Simulating the spectrum of the water dimer in the far infrared and visible Ross E. A. Kelly, Matt J. Barber, Jonathan Tennyson Department 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 Consortium UCL Lab & Theory Meeting 30 th April 2010

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: good test for a water dimer potentialLowest Vibration-Rotation Tunnelling (VRT) states: good test for a water dimer potential –Rigid 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. m 1 = water monomer 1 vibrational wavefunction m 2 = water monomer 2 vibrational wavefunction d = dimer VRT wavefunction

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

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 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) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Band intensities Simulate 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, (2008) Issues: PES used to generate monomer wavefunctions (Cut) through 12 D DMS used

Vibrational band intensities: at equilibrium

Vibrational band intensities: at R < R eq

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 Monomer well

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>

Need effective 6D PES, dependent on monomer state Averaging Technique

(a) 6D averaging: (b) 3D+3D averaging: C Leforestier et al, J Chem Phys, 117, 8710 (2002) Averaging Technique

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 –1,080 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

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 = points for both monomers –2 160 x 2,894,301 intermolecular points = only points But requires monomer wavefunctions at each r Parallel computing: Legion 60 computers, 16 days

Allowed Permutations with excited monomers 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 Dimer VRTGround State G4 symmetry so each dimer state has 4 similar transitions but with different energy

Full Vibrational Stick Spectra (low T ~100K?) Strongest absorption on bend – difficult to distinguish from monomer features More structure between 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: ( cm -1 )

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