Simulating the spectrum of the water dimer in the far infrared and visible

Ross E. A. Kelly, Matt J. Barber, Jonathan TennysonDepartment of Physics and Astronomy

University College London

Thanks to: Gerrit C. Groenenboom, Ad van der Avoird Theoretical Chemistry Institute for Molecules and Materials

Radboud University

CAVIAR ConsortiumUCL Lab & Theory Meeting

30th April 2010

0.0E+00

5.0E-09

1.0E-08

1.5E-08

2.0E-08

2.5E-08

3.0E-08

3.5E-08

4.0E-08

4.5E-08

5.0E-08

606 608 610 612 614 616 618 620 622

Wavelength / nm

Ab

sorp

tio

n C

oef

fici

ent

/ cm

-1

Measured

UCL '08

0.0E+00

5.0E-09

1.0E-08

1.5E-08

2.0E-08

2.5E-08

3.0E-08

3.5E-08

4.0E-08

4.5E-08

5.0E-08

606 608 610 612 614 616 618 620 622

Wavelength / nm

Ab

so

rpti

on

Co

eff

icie

nt

/ c

m-1

Measured

HITRAN '06

Lab observations in the visible (broad band CRDS)

For dimer spectroscopy

Need accurate description of water monomer contribution

Including weak lines

A.J.L. Shillings, S.M. Ball, M.J. Barber, J. Tennyson & R.L. Jones, Atmos. Chem. Phys. (to be submitted)

Improved Water Dimer Characteristics

• Monomer corrected HBB potential

• Corrects for monomer excitation

R.E.A. Kelly, J. Tennyson, G C. Groenenboom, A. Van der Avoird, JQRST, 111, 1043 (2010).

Water Dimer Characteristics

• Lowest Vibration-Rotation Tunnelling (VRT) states: Lowest Vibration-Rotation Tunnelling (VRT) states: good test for a water dimer potentialgood test for a water dimer potential– Rigid monomer HamiltonianRigid monomer Hamiltonian

• Compare with 5 K Tetrahertz Spectra.Compare with 5 K Tetrahertz Spectra.

G. Brocks et al. Mol. Phys. 50, 1025 (1983).

Water Dimer VRT Levels

• In cm-1

• Red – ab initio potential• Black – experimental

• GS – ground state

• DT – donor torsion

• AW – acceptor wag

• AT – acceptor twist

• DT2 – donor torsion overtone

R.E.A. Kelly, J. Tennyson, G C. Groenenboom, A. Van der Avoird, JQRST, 111, 1043 (2010).

Model for high frequency absorption

• Approximate separation between monomer and dimer modes

• Assume monomers provide chromophores

• Franck-Condon approximation for vibrational fine structure

• Rotational band model (so far)

Adiabatic Separation

Adiabatic Separation of vibrational Modes Separate intermolecular and intramolecular modes.

m1 = water monomer 1 vibrational wavefunction

m2 = water monomer 2 vibrational wavefunction

d = dimer VRT wavefunction

dmm 21

Allowed Transitions in our Model

1. Acceptor 2. Donor

All transitions from ground monomer vibrational states

Assume excitation localised on one monomer

2

2121

2fffiii

fi dmmdmmI

22

1122

fifi

mmddmmfi

Franck-Condon Approx for overtone spectra

Assume monomer m1 excited, m2 frozen

m2i = m2

f

I

22

1122

fifi

mmddmmfi

(2) Franck-Condon factor

(square of overlap integral):

Gives dimer vibrational fine structure

(1) Monomer vibrational band Intensity

Franck-Condon Approx for overtone spectra

Calculating dimer spectra with FC approach

Vibrationally average potential on

parallel machine(large jobs!)

Create Monomer band origins in the

dimer (with DVR3D)

CreateG4 symmetry

Hamiltonian blocks

Solve eigenproblemsObtain energies

and wavefunctions

Create dot productsbetween eigenvectors

to get FC factors

Combine with Band intensitiesSimulate spectra

Vibrational band intensities

• Calculate from (perturbed) monomer vibrational wavefunctions• Requires Eckart embedding of axis frame• Use HBB 12 D dipole moment surface (DMS) corrected with

accurate monomer DMS CVR: L. Lodi et al, J Chem Phys., 128, 044304 (2008)

Issues:• PES used to generate monomer wavefunctions• (Cut) through 12 D DMS used

Vibrational band intensities: at equilibrium

Vibrational band intensities: at R < Req

Franck-Condon factors

– Overlap between dimer states on adiabatic potential energy surfaces for water monomer initial and final states

– Need the dimer states (based on this model).

Adiabatic Surfaces

1. Acceptor bend 2. Donor bend

1597.5 1608.21594.8 1594.8

Monomer well

Outline of full problem

• Need to ultimately solve (6D problem)

• H=K+Veff

• Veff sampled on a 6D grid

dd EH • Calculate states for donor

• Calculate states for acceptor

• Vibrationally average potential for each state-state combination– Really only |0j> and |i0>

Need effective 6D PES, dependent on monomer state

Averaging Technique

)()(|);,(|)()()( BBAABABBAAmm

eff mmVmmV BA QQRQQQQR

(a) 6D averaging:

(b) 3D+3D averaging:

C Leforestier et al, J Chem Phys, 117, 8710 (2002)

Averaging Technique

);,()()(

)()(|);,(|)()()(22 RQQQQ

QQRQQQQR

BABBAqq

A

BBAABABBAAeff

Vmm

mmVmmV

BA

);,()(|);,(|)(

)(|);,(|)()(minminmin

min

RQQQRQQQ

QRQQQR

BABBBABB

AABAAAeff

VmVm

mVmV

Vibrational Averaging: 6D

• Energies up to 16,000 cm-1 sufficient.• Computation:

