Accurate reference spectroscopic information for the water molecule from the microwave to the near-ultraviolet is of paramount importance in atmospheric research. A semi-empirical potential energy surface for the ground electronic state of

Combining this potential with the latest dipole moment surface for water vapour, a line list has been calculated which extends reliably to 37 000 cm

Water vapour is a major absorber of light in the terrestrial atmosphere, and it interferes with atmospheric retrievals from the microwave to the near-ultraviolet

Observations also indicate that water vapour overlaps with near-ultraviolet absorption features of trace molecules such as

Satellite missions possessing spectrometers with detection limits extending into the near-ultraviolet are becoming more popular for both Earth and planetary studies: Hubble Space Telescope (HST) (NASA), MAVEN (NASA), CUTE

Computing an accurate line list requires three elements

Semi-empirical adjustments which start from a high-quality ab initio PES allow energy levels to be calculated to within a fraction of a wavenumber when compared to experimental measurements

The POKAZATEL line list was also designed for high-temperature applications (it is complete), yet as shown below, the POKAZATEL PES only calculates energy levels to high precision for states with low values of total angular momentum

Recent near-ultraviolet broadband cavity ring-down measurements by

In contrast,

In this work we create a new semi-empirical potential energy surface that accurately models the rotational behaviour of those high

Approximately 16 000 electronic structure calculations were previously performed for a dipole moment surface at the MR-CI (multi-reference configuration interaction) level of theory utilizing an aug-cc-pCV6Z basis set

These points need to be fitted to a functional form to obtain an ab initio PES; in the fit each data point was weighted as a function of their energy, with weights

While constructing the POKAZATEL

Due to the difficulty of fitting data in different energy regions, it is helpful to begin with a well-defined functional form; hence, the starting point for

The number of parameters,

For quanta in

The non-adiabatic correction is an important contribution to any high-accuracy potential

We use the DVR3D

These parameters have been optimized for the initial

PES refinement is a technique where one adjusts the underlying ab initio surface to reproduce measured data to a high degree of accuracy, often to within a fraction of a wavenumber

Overall, we are trying to minimize

The Hellman–Feynmann theorem allows us to efficiently calculate the derivative of an energy level with respect to a particular parameter in our potential, required for the least-squares fit. With this, we can iterate and optimize the parameters of the PES to reduce the deviation of our semi-empirical energies from the observed levels.
The MARVEL (measured active rotational–vibrational energy levels) procedure

The only near-ultraviolet energy levels available for

For our initial unrefined ab initio PES, the average deviation from the MARVEL

For the first refinement of

For the second step, the ratio of weights for those states below 26 000 cm

For the third stage, we return to

Next, for step four, we apply the weighting criteria of step two; refine

For the final optimization of our potential, we refine

The average deviation of calculated levels from those in MARVEL

It is common to provide a breakdown of residuals for the VBOs in a large table; however, as already described, these states alone cannot be used to measure how well a potential can calculate energy levels. Hence, we calculate the average deviation of the calculated energy levels using our new potential, the POKAZATEL potential and the PES15K potential to those MARVEL states with

Figure

Calculated energy levels obtained from the POKAZATEL

Transition intensities from the POKAZATEL line list

To generate transition intensities, we require an accurate dipole moment surface. The CKAPTEN

In an earlier study

In Fig.

Cross sections calculated using our new PES with the CKAPTEN DMS

Comparing our new line list to the old calculations indicates that the new potential does not greatly alter the intensities, which was expected as, for stable transitions, the DMS controls the magnitude of the absorption

In 2013,

Both

Our calculated line list is available in the Supplement and assumes 100 %

A new semi-empirical potential energy surface for the main water vapour isotopologue is created by refining

Combining our new surface with the CKAPTEN

This DMS has previously been verified through a significant number of comparisons against experimental and theoretical sources

For wavelengths below 400 nm, the POKAZATEL absorption features drop almost systematically, which explains the under-absorption observed at 363 nm

Considering the improvements this new potential surface has to offer for high-temperature spectra, future work is planned for this. The potential energy surface is available in the Supplement as a FORTRAN F90 file along with the calculated line list assuming 100 % abundance. This line list will be proposed for the HITRAN2020 water line list in the visible and ultraviolet where it will be supplied with best available experimental data, including that by

The Fortran code for the potential energy surface is provided in the Supplement. The data for this article is also provided in the Supplement.

The supplement related to this article is available online at:

EKC performed the theoretical calculations and created all figures and tables under the supervision and guidance of IEG, JT, OLP, SNY and KC. SNY contributed to the refinement procedure of the potential energy surface. EKC wrote the initial article, and all authors contributed to the final article.

The authors declare that they have no conflict of interest.

The authors would like to thank Tibor Furtenbacher and Attila G. Császár for providing energy levels originating from a provisional update to the MARVEL database.
The computations performed for this paper were conducted on the Smithsonian High Performance Cluster (SI/HPC), Smithsonian Institution.

This research has been supported by the UK Natural Environment Research Council (grant no. NE/T000767/1), NASA Aura (grant no. NNX17AI78G), NASA PDART (grant no. NNX16AG51G), and the STFC (Science and Technology Facilities Council) (grant no. ST/R000476/1).

This paper was edited by Sergey A. Nizkorodov and reviewed by Alain Campargue and two anonymous referees.