Modelling Water Dimer BandIntensities and Spectra

Matt Barber

Jonathan Tennyson

University College London

10th February 2011

matt@theory.phys.ucl.ac.uk

Band Intensities

• Calculated using the “forbidden” J=0-0 transition.• Water dimer is too complicated for full ro-

vibrational modelling.• However, we can model vibrations of monomers

within dimer and simulate additional rotational structure.

• Need to use 1992 version of DVR– Band models subsequently superseded– Calculate monomer bands from recent line lists

Band Intensities

1.00E-025

1.00E-024

1.00E-023

1.00E-022

1.00E-021

1.00E-020

1.00E-019

1.00E-018

1.00E-017

1.00E-016

0 2000 4000 6000 8000 10000

Frequency

Inte

nsity HITRAN

BT2

DIPJ0

Dimer 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, 044304 (2008)

Issues:• PES used to generate monomer wavefunctions• Cut through 12 D DMS used

1500 2500 3500 4500 5500 6500 7500 8500 9500 10500 11500

1.00E-028

1.00E-026

1.00E-024

1.00E-022

1.00E-020

1.00E-018

1.00E-016

Donor (equilibr ium)

A c c eptor(equilibr ium)

Monomer

Perturbing the dimer configuration

• Many possible configurations• Transition intensities vary considerably from small

changes in geometry• Equilibrium may not be best choice• Pick to strengthen donor bound stretch

1500 2500 3500 4500 5500 6500 7500 8500 9500 10500 11500

1.00E-028

1.00E-026

1.00E-024

1.00E-022

1.00E-020

1.00E-018

1.00E-016

Donor (per turbed)

A c c eptor (per turbed)

Monomer

Estimating transition frequencies

Band centre from monomer DVR3D calculation

Blue/red shift from calculation on perturbed PES

Vibrational fine structure from dimer dimer transitions

Rotational structure simulated by overlaid Lorentzian

Partition function and equlibrium constant

• 800 vibrational energy levels• J up to 5 calculated, extrapolated up to 50

• Dissociation energy?

• Equilibrium constant at room temperature:– Around 0.03 to 0.05 for bound states– Possibly up to 0.08 for metastable

Simulate spectra at “296 K”

• Assume 0.045 equilibrium constant for typical atmospheric conditions• Rotational band profile 30 cm-1 HWHM• Vibrational fine structure mostly hidden beneath rotational structure

But: • Vibrational substructure still only for low T

(8 J=0 states per symmetry)• Possible contribution from metastable dimers

1300 1400 1500 1600 1700 1800 19000.00E+000

1.00E-021

2.00E-021

3.00E-021

4.00E-021

5.00E-021

6.00E-021

7.00E-021

8.00E-021

9.00E-021

UCL

Salmi

MTCKD-1.1, 293K

WD(S&K-2003)

RAL-2007/295K/

Further Work

• 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.

• Need all states up to dissociation for RT spectra– Only 8 states per symmetry here– It is a challenge for a much higher number of states

• Improved band origins