Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bonds

Hydrogen bonds are of outstanding importance for many processes in Chemistry, Biology, and Physics. From the theoretical perspective the small mass of the proton in a hydrogen bond makes it the primary quantum nucleus and the phenomena one expects to surface in a particular clear way are, for instance, zero-point energy effects, quantum tunneling, or coherent wave packet dynamics. While this is well established in the limit of one-dimensional motion, the details of the multidimensional aspects of the dynamics of hydrogen bonds are just becoming accessible to experiments and numerical simulations. In this review we discuss the theoretical treatment of multidimensional quantum dynamics of hydrogen-bonded systems in the context of infrared spectroscopy. Here, the multidimensionality is reflected in the complex shape of linear infrared absorption spectra which is related to combination transitions and resonances, but also to mode-selective tunneling splittings. The dynamics underlying these spectra can be unravelled by means of time-resolved nonlinear infrared spectroscopy. As a fundamental theoretical ingredient we outline the generation of potential energy surfaces for gas and condensed phase nonreactive and reactive systems. For nonreactive anharmonic vibrational dynamics in the vicinity of a minimum geometry, expansions in terms of normal mode coordinates often provide a reasonable description. For reactive dynamics one can resort to reaction surface ideas, that is, a combination of large amplitude motion of the reactive coordinates and orthogonal harmonic motion of the remaining coordinates. For isolated systems, dynamics and spectroscopy follow from the time-dependent Schrodinger equation. Here, the multiconfiguration time-dependent Hartree method is shown to allow for describing the correlated dynamics of many degrees of freedom. Classical trajectory based methods are also discussed as an alternative to quantum dynamics. Their merits and shortcomings are scrutinized in the context of incorporating tunneling effects in the calculation of spectra. For the condensed phase, reduced density operator based approaches such as the quantum master equation are introduced to properly account for the energy and phase relaxation processes due to the interaction of the hydrogen bond with its surroundings. (c) 2006 Published by Elsevier B.V.