Magic Numbers in Large Hydrated Alkali Metal Clusters: K + and Cs + Matthew L. Ackerman, Jason D. Rodriguez, Dorothy J. Miller, and James M. Lisy University of Illinois at Urbana-Champaign

K + (H 2 O) n Mass Spectrum n = 20

K + (H 2 O) n IRPD Spectra DA DAA

K + (H 2 O) n IRPD Spectra

Lorentzian Fits

Cs + (H 2 O) n Mass Spectrum n = 20

Cs + (H 2 O) n IRPD Spectra DAA

Cs + (H 2 O) n IRPD Spectra

Lorentzian Fits

Conclusions There are no IR signatures of the magic number observed in the mass spectrum; only AAD bands arise in the magic number region for K + and Cs + No observed relationship between appearance/ disappearance of AD bands and increased/ decreased intensity in mass spec n = 20 n = 21 DAA DA

Multi-photon Absorption in Cs + (H 2 O) n clusters Dip in intensity when monitoring loss of 1 water For n = 22, loss of 2 waters has a higher cross section than loss of 1 water Significant dissociation when monitoring loss of 3 or more waters Multi-photon absorption! n = 16 n = 22

Mechanism of Multi-photon Absorption The OH stretch potential energy curve is sufficiently anharmonic that a single oscillator cannot absorb more than one photon However, the free OH oscillators in the cluster are highly uncoupled  Each one can absorb a photon There are generally uneven numbers of DA and DAA waters in a given cluster, so it is critical to understand these processes when analyzing the action spectra of these clusters 8 DAA Water 1 DA Water K + (H 2 O) 17 Calculated Global Minimum Structure Schulz, F. and Hartke, B Theor Chem ACC, 114 (2005)

Poisson Statistics I = I o e -  F ~ I o (1-  F) (I/I o ) = 1-  F  F = 1-(I/I o ) = Depletion of Parent Cluster Poisson Distribution – P(x) = (h) x e -h /(x!)  P(x) = (  F) x e -  F /(x!)

Experimental Data Preliminary data shows that experimental values track closely with Poisson probabilities As n increases, one photon absorption leads to loss of more than one water

Difference between Free and H-Bonded OH Stretches Drop in relative cross section in hydrogen bonded region Free OH Bands Scaled

Internal Energy Distribution of Cs + (H 2 O) 22 FWHM decreases going from 1 water loss to 6 water loss We can now probe the coldest part of the cluster distribution

Conclusions and Future Work We observed Cs + (H 2 O) n clusters undergo multi-photon absorption Each free OH oscillator can absorb only one photon, but more than one oscillator can be excited Poisson statistics correctly predict the probability of multi-photon absorption As more waters are lost, the colder part of the internal energy distribution is sampled The branching ratio between one and two water loss subsequent to 1  absorption needs to be characterized Previously collected spectra need to reexamined in light of these new multi-photon absorption discoveries

Acknowledgements Lisy Group Members –James Lisy –Dorothy Miller –Jason Rodriguez –Amy Willmarth –Jordan Beck