1. 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.

3. 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.

4. 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.

5. Water dimer, H2O•H2O CCSD(T)/aug-cc-pV5Z optimized geometry H donor
CCSD(T)/CBS
ROO = Å
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.

6. 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.

7. HCAO model for donor unit
Dipole moment function

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

9. 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

10. Equilibrium constants
Region
(cm-1)
Keq (atm-1)
VPT2
HCAO
4.77 × 10-2
5.41 × 10-2
1.61 × 10-2
1.10 × 10-2
3.19 × 10-2
3.26 × 10-2
4.38 × 10-2
4.72 × 10-2
Comparison of calculated (HCAO and VPT2) and observed vapor phase intensities in different regions cm-1 lead to Keq in the range to atm-1 at 298K

11. 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

13. 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.

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

15. Larger diols
Propanediol, and Butanediol have similar structures to Ethylene Glycol. EG
QCISD/ 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.

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

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

18. 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

19. 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

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

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

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

23. 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

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Garden unpublished

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Garden unpublished

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

27. 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.

29. 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

31. Copenhagen by night

32. 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