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Contribution of water dimers in atmospheric absorption: methodology. Ross E. A. Kelly , Matt J. Barber, Jonathan Tennyson Department of Physics and Astronomy, University College London Gerrit C. Groenenboom, Ad van der Avoird Theoretical Chemistry Institute for Molecules and Materials, - PowerPoint PPT Presentation
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Contribution of water dimers in atmospheric absorption: methodology
Ross E. A. Kelly, Matt J. Barber, Jonathan TennysonDepartment of Physics and Astronomy,
University College London
Gerrit C. Groenenboom, Ad van der Avoird Theoretical Chemistry Institute for Molecules and Materials,
Radboud University
Caviar Consortium Meeting, NPL29th September 2010
• (1) Need to solve the nuclear motion Hamiltonian– 12D problem! Approximations required.
• (2) Fully dimensional potential energy surface required– Huang, Braams and Bowman (HBB) potentials
• 30-40,000 configurations sampled.• Calculated at coupled-cluster, single and double and perturbative
treatment of triple excitations method.• Augmented, correlation consistent, polarized triple zeta basis set.• Polynomial fit with 5227 coefficients.
Water Dimer Method
HBB – X. Huang et al. J. Chem. Phys. 128, 034312 (2008).HBB2 – X. Huang et al. J. Chem. Phys. 130, 144314 (2009).
(2) Fully Dimensional Water Dimer Potential
Monomer corrected* HBB potential • Corrects for monomer excitation
– Accurate modes for the monomer
* S. V. Shirin et al., J. Chem. Phys. 128, 224306 (2008).R.E.A. Kelly, J. Tennyson, G C. Groenenboom, A. Van der Avoird, JQRST, 111, 1043 (2010).
• Diffusion Monte Carlo may be used– Start with a number of walkers– Allow them to follow a random walk in space– Propagate in imaginary time– Decide whether to replicate or destroy the walker
(1) Fully Dimensional (12D) Solution
• Only useful for 12D vibrational ground state.
Solving the 6D intermolecular problem
• Brocks Brocks et alet al. Hamiltonian*. Hamiltonian*
• Monomers fixed in Monomers fixed in – Equilibrium geometry, or Equilibrium geometry, or – Vibrational ground state geometryVibrational ground state geometry
* G. Brocks et al. Mol. Phys. 50, 1025 (1983).
Solving the 6D intermolecular problemSolving the 6D intermolecular problem
AcceptorTwist (AT)
AcceptorWag (AW)
Donor Torsion (DT)
In PlaneBend (IPB) Stretch
Out-of-PlaneBend (OPB)
Generated by Matt Hodges and Anthony Stone. C. Millot et al. J. Phys. Chem. A 1998,102, 754. http://www-stone.ch.cam.ac.uk/research/water.dimer/modes.html
1 1
1 1
5 5
5 5
2 2
2 2
6 6
6 6
6 6
6 6
5
5 5
5
4
4
4
4
3
3
3
3
3 3
3 3
4
4
4
4
1 1
1 1
2
2 2
2
Isomorphic to D4h
with Irreducible Elements:
A1
+, A2
+, A1
-, A2
-, B1
+, B2
+, B1
-, B2
-, E+, E-
-> Water Dimer Spectroscopic Labels
Tunneling Splittings
Tunneling Splittings
Very good agreement with:
• Ground State Tunnelling splittings• Rotational Constants
Not so good agreement with:
• Acceptor Tunnelling
Solving the 6D intermolecular problem
• Brocks Brocks et alet al. Hamiltonian*. Hamiltonian*
• Monomers fixed in Monomers fixed in – Equilibrium geometry, or Equilibrium geometry, or – Vibrational ground state geometryVibrational ground state geometry
* G. Brocks et al. Mol. Phys. 50, 1025 (1983).
Is there another way to help us probe the 12D problem?
Adiabatic Separation
• Approximate separation between monomer and dimer modes– Separate intermolecular and intramolecular modes.
mD – water donor vibrational wavefunction
mA – water acceptor vibrational wavefunction
d – dimer VRT wavefunction
dmm AD
)()(|);,(|)()()( BBAABABBAAmm
eff mmVmmV BA QQRQQQQR
• Now we can vibrationally average the potentialNow we can vibrationally average the potential
• Input for 6D calculationsInput for 6D calculations
donordonor acceptoracceptor
State mState m State nState n
• How well does it perform for |0 0> calculationsHow well does it perform for |0 0> calculations
Solving the 6D intermolecular problem
• 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).
Vibrational Averaging
Vibrational Averaging: 6D Costs!
• 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
But we have a way to probe high frequency dimer spectra
Full model for high frequency absorption
• Approximate separation between monomer and dimer modes
• Franck-Condon approximation for vibrational fine structure
• Rotational band model
Adiabatic Separation
• Approximate separation between monomer and dimer modes– Separate intermolecular and intramolecular modes.
mD – water donor vibrational wavefunction
mA – water acceptor vibrational wavefunction
d – dimer VRT wavefunction
dmm AD
Model for high frequency absorption
• Approximate separation between monomer and dimer modes
• Franck-Condon approximation for vibrational fine structure
• Rotational band model
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
(2) Franck-Condon factor
(square of overlap integral):
Gives dimer vibrational fine structure
(1) Monomer vibrational band Intensity
Allowed Transitions in our Model
1. Excited donor 2. Excited acceptor
All transitions from ground monomer vibrational states
Assume excitation localised on one monomer
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).
