Potential energy surface, dipole moment surface and the intensity calculations for the 10 micron, 5 micron, and 3 micron bands of ozone
Oleg L. Polyansky Nikolai F. Zobov Irina I. Mizus Aleksandra A. Kyuberis Lorenzo Lodi Jonathan Tennyson






Department of Physics and Astronomy, University College London,
Gower Street, London WC1E 6BT, United Kingdom;
Institute of Applied Physics, Russian Academy of Science,
Ulyanov Street 46, Nizhny Novgorod, Russia 603950


Institute of Applied Physics, Russian Academy of Science,
Ulyanov Street 46, Nizhny Novgorod, Russia 603950


Department of Physics and Astronomy, University College London,
Gower Street, London WC1E 6BT, United Kingdom





Monitoring ozone concentrations in the Earth's atmosphere using
spectroscopic methods is a major activity which undertaken both from the ground and from space. However there are long-running
issues of consistency between measurements made at infrared (IR)
and ultraviolet (UV) wavelengths. In addition, key
O_3 IR bands at 10 , 5  and 3  also yield results
which differ by a few percent when used for retrievals. These problems
stem from the underlying laboratory measurements of the line intensities.
Here we use quantum chemical techniques, first principles
electronic structure and variational nuclear-motion calculations, to address this problem. 
A new high-accuracy   dipole moment 
surface (DMS) is computed. Several spectroscopically-determined
 potential energy surfaces (PESs)  are constructed by
fitting to empirical energy levels in the region below 7000  starting
from an  PES. 
Nuclear motion calculations using these new surfaces allow the
unambiguous determination of the  
intensities of 10  band transitions, and the computation of
the intensities of 10  and 5  
bands within their experimental
error. A decrease in intensities within the 3   is predicted which
appears consistent with atmospheric retrievals. The PES and DMS form a suitable
starting point both for the computation of comprehensive ozone line lists
and for  future calculations of electronic transition
intensities.




ozone potential energy surface dipole moment surfaces
line intensities  calculations






§ INTRODUCTION

The ozone molecule, O_3, is an important constituent of the 
Earth's atmosphere. At high altitudes its ultraviolet (UV) 
absorption bands protect life
from deadly solar UV radiation, while at low altitude ozone represents
a dangerous, poisonous pollutant. 
Monitoring of ozone concentration in the Earth's atmosphere is thus a major and important activity <cit.>
which undertaken both from the ground and from space. Much of this monitoring
is based on the use of remote sensing and therefore relies
on the availability of reliable laboratory spectroscopic data.

Another potential use of ozone spectroscopy is provided by remote
sensing of other planets, particularly exoplanets. The use of spectra
of key molecules whose presence in the atmosphere of an exoplanet could
point towards the possible presence of life, so-called biomarkers, is
the subject of active discussion <cit.>.
One of the most important biomarkers is the presence of methane
in an oxygen-rich atmosphere  <cit.>.
As diatomic oxygen does not
have a strong IR spectrum due to its symmetry, oxygen's first
derivative ozone takes on the role as an important biomarker <cit.>
alongside the O_2 A band.

Ozone can be monitored at both ultraviolet (UV) and infrared (IR)
wavelengths.
There are extensive compilations of spectroscopic data on ozone in
general spectroscopic databases such as HITRAN <cit.>, GEISA
<cit.> and the UV/Vis+ Spectral data base <cit.>, as
well as the specialist compilations for missions such as MIPAS
<cit.> and the ozone-specific 
Spectroscopy and Molecular Properties  of Ozone (SMPO) database
<cit.>. Recommended cross sections for UV absorption
by ozone are regularly reviewed <cit.>
and display a reasonable measure of self-consistency <cit.>.
The same is not true of the IR transition intensities which are
neither consistent between IR or bands between the IR and UV
<cit.>.

For atmospheric retrievals and monitoring, sub-1% accuracy in
intensity is highly desirable. However, the 3 to 4 % inconsistency
between various experimental observations of intensities of the ozone
IR absorption lines represents the present state of knowledge.  As
described in detail by Smith et al. <cit.>, the
major inconsistency is between several measurements of the strong 10
 absorption IR bands, which differ by 4 %. Some of these
measurements give atmospheric retrievals in line with the UV observation of the Hartley band at
254 nm and some of them do not.  The second important inconsistency,
between retrievals based on the 10  bands and 5  bands
intensities, is described by Janssen et al.  <cit.>.
Based on measurements due to Thomas et al. <cit.>,
it was shown by Janssen et al.  that the concentration of ozone
determined by a retrieval based on data for the 10  band is 2 to 3 %different from that based on the 5  band when using 
spectroscopic data from HITRAN 2012
<cit.>.

Recently Drouin et al.  <cit.>
attempted to validate the 10  intensities by the simultaneous
measurement of IR and microwave absorption line intensities of ozone. This study
confirmed the
HITRAN 2012  intensities for the 10  band within 1.5 %;
however, the accuracy was limited by the signal to noise ratio
of the IR data. As 10  band consists  of two vibration bands, namely ν_1 and
the much stronger ν_3 band, the signal to noise limitations should mean that for ν_3
band the discrepancy should be even less.

Finally there also appears to be a consistency problem with ozone
intensities in the 3  region. For this band the HITRAN 2016
<cit.> compilation is based on measurements due to Bouazza et al <cit.> and the SMPO database <cit.>. However
analysis by Toon <cit.> suggests that here too there are
systematic differences with line intensities when compared with results
for other wavelengths, in this case in the region of 9%.

The ozone molecule has been studied extensively both experimentally
and theoretically, see Ref. <cit.> and references therein.
In particular, an accurate ground state potential energy surface (PES)
of ozone was determined long ago by Tyuterev and coworkers
<cit.>. This PES was  subsequently further improved
<cit.>. More recently   Tyuterev et al.  <cit.>
calculated an
 dipole moment surface (DMS) and  used it to
compute intensities of the 10  band lines belonging to the  and
 band. More details of and comparisons with this work are given below.


