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Preliminary Results for Water Dimer Spectroscopy Simulations Ross E. A. Kelly, Matt J. Barber, and Jonathan Tennyson Department of Physics and Astronomy UCL Gerrit C. Groenenboom, Ad van der Avoird Theoretical Chemistry Institute for Molecules and Materials Radboud University CAVIAR AGM STFC, Cosener's House December 15, 2009

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Contents I. Motivations II. Improved Water Monomer Parameters III. Water Dimer Characteristics IV. Water Dimer VRT states V. New Methodology VI. Summary

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I. Motivations to understand water dimer absorption throughout visible and IR region in the atmosphere. To create a high accuracy water dimer spectra in agreement with experiments. To create a linelist of all possible water dimer transitions.

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II. Improved Water Monomer Parameters To get the water dimer spectroscopy correct we need an accurate understanding of the water monomer contribution to the observed experimental spectra [*] Courtesy of R. L. Jones & A. J. L. Shillings, University of Cambridge.

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III. Improved Water Dimer Characteristics May exist in various configurations Has feasible tunnelling between equivalent geometries Has a complex potential energy landscape Full dimensional potential exists* [*] X. Huang et al. J. Phys. Chem. A 110, 445 (2006); X. Huang et al. J. Chem. Phys. 128, 034312 (2008).

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III. Improved Water Dimer Characteristics Monomer corrected Bowman dimer potential used*. Corrects for monomer excitation [*] R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. Van der Avoird, JQRST. Submitted.

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III. Water Dimer Characteristics Dimer VRT states complicated by tunnelling effects Tunnelling between equivalent states in the PES is feasible! Acceptor Tunnelling: –No bond breaking here –Lowest tunnelling barrier Also, by breaking the Hydrogen bond, other tunnelling paths possible: –Donor-Acceptor interchange –Donor Bifurcation Tunnelling

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III. Water Dimer Characteristics Calculating the lowest energy Vibration-Rotation Tunnelling states is a good test for a water dimer potentialCalculating the lowest energy Vibration-Rotation Tunnelling states is a good test for a water dimer potential –Rigid monomer Hamiltonian* There exists Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), around 5 K.There exists Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), around 5 K. [*] G. Brocks et al. Mol. Phys. 50, 1025 (1983).

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IV. 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. Submitted.

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IV. Water Dimer VRT Levels Very good agreement with: –Ground State Tunnelling splittings –Rotational Constants Not so good agreement with: –Acceptor Tunnelling [*] R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. Van der Avoird, JQRST. Submitted.

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Water Dimer Characteristics ZPE = 9899 ± 5 cm -1 9854 ± 3 cm -1 StructureSymmetryHBBHBB+SHI08Benchmark* 1Cs0.0 0 2C1161.4159.6181 3Cs198.5193.5198 4Ci244.0241.1245 5C2329.3323.9323 6C2h348.1340.6348 7Cs603.0601.3635 8C2h1181.81178.91249 9C2v590.2588.2625 10C2v898.3894.8948 * G. S. Tschumper et al. JCP 116, 690 (2002).

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V. Adiabatic Separation Adiabatic Separation of Vibrational Modes Adiabatic Separation of Vibrational Modes Separate intermolecular and intramolecular modes. Separate intermolecular and intramolecular modes. m 1 = water monomer 1 Vibrational Wavefunction m 1 = water monomer 1 Vibrational Wavefunction m 2 = water monomer 2 Vibrational Wavefunction m 2 = water monomer 2 Vibrational Wavefunction d = dimer Vibration-Rotation Wavefunction d = dimer Vibration-Rotation Wavefunction

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Transition: Approximation: (Franck Condon type). 0 th Order Model =1 (2) Franck Condon Factor (square of overlap integral) (1) Monomer Vibrational Band Intensity V. New Methodology Franck-Condon Type Approx for IR spectra

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1. Vibrational Band Intensities

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2. 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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Calculating Dimer States with New Approach Vibrationally average potential on Condor machine (large jobs!) Create Monomer band origins in the dimer (with DVR3D) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matts Band intensities to get spectra

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Complete Water Dimer Energy Level Diagram Intramolecular/ Intermolecular distance Slightly complicated by Localisation of monomer excitations

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Allowed Transitions in our Model 1. Acceptor 2. Donor Also not between excited monomer states Assume excitation localised on one monomer

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Adiabatic Surfaces 1. Acceptor bend 2. Donor bend 1597.51608.2 1594.8 Monomer well Have perturbed monomer wavefunctions from these DVR3D calculations

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Calculating Dimer States Vibrationally average potential on Condor machine (large jobs!) Create Monomer band origins in the dimer (with DVR3D) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matts Band intensities to get spectra

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Large grid calculations performed with these new perturbed monomer wavefunctions For each dimer geometry on 6D grid (~3 million points) Up to 10,000 cm-1 Took around 2 weeks on 500 machines New run up to 16,000 cm-1 running Averaging Technique Now we averaged the potential, we can start the dimer energy level (and wavefunction) calculations

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Vibrational Averaging larger calculations 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 (cf. 17,864) –1,080 2 = 1,166,400 points for the dimer (cf. 319,122,496) –1,166,400 * 2,894,301 intermolecular points = 3,374,862,926,400 points

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Calculating Dimer States Vibrationally average potential on Condor machine (large jobs!) Create Monomer band origins in the dimer (with DVR3D) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matts Band intensities to get spectra

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Allowed Permutations with excited monomers 1 1 5 5 2 2 66 4 4 3 3 11 5 5 226 6 6 6 6 6 5 55 5 4 4 3 3 3 3 3 3 4 4 4 4 1 1 1 1 2 2 2 2

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G16 Symmetry of Hamiltonian for GS mononers –> replaced with G4 Dimer program modified substantially to print Hamiltonian into G4 symmetry blocks Separate eigensolver to obtain energy levels and dimer wavefunctions Symmetry

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Calculating transition energies Combing monomer DVR3D c alculations and dimer energies E trans From monomer DVR3D calculations

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Calculating Dimer States Vibrationally average potential on Condor machine (large jobs!) Create Monomer band origins in the dimer (with DVR3D) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matts band intensities to get spectra

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Donor and Acceptor Bend FC factors Dimer VRTGround State G4 symmetry so each dimer state has 4 similar transitions but with different energy

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Calculating Dimer States Vibrationally average potential on Condor machine (large jobs!) Create Monomer band origins in the dimer (with DVR3D) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matts band intensities to get spectra

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Full Vibrational Stick Spectra (low T ~100K?) Strongest absorption on bend – difficult to distinguish from monomer features Looks like area of interest – lots going on between 6000-9000cm-1

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

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VII. Conclusions Preliminary Stick spectra for up to 10,000cm-1 produced. –Band profiles provided by Igor show some encouraging signs. –Larger calculations were performed to check convergence. –Effects of the sampling of the potential being investigated. New averaging job running for input for spectra up to 16,000cm-1. All states up to disociation –Only 8 states here

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