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Complete Spectroscopy of Water: Experiment and Theory
INTAS grant 03-51-3394



The overall objective of the proposal is to provide a comprehensive solution to the problem of the rotation-vibration spectrum of water. This solution will embrace both high quality experimental measurements and sophisticated theoretical models. To achieve this goal a number specific scientific objectives will be addressed:

  1. To analyze Fourier Transform (FT) spectrum of water vapour at room temperature from the infrared to the ultraviolet region, 9000 - 26000 cm-1, (over 16000 lines).
  2. To measure the water vapour high temperature absorption spectra (up to T=800 K) in the region of 10000 - 16000 cm-1, the emission spectra of oxygen-hydrogen flame (T=2000 K) in the region 10000 - 16000 cm-1.
  3. To analyze flame emission spectra (T=3000 K) in the 600 - 13000 cm-1 region (over 50000 lines), sun spot absorption spectra 400-8000 cm-1 (over 10000 lines), D2O emission laboratory spectrum, 400-8000 cm-1, 1800 K (over 45000 lines).
  4. To obtain the absorption spectrum of extremely weak transitions of HDO. To obtain the line positions and intensities of H2O in spectral windows corresponding to extremely weak transitions (1.5-1.6 micron and 1.0-1.1 micron).
  5. To obtain new energy levels of water molecule and its isotopomers from the analysis experimental data.
  6. To improve ab initio potential energy surface (PES) and dipole moment surface (DMS) by extending previous ultra-high accuracy calculations, by performing better treatment of corrections to Born-Oppenheimer (BO) approximation and increasing the level of electronic structure theory.
  7. To create theoretical models within the Effective Hamiltonian (EH) and Effective Dipole Moment (EDM) approaches which are able to predict all the H2O and H2S vibration-rotation transitions within the ground electronic state.
  8. To obtain new data on line intensities, N2 and air broadening and shifting. To model pressure broadening and pressure shifts taking into account strong excitation effects. To use these data to study the H2O line broadening and shifting under strong excitation and to create the databases for various applications.
  9. To fit ab initio PES using existing and new experimental energy levels which give levels with an accuracy close to 0.01 cm-1 (the average experimental accuracy).
  10. To compile new line lists based on both variational calculations and more accurate EH calculations. To create a new database of H2O, and possibly H2S, experimental energy levels.
  11. To prepare new experimental and theoretical data for inclusion to present spectroscopic databases (HITRAN, GEISA...) and to distribute this data using appropriate means such as the World Wide Web.

Background and Justification

The spectrum of water is arguably the single most important spectrum of any molecule. Therefore many years of work, both experimental and theoretical, have been devoted to trying to both catalogue and understand this spectrum. Despite these efforts, short-wavelength (near infrared, visible and even near ultraviolet) spectra which probe highly excited vibrational states and high temperature spectra, which also probe highly excited rotational states remain poorly characterised.

These spectra are of vital importance for a range of applications including atmospheric transmission, combustion modelling and astrophysical applications such the atmosphere of dwarf stars and even sunspots. Modellers rely on data bases of transitions (line positions, intensity, assignments and pressure-dependent parameters). Typical atmospheric databases contain over 30,000 transitions due to water. Recent theoreticallydriven attempts to solve all aspects of the water spectroscopy problem have produced data bases with approaching a billion transitions. So far none of these huge data bases offer the required accuracy.

Recent years have seen major advances in water spectroscopy driven experimentally by the use of lasers to give ultra-long path-lengths and therefore, in principle, very high sensitivity. On the theoretical side, the use of variational calculations has revolutionised the taxing problem of assigning the spectra involving highly excited states, an essential step for applications using this data. Furthermore, recent advances in ab initio theory, breaching the 1 cm-1 accuracy barrier for water for the first time, raise the real possibility that accurate spectra could be calculated using first principles quantum mechanics.