In this paper we concentrate only on . We present a new  and
several fitted PESs for the ground electronic state of ozone, as well
as a new  DMS constructed for the purpose of calculating the
intensities of the 10 , 5  and 3  bands of ozone.
Section II presents our  PES and DMS calculations.  The  PES
is constructed mainly to be the starting point for obtaining a
spectroscopically-determined PES. Conversely, semi-empirical
adjustment of the DMS usually leads to a deterioration in the intensity
calculations <cit.>. Thus we use our  DMS for all
intensity calculations.  Section III describes the fit of the ozone
PES to spectroscopic data; we also provide a comparison of the
resulting PES with the existing ones. Section IV describes the
intensity calculations which are compared to the experimental values
and previous theoretical results.  Section V gives our conclusions and
plans for further work.




§ CALCULATION OF THE  PES AND DMS


A completely global, , ozone PES was recently constructed
<cit.> which removed previous problems with a spurious
hump in the dissociation region; this means that there is an available
 PES which is well-characterized for every geometry.

For our purposes we need both an analytical  PES and the values of
the  energies at hundreds of geometries, as both are used in our
procedure to fit the PES to experimental data; see, for example,
Bubukina et al. <cit.>.  This is because our fit
procedure uses both empirical energies and  points with a reduced
weight; including these points prevents the final PES from moving too far away
from the  surface <cit.>. This is done in order to
both avoid “holes” in the resulting PES, and to be able to fit more
PES parameters than is possible when only a limited number of
vibrational band origins are known.

We calculated both the PES and DMS at the same level of quantum
chemical theory. Experience with calculations of the DMS for  CO_2
<cit.>  shows
that, if the fundamental band origins of the molecule are predicted to better
than 1 , one can expect the sub-percent accuracy in the intensity
calculations provided the same level
 of theory is used for the DMS calculation and very accurate nuclear-motion wave
functions are used from a spectroscopically-determined PES.

These considerations resulted in the choice of the aug-cc-pwcVQZ basis
set <cit.> and of the multi-reference configuration interaction (MRCI) method
for both PES and DMS calculations. Specifically, we used the
full-valence complete active space, in which the 12 valence electrons
are free to populate all 18 valence orbitals; with this choice of
active space the electronic wave function comprises 8,029
configuration state functions at the complete active space
self-consistent field (CASSCF) and 109,785 ones at the MRCI level.  We
used the newer MRCI code implemented in the Molpro package
<cit.> using the Celani-Werner internal contraction scheme
<cit.>.  


Calculations at this level of theory took about 6 hours per geometry
running on a single modern CPU. 
 
We performed  
calculations for 4300 geometries, 2637 of which are 
below 7000  with respect to the bottom of the potential well.
The  Molpro package <cit.> was  used for all electronic structure 
calculations. 

We fitted the  energies to the following functional form

    V(S_1,S_2,S_3)= V_0+[∑_i,j,kK_ijkS_1^iS_2^jS_3^k]exp[-b_1(Δr_1^2+Δr_2^2)]+


    +E_0[exp(-2αΔr_1)-2exp(-αΔr_1)]+


    +E_0[exp(-2αΔr_2)-2exp(-αΔr_2)]+


    +exp[-b_2(θ-θ_e)]


    S_1=(r_1 +r_2)/2 -r_e, S_2=(r_1 -r_2)/2, S_3 = cosθ -cosθ_e, Δr_i=r_i-r_e

E_0=11500 , α=3.31, b_1=2.15, b_2=10, r_e=1.282 Å, 
θ_e=116.88 degrees.

Using 50 constants a root mean square (rms)  for the  energies of 1  was obtained.
Table 1 presents the J =0 energy levels calculated using the resulting  PES
and compares them to  experimental values.
 Details
of the nuclear motion calculations for rovibrational energy levels
are given in the next section.

The dipole moment points were calculated using the finite field
procedure.  We have demonstrated for both water <cit.> and
carbon dioxide <cit.> that even though the finite field method
requires more calculations, the resulting DMS is more accurate.

A polynomial functional form is used to represent the DMS: 

    μ_x(r_1, r_2, θ) = ∑_i,j,kK_ijk^xS_1^iS_2^jS̃_3^k


    μ_y(r_1, r_2, θ) = ∑_i,j,kK_ijk^yS_1^iS_2^jS̃_3^k

where the angular valence coordinates differs from that used for the potential and is given by:

    S̃_3 =θ_e -θ

where the X axis bisects the valence angle, the Y axis is perpendicular to X, 
and the  Z axis, for which μ_z=0, is perpendicular 
to the molecular plane.
The X and Y components of the dipole were fitted separately.
μ_x has the symmetry properties μ_x(r_1, r_2, θ)=μ_x(r_2, r_1, θ); the indices
were therefore selected by j = 0, 2, 4, . . . . For μ_y, the symmetry property is
μ_x(r_1, r_2, θ)=-μ_x(r_2, r_1, θ) and the indices were restricted
to j = 1, 3, 5, . . . .

For μ_X, 53 constants were fitted and 730 
 points were used. 
The root-mean-square 
(RMS) deviation of the fit was σ = 2.64 × 10^-5 au. 
For μ_y, 43 constants were fitted and 2404  points were used. The RMS
deviation of the fit was almost identical, σ = 2.65 × 10^-5 au. 
A Fortran file containing the DMS is presented in the supplementary material.



§ FITTING THE PES TO EXPERIMENTAL ENERGY LEVELS

In many different cases, such as for recent calculation for water
<cit.>, it has been shown that the accuracy of the predicted
intensities for computed absorption lines depends on the quality of
the wave functions used to represent the lower and upper states in the
corresponding transitions. Our  PES is not good enough if we want
to aim for intensity predictions accurate to better than 1 %.  Thus
fitting of the PES to the empirical energy levels is necessary.
The ab initio PES was then fitted to selected experimental
energy levels using an iterative procedure based on the method
developed by Yurchenko et al. <cit.>.

Studies on the water molecule <cit.> have shown that a
significantly more accurate PES can be obtained if we limit ourselves
to a restricted set of empirical energy levels.  In particular for
water, the highest energy involved in the fitting procedure
<cit.> was 15 000 , whereas the levels known from
conventional spectroscopy extends to 26 000 ; indeed
multi-resonance spectra <cit.> even reach
and go beyond dissociation <cit.>.  If we do not aim at
completeness or to cover all the available experimental data and
concentrate on the lower energies, significantly more accurate results
can be obtained. In particular, for H_2^16O when we fitted the
data up to 26 000  <cit.>, the standard deviation of
the fit was about 0.025 . While limiting energies to below 15 000
, more than a twofold improvement in accuracy was achieved with a
standard deviation of 0.011  <cit.>. Here we opted to fit
data significantly higher than the energies of the bands we are
interested in, but lower than the highest experimentally known energy
levels.



