Proton transfer is of vital importance in many chemical and biological systems and processes.1 The conduction of protons plays a central role in the function of many devices, including polymer electrolyte membrane (PEM) fuel cells.2 Recently, the ability of fuel cells to generate electric power with no greenhouse gas emissions and at high efficiency has generated tremendous interest from various research and industrial communities. The search for novel high-performance electrolytes suitable for low- and intermediate-temperature operation where no exte al humidification is required has spurred efforts including synthesis and characterization of a wide range of materials suitable as the separator. The development of new materials requires a fundamental understanding of the protonconduction process at the atomic level, and an Edisonian approach for synthesizing new membrane materials is insufficient. 3 Proton transfer involves bond-breaking and -forming processes and the transfer of H+ between two entities accompanied by a local redistribution of electron density.4 Despite the diversity of proton-conducting electrolyte materials,5,6 the protonic defects in these materials are solvated by very few species,7 water, oxide ions, heterocycles, and oxo acids and anions. These species are typically responsible for the intrinsic generation of charge carriers, but a molecular description of the mechanism of proton transfer has only been secured for an excess proton in water.8 A complete understanding of the solvation structure and dynamics of an excess proton in water, however, remains elusive.9 It is widely recognized that hydrogen bonding is a key feature in all systems exhibiting proton transport. Of relevance for understanding proton conduction in PEMs is the consideration of ingredients that encompass complexity, connectivity, and cooperativity.10,11 Investigation of hydrogen bonding from structural as well as dynamical aspects is warranted in order to understand the phenomena at a molecular level. There are few experimental techniques capable of probing the effects accompanying the hydrogen-bond formation or breaking at this scale, and therefore, various simulation methods have been utilized for describing these processes. Proton mobility in liquid water surpasses the hydrodynamic limit by a factor of more than 4.5 and is approximately five times higher than that of Li+ in water.12 The first hypothesis in trying to explain this behavior comes with a picture of highly correlated charge-transfer events along the hydrogen-bonded chains, also known as structure diffusion or Grotthuss hopping.13 However, a process involving only proton-transfer events between water molecules along the chains leads to a local polarization of the network and no net conduction. Thus, a successive reorientation of the molecules in the outer hydration shell is necessary in order to depolarize the network and yield a new configuration permitting the next proton-transfer event. The first mechanistic picture for the overall excess protontransfer mechanism in water was determined from NMR data interpreted by Agmon4 and confirmed by Tuckerman et al.14,15 with Car-Parrinello ab initio molecular dynamics (AIMD) simulations.16 The region containing the excess proton corresponds to either a hydrated hydronium ion (i.e., H9O4 + or Eigen cation17,18) or a dimeric form sharing the excess charge between two water molecules (i.e., a H5O2 + or Zundel cation19). The proton-transfer mechanism in water proceeds via a series of structural rearrangements between these patte s; in this manner, an Eigen ion is transformed into a Zundel ion, which itself is converted to an Eigen ion (i.e., EZE mechanism8). The main qualitative features complemented with some significant quantitative corrections of the above-described mechanism were later * To whom correspondence should be addressed. E-mail: spaddison@ utk.edu. † Max-Planck-Institut fu¨r Festko¨rperforschung. ‡ University of Tennessee. J. Phys. Chem. A XXXX, xxx, 000 A 10.1021/jp903005r CCC: $40.75 XXXX American Chemical Society Downloaded by AUSTRIA CONSORTIA on July 6, 2009 Published on July 1, 2009 on http://pubs.acs.org | doi: 10.1021/jp903005r confirmed by more sophisticated techniques involving nuclear quantum effects.20-24 The structure of neat liquid phosphoric acid (H3PO4) consists of an extended intermolecular network of hydrogen bonds and exhibits high proton conductivity, making it of particular interest for use in fuel cells. Phosphoric acid fuel cells (PAFCs), in contrast to PEM fuel cells, use phosphoric acid (instead of a solid polymer) as the electrolyte, do not require water for operation, and operate at higher temperature (150-200 °C). Although PAFCs dominate the stationary fuel cell market, there are some serious drawbacks due to low efficiency and a much lower power to size ratio when compared to those for other fuel cells.25 Recently, phosphoric acid has become an important constituent of alte ative proton-conducting membranes, particularly in complexes with basic polymers, such as poly(benzimidazole) for use as the electrolyte in PEM and direct methanol fuel cells.26 Despite the fact that the PBI/PA composite has a very low conductivity (∼2 × 10-3 S/cm), it has extraordinary thermomechanical and chemical stabilities, which are crucial for fuel cell applications.27,28 Drawbacks in these systems indicate the fact that H3PO4 is not strongly bound to the polymer and therefore leaches out by water during fuel cell operation and also that the proton conductivity dramatically decreases with decreasing concentration of PA. The latter is a common feature in both phosphoric and phosphonic acid systems.29 Obviously, proton conduction in phosphoric acid is very sensitive toward perturbations, but it is not clear to what extent these perturbations are the consequences of chemical interaction or just the confinement in the diverse matrixes. Of course, such questions can only be addressed in a meaningful way on the basis of a better understanding of proton dynamics in pure bulk phosphoric acid. The H3PO4 molecule has three proton-donor sites and one proton-acceptor site. As a liquid, it is able not only to solvate the excess charge but also generate the charge carriers through self-dissociation (∼7.4%) along with some condensation, mainly yielding pyrophosphoric acid (H4P2O7).30 The acid has a low diffusion coefficient of phosphate “blocks” but an extremely high proton mobility, which presumably proceeds via proton transfer between phosphate species and is facilitated by structural rearrangement. The contribution of Grotthuss-type hopping is ∼98%, with the remaining 2% coming from hydrodynamic diffusion of charged species.31,32 Greenwood and Thompson33,34 were the first to suggest a mechanism for proton conduction in phosphoric acid by introducing Grotthuss chains and a mechanism where the proton hops between neighboring phosphate species. The observation of almost negligible changes in the mobility with an exchange of H with D suggests that the transfer of the proton between phosphate units occurs with very small barriers, and quantum effects might be excluded from the description of the structural mechanism. Most of the previous simulation work aimed at modeling the structure of liquid and solid states was performed using empirical interatomic potentials, which are unable to describe bond-breaking and -forming processes in such a complex system as phosphoric acid.35 A more recent AIMD study36 was unable to provide insight into the mechanism of proton transfer in this system in part due to the short time of the simulations. The aim of this study is to investigate the hydrogen-bonding and proton-transfer energetics in phosphoric acid clusters with ab initio electronic structure calculations. Clusters of up to six molecules are investigated using density functional theory and a moderate size basis set in order to probe collective effects on the proton-transfer potentials and the critical number of molecules necessary for an effective proton-transfer event. Previous studies of similar scope and employing the same computational protocol performed on phosphonic acid, sulfonic acid, and imidazole systems have proved to yield results which were in good agreement with experimental data.37 The paper is organized as follows; the first section contains a short description of the computational methods used to determine the structures and energetics for all molecular systems. This methods section is followed by a discussion section describing the structures and binding energies for each of the phosphoric acid clusters.
