High High ResolutionResolution SpectroscopySpectroscopyof the water of the water moleculemolecule

PhD student: Lorenzo Lodi

Thesis Advisor: Jonathan Tennyson

University College London

Department of Physics and Astronomy

Who am I?

• Degree: Materials Science, University of Milan, Italy (2005)

• Now: physics PhD student at UCL from October 2005

What do I do ?• High-resolution ab-initio prediction of vibrational-rotational spectrum of water

Importance of water• Atmospheric science: modelling of the Earth’s

atmosphere, greenhouse effect• Combustion science: rocket exaust plumes, forest fires

• Astrophysics

• Water is found in virtually all environments with temperatures inferior to ca. 4000K

• Celestial bodies within the solar system (comets, planets, moons) • In the Sun• In the interstellar medium (nebulae, star forming regions…)• Stars with low termperatures like red supergiant• Distant quasars

• Very recently, water has been found on the extra-solar planet HD 209458 b

Method of computation• 1) One calculates Potential Energy Surface and Dipole Moment Surface• 2) The Schrodinger equation for the nuclear motion is numerically solved

“exactly” using the program suite DVR3D• Computed line frequences and intensities may then be compared with

experimental data• The main source of error for vibrational states is the quality of the PES and

DMS• Our group (with Budapest et al.) have recently set up a new ab-initio DMS

which has been thoroughly tested)• It comprises a main surface based of a set of ~1500 ab-initio points and two

small corrections due to core correlation and relativistic corrections• A major difficulty was in the fitting of the data to obtain a smooth surface

without artifacts

1e-27 1e-24 1e-21 1e-18Line intensities (cm/molecule)

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• It’s been helpful in identifying some mistakenly assigned lines in HiTran• Good overall agreement for the intesities (ab. 5%) but we now now that the

reference space used is too small (not the basis set as in the PES)

Comparison with accurate data from GrenobleComparison with S. Kassi et al., Phys.Chem.Chem.Phys., 2005, 7, 2460-2467

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SP2000 This work

Other remarks• Agreement with highly accurate data is only slightly better than

the previously best surface (Schwenke and Partridge, 2000)

• The main source of error in the main surface so that the core and relativistic corrections are useless

• Subsequent test of covergence of the dipole showed that our values are basis-set converged but not correlation converged

• Some technical differences in the way the dipole is calculated from the electronic wavefunctions become of importance at our level of accuracy

Purely rotational linelist• Purely rotational transitions are important in astrophysics but their intensities

can be difficult to measure accurately (especially “forbidden” transitions, with∆Ka > 1 or ∆Kc > 1

• They have been observed in many stellar enviroments (i.e. red giants Arcturusand Betelgeuse; Orion KL star-forming region)

• Experimental accuracy is high for line frequencies (~0.01 cm-1) but not forintensities

• We considered transition within the vibrational ground state (000) → (000) and with Jmax = 15

• We compared our calculations with the available data in HiTran, in the JPL database (and others)

Allowed lines, (000) bandIntensity ratios for purely rotational (allowed) lines

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Line intensity (cm/molecule)

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Analysis of the results

• Agreement with experiment is usually at the 3% level or better (our new DMS is good!)

• We identified several probable mistakes in HiTran

• The JPL database seems to be affected by a systematicerror which makes weak lines too intense. This issue isbeing discussed.

PES accurate to dissociation

• Recent multi-laser techniques in Lausanne allowed to probe high-energystates near or above dissociation(~41,000 cm-1)

• Available PES’s for water are notadeguate to analyse data from Lausanne

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• We have extended our pre-existing PES with ~ 800 points near dissociationgeometries selected by hand

• The major problem is to fit the data toproduce a smooth surface

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Surface building methods• Least-square fit to a functional form => often spurious oscillations because of

the high degree of the polynomials included• Numerical interpolation (3D splines, Reproducing Kernel Hilbert Space,

Shepard’s method…• => requires too many points• => it’s difficult/impossible to implement correct asyptotics

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• Another complication for complete PES is a potential surface crossing at linear geometries which introduces a cusp

Acknowledgments

• The QUASAAR network for financial support

• Professor Jonathan Tennyson

• The TAMPA group at University College London