 §.§ Nuclear motion calculations


The nuclear-motion Schrödinger equation was solved using program
DVR3D <cit.>, which makes use of an exact kinetic energy
operator. These calculations were performed in Radau coordinates and
used Morse-like oscillators <cit.> with the values of parameters
r_e = 2.8, D_e = 0.1 and ω_e = 0.0024 in atomic units
for both radial coordinates, and associated Legendre functions for the
angular coordinate as basis functions.  The corresponding DVR grids
contained 20, 20 and 70 points for these coordinates, respectively.
The final diagonalized vibrational matrices had dimension 1500. For
the rotational problem, the dimensions of the final matrices were
obtained using the expression 400(J + 1 - p), where J is the total
angular momentum quantum number and p is the value of parity.
Atomic masses equal to 15.994915 Da were used for oxygen; using
atomic rather than nuclear masses very approximately accounts for
non-adiabatic effects <cit.>.
 


 §.§ Optimization results


Empirical
J=0 energy levels were taken from the table in SMPO data base <cit.>,
J=2 and J=5 levels were obtained from HITRAN frequencies. This gave
a total of 371 levels with energies up to  6000 cm^-1.
We varied the values of 36 
non-zero potential parameters of the starting PES, henceforth
PES ai, to obtain best agreement
with three separate sets of experimental energy levels;
as a result, we obtained three new 
potentials: 

 
  PES1  reproduces a set of 301 (70 were excluded from the fit)
empirical energy levels 
with a standard deviation of 0.027cm^-1. 

  PES2 reproduces a set of 350 (21 excluded) empirical energy levels
with a standard deviation of 0.225 cm^-1. 

  PES3   reproduces the complete set of 371 empirical energy levels
with a standard deviation of 0.693 . This rms is
dominated by the residues for so-called dark states which are only
reproduced with an rms of 1.6 . The other levels have an rms 
of 0.3 .

Most of the excluded energy levels are highly excited or have high 
values of bending quantum number ν_2; these levels are not well-described 
within our method which concentrated on getting a very accurate representation
of the stretching motions.

The method by Yurchenko et al. <cit.> allows us to
optimize simultaneously with respect to both the experimental rovibrational energy
levels and ab initio energies. This avoids creating nonphysical
features in the optimized PES. For this purpose we used a set of 2637
ab initio electronic energies in the energy region up to
7000 cm^-1 (about 2.4% of ab initio points from
the original set of 2701 energies were excluded from the fit).
Standard deviations of our final PESs from this set of ab
  initio data are about 69cm^-1,
87.2cm^-1, and 75.1cm^-1, respectively. At
the final stages of our fits the weights of ab initio points
were 3×10^-9 for PES1 and 10^-8 for PES2 and PES3, with the
empirical data unit weighted.  This was sufficient to ensure the
physically correct behavior of the fitted potentials.

rrrrrrrr
Observed band origins, in , of ^16O_3 used in the
 fitting procedures and differences between observed and calculated 
 values (in cm^-1) for three new 
spectroscopically-determined potentials.