Transitions: Example
Donor – Vibrational ground state (VGS)Acceptor – VGS
Donor –VGS Acceptor – bend
Acceptor Twist (AT)
Acceptor Wag (AW)
Donor Torsion (DT)
Ground State (GS)
Acceptor Twist (AT)
Acceptor Wag (AW)
Donor Torsion (DT)
Ground State (GS)
Transitions: Example
Acceptor Twist (AT)
Acceptor Wag (AW)
Donor Torsion (DT)
Ground State (GS)
Acceptor Twist (AT)
Acceptor Wag (AW)
Donor Torsion (DT)
Ground State (GS)
Donor – Vibrational ground state (VGS)Acceptor – VGS
Donor –VGS Acceptor – bend
Transitions: Example
Acceptor Twist (AT)
Acceptor Wag (AW)
Donor Torsion (DT)
Ground State (GS)
Acceptor Twist (AT)
Acceptor Wag (AW)
Donor Torsion (DT)
Ground State (GS)
Donor – Vibrational ground state (VGS)Acceptor – VGS
Donor –VGS Acceptor – bend
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>
(a) 6D averaging:
(b) 3D+3D averaging:
1 C Leforestier et al, J Chem Phys, 117, 8710 (2002)2 R. E. A. Kelly et al. To submit shortly.
);,()()(
)()(|);,(|)()()(22 RQQQQ
QQRQQQQR
BABBAqq
A
BBAABABBAAeff
Vmm
mmVmmV
BA
);,()(|);,(|)(
)(|);,(|)()(000
0
RQQQRQQQ
QRQQQR
BABBBABB
AABAAAeff
VmVm
mVmV
Averaging Techniques
Averaging Techniques
• Form of the wavefunction:– (I) Uncoupled free monomer
– (II) Uncoupled perturbed (fixed) monomer
R. E. A. Kelly et al. To submit shortly.
Problems with Fixed Wavefunction approach (uncoupled methods)
• Donor bend • (Donor) Free OH stretch • (Donor) Bound OH stretch
• (Donor) Free OH stretch • (Donor) Bound OH stretch
Averaging Techniques
• Form of the wavefunction:– (I) Uncoupled free monomer
– (II) Uncoupled perturbed (fixed) monomer
– (III) Coupled Adiabatic
R. E. A. Kelly et al. To submit shortly.
Averaging Techniques
• Form of the wavefunction:– (I) Uncoupled free monomer
– (II) Uncoupled perturbed (fixed) monomer
– (III) Coupled Adiabatic
R. E. A. Kelly et al. To submit shortly.
Averaging Techniques
• Form of the wavefunction:– (I) Uncoupled free monomer
– (II) Uncoupled perturbed (fixed) monomer
– (III) Coupled Adiabatic
R. E. A. Kelly et al. To submit shortly.
Averaging Techniques
• Form of the wavefunction*:– (I) Uncoupled free monomer– (II) Uncoupled perturbed monomer – (III) Coupled Adiabatic
• Coupled Adiabatic methods are the most suitable– Requires wavefunction calculations at each intermolecular grid
point! 2,893,401 * 2 DVR3D calculations!– So we use cheaper (3+3)D averaging technique.
– Still costs! 500-700 CPUs for 3-4 weeks.
*R. E. A. Kelly et al. To submit shortly.
Calculating dimer spectra with FC approach
• Solved for monomers • Coupled adiabatic appoach
• Vibrationally averaged potential for donor-acceptor state-state combinations |0j> and |i0>• Input for 6D intermolecular problem
• Now we can solve 6D intermolecular problem• Obtain vibrational fine structure
Solving the 6D intermolecular problem:Allowed permutations
1 15 5
2 26 6
4
4
3
3
1 1
5 5
2 26 6
6 6
6 6
5
5 5
5
4
4
3
3
3 3
3 3
4
4
4
4
1 1
1 1
2
2 2
2
1 15 5
2 26 6
4
4
3
3• G16 Symmetry of Hamiltonian for GS monomers
– > replaced with G4 • Greatly increases computational requirements
• Reduced angular basis• Small radial basis• 320 diagonalizations for 0-10,000 cm-1
• Each at 16GB• 8 states per symmetry block
• Leading to 20,480 transitions
Solving the 6D intermolecular problem:Allowed permutations for excited monomers
Full Vibrational Stick Spectra
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
Model for high frequency absorption
• Approximate separation between monomer and dimer modes
• Franck-Condon approximation for vibrational fine structure
• Rotational band model – Matt will discuss this
• We have a new model to probe near IR and visible regions of the water dimer spectra.– With first vibrational fine structure reported.
• Spectra for up to 10,000 cm-1 produced.– Much better agreement with experimental and theoretical work
than our previous calculations.
• We have finished new averaging calculations which will allow us to probe spectra up to 18,000 cm-1
• And all states up to dissociation to be calculated.– Only 8 states per symmetry here (32 states per state-state job)– up to 800, or 3200 per job.
Conclusions