“Protonated water clusters – where is the proton

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					“Protonated water clusters – where is the proton?”
Kenneth D. Jordan
Department of Chemistry
and Center for Materials and Molecular Simulations

University of Pittsburgh

Support National Science Foundation

Department of Energy Co-workers
R. A. Christie, J. Cui - Univ. of Pittsburgh M. A. Johnson, J. -W. Shin, N. I. Hammer, E. G. Diken - Yale M. A. Duncan, R. S. Walters, T. D. Jaeger - Univ. of Georgia Computational resources Maui High Performance Computing Center

Pittsburgh Supercomputer Center


The importance of interstitial water in determining protein structure Proton transfer is a fundamental process in biological systems
Proton transfer in aqueous solution

Protonated water clusters; structures and vibrational spectra Insight into a magic number protonated water cluster; H+(H2O)21

The importance of interstitial water in determining protein structure
water comprises 70% by weight of cells the presence of water dictates the structure (and function) of proteins water is present both on the exterior of the protein and in internal protein cavities example: water molecules (blue spheres) inside an internal cavity of the lipid binding protein I-FABP

“Protein function mediated by water molecules”, http://www.fkem2.lth.se/research/areas/projects/function_water/

Long-lived water clusters are found in biomolecular, organic and inorganic environments

e.g. (H2O)8 in an organic host crystal

D. R. Alfonso, K. Karapetian, D. Sorescu, and K. D. Jordan, J. Phys. Chem. B, 108, 34313436 (2004).

Water present in protein cavities can differ appreciably from water in “bulk” solution
specifically, water at the interface may be less polarized than water in the bulk this, in turn, impacts the water-protein interaction

Models of water designed for the bulk may not be reliable for describing water at interfaces

Proton transfer in biological systems; systems: a case example Rhodobacter sphaeroides - Rhodobacter sphaeroides

purple photosynthetic bacteria; absorption of photon drives ATP synthesis via proton transfer events the mechanism of photosynthesis in Rhodobacter sphaeroides can be explained in a four-step mechanism

Reaction center of Rhodobacter sphaeroides

The proton-accepting quinone molecules

H+ transfer pathways

mediated by hydrogen bonded water cluster (shown as red spheres)

M. L. Paddock, G. Feher, M. Y. Okumura, FEBS Letters, 555, 45 (2003)

Proton transfer in aqueous solution
The proton in solution has an anomolously high mobility H+ mobility 36 x 10-8 m2s-1V-1 at T = 298 K Li+ mobility 4 x 10-8 m2s-1V-1 The high mobility is due to proton “hopping” rather than H+ ion diffusion

Grotthuss mechanism for proton transfer
(C. von Grotthuss, Ann. Chim. LVII, 54 (1806))

Simulation of H+ in “bulk” water using OSS41 model potential

Animation reproduced with permission from L. Ojamäe from http://www.ifm.liu.se/compchem/former/htransf.html
1. L. Ojamäe, I. Shavitt and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)

Protonated water clusters; structures and vibrational spectra
H3O+ vs


Eigen structure
OH bond strength in H3O+ ≈ 260 kcal/mol given the strong OH bonds in H3O+, why is the proton so mobile?

Zundel structure

involvement of Zundel species in proton transfer

The key species for proton transfer: H5O2+ (Zundel cation)


proton transfer barrier free for R(OO) ≤ 2.50 Å

accounts for Grotthuss mechanism and high H+ mobility



1. Y. Xie, R. B. Remington, H. F. Schaefer III, J. Chem. Phys., 101, 4878 (1994)

Is the proton in larger clusters and bulk water Eigen-like, Zundel-like or both?

Eigen structure proton relatively localized on H3O+ barrier to proton transfer

Zundel structure
proton delocalized over 2 H2O

no barrier to proton transfer

ab initio simulations (Tuckerman et al.1) reveal that both species are present in bulk water
1. M.Tuckerman, K. Laasonen, M. Sprik, M. Parinello, J. Chem. Phys. 103, 150 (1995)

Spectroscopic studies of H+(H2O)n, n=2-8 water clusters Prof. M. A. Duncan, University of Georgia vibrational predissociation Infrared (IR) spectroscopy hv Ar•H+(H2O)n

H+(H2O)n + Ar

temperature of clusters is T ≈ 100-200 K

Experimental vibrational spectra
H (H 2 O ) n A r
n=8 n=7 n=6 n=5 n=4 n=3 n=2 *

free OH
* bad parent signal

Eigen H-stretch










Calculated (DFT, harmonic approx.) vibrational spectra

Structural assignment of H+(H2O)n, n=2-8 spectra H+(H2O)



Zundel species

(with Argon) Eigen species

Eigen species

starting configurations from Wales' Cambridge Cluster database1 and Monte Carlo simulations employing a model potential
1. http://www-wales.ch.cam.ac.uk/CCD.html




Eigen species

Zundel species Zundel species

spectra of n=5,6,8 clusters; so not arise from global minimum structures species with “dangling” H2O molecules favored by vibrational ZPE and by finite temperature effects (entropy!)