Application of these methods has led to numerous experimental and theoretical studies of water spectra. Thousands of new energy levels have been obtained experimentally. Overall these have led to an increase in the number of known experimentally energy levels by a factor of about three and a similar increase in the assigned transitions. Despite this work, there remains significant problem with the spectrum of water: many spectra remain poorly analyzed, for example only 15% of the transitions observed in sunspots actually have quantum number assignments. The incompleteness of our knowledge of water spectra has significant practical consequences: for example the exact contribution of absorptions by water vapour to the earth’s energy budget remains a subject of debate and the analysis of data obtained from earth remote sensing experiments on board satellites such as ENVISAT is severely hampered by the uncertainties in the laboratory data for water. There is thus the utmost need for a coordinate attack on the spectroscopy of water which combines both high class theory and state-of-the-art laboratory work.

This proposal aims to provide a comprehensive solution to the rotation-vibration spectrum of water by combining world-leading laboratories that specialise in the measurement, calculation and analysis of the spectra of small molecules and in particular water. To do this it is necessary to characterize line positions, intensities, assignments and behaviour under different physical conditions (temperature and pressure). This goal requires thorough experimental coverage of key spectral regions which can be used to validate high accuracy ab initio and semiempirical models. A major deliverable will be the provision comprehensive data on water spectra for use by modellers.

To achieve these aims the complementary theoretical approaches will be employed: semiempirical and ab initio. Semiempirical methods are capable, in principle, of achieving experimental accuracy. These methods use either variational calculations based on potential surfaces fitted to spectroscopic energies or effective Hamiltonians expansions. As yet ab initio approaches do not give this accuracy but are important as they are complete (i.e. can probe all wavelengths and even transitions of vanishingly small intensity), are used to seed the semiempircal fits and provide accurate dipole surfaces which are necessary to generate line intensities.

This proposal combines the efforts of laboratories, which have made a major contribution to the development of theoretical and experimental studies of water spectra. They will deliver a comprehensive solution to the water spectral problem which has many important uses. Application of the methods developed to related triatomic molecules such as H2S will also be explored.

The participating teams have immense experience developing spectroscopic experimental and theoretical methods and applying them for measuring and analyzing molecular spectra. Highly sensitive intracavity laser spectrometers were developed and used for weak line investigations in 70-90s in Institute of Atmospheric Optics (IAO team). Since 1972, when the team had began to build up such spectrometers there is a continuing work in the field, and the team has published first monographs in this subject in Russian and English , [1]. These spectrometers allowed recording of many weak lines of H2O, CO2, C2H2, CH4, and their isotopomers in the spectral region higher 8000 cm-1. At the present highly sensitive laser spectrometers are widely used in the IAO for study of molecules at high excitation (at high temperature, in flame, in discharge); and new type of spectrophotometric gas analyzers are being developing for atmospheric tasks.

In the University Joseph Fourier of Grenoble, France (UNIJFG team) a number of ultra sensitive absorption laser techniques were developed in recent years, including Intracavity Laser Absorption Spectroscopy, Cavity-Ring Down Spectroscopy, Cavity Enhanced Absorption Spectroscopy [2], [3]. The investigated molecules include water, acetylene, hydrogen sulfur, methane, silanes and their isotopic derivatives. The higher sensitivity of UNIJFG methods in comparison with say Fourier Transform Spectroscopy methods allows for a considerable increase of the number of observed weak lines.

Until recent years the main theoretical method of analyzing spectra of water and related molecules were Effective Hamiltonian (EH) approach. The theoreticians from IAO team since 80-s are taking part in development of models within the EH and Effective Dipole Moment (EDM) approaches. This work was done in parallel with analyzing experimental spectra with results published in tens of papers [4]. The team from Institute of Applied Physics of Russian Academy of Sciences (IAP team) also has long and successful history in studying light molecules. First theoretical works studying water spectrum were published in early 80-s. Originally the analysis was done using Effective Hamiltonian approach. Leader of the IAP team O.L. Polyansky in 1985 proposed Pade-Borel method of EH series summation [5] since then widely used for studying water and related molecules spectra.

