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used in protein folding and the structures of DNA. H bond is also the path of
H-atom transfer that is one of the most elementary and significant reactions in
synthetic, environmental and biological processes. For instance, H-atom transfer is
essential in biological catalysis because the transportation of H atom into the
correct site and timing can enhance the process in enzyme reactions.
H bond in water is a quite ubiquitous question in nature. The H bond is formed
between an H atom and an electronegative O atom, which provides unique
properties of water [ 1 ], e.g., the relatively high boiling point, the lower density in
solid than that in liquid, and the tendency to form dome-like droplets on solid
surfaces. A water molecule can form four H bonds, thus two donating and two
accepting H atoms. Although water molecules build three-dimensional networks in
the liquid, continuous annihilation/re-creation of H bond and changes of molecular
orientations/distances takes place with the time scale from femtosecond to
picosecond. This flexibility of H bond gives rise to an abundant phase behavior in
the pressure-temperature diagram. The dynamical fluctuation of H bond is also
associated with various chemical and physical processes, e.g., solvation, acid-base
reactions in solution, and freezing processes. For this reason, it has been a long-
standing challenge to elucidate the net structure and dynamics of H bond in liquid
water and numerous experimental [ 2 - 21 ] and theoretical [ 22 - 34 ] efforts have been
devoted in the past. Infrared absorption, Raman scattering, depolarized light scat-
tering, inelastic neutron scattering, and x-ray absorption spectroscopy have been
employed to probe H-bond dynamics indirectly. The vibrational spectroscopies
have been proven to be a powerful tool observing H-bonding nature and dynamics
of water. A water molecule has three fundamental vibrations, i.e., the symmetric
and asymmetric stretching modes at 3657 and 3756 cm -1 , respectively and the
bending mode at 1595 cm -1 [ 34 ]. Especially, it is beneficial to detect the O-H
stretching mode of water molecules because its frequency is quite sensitive to the H-
bonding nature, like the number and relative strengths of H bond. Specifically, the
frequency shows redshift as a water molecule forms H bond due to a weakening of
the covalent OH bond. This weakening results from the substantial charge transfer
from covalent O-H bond to the vicinity of H bond. In addition to the redshift,
a spectral broadening can also arise from several reasons; anharmonic coupling to
low-frequency modes, Fermi resonances with overtone and inhomogeneous
broadening due to different H-bonding geometries [ 35 - 38 ]. Although linear
vibrational spectroscopy provides a direct evidence of H-bonding interaction of
steady states, it is quite difficult to gain insights of its dynamics because such
spectroscopy gives only time-averaged signals. Ultrafast time-resolved vibrational
spectroscopy is a powerful tool to investigate the dynamics of liquid water, which
enables us to probe H-bond dynamics in real-time. Infrared pump-probe spectros-
copy has often used to observe the ultrafast dynamics of the H-bond network of
water [ 39 - 46 ]. However, the experimental data have often interpreted in only
qualitative way. The difficulty to reproduce H-bonding dynamics mainly results
from the complex potential energy landscape as well as a large number of possible
network configurations. Moreover, quantum effects, i.e., tunneling, zero-point
energy, become pronounced due to its small mass of H-atom, making it further
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