Calculated Band Widths of Water Dimer Transitions CAVIAR, The Cosener’s House, December 15, 2009 Henrik G. Kjaergaard Department of Chemistry, University of Copenhagen, Copenhagen, Denmark.

Solar flux at Earth’s surface Visible NIR IR O3 Electronic transitions O2 H2O, v=3 Vibrational transitions H2O H2O, v=2 H2O Calculated clear sky direct solar flux at Earth’s surface from known absorbers in the atmosphere.

Complexes in the Atmosphere O2•O2 and O2•N2 complexes have been shown to absorb about 1 W/m2 of incoming solar radiation. Solomon, Portmann, Sanders, Daniel, JGR 1998. Hydrated complexes, H2O•X, are likely to contribute. H2O•H2O H2O•O2 H2O•N2 Contribution depends on position, intensity and shape of spectroscopic transitions as well as atmospheric abundance. Nature, 1969. Vaida, Daniel, Kjaergaard, Goss, Tuck, QJRMS 2001.

Water dimer, H2O•H2O CCSD(T)/aug-cc-pV5Z optimized geometry H donor CCSD(T)/CBS ROO = 2.9125Å 0.965Å 0.958Å +anharm corr ROO = 2.97Å 0.960Å Water monomer, ROH = 0.959Å Expt. (Dyke) ROO = 2.976Å H donor H acceptor OH bond involved in hydrogen bonding is significantly longer  frequency red shift Lane, Kjaergaard, JCP 2009.

Water dimer, H2O•H2O Simple vibrational model for water dimer Each H2O unit is modeled by two OH-stretching and one HOH-bending local mode oscillator. We use the Harmonically Coupled Anharmonic Oscillators (HCAO) local mode model for each of the H2O units. Determine local mode parameters and dipole moment functions from ab initio calculations. Low, Kjaergaard, JCP 1999. Schofield, Kjaergaard, PCCP 2003.

HCAO model for donor unit Dipole moment function

Stretch fundamental region Long path length 351K with water monomer abs subtracted. Paynter, Ptashnik, Shine, Smith, GRL 2007 Schofield, Kjaergaard, PCCP 2003

Band frequencies (cm-1) Water dimer, far-IR Matrix isolation experiment versus anharmonic calculation Mode Band frequencies (cm-1) Ne-matrix p-H2-matrix VPT2 (calc) 7 522.4 485 495 8 309.1 299.1 304 9 173 145.9 144 10 151 121.2 122 11 122.2 121 12 75.7 85 Ceponkus et al, JPCA 2008 Kjaergaard et al, JPCA 2008

Equilibrium constants Region (cm-1) Keq (atm-1) VPT2 HCAO 1200-2000 4.77 × 10-2 5.41 × 10-2 3000-4000 1.61 × 10-2 1.10 × 10-2 5000-5600 3.19 × 10-2 3.26 × 10-2 6800-7500 4.38 × 10-2 4.72 × 10-2 Comparison of calculated (HCAO and VPT2) and observed vapor phase intensities in different regions 1200-7500 cm-1 lead to Keq in the range 0.011 to 0.054 atm-1 at 298K

Water dimer in the atmosphere DvOH = 3½ DvOH = 4 H2O•H2O (calc) H2O (observed) Water dimer conc. depends on water conc. squared! 11500 13100 14750 wavenumber (cm-1) Schofield, Kjaergaard, PCCP 2003

Ethylene Glycol Different conformers present at room temperature and seen in the overtone spectra. Hydrogen bonding (~58%) (~26%) (~10%) Small molecule, so high level ab initio calculations are possible: CCSD(T)/aug’-cc-pVTZ. Howard, Jørgensen, Kjaergaard, JACS 05.

Ethylene Glycol 1f 1b 2f 2b Higher overtones better but also more difficult!

Larger diols Propanediol, and Butanediol have similar structures to Ethylene Glycol. EG QCISD/6-311++G(2d,2p) calculations show stronger hydrogen bonding from EG - PD - BD. Larger frequency red shifts PD BD AO local mode calculation indicate similar intensities of bonded and free OH modes. Howard and Kjaergaard, JPC A 06.

OH-stretching in diols V=3 V=4 What happens to the hydrogen bonded OH-stretching vibrations?

Hydrated complexes Vibrational band profile important for detection and effect. Kjaergaard, Robinson, Howard, Daniel, Headrick, Vaida, JPCA 2003

Water dimer, band profile Vibrational band profile important for detection and effect. Rotational profiles depend on direction of TDM Hf Hb Garden, Halonen, Kjaergaard, JPCA 2008

Water dimer, band profile Effect of coupling to low frequency modes? Third CH-stretch overtone, p-xylene. 10800 11000 11200 Adiabatic separation of methyl torsion and CH-stretching has explained CH-stretching overtone spectra in toluenes and xylenes. We can separate adiabatically, the fast OH-stretching motion from the slow intra-molecular motion. Rong, Kjaergaard, JPCA 2002

OO-stretch coupling Use variation in OH-stretch mode with OO displacement to construct effective OO-stretch potential Garden, Halonen, Kjaergaard, JPCA 2008

OO-stretch coupling Shift in position of minimum. Both in s and E. Little change for OHf. Garden, Halonen, Kjaergaard, JPCA 2008

OO-stretch coupling <0|0> <1|0> Garden, Halonen, Kjaergaard, JPCA 2008

OO-stretch coupling Direction of TDM changed. Hf Direction of TDM changed. Hb OHb-stretching transition is wide, OHf-stretch is not. Garden, Halonen, Kjaergaard, JPCA 2008

Accepter wag coupling Separate adiabatically, the fast OH-stretching motion from the slow acceptor wag motion. Garden unpublished

Accepter wag coupling Similar spreading of intensity. Closer to 1D transition. Double well changes order. <0|0> <1|0> Garden unpublished

Water dimer, band profile Combining OH-stretch + OO-stretch + Acceptor wag Four more intermolecular modes! Garden, unpublished

Conclusion The local mode model gives a good description of the dominant OH-stretching overtone transitions. We can calculate quite accurate absolute overtone intensities ab initio for species that have not been observed. Guide experimental efforts to observe these species. Provide input for atmospheric impact studies. Water dimer band profile/width of OHb stretching transitions is very wide - making observation elusive - but increases impact on solar radiative transfer.

Acknowledgements Bryan R. Henry, Guelph Geoffrey R. Low Timothy W. Robinson Daniel P. Schofield Joseph R. Lane Anna L. Garden Daryl Howard Ben Miller Bryan R. Henry, Guelph Veronica Vaida, Boulder Poul Jørgensen, Aarhus Lauri Halonen, Helsinki John Stanton, Austin Benny Gerber, Irvine Keith Shine, Reading Igor Ptasnik, Reading John S. Daniel, NOAA MARSDEN FUND

Copenhagen by night

Continuum Optical depth of self continuum (H2O only) compared to that calculated for water dimer (K = 0.01 to 0.12 atm-1). Daniel, Solomon, Kjaergaard, Schofield, GRL 2004