ν_1     ν_2     ν_3     E_obs     PES ai     PES1     PES2    PES3

0     1     0      700.9310     4.43     0.0174     0.0570     0.0627 

1     0     0     1103.1370     -1.86     0.0160     0.0249     0.0291 

0     2     0     1399.2730      8.70     -0.0092     -0.0120     -0.0330 

1     1     0     1796.2620      2.51     0.0171     -0.0153     -0.0295 

0     0     2     2057.8910     -9.38     0.0666     0.0453     0.0387 

0     3     0     2094.9920     12.81     -0.0562     -0.0588     -0.1328 

2     0     0     2201.1550     -3.92     -0.0103     0.0146     0.0347 

1     2     0     2486.5760      6.72     -0.0499     -0.1087     -0.1443 

0     1     2     2726.1070     -5.13     0.0580     0.0983     0.1096 

0     4     0     2787.9000     16.66          0.5974     0.4494 

2     1     0     2886.1780      0.41     -0.0228     -0.0089     -0.0205 

1     0     2     3083.7030     -9.80     0.0036     0.1731     0.1679 

1     3     0     3173.9290     10.77          0.4359     0.3818 

3     0     0     3289.9300     -5.63     0.0073     0.0254     0.0252 

0     2     2     3390.9180     -0.97     0.0346     0.0494     0.0535 

0     5     0     3478.4000     20.73          0.0972     -0.0892 

2     2     0     3568.0700      9.42          0.2299     0.2006 

1     1     2     3739.4270     -5.63     -0.0137     0.0236     -0.0082 

1     4     0     3858.6000     15.19               -1.7993 

3     1     0     3966.7000     -1.43     0.0021     0.0799     0.0479 

0     0     4     4001.3140     -13.92     0.0155     -0.0096     -0.0403 

2     0     2     4141.4180     -0.06     0.0271     -0.0015     -0.0045 

2     3     0     4246.7000      8.84          -1.0634     -1.1265 

4     0     0     4370.3000     -6.76          -0.4440     -0.5366 

1     2     2     4390.5000     -1.43          -0.1839     -0.2234 

0     1     4     4632.8880     -2.34          -0.0333     -0.1013 

3     2     0     4643.8000     -4.54          0.0761     0.0251 

2     1     2     4783.4610     -9.25     -0.0460     -0.0089     -0.0272 

1     0     4     4922.5720     -11.67          0.1503     0.2291 

4     1     0     5038.5000     -3.08          -1.2119     -1.2083 

3     0     2     5172.0000     -13.28     -0.0653     -0.4313     -0.5617 

0     2     4     5266.9000     -3.06          -0.7619     -0.8423 

3     3     0     5310.5000      5.94     -0.1129     0.4639     0.6248 

5     0     0     5443.0000     -6.07               -3.0049 

1     1     4     5540.8980     -6.23               1.6853 

4     2     0     5701.6000      0.48          -0.0513     -0.1379 

2     0     4     5766.3200     -9.90          0.8783     1.3582 

3     1     2     5812.6000     -9.55          0.3437     0.3426 

0     0     6     5997.0000     -3.61               -2.8861 

5     1     0     6100.2100     -4.59          -0.4007     -0.5910 

0     0     1     1042.0840     -5.10     -0.0082     -0.0696     -0.0794 

0     1     1     1726.5220     -0.76     0.0054     -0.0051     0.0120 

1     0     1     2110.7840     -6.45     0.0256     0.1036     0.1026 

0     2     1     2407.9350      3.41     -0.0326     -0.0952     -0.0851 

1     1     1     2785.2390     -2.25     0.0387     0.0256     0.0224 

0     0     3     3046.0880     -12.59     0.0186     0.0639     0.0466 

0     3     1     3086.2180      7.43     -0.0419     -0.1323     -0.1696 

2     0     1     3186.4110     -8.92     0.0261     0.0822     0.0687 

1     2     1     3455.8240      1.78     -0.0313     -0.1369     -0.1418 

0     1     3     3698.2920     -8.33     -0.0006     0.0951     0.0638 

2     1     1     3849.9110     -4.81     -0.0066     0.0304     0.0207 

1     0     3     4021.8500     -11.70     0.0099     0.0544     0.0387 

1     3     1     4122.0690      5.61          0.2899     0.2788 

3     0     1     4250.2230     -10.27     -0.0069     -0.0404     -0.1484 

0     2     3     4346.7270     -4.03     0.0997     0.2117     0.1666 

2     2     1     4508.1320     -0.99          0.1729     0.1588 

1     1     3     4658.9500     -7.15     0.0201     -0.1270     -0.1879 

1     4     1     4783.2000      9.21          -0.9981     -0.9682 

3     1     1     4897.2770      2.43     0.0222     -0.0288     -0.0254 

0     0     5     4919.2030     -21.86          0.0359     0.0371 

2     0     3     5077.0950     -4.79     -0.0087     -0.3957     -0.3887 

1     2     3     5291.1710     -2.47     0.0076     0.0836     0.0483 

4     0     1     5307.7900     -11.83     0.0217     -0.4022     -0.6822 

0     1     5     5518.8120     -6.70          0.0990     0.2440 

3     2     1     5562.0000     -1.18               -2.8649 

2     1     3     5697.3230     -12.88          -0.0054     0.0216 

1     0     5     5783.7850     -9.48               1.7396 

4     1     1     5947.0700     -8.37          -0.7589     -0.8447 

1     0     5     6063.9220     -5.57          -1.1198     -1.2258 




Table 1 presents the values of the J=0 band origins
calculated using  the ab initio PES, PES1, PES2  and PES3.  
Fortran files representing all
the PESs are provided as part of
the supplementary material. Figure 1 shows a cuts through the potential (PES1) and  DMS.






§ INTENSITY OF OZONE ABSORPTION LINES IN THE 10 , 5  AND 3   BANDS


All absolute intensities quoted in are in HITRAN units” of
cm^2/(molecule cm) and converted to 100 % .

In order to calculate
line intensities analytical forms for both the PES and DMS must
be provided to the DVR3D program suite. Comparisons were made for
various PESs and DMSs: our  DMS, PES1 and surfaces from the 
recent work of Tyuterev et al. <cit.>.

Table 2 and 3 present comparisons of calculated intensities with
empirical data used in  HITRAN 2016 
and which are taken from the SMPO <cit.>
database. 
Table 2 presents a comparison of the calculated intensities using DMS
F2 of Tyuterev et al. <cit.> and our DMS using the
wave functions produced by our PES1 for the 10  (001) band which
is ozone's strongest IR band.  Comparison of the results shows that
use of DMS F2 gives results that differ from those given by our DMS by
almost 4 % when the same PES is used. We do not have access to the
PES used by Tyuterev et al. <cit.>, hence we cannot
present the results using their PES and our DMS. The results using
their PES and DMS are therefore taken from the table X of their paper
<cit.>. The difference with our results (last column) is
slightly lower – only 3 %. It would seem that the difference of 4%between different DMSs is compensated by about 1 % due to the use of
different PESs. The discrepancy with experiment given by our PES1
and DMS is significantly lower than other combinations: less than 1 %.

Table 3 gives a similar comparison for the much weaker (100) band at
9 . The difference between calculations performed with Tyuterev
et al.'s DMS F2 and our DMS is the same 4 %.  However, for this
band the discrepancy with HITRAN 2016 is slightly worse in our
calculations.

Results for the 5  (101) band line intensities are presented in
the Table 4. One can see that as for the strong (001) 10  band,
that our 5  band predicted intensities agree with the observed
intensities within the experimental uncertainties <cit.>.

The last region of interest for the problem of retrieval
inconsistencies is 2900  – 3000  region. As reported by Toon
<cit.> “The 2900-3000  also produce 8-9% too low amounts in all line lists.” This means that intensities of the
experimental lines presented in these line lists are too large by about
9%. Table 5 presents intensities for the (003) band. It can be seen
that our calculated intensities are between 7 and 11 % lower than the
HITRAN values.  This indicates that our calculated intensities should
solve the 3000  region inconsistency problem as well.
We note that our results show a distinct difference between P-branch
transitions  (difference relative to HITRAN about 7%) and R-branch
ones (difference 11%). At this stage it is unclear if this issue
is associated with the measurements or our calculations.


rrrccc
Intensities of the   band  calculated using PESs and DMSs
from Tyuterev et al.<cit.> and this work.
HITRAN intensities are given as 100% abundance in units of cm/molecule
with powers of 10 in parenthesis. Other intensities are given
as a percentage difference to these values.

