Vibrational averaging techniques to calculate the role of water dimers in atmospheric absorption Jonathan Tennyson, Matt J. Barber, Ross E. A. Kelly, Lorenzo.

Vibrational averaging techniques to calculate the role of water dimers in atmospheric absorption

Jonathan Tennyson, Matt J. Barber, Ross E. A. Kelly, Lorenzo Lodi

Department of Physics and Astronomy, University College London

CAVIAR meetingCambridge, Feb 2011

CAVIAR - Continuum Absorption at Visible and Infrared wavelengths and its Atmospheric Relevance

• (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).

Solving the 6D intermolecular problem

• Brocks Brocks et alet al. Hamiltonian*. Hamiltonian*

Solved using Dimer code ofSolved using Dimer code of

Groenboom and van der Avoird:Groenboom and van der Avoird:

Gives dimer “VRT” statesGives dimer “VRT” states

* 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

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. Donor2. 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.

This part is complete

.

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

For T=296 K requires all vibrational states

1 15 5

2 26 6

4

4

3

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

• Greatly increases computational requirements

So far• Reduced angular basis• Small radial basis• 320 diagonalizations for 0-10,000 cm-1

• Each at 16 GB• 8 states per symmetry block

• Gives 20,480 transitions: results presented by Matt

Solving the 6D intermolecular problem:Allowed permutations for excited monomers

Model for high frequency absorption

• Approximate separation between monomer and dimer modes

• Franck-Condon approximation for vibrational fine structure

• Rotational band model

• G4 Symmetry of Hamiltonian• Require all vibrational bound states • Greatly increases computational requirements

So far• Reduced angular basis• Small radial basis• 320 diagonalizations• Each at matrix 320,000 x 320,000 means ~ 1 TB RAM• ~400 states per symmetry block• 3 – 5 days CPU• Ongoing (problems with UCL computers)

Solving the 6D intermolecular problem: For atmospheric temperatures

• New Model to probe near IR and visible regions of the water dimer spectra.– vibrational fine structure

• Aim for spectra for up to 15,000 cm-1 produced.

• And all states up to dissociation to be calculated.

-- Computer resources a big issue

Conclusions