Analysis of Hydrogen Bonding in the OH Stretch Region of Protonated Water Clusters Laura C. Dzugan and Anne B. McCoy June 26, 2015

Chemical and biological systems Scientists would like to understand the dynamics of this highly mobile proton Zundel and Eigen Numerous theoretical and experimental studies M.A. Duncan, M.A. Johnson, K. Asmis, M. Okumura, K.D. Jordan, N. Agmon, G.A. Voth, etc. Protonated Water Clusters 1000 cm – cm –1

Experimental Spectra of H + (H 2 O) 3 and H + (H 2 O) 4 Johnson, M.A., Wolke, C.T., Fournier, J.A. Narrow peaks due to free OH stretches Broad, red-shifted peaks due to OH stretches involved in strong H- bonding This broad region is seen in other strongly H-bonded systems, such as CaOH + (H 2 O) 4 Intensity Photon Energy, cm –1

Harmonic – black Experiment – red Previous Study of CaOH + (H 2 O) 4 Johnson, C. J.; Dzugan, L. C.;…; McCoy, A. B.; Johnson, M. A. J. Phys. Chem. A 2014, 118, 7590.

Harmonic – black Experiment – red Calculations on CaOH + (H 2 O) 4 Similar geometries and energies Peaks are similar in the 3600 cm –1 to 3800 cm –1 region Other peaks are different by hundreds of cm –1 65 cm -1 0 cm cm cm -1 Johnson, C. J.; Dzugan, L. C.;…; McCoy, A. B.; Johnson, M. A. J. Phys. Chem. A 2014, 118, 7590.

Broadening was thought to be caused by coupling between the low frequency modes to the OH vibrational modes Developed a theoretical method to model this coupling by only focusing on the optimization of the high frequency modes Defined normal modes in internal coordinates because we do a partial optimization in internal coordinates Previous Study of CaOH + (H 2 O) 4 Johnson, C. J.; Dzugan, L. C.;…; McCoy, A. B.; Johnson, M. A. J. Phys. Chem. A 2014, 118, Experiment Scaled Harmonic Can we use the same method to model the broadening observed in H + (H 2 O) 3 and H + (H 2 O) 4 ? Can we determine the physics behind the broadening?

O-O-O angle |X(R)| 2 Procedure 1.Calculate the harmonic oscillator probability amplitude 2.Model low frequency modes Ψ(q w,R) = Φ(q w ;R)Χ(R), where q w are the OH stretch modes and the intramolecular HOH bends Randomly sample geometries from |X(R)| 2 using Monte Carlo sampling 3.Optimize geometries in OH stretch modes and the intramolecular HOH bends 4.Calculate the harmonic frequencies and intensities 5.Construct spectrum as sum of spectra for sampled geometries

Harmonic Spectra for H + (H 2 O) 3 & H + (H 2 O) 4 Method works for protonated water clusters, but could use modification Compare to electronic structure theory calculations done in normal modes based on Cartesian coordinates Can we extend our method through 2 nd order perturbation theory in internal coordinates? Intensity Photon Energy (cm –1 ) Experiment Scaled Harmonic VPT2 Calculation Level of theory/basis: MP2/aug-cc-pVDZ Intensity Photon Energy (cm –1 )

2 nd Order Perturbation Theory Harmonic approximation: Real molecules are not harmonic 2 nd order perturbation theory for internal coordinates rere r V(r) rere r rere Zero-order energy: 1 st order correction to the energy: 2 nd order correction to the energy : Can calculate transition energy for a vibration: E 1 – E 0 n=0 n=1 n=2

Determination of Hamiltonian Hamiltonian in internal coordinates: Need H 0, H 1, and H 2 for 2 nd order perturbation theory Taylor series expansion on H H1H1 H2H2 H1H1 H2H2 0 equil. H0H0 H0H0

Intensity Calculations With the 2 nd order frequencies and intensities determined, the anharmonic spectra for the protonated water clusters can be determined Expand the dipole in a Taylor series McCoy, A.B.; Sibert, E.L. J. Chem. Phys. 1991, 95, µ1µ1 µ2µ2 µ0µ0

2 nd Order Perturbation Theory Results More red-shifted than harmonic Shape is similar to harmonic Not noticeably “better” than harmonic Experiment Scaled Harmonic Anharmonic Intensity Photon Energy (cm –1 ) Intensity Photon Energy (cm –1 )

Anharmonicities Experiment VPT2 calculation Anharmonic calculation of all modes Anharmonic calculation of only HOH bends/OH stretches Fermi resonance causes shift from VPT2 calculation compared to anharmonic calculations Decoupling of the low frequency modes from the high frequency modes causes shift between our two anharmonic calculations There is coupling between the lower frequency and high frequency modes our model does not take into account - yet 1 1 Intensity Photon Energy (cm –1 )

Anharmonicities Experiment VPT2 calculation Anharmonic calculation of all modes Anharmonic calculation of only HOH bends/OH stretches Resonances causes slight shift from VPT2 calculation compared to anharmonic calculations Decoupling of the low frequency modes from the high frequency modes causes shift and split between our two anharmonic calculations There is coupling between the lower frequency and high frequency modes our model does not take into account – yet Can still investigate the cause of the broadening Intensity Photon Energy (cm –1 )

Correlations Can see correlations with H-bonded OH stretches w1 OH w2 OH Frequency (cm –1 ) r (Å) Lowest OH stretch frequency w1 w Frequency (cm –1 ) r (Å) 2nd lowest OH stretch frequency w1 OH w2 OH

Correlations w1 OH w2 OH w3 OH Frequency (cm –1 ) r (Å) Low OH stretch frequency w1 OH w2 OH w3 OH Frequency (cm –1 ) r (Å) Middle OH stretch frequency w1 OH w2 OH w3 OH Frequency (cm –1 ) r (Å) High OH stretch frequency w2 w1 w3

Conclusions Method works well in modeling the coupling between the low frequency modes and high frequency modes Harmonic is not accurate enough for protonated water clusters Extend through 2 nd order perturbation theory 2 nd order perturbation theory is more red-shifted, but shape of curve is the same Strongest correlation for the cause of the broadening is seen in the OH bond distances Future Work Higher order terms in the intensities Determine which other modes should be included in the reduced dimensional Hamiltonian

Acknowledgements Johnson Lab: Mark A. Johnson Joseph A. Fournier Conrad T. Wolke Back row: Bernice Opoku-Agyeman, Melanie Marlett, Zhou Lin, Laura Dzugan Front row: Jason Ford, Scott Garner, Anne B. McCoy, Meng Huang