Assignment    ν̃    HITRAN    (o-c)/c%                   (o-c)/c%                   (o-c)/c%  

 (001)         ()            DMS F2 <cit.>   DMS F2 <cit.>   DMS(this work)
 
                                PES <cit.>      PES1(this work)             PES1(this work)
 
15 0 14 0       1052.848      4.09(-20)        -2.7         -3.6      0.8    

17 0 16 0       1053.966      4.07(-20)        -2.7         -3.7      0.8    

16 1 15 1       1053.168      4.05(-20)        -2.8         -3.7      0.8    

15 1 14 1       1053.692      4.02(-20)        -2.5         -3.5      0.9    

14 1 13 1       1051.985      3.99(-20)        -2.7         -3.6      0.8    

17 1 16 1       1055.006      3.99(-20)        -2.6         -3.5      0.9    

18 1 17 1       1054.289      3.98(-20)        -2.8         -3.7      0.8    

13 0 12 0       1051.657      3.97(-20)        -2.6         -3.6      0.8    

15 0 16 0       1027.456      3.97(-20)        -2.4         -3.3      1.0    

14 1 15 1       1028.495      3.94(-20)        -2.4         -3.3      1.1    

13 0 14 0       1029.433      3.94(-20)        -2.4         -3.3      1.0    

19 0 18 0       1055.016	    3.93(-20)        -2.8         -3.7      0.8   
     
16 1 17 1       1026.476	    3.92(-20)        -2.4         -3.2      1.1   

13 1 12 1       1052.308	    3.91(-20)        -2.5         -3.5      0.9  

17 0 18 0       1025.426	    3.89(-20)        -2.4         -3.3      1.1  

19 1 18 1       1056.244	    3.84(-20)        -2.7         -3.6      0.9  

12 1 13 1       1030.463	    3.83(-20)        -2.3         -3.3      1.0  

16 2 15 2       1053.680	    3.81(-20)        -2.7         -3.6      0.8  

15 2 14 2       1053.520	    3.81(-20)        -2.6         -3.5      0.9  

17 2 16 2       1054.968	    3.81(-20)        -2.6         -3.5      0.9  

20 1 19 1       1055.350	    3.80(-20)        -2.9         -3.7      0.8  

15 1 16 1       1027.103	    3.79(-20)        -2.6         -3.5      0.9  

12 1 11 1       1050.741	    3.79(-20)        -2.6         -3.6      0.8  

18 1 19 1       1024.406	    3.79(-20)        -2.3         -3.6      0.7  

13 1 14 1       1029.095      3.78(-20)        -2.6         -3.5      0.9  

11 0 12 0       1031.360      3.76(-20)        -2.4         -2.2      1.0  

14 2 13 2       1052.392      3.75(-20)        -2.7         -3.6      0.8  

18 2 17 2       1054.911      3.75(-20)        -2.8         -3.6      0.9  

11 0 10 0       1050.385      3.71(-20)        -2.6         -3.6      0.8  

19 0 20 0       1023.342      3.70(-20)        -2.4         -3.2      1.1  

21 0 20 0       1056.007      3.69(-20)        -2.9         -3.7      0.8  

17 1 18 1       1025.073      3.69(-20)        -2.6         -3.4      0.9  

19 2 18 2       1056.376      3.69(-20)        -2.7         -3.5      0.9  

13 2 12 2       1052.043      3.68(-20)        -2.5         -3.5      0.9  

14 2 15 2       1028.139      3.65(-20)        -2.4         -3.4      1.0  

11 1 10 1       1050.863      3.64(-20)        -2.4         -3.5      0.9  

16 2 17 2       1026.120      3.62(-20)        -2.5         -3.4      1.0  

11 1 12 1       1031.051      3.62(-20)        -2.5         -3.5      0.9  

15 2 16 2       1026.979      3.62(-20)        -2.6         -3.4      0.9  

21 1 20 1       1057.397      3.60(-20)        -2.7         -3.6      0.9  

13 2 14 2       1029.002      3.59(-20)        -2.5         -3.5      0.9  

20 2 19 2       1056.081      3.58(-20)        -2.9         -3.6      0.8  

10 1 11 1       1032.381      3.57(-20)        -2.3         -3.3      1.0  

20 1 21 1       1022.285      3.56(-20)        -2.4         -3.9      0.9  

12 2 11 2       1051.047      3.55(-20)        -2.6         -3.6      0.9  

12 2 13 2       1030.115      3.54(-20)        -2.4         -3.4      1.0  

22 1 21 1       1056.351      3.54(-20)        -3.0         -3.7      0.7  

17 2 18 2       1024.922      3.52(-20)        -2.6         -3.5      0.9  

18 2 19 2       1024.056      3.49(-20)        -2.6         -3.3      1.0  

19 1 20 1       1023.003      3.49(-20)        -2.7         -3.4      0.9  




rrrccc
Intensities of the   band  calculated using PESs and DMSs
from Tyuterev et al.<cit.> and this work.
HITRAN intensities are given as 100% abundance in units of cm/molecule
with powers of 10 in parenthesis. Other intensities are given
as a percentage difference to these values.

Assignment    ν̃      HITRAN     (o-c)/c%                    (o-c)/c%                    (o-c)/c%  

(100)          ()                  DMS F2 <cit.>    DMS F2 <cit.>    DMS(this work) 
 
                                            PES <cit.>       PES1(this work)              PES1(this work)
 