Since early 90-s progress in development of computational hardware and ‘software’ lead to variational calculations taking the bigger part in analyzing spectra of triatomic molecules. In particular the program suit DVR3D [[6]] for variational calculations of vibration-rotation energy levels using the exact kinetic energy operator for nuclear motion was developed in the University College London, UK (UCL). The accuracy of variational calculations is mostly determined by the quality of potential energy surface (PES). The UCL and IAP teams had developed semiemperical PESes for H2O and H2S which were the best at the time [7], [8]. The difficulties in getting spectroscopic accuracy (0.01 cm-1) with variational calculations meant that it was necessary to take into consideration corrections to Born-Oppenheimer (BO) surface. In 1997 H. Partridge and D.W. Schwenke calculated ab initio PES of water (J. Chem. Phys., 106, 4618 (1997)) with highest for the time accuracy. They also optimized the ab initio surface to get semiempirical PES with standard deviation of about 0.1 cm-1 for energy levels included in the fitting. Adding of adiabatic correction to the surface allowed IAP team in cooperation with UCL to start analyzing complicated experimental spectra of water. In particular the absorption spectra of sun spots were studied [9].

In cooperation of IAP, UCL and team from Eotvos Lorand University, Hungary (ELTE) electronic relativistic and quantum electrodynamics corrections to BO PES of water were calculated [10], [11] giving significant improvement in theoretical predictions. In parallel with development of theoretical calculations methods UCL and IAP analyzed a number of spectra of H2O and it’s isotopomers, including sun spot spectra (T=3300 K), room temperature spectra in 9000 – 26000 cm-1 region, hot (T=1800 K) emission laboratory spectra. Tens of thousands of lines were analyzed and assigned. This leaded to doubling of the number of observed energy levels of water molecule from about 6000 to 12000. The new compilation of energy levels was published in [12]. Using of corrections to BO surface and newly determined energy levels allowed IPF and UCL teams to optimize PS ab initio PES to get semiemperical potential with 0.1 cm-1 standard deviation for almost all known energy levels [13] of H216O.

In cooperation of ELTE, UCL and IAP teams very elaborate non-relativistic electronic structure calculations of water were performed, also considering a variety of small physical effects arising from a fully relativistic treatment, breakdown of the BO approximation, and even quantum electrodynamics. The result was ab initio PES of water determining the vibration-rotation energy level structure to better than 1 cm-1 on average [14]. Ab initio improvements of this PES with it’s optimization using now known and obtained during the project energy levels should lead to determining of semiempirical PES with about 0.01 cm-1 accuracy.

The problem of calculating line intensities is much less developed then that of line frequencies. The calculations of dipole moments converge differently from those of energies. Empirical DMSs rely on absolute spectroscopic intensity measurements, which are notoriously difficult to carry out with high accuracy. In [15] dipole moments of highly vibrationally excited water were measured for the first time and calculated by ELTE, UCL and IAP teams. The calculations suggested that the best currently available potential and dipole surfaces do not accurately model intensities in the optical spectrum of water. The IAO and UNIJFG teams have a long experience of experimental studies of transition intensities and pressure effects on lineshape. IAO team developed a number of methods using Effective Dipole Moments for its modelling.

Semiempirical methods of using experimental data for calculations of energy levels and intensities open possibility of obtaining results with experimental accuracy. EH methods give better accuracy but for limited spectral regions while variational calculations can provide overall outline of whole water spectrum. Their combination in one project gives unique opportunity to solve the problem of high resolution water spectrum.

The project teams publications:


