calculated band widths of water dimer transitions henrik g. kjaergaard department of chemistry,...
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Calculated Band Widths of Water Dimer Transitions
Henrik G. KjaergaardDepartment of Chemistry,
University of Copenhagen,
Copenhagen, Denmark.
CAVIAR, The Cosener’s House, December 15, 2009
Calculated clear sky direct solar flux at Earth’s surface from known absorbers in the atmosphere.
Visible NIR IR
O2
O3
H2O, v=2
Solar flux at Earth’s surface
H2O
H2O, v=3
H2O
Electronic transitions
Vibrational transitions
Contribution depends on position, intensity and shape of
spectroscopic transitions as well as atmospheric abundance.
O2•O2 and O2•N2 complexes have been shown to
absorb about 1 W/m2 of incoming solar radiation.
O2•O2 and O2•N2 complexes have been shown to
absorb about 1 W/m2 of incoming solar radiation.
Hydrated complexes, H2O•X, are likely to contribute.Hydrated complexes, H2O•X, are likely to contribute.
H2O•H2OH2O•H2O H2O•O2H2O•O2H2O•N2H2O•N2
Complexes in the Atmosphere
Nature, 1969.
Vaida, Daniel, Kjaergaard, Goss, Tuck, QJRMS 2001.
Solomon, Portmann, Sanders, Daniel, JGR 1998.
0.960Å0.960Å
0.965Å0.965Å0.958Å0.958Å
H donorH donor H acceptorH acceptor
CCSD(T)/aug-cc-pV5Z optimized geometry CCSD(T)/aug-cc-pV5Z optimized geometry
Water monomer,ROH = 0.959Å
Water dimer, H2O•H2O
OH bond involved in hydrogen bonding is significantly longer frequency red shift
CCSD(T)/CBSROO = 2.9125Å
+anharm corrROO = 2.97Å
Expt. (Dyke)ROO = 2.976Å
Lane, Kjaergaard, JCP 2009.
ˆ ˆ ˆacceptor donorH H H
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.
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.
Water dimer, H2O•H2O
Simple vibrational model for water dimer Simple vibrational model for water dimer
Each H2O unit is modeled by two OH-stretching and one HOH-bending local mode oscillator.Each H2O unit is modeled by two OH-stretching and one HOH-bending local mode oscillator.
Low, Kjaergaard, JCP 1999. Schofield, Kjaergaard, PCCP 2003.
1 2 3 1 2 3, ,
, , i j kijk
i j k
q q q q q q
2 21 1 1 1 1 1 2 2 2 2 2 200 0
23 3 3 3 3 3
2
1 2 1 2 3 3 3 31
ˆ / +v v v +v v v
+v v v
( )i i ii
H E hc x x
x
a a a a fr a a a a a a
Dipole moment function
HCAO model for donor unit
12 12
11 22 11 22
2 233 3 3 3 3 3
333
2
1
4 2 2 2 4 2ci c i ci c c ci c
i ii e e
g f
g g f f
g q p g p q p q qfr f
q q hc
Stretch fundamental region
Long path length 351K with water monomer abs subtracted.
Paynter, Ptashnik, Shine, Smith, GRL 2007 Schofield, Kjaergaard, PCCP 2003
Water dimer, far-IR
Matrix isolation experiment versus anharmonic calculation
ModeBand 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
Kjaergaard et al, JPCA 2008Ceponkus et al, JPCA 2008
Equilibrium constants
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
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
11500 14750
H2O•H2O (calc)
H2O (observed)
wavenumber (cm-1)13100
Water dimer in the atmosphere
DvOH = 3½ DvOH = 40 4f b
Water dimer conc. depends on water conc. squared!
Schofield, Kjaergaard, PCCP 2003
Different conformers present at room temperature and seen in the overtone spectra.
Ethylene Glycol
(~58%) (~26%) (~10%)
Small molecule, so high level ab initio calculations are possible: CCSD(T)/aug’-cc-pVTZ.
Howard, Jørgensen, Kjaergaard, JACS 05.
Hydrogen bonding
Ethylene Glycol
1f1b
2b2f
Higher overtones better but also more difficult!
Larger diols
QCISD/6-311++G(2d,2p) calculations show stronger hydrogen bonding from EG - PD - BD.
Larger frequency red shifts
QCISD/6-311++G(2d,2p) calculations show stronger hydrogen bonding from EG - PD - BD.
Larger frequency red shifts
AO local mode calculation indicate similar intensities of bonded and free OH modes.
AO local mode calculation indicate similar intensities of bonded and free OH modes.
Propanediol, and Butanediol have similar structures to Ethylene Glycol.
Propanediol, and Butanediol have similar structures to Ethylene Glycol.
Howard and Kjaergaard, JPC A 06.
EGEG
PDPD
BDBD
V=3 V=4
OH-stretching in diols
What happens to the hydrogen bonded OH-stretching vibrations?What happens to the hydrogen bonded OH-stretching vibrations?
Vibrational band profile important for detection and effect.
Kjaergaard, Robinson, Howard, Daniel, Headrick, Vaida, JPCA 2003
Hydrated complexes
Water dimer, band profile
Vibrational band profile important for detection and effect.
Rotational profiles depend ondirection of TDM
Garden, Halonen, Kjaergaard, JPCA 2008
1f
1b
Hb
Hf
Water dimer, band profile
Effect of coupling to low frequency modes?
Adiabatic separation of methyl torsion and CH-stretching has explained CH-stretching overtone spectra in toluenes and xylenes.
Rong, Kjaergaard, JPCA 2002
10800 11000 11200
Third CH-stretch overtone, p-xylene.
We can separate adiabatically, the fast OH-stretching motion from the slow intra-molecular motion.
OO-stretch coupling
Use variation in OH-stretch mode with OO displacement to construct effective OO-stretch potential
2
v
1 1/ ( ) v v
2 2
( )
OO OO OO
OO OO
H hc T V s F F
T V s
2 3[1, , , ]TF s s s
Garden, Halonen, Kjaergaard, JPCA 2008
OO-stretch coupling
vOOV
Garden, Halonen, Kjaergaard, JPCA 2008
Shift in position of minimum.
Both in s and E.
Little change for OHf.
OO-stretch coupling
4b
Garden, Halonen, Kjaergaard, JPCA 2008
6 4
0 1
( , ) i ii i
i i
q s a q b sq
4f
1b
<0|0>
<1|0>
4f
OHb-stretching transition is wide, OHf-stretch is not.
Direction of TDM changed.
4b
Garden, Halonen, Kjaergaard, JPCA 2008
Hb
Hf
OO-stretch coupling
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.
Garden unpublished
4b<0|0>
<1|0>
Water dimer, band profile
Garden, unpublished
Combining OH-stretch +OO-stretch +Acceptor wag
Four moreintermolecular modes!
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, GuelphVeronica Vaida, BoulderPoul Jørgensen, AarhusLauri Halonen, HelsinkiJohn Stanton, AustinBenny Gerber, IrvineKeith Shine, ReadingIgor Ptasnik, Reading
MARSDEN FUND
John S. Daniel, NOAAJohn S. Daniel, NOAA
Geoffrey R. LowTimothy W. RobinsonDaniel P. SchofieldJoseph R. LaneAnna L. GardenDaryl HowardBen Miller
Copenhagen by night
Optical depth of self continuum (H2O only) compared to that calculated for water dimer (K = 0.01 to 0.12 atm-1).
Optical depth of self continuum (H2O only) compared to that calculated for water dimer (K = 0.01 to 0.12 atm-1).
Continuum
Daniel, Solomon, Kjaergaard, Schofield, GRL 2004