25 1 24 0      1123.946      2.04(-21)        2.3          1.4     5.4     

26 0 25 1      1124.295      2.03(-21)        2.1          1.3     5.3     

24 0 23 1      1122.544      2.01(-21)        2.4          0.8     6.4     

27 1 26 0      1125.524      2.01(-21)        2.0          1.2     5.0     

23 1 22 0      1122.401      1.99(-21)        2.6          1.7     5.6     

28 0 27 1      1126.022      1.98(-21)        1.9          1.1     5.1     

22 0 21 1      1120.763      1.95(-21)        2.7          1.8     5.7     

29 1 28 0      1127.129      1.93(-21)        1.8          1.1     5.1     

21 1 20 0      1120.899      1.88(-21)        2.9          2.0     5.9     

30 0 29 1      1127.731      1.87(-21)        1.6          1.1     5.0     

20 0 19 1      1118.945      1.80(-21)        3.0          2.1     6.0     

31 1 30 0      1128.752      1.79(-21)        1.5                  4.9     
 
32 0 31 1      1129.426      1.72(-21)        1.4                  5.7     
 
19 1 18 0      1119.446      1.70(-21)        3.2          2.3     6.2     
 
18 0 17 1      1117.083      1.60(-21)        3.3          2.4     6.3     
 
32 0 31 1      1129.426      1.72(-21)        1.2          1.7     5.7     
 
34 0 33 1      1131.110      1.54(-21)        3.6                  4.6     
 
17 1 16 0      1118.049      1.48(-21)        1.1          2.7     6.5     
 
35 1 34 0      1132.024      1.44(-21)        3.7                  4.7     
 
16 0 15 1      1115.177      1.35(-21)        1.1          2.8     6.6     
 
36 0 35 1      1132.786      1.34(-21)        0.9                  4.6     
 
37 1 36 0      1133.671      1.24(-21)        4.0                  4.6     
 
15 1 14 0      1116.703      1.22(-21)        0.8          3.1     6.8     
 
38 0 37 1      1134.454      1.14(-21)        1.9                  4.5     
 
28 1 27 2      1123.772      1.11(-21)        2.0          1.3     5.3     
 
29 2 28 1      1129.009      1.10(-21)        1.8          1.3     5.3     
 
30 1 29 2      1125.905      1.10(-21)        2.3          1.1     5.2     
 
27 2 26 1      1127.967      1.09(-21)        2.3          1.4     5.4     
 
26 1 25 2      1121.562      1.09(-21)        4.1          1.4     5.5     
 
14 0 13 1      1113.231      1.08(-21)        1.8          3.3     7.0     
 
31 2 30 1      1130.139      1.07(-21)        2.4                  5.1     
 
25 2 24 1      1127.001      1.06(-21)        1.6          2.6     6.5     
 
32 1 31 2      1127.953      1.05(-21)        0.7          0.9     5.0     
 
39 1 38 0      1135.318      1.05(-21)        2.4                  4.5     
 
24 1 23 2      1119.287      1.03(-21)        1.6          1.6     5.6     
 
33 2 32 1      1131.357      1.01(-21)        2.8          1.0     5.0     
 
23 2 22 1      1126.090      9.75(-22)        1.4          1.9     5.8     
 
34 1 33 2      1129.918      9.65(-22)        4.5                  4.9     
 
13 1 12 0      1115.399      9.61(-22)        0.6          3.6             
 
40 0 39 1      1136.114      9.50(-22)        2.6                          
 
22 1 21 2      1116.967      9.44(-22)        1.3          1.8     5.8     
 
35 2 34 1      1132.657      9.17(-22)        3.1                  4.9     
 
21 2 20 1      1125.209      8.81(-22)        1.2          2.2     6.0     
 
36 1 35 2      1131.808      8.65(-22)        0.5                  4.9     
 
41 1 40 0      1136.964      8.60(-22)        2.9                          
 
20 1 19 2      1114.626      8.35(-22)        4.6          2.1     6.0     
 
12 0 11 1      1111.255      8.19(-22)        1.1          3.8             
 
37 2 36 1      1134.029      8.10(-22)        3.5                  4.8     
 
19 2 18 1      1124.329      7.74(-22)        0.4          2.5     6.3     
 
42 0 41 1      1137.768      7.74(-22)        1.0                  4.4     
 
38 1 37 2      1133.632      7.52(-22)                             4.8     
 


rrrrrr
Calculated  intensities  (PES1 and our DMS) of the (001), (100) and (101) bands compared with 
the measurements of Thomas et al. <cit.>.
Measured intensities are given as 100% abundance in units of cm/molecule
with powers of 10 in parenthesis. Our intensities are given
as a percentage difference to these values.

ν̃ ()     Intensity     exp. unc.%    Assign E_up     Assign  E_low   (o-c)/c % 

973.0979     1.94(-22)     2.3     58 2 57 (001)     59 2 58 (000)    	 2.6     

 974.5576     2.92(-22)     2.2     57 0 57 (001)     58 0 58 (000)    	 1.5     

 974.5809     2.36(-22)     1.5     57 1 56 (001)     58 1 57 (000)    	 0.6      

 974.5987     8.80(-23)     3.9     55 9 46 (001)     56 9 47 (000)    	-1.9     

 988.8183     1.07(-21)     0.8     47 5 42 (001)     48 5 43 (000)    	 0.6      

 994.5107     1.09(-21)     1.1     39 10 29 (001)    40 10 30 (000)   	 0.2     

1048.6125     1.53(-21)     1.6     19 13 6 (001)     18 13 5 (000)    	 0.6      

1051.3383     1.15(-21)     0.8     27 12 15 (001)    26 12 14 (000)                

1054.0585     1.63(-21)     1.6     23 12 11 (001)    22 12 10 (000)         1.0     

1058.0241     1.27(-21)     1.5     36 11 26 (001)    35 11 25 (000)         0.0     

1059.5267     1.99(-21)     1.1     36 10 27 (001)    35 10 26 (000)   	 0.1      

1065.9838     1.63(-21)     1.4     44 7 38 (001)     43 7 37 (000)    	-0.1     

1066.0126     2.14(-21)     1.5     47 1 46 (001)     46 1 45 (000)    	-0.8     

1070.4355     1.83(-21)     1.4     47 3 44 (001)     46 3 43 (000)    	 0.4      

1071.0834     1.71(-21)     1.0     47 4 43 (001)     46 4 42 (000)             

1071.9168     1.19(-21)     0.8     49 4 45 (001)     48 4 44 (000)      0.0     

                               	                 	                          