  1. Sinitsa L.N,
    Encyclopedia of Optical Engineering.,
    (EOE). Published by Markel Dekker, Inc. No 120009765, 1990.
  2. Bertseva E., A. Kachanov and A. Campargue,
    Intracavity laser absorption spectroscopy of N2O with a vertical external cavity surface emitting laser,
    Chemical Physics Letters, 2002, Volume 351, Issue 1-2, Pages 18-26,
    DOI: 10.1016/S0009-2614(01)01321-5.
  3. Ding Y., O. Naumenko, S-M. Hu, E. Bertseva, and A. Campargue,
    The absorption spectrum of H2S between 9540 and 10 000 cm-1 by intracavity laser absorption spectroscopy with a vertical external cavity surface emitting laser,
    Journal of Molecular Spectroscopy, 2003, Volume 217, Issue 2, Pages 222-238,
    DOI: 10.1016/S0022-2852(02)00037-1.
  4. Bykov A., O.Naumenko, A.M.Pshenichnikov, A.Scherbakov, and L.Sinitsa,
    Expert System for line identifications in rovibrational spectra,
    Optics and Spectroscopy, 2003, Volume 94, no. 4, Pages 528-537,
    DOI: 10.1134/1.1570477.
  5. O.L. Polyansky,
    One-dimensional approximation of the effective rotational Hamiltonian of the ground state of the water molecule,
    Journal of Molecular Spectroscopy, 1985, Volume 112, Issue 1, Pages 79-87,
    DOI: 10.1016/0022-2852(85)90193-6.
  6. Tennyson, J.R. Henderson and N.G. Fulton,
    DVR3D: for the fully pointwise calculation of ro-vibrational spectra of triatomic molecules,
    Computer Physics Communications, 1995, Volume 86, Issue 1, Pages 175-198,
    DOI: 10.1016/0010-4655(94)00139-S.
  7. Polyansky O.L., P. Jensen and J. Tennyson, J,
    A spectroscopically determined potential energy surface for the ground state of H216O: A new level of accuracy,
    Journal of Chemical Physics, 1994, Volume 101, Pages 7651-7657,
    DOI: 10.1063/1.468258.
  8. Polyansky O.L., P. Jensen and J. Tennyson, J.,
    The potential energy surface of H216O,
    Journal of Chemical Physics, 1996, Volume 105, Pages 6490-6497,
    DOI: 10.1063/1.472501, http://link.aip.org/link/?JCPSA6/105/6490/1.
  9. Polyansky O.L., N.F. Zobov, J. Tennyson, S. Viti, P.F. Bernath and L. Wallace,
    Water on the Sun: Line Assignments Based on Variational Calculations,
    Science, 1997, Volume 277, no. 5324, Pages 346-348 DOI: 10.,
  10. Harry M. Quiney, Paolo Barletta, György Tarczay, Attila G. Császár, Oleg L. Polyansky, Jonathan Tennyson,
    Two-electron relativistic corrections to the potential energy surface and vibration-rotation levels of water,
    Chemical Physics Letters, 2001, Volume 344, Pages 413-420,
    DOI: 10.1016/S0009-2614(01)00784-9.
  11. P. Pyykko, K.G. Dyall, A.G. Csaszar, G. Tarczay, O.L. Polyansky, J. Tennyson,
    Physical Review, A, 2001, Pages art. no. 024502.
  12. Tennyson J., N.F. Zobov, R. Williamson, O.L. Polyansky and P.F. Bernath,
    Experimental Energy Levels of the Water Molecule,
    Journal of Physical and Chemical Reference Data, 2001, Volume 30, Issue 3, Pages 735-831,
    DOI: 10.1063/1.1364517, http://link.aip.org/link/?JPCRBU/30/735/1.
  13. Shirin S.V., O.L. Polyansky, N.F. Zobov, P. Barletta and J. Tennyson,
    Spectroscopically determined potential energy surface of H216O up to 25 000 cm-1,
    Journal of Chemical Physics, 2003, Volume 118, Issue 5, Pages 2124-2129,
    DOI: 10.1063/1.1532001.
  14. Polyansky O.L., A. G. Császár, S.V. Shirin, N.F. Zobov, P. Barletta, J. Tennyson, D.W. Schwenke and P.J. Knowles,
    High-Accuracy ab Initio Rotation-Vibration Transitions for Water,
    Science, 2003, Volume 299, no. 5606, Pages 539-542,
    DOI: 10.1126/science.1079558.
  15. Callegari A., P. Theule, R.N. Tolchenov, N.F. Zobov, O.L. Polyansky, J. Tennyson, J.S. Muenter and T.R. Rizzo,
    Dipole moments of highly vibrationally excited water,
    Science, 2002, Volume 297, Pages 993-995,
    DOI: 10.1126/science.1073731.

Грант INTAS 00-189