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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, Radboud University Caviar Consortium Meeting, NPL 29 th September 2010

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(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, (2008). HBB2 – X. Huang et al. J. Chem. Phys. 130, (2009).

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(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, (2008). R.E.A. Kelly, J. Tennyson, G C. Groenenboom, A. Van der Avoird, JQRST, 111, 1043 (2010).

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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.

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Solving the 6D intermolecular problem Brocks et al. Hamiltonian*Brocks et al. Hamiltonian* Monomers fixed inMonomers fixed in –Equilibrium geometry, or –Vibrational ground state geometry * G. Brocks et al. Mol. Phys. 50, 1025 (1983).

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Solving the 6D intermolecular problem Acceptor Twist (AT) Acceptor Wag (AW) Donor Torsion (DT) In Plane Bend (IPB) Stretch Out-of-Plane Bend (OPB) Generated by Matt Hodges and Anthony Stone. C. Millot et al. J. Phys. Chem. A 1998,102, 754.

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Isomorphic to D 4h with Irreducible Elements: A 1 +, A 2 +, A 1 -, A 2 -, B 1 +, B 2 +, B 1 -, B 2 -, E +, E - -> Water Dimer Spectroscopic Labels Tunneling Splittings

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Very good agreement with: Ground State Tunnelling splittings Rotational Constants Not so good agreement with: Acceptor Tunnelling

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Solving the 6D intermolecular problem Brocks et al. Hamiltonian*Brocks et al. Hamiltonian* Monomers fixed inMonomers fixed in –Equilibrium geometry, or –Vibrational ground state geometry * G. Brocks et al. Mol. Phys. 50, 1025 (1983). Is there another way to help us probe the 12D problem?

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Adiabatic Separation Approximate separation between monomer and dimer modes –Separate intermolecular and intramolecular modes. m D – water donor vibrational wavefunction m A – water acceptor vibrational wavefunction d – dimer VRT wavefunction

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Now we can vibrationally average the potentialNow we can vibrationally average the potential Input for 6D calculationsInput for 6D calculations donoracceptor State mState n How well does it perform for |0 0> calculationsHow well does it perform for |0 0> calculations Solving the 6D intermolecular problem

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In cm -1 Red – ab initio potential Black – experimental GS – ground state DT – donor torsion AW – acceptor wag AT – acceptor twist DT 2 – donor torsion overtone R.E.A. Kelly, J. Tennyson, G C. Groenenboom, A. Van der Avoird, JQRST, 111, 1043 (2010). Vibrational Averaging

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Vibrational Averaging: 6D Costs! Computation: –typical number of DVR points with different Morse Parameters: –{9,9,24} gives 1,080 points for monomer –1,080 2 = 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

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Full model for high frequency absorption Approximate separation between monomer and dimer modes Franck-Condon approximation for vibrational fine structure Rotational band model

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Adiabatic Separation Approximate separation between monomer and dimer modes –Separate intermolecular and intramolecular modes. m D – water donor vibrational wavefunction m A – water acceptor vibrational wavefunction d – dimer VRT wavefunction

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Model for high frequency absorption Approximate separation between monomer and dimer modes Franck-Condon approximation for vibrational fine structure Rotational band model

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Franck-Condon Approx for overtone spectra Assume monomer m 1 excited, m 2 frozen m 2 i = m 2 f I (2) Franck-Condon factor (square of overlap integral): Gives dimer vibrational fine structure (1) Monomer vibrational band Intensity

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Allowed Transitions in our Model 1. Excited donor 2. Excited acceptor All transitions from ground monomer vibrational states Assume excitation localised on one monomer

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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).

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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)

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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

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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

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Outline of full problem Need to ultimately solve (6D problem) H=K+V eff V eff sampled on a 6D grid Calculate states for donor Calculate states for acceptor Vibrationally average potential for each state- state combination –Really only |0j> and |i0>

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(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. Averaging Techniques

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Form of the wavefunction: –(I) Uncoupled free monomer –(II) Uncoupled perturbed (fixed) monomer R. E. A. Kelly et al. To submit shortly.

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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

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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.

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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.

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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.

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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! CPUs for 3-4 weeks. *R. E. A. Kelly et al. To submit shortly.

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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

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Solving the 6D intermolecular problem: Allowed permutations

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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

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Full Vibrational Stick Spectra Strongest absorption on bend – difficult to distinguish from monomer features More structure between cm -1

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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

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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

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