1077.9813     3.69(-22)     1.1     33 8 26 (100)     32 9 23 (000)    	 4.5   

1078.8580     3.44(-22)     1.2     30 0 30 (100)     31 1 31 (000)    	-4.9   

1079.4090     4.06(-22)     0.9     20 6 14 (100)     19 7 13 (000)    	 4.8   

1083.0592     3.39(-22)     1.3     17 5 13 (100)     16 6 10 (000)    	 5.2   

1100.0901     5.00(-22)     0.8     22 3 19 (100)     21 4 18 (000)      4.5     

1101.7616     4.93(-22)     0.7     25 3 23 (100)     24 4 20 (000)      4.5     
  
1104.0767     4.94(-22)     0.9     26 3 23 (100)     25 4 22 (000)      4.4     
  
1109.2699     5.71(-22)     0.7     10 0 10 (100)     9 1 9 (000)        6.7     
  
1111.5000     3.25(-22)     1.4     7 1 7 (100)       6 0 6 (000)        8.2     
  
1115.1773     1.32(-21)     0.7     16 0 16 (100)     15 1 15 (000)      4.2      
 
1116.7032     1.20(-21)     1.2     15 1 15 (100)     14 0 14 (000)      5.3     
  
1118.0486     1.45(-21)     1.1     17 1 17 (100)     16 0 16 (000)      4.6      
 
1119.2868     1.02(-21)     0.8     24 1 23 (100)     23 2 22 (000)      4.4    
   
1119.4463     1.67(-21)     1.0     19 1 19 (100)     18 0 18 (000)      4.3     
  
1121.5617     1.07(-21)     0.9     26 1 25 (100)     25 2 24 (000)      3.7     
  
1122.4009     1.95(-21)     1.3     23 1 23 (100)     22 0 22 (000)      3.6      
 
1122.5439     1.98(-21)     1.3     24 0 24 (100)     23 1 23 (000)      3.3     
  
1123.8503     1.51(-22)     1.0     6 3 3 (100)       5 2 4 (000)        8.2     
  
1123.9457     2.00(-21)     1.2     25 1 25 (100)     24 0 24 (000)      3.6      
 
1124.2947     1.99(-21)     1.3     26 0 26 (100)     25 1 25 (000)      3.2    
   
1124.3286     7.61(-22)     1.0     19 2 18 (100)     18 1 17 (000)      4.5     
  
1126.6751     4.60(-22)             36 2 34 (100)     35 3 33 (000)      5.5    
   
1127.2348     2.64(-22)             10 3 7 (100)      9 2 8 (000)        8.1      
 
1129.2358     3.53(-22)             13 3 11 (100)     12 2 10 (000)      7.0     
  
1129.2765     1.37(-22)             5 4 2 (100)       4 3 1 (000)        8.9      
 
1132.6569     9.07(-22)     0.5     35 2 34(100)      34 1 33 (000)      3.7      
 
1132.7860     1.33(-21)     0.5     36 0 36 (100)     35 1 35 (000)      3.6     
  
1132.8114     4.83(-22)     0.7     19 3 17 (100)     18 2 16 (000)      5.7     
  
1133.4335     2.65(-22)     0.7     10 4 6 (100)      9 3 7 (000)        8.1     
  
1133.5869     1.37(-22)     1.2     18 2 16 (100)     17 1 17 (000)      5.2     
  
1133.6317     7.44(-22)     1.1     38 1 37 (100)     37 2 36 (000)      3.6     
  
1133.6712     1.23(-21)     1.0     37 1 37 (100)     36 0 36 (000)      3.7      
 
1133.7245     5.04(-22)     0.4     21 3 19 (100)     20 2 18 (000)      4.5     
  
1133.9786     3.02(-22)     1.4     42 2 40 (100)     41 3 39 (000)      3.1      
 
1134.0288     8.00(-22)     1.2     37 2 36 (100)     36 1 35 (000)      3.4    
   
1134.2514     2.91(-22)     0.6     11 4 8 (100)      10 3 7 (000)       7.5     
  
                                                                                
  
2086.1304     4.94(-22)     0.5     19 10 9 (101)     20 10 10 (000)     -1.4     
 
2086.4723     8.82(-22)     0.5     21 8 13 (101)     22 8 14 (000)      -2.1    
  
2086.9846     3.64(-22)     0.9     18 9 10 (101)     19 9 11 (000)      -1.0    
  
2087.5873     9.23(-22)     0.8     20 8 13 (101)     21 8 14 (000)      -1.4     
 
2088.2490     3.68(-22)     0.3     17 9 8 (101)      18 9 9 (000)       -0.8   
   
2088.6874     9.44(-22)     0.5     19 8 11 (101)     20 8 12 (000)      -2.0    
  
2089.7729     9.59(-22)     0.7     18 8 11 (101)     19 8 12 (000)      -2.4   
   
2103.2106     7.43(-22)     0.4     12 12 1 (101)     12 12 0 (000)      -0.7     
 
2106.5742     8.25(-22)     0.2     14 8 7 (101)      14 8 6 (000)       -2.3    
  
2116.8712     4.77(-22)     0.7     15 10 5 (101)     14 10 4 (000)      -1.7     
 
2116.9201     9.11(-22)     0.8     11 7 4 (101)      10 7 3 (000)       -2.8     
 
2117.4047     5.21(-22)     0.7     16 10 7 (101)     15 10 6 (000)      -1.8    
  
2117.9200     5.54(-22)     0.9     17 10 7 (101)     16 10 6 (000)      -1.7    
  
2125.2044     6.59(-22)     0.7     26 8 19 (101)     25 8 18 (000)      -5.2    
  
2125.6791     6.33(-22)     2.0     27 8 19 (101)     26 8 18 (000)              
  
2132.7605     1.97(-22)     0.9     44  5 40 (101)    43  5 39 (000)     -3.6    
  
2132.8026     2.36(-22)     1.0     43  5 38 (101)    42  5 37 (000)     -1.2     
 


rrrrr
Calculated  intensities  (PES1 and our DMS) of the   (003) band compared with 
the HITRAN 2016. 
HITRAN intensities are given as 100% abundance in units of cm/molecule
with powers of 10 in parenthesis. Our intensities are given
as a percentage difference to these values.

ν̃      intensity           Assignment         Assignment        (o-c)/c % 

()    HITRAN               upper              lower                       

                                                                                   

3002.8414   	1.39(-22)          32 2 31 (003)     33 2 32 (000)         10.1  

3007.9106   	1.73(-22)   	29 3 26 (003)     30 3 27	(000)         10.8  

3014.1642   	2.41(-22)   	25 3 22 (003)     26 3 23	(000)         10.7  

3020.9156   	3.46(-22)   	21 1 20 (003)   	22 1 21 (000)         11.5  

3022.5631   	3.78(-22)   	20 1 20 (003)   	21 1 21 (000)         11.3  

3025.3709   	4.04(-22)   	18 1 18 (003)   	19 1 19 (000)         11.2  

3036.4846   	3.73(-22)   	 9 0  9 (003)     10 0 10	(000)         10.2  

3050.7231   	2.50(-22)   	 7 2  5 (003)      6 2  4	(000)    	     8.3  

3052.3788   	3.14(-22)   	11 3  8 (003)     10 3  7	(000)          7.8  

3056.9845   	3.93(-22)   	19 1 18 (003)   	18 1 17 (000)          7.8  

3057.6913   	3.27(-22)   	23 1 22 (003)   	22 1 21 (000)          7.2  

3057.7125   	2.46(-22)   	27 1 26 (003)   	26 1 25 (000)          6.4  

         








§ CONCLUSIONS


This work addresses from a theoretical perspective the long 
standing problem of inconsistency  of the IR intensities of ozone.
For the 10  band,  for which different laboratory measurements yield
results which differ by up to 4 %,  our calculations
coincide within 1 % with the measurements selected by HITRAN
and confirmed recently by simultaneous  microwave and infrared
measurements <cit.>. Furthermore, our calculations for absorption lines in the 5  band 
using the same surfaces gives results within
the experimental accuracy of about 2%. 
Finally, our results for 3  suggest that a significant
lowering of the intensities given by HITRAN in this region
is needed; this result would appear also
to be in line with recent atmospheric observations <cit.>.

