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