Insight into the magic number H+(H2O)21 cluster
mass spectrum of H+(H2O)n clusters

recorded by M. A. Johnson (Yale) and M. A. Duncan (Georgia)

History of H+(H2O)21 magic number problem

Lin1 (1973) first observed the hight intensity of the n=21 cluster mass spectroscopically and ascribed it to contamination
Searcy and Fenn2 (1974) also observed this feature and concluded that is was an inherent feature of the n=21 cluster proposed a dodecahedral structure with a H2O inside the cage Castleman group3 used a novel “titration” method for counting the free-OH groups concluded that the structure of H+(H2O)21 was based upon a water dodecahedron with the H3O+ inside the cage

1. S. -S. Lin, Rev. Sci. Instrum. 44, 516-517 (1973) 2. J. Q. Searcy, J. B. Fenn, J. Chem. Phys., 61, 5282-5288 (1974) 3. S. Wei, Z. Shi, A. W. Castleman, Jr., J. Chem. Phys. 94, 3268 (1991).

Main motivation for assignment of H+(H2O)21 as a water dodecahedra anticipated analogy with gas hydrates (clathrates) Clathrates are an abundant source of methane in sediment deposits in the sea-bed

methane molecule (green) inside water (H2O)20 dodecahedron

Castleman's hypothesis: H+(H2O)21 - analogous structure, but with H3O+ inside

Is the proton located inside the dodecahedral cage? New experiments

IR vibrational spectra have recently been obtained for H+(H2O)n, n=6-27
carried out by M. A. Duncan (Univ. of Georgia) and M. A. Johnson (Yale)1 New theoretical studies (our group)1 DFT and MP2 ab initio calculations of low energy local minima and vibrational spectra

1. “J. -W. Shin, N. I. Hammer, E. G. Diken, M. A. Johnson, R. S. Walters, T. D. Jaeger, M. A. Duncan, R. A. Christie, K. D. Jordan, Science Express, 29th April 2004, DOI: 10.1126/science.1096466

vibrational spectra of H+(H2O)n, n = 6-27

free-OH region of spectra reflect structural transitions at n = 12 and n = 21

The free-OH region of the IR spectrum of H+(H2O)n, n = 6-12

four different types of free-OH peaks a, b, c and d for n=6, 8, 10

a, d – due to “dangling” waters
b, c – due to water molecules donating an H-atom to the H-bonding network

for n=12 only peaks, b and c remain

example: H+(H2O)8

a and d are the asymmetric and symmetric free-OH stretches of acceptor-only (type A) H2O molecules




AD A b is free-OH stretch of an acceptor-acceptor-donor (type AAD) H2O

c is free-OH stretch of an acceptor-donor (type AD) H2O

Structural transitions of the smaller water clusters

the dominant clusters, up through n = 11 have a chain-terminating A-type H2O molecule
these are not necessarily the global (Eel) minimum. Vibrational zero-point energy and finite-temperature effects (entropy) reorder structures

n ≥ 12: no A-type H2O molecules present [other than (possibly) in minor population isomers)
implies “fused-ring” structures

Structural transition at n = 21 at n = 21 and n = 22, there is only one free-OH peak peak is of type b, i.e., AAD

this implies a cage structure

Lowest-energy n=21 structure found in ab initio optimizations dodecahedron with H3O+ on surface (blue) and H2O (purple) inside cage
Note: 4 H-bonds with interior H2O this causes a rearrangment of the H-bonding in the dodecahedron there are only 9 free-OH groups (Castleman's experiments suggest 10) all free-OH associated with AAD waters

Comparison of n = 20 and n = 21 clusters

n = 20

n = 21


theoretical (expt. Duncan group)
(expt. Johnson group)



free-OH spectra

low T

high T

Comparison of experimental and calculated spectra for H+(H2O)21

theory – very intense lines due to H3O+ not seen experimentally

Unanswered questions clusters near n=21 have T=100-200 K ? internal energies estimated to be ≈ 1.5 eV why does the global minimum structure (apparently) dominate? why is there no evidence of H3O+ H-bond stretching modes in the experimental spectra ?

is this a consequence of the “action” spectroscopy employed? could it be that the actual structures are Zundel-like rather than Eigen-like, or that there is rapid Eigen-Zundel conversion?
could anharmonicities shift the H3O+ OH stretch modes below 2000 cm-1? New theoretical studies are planned to address these issues

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