginary time by using P=64 replicas, and the reported quantities were computed from trajectories of 10000–30000 steps depending on the regime; further technical details can be found in refs. [12–14]. A first pictorial impression can be gleaned from Figure 1. In the molecular regime (a) characterized by rather long HBs (dOO=2.85 @), each proton remains bonded to a given oxygen site and assumes a disklike shape with the short axis oriented along the HB axis. This regime of ice corresponds to “normal HBs”, Oa H···Ob, such as those encountered, for instance, in liquid water or molecular ices having a unimodal proton density distribution function P(d) along the proton-transfer coordinate d=ROaH RObH; note that d=0 for centered HBs. The [a] Dr. M. Benoit Centre d’Elaboration de Mat riaux et d’Etudes Structurales 29 rue Jeanne Marvig, BP 94347, 31055 Toulouse Cedex 4 (France) Fax: (+33)562-257-999 E-mail : mbenoit@cemes.fr [b] Prof. Dr. D. Marx Lehrstuhl f1r Theoretische Chemie, Ruhr-Universit3t Bochum 44780 Bochum (Germany)