– typical number of DVR points with different Morse Parameters:

– {9,9,24} gives 1,080 points for monomer

– 1,0802 = 1,166,400 points for both monomers

– 1,166,400 x 2,894,301 intermolecular points

= 3,374,862,926,400 points• Same monomer wavefunctions for all grid points• Distributed computing: Condor 1000 computers, 10 days

Problems with Fixed Wavefunction approach (6D method)

• Donor bend

Problems with Fixed Wavefunction approach (6D method)

• (Donor) Free OH stretch • (Donor) Bound OH stretch

Problems with Fixed Wavefunction approach (6D method)

• (Donor) Free OH stretch • (Donor) Bound OH stretch

Vibrational Averaging: 3D+3D

• Energies up to 16,000 cm-1 sufficient.• Computation “reduced”

– typical number of DVR points with different Morse Parameters:

– {9,9,24} gives 1,080 points for monomer

– 2 x 1,080 = 2 160 points for both monomers

– 2 160 x 2,894,301 intermolecular points

= ‘only’ 624 890 160 points• But requires monomer wavefunctions at each r• Parallel computing: Legion 60 computers, 16 days

Allowed Permutations with excited monomers

1 15 5

2 26 6

4

4

3

3

• G16 Symmetry of Hamiltonian for GS monomers– > replaced with G4

• Dimer program modified:

Hamiltonian in G4 symmetry blocks• Separate eigensolver to obtain energy levels and

dimer wavefunctions

Donor and Acceptor Bend FC factors

Dim

er VR

T

Ground

State

G4 symmetry so each dimer state has 4 similar transitions but with different energy

Full Vibrational Stick Spectra (low T ~100K?)

1.00E-56

1.00E-50

1.00E-44

1.00E-38

1.00E-32

1.00E-26

1.00E-20

1.00E-14

1.00E-08

1.00E-02

1000 4000 7000 10000

Frequency (cm-1)

Ab

sorp

tio

n (

Hit

ran

un

its)

1.00E-281.00E-271.00E-261.00E-251.00E-241.00E-231.00E-221.00E-211.00E-201.00E-191.00E-181.00E-171.00E-16

1000 4000 7000 10000

Strongest absorption on bend – difficult todistinguish from monomer features

More structure between 6000-9000 cm-1

Estimating transition frequencies

Band centre from monomer DVR3D calculation

Blue/red shift from calculation on perturbed PES

Vibrational fine structure from dimer dimer transitions

Simulate spectra at “295 K”

• Assume 4.5% dimer concentration• Rotational band profile 30 cm-1 (too narrow?)• Predictions give absolute intensities• 6D averaging

But:

Vibrational substructure still only for low T

(8 J=0 states per symmetry)

Results preliminary (main calculations in progress)

CAVIAR measurements & theory: (1600-8000 cm-1)

1300 1400 1500 1600 1700 1800 19000.0

0.2

0.4

0.6

0.8

1.0

1.2Keq=0.039 atm-1, HWHM=30 cm-1

17.85 mb pure H2OThreshold=3; Grad.=0.05

Cs

(1

0-20

cm

2 m

ole

c-1a

tm-1

)

Wavenumber (cm-1)

MT_CKD RAL (2007) /295K, 128m/ Tobin et al. 1996 /296 K/ Burch, 1981 /308K/ WD (S&K, 2003) WD (KjSaGaVi-2009) WD (UCL-2009 v1) / 48 WD (UCL-2009 v2) / 48

3400 3500 3600 3700 3800 39000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Wavenumber, cm-1

/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/

Keq=0.041 atm-1, hwhm=25 cm-1

15.3 mb purer H2O

Cs,

10

-20 c

m2 *

mo

lec

-1at

m-1

CKD-2.4 MT_CKD WD (S&K-2003) MSF (RAL-2007) Burch cont. corr. to Hit04 WD (KjSaGaVi-2009) WD (UCL-2009 v1) / 24 WD (UCL-2009 v2) / 24

5000 5100 5200 5300 5400 5500 56000.0

0.2

0.4

0.6

0.8

1.0

1.2

/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/

Keq=0.041 atm-1, hwhm=30 cm-115.3 mb pure H2O

opt.depth/273.15*293/2.69e19/0.0151^2/51275

Everything (excluding Burch data) is with the 'Base term' subtracted !!!

Wavenumber, cm-1

/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/

Cs,

1

0-21

cm

2 *m

ole

c-1a

tm-1

WD (S&K-2003) MSF (RAL-2007) Ptashnik et al. (2004) 299K CKD 2.4, 293K MT_CKD 1.10, 293K WD (KjSaGaVi-2009) WD (UCL-2009 v.1) / 48 WD (UCL-2009 v.2) / 48

6900 7000 7100 7200 7300 7400 75000.0

0.1

0.2

0.3

0.4

0.5

0.6/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/

Keq=0.041 atm-1, hwhm=30 cm-1

Wavenumber, cm-1

15.3 mb pure H2O

Cs,

10

-21 c

m2

mo

lec

-1at

m-1

CKD-2.4 MT_CKD MSF RAL (2007), 293K WD (S&K-2003) WD (KjSaGaVi-2009) WD (UCL-2009 v.1) / 24 WD (UCL-2009 v.2) / 24

Conclusions

• Careful treatment of weak monomer spectra essential

• Preliminary spectra for up to 10,000 cm-1 produced.

– Band profile comparisons show some encouraging signs..– Effects of the sampling of the potential being investigated.

• New averaging job (3D+3D) running for input for spectra up to 16,000 cm-1.

• Need all states up to dissociation– Only 8 states per symmetry here– It is a challenge for a much higher number of states