The next step in this study is to produce comprehensive line lists
for  and its isotopologues, and use them as input to atmospheric
 radiative transfer models to demonstrate that their use does indeed lead to consistent
retrievals. This involves producing multiple line lists for each isotopologue
as a check on line-by-line accuracy and stability <cit.>. 
Work in this direction is currently in progress.  

The most important absorption of solar radiation by ozone is in the
UV.  The consistency between IR and UV intensity measurements is a
major outstanding problem of ozone spectroscopy.  An important step towards resolving this consistency
problem would be achieved with the accurate (within 1 %) computation of both IR and UV
bands absorption. For the UV intensity calculation several components
are necessary. A program to compute rovibronic transition intensities
for triatomic molecules has been published recently by one of us
<cit.>.  An accurate ground electronic state PES is an important
part of the electronic spectra calculations; this is presented here.
Accurate  calculated transition dipole moment surfaces and
electronic excited states PES are available in the literature <cit.>.           

Fitting of the excited-state PES to 
experimental data and further improvement of the dipole moment
calculations are in progress. This should yield accurate electronic
transition intensities calculations. Again, part of this procedure is
the accurate ground electronic state PES, presented in this work.

We include  as supplementary
material the fitted ozone PES. 
We searched the literature carefully and failed to find any freely available 
ozone PES which
had been accurately fitted to reproduce the known empirical energy levels of the ozone ground electronic state,
though results using such PESs have been presented many times.
Thus, the present PES, given in the supplementary material  as
a Fortran program, is the first freely-available, accurate  PES for ozone.



§ ACKNOWLEDGMENT

We thanks Geoff Toon (JPL) for sharing his assessment  of the HITRAN 2016
ozone line list with us and for helpful discussions.
This work was supported by  the UK Natural Environment
Research Council under grant NE/N001508/1. NFZ, IIM and AAK
acknowledge support by State Project IAP RAS No.0035-2014-009.



elsarticle-num



10
url<#>1urlprefixURL href#1#2#2 #1#1

99Solomo.O3
S. Solomon, Stratospheric ozone depletion: A review of concepts and history,
  Rev. Geophys. 37 (1999) 275–316.
http://dx.doi.org/10.1029/1999RG900008
  doi:10.1029/1999RG900008.

14FrLiLo
K. France, J. L. Linsky, R. O. P. Loyd, The ultraviolet radiation environment
  in the habitable zones around low-mass exoplanet host stars, Astron.
  Astrophys. Suppl. 354 (2014) 3–7.
http://dx.doi.org/10.1007/s10509-014-1947-2
  doi:10.1007/s10509-014-1947-2.

93SaThCa.CH4
C. Sagan, W. R. Thompson, R. Carlson, D. Gurnett, C. Hord, A search for life on
  earth from the Galileo spacecraft, Nature 365 (1993) 715–721.
http://dx.doi.org/10.1038/365715a0
  doi:10.1038/365715a0.

13GrGeGo
J. L. Grenfell, S. Gebauer, M. Godolt, K. Palczynski, H. Rauer, J. Stock,
  P. von Paris, R. Lehmann, F. Selsis, Potential Biosignatures in Super-Earth
  Atmospheres II. Photochemical Responses, Astrobiology 13 (2013)
  415–438.
http://dx.doi.org/10.1089/ast.2012.0926
  doi:10.1089/ast.2012.0926.

jt691
I. E. Gordon, L. S. Rothman, C. Hill, R. V. Kochanov, Y. Tan, P. F. Bernath,
  M. Birk, V. Boudon, A. Campargue, K. V. Chance, B. J. Drouin, J.-M. Flaud,
  R. R. Gamache, J. T. Hodges, D. Jacquemart, V. I. Perevalov, A. Perrin, K. P.
  Shine, M.-A. H. Smith, J. Tennyson, G. C. Toon, H. Tran, V. G. Tyuterev,
  A. Barbe, A. G. Császár, V. M. Devi, T. Furtenbacher, J. J. Harrison,
  J.-M. Hartmann, A. Jolly, T. J. Johnson, T. Karman, I. Kleiner, A. A.
  Kyuberis, J. Loos, O. M. Lyulin, S. T. Massie, S. N. Mikhailenko,
  N. Moazzen-Ahmadi, H. S. P. Müller, O. V. Naumenko, A. V. Nikitin, O. L.
  Polyansky, M. Rey, M. Rotger, S. W. Sharpe, K. Sung, E. Starikova, S. A.
  Tashkun, J. Vander Auwera, G. Wagner, J. Wilzewski, P. Wcisło, S. Yu,
  E. J. Zak, The HITRAN 2016 molecular spectroscopic database, J.
  Quant. Spectrosc. Radiat. Transf. 203 (2017) 3–69.
http://dx.doi.org/10.1016/j.jqsrt.2017.06.038
  doi:10.1016/j.jqsrt.2017.06.038.

jt636
N. Jacquinet-Husson, R. Armante, N. A. Scott, A. Chédin, L. Crépeau,
  C. Boutammine, A. Bouhdaoui, C. Crevoisier, V. Capelle, C. Boonne,
  N. Poulet-Crovisier, A. Barbe, D. C. Benner, V. Boudon, L. R. Brown,
  J. Buldyreva, A. Campargue, L. H. Coudert, V. M. Devi, M. J. Down, B. J.
  Drouin, A. Fayt, C. Fittschen, J.-M. Flaud, R. R. Gamache, J. J. Harrison,
  C. Hill, Ø. Hodnebrog, S. M. Hu, D. Jacquemart, A. Jolly, E. Jiménez,
  N. N. Lavrentieva, A. W. Liu, L. Lodi, O. M. Lyulin, S. T. Massie,
  S. Mikhailenko, H. S. P. Müller, O. V. Naumenko, A. Nikitin, C. J.
  Nielsen, J. Orphal, V. I. Perevalov, A. Perrin, E. Polovtseva,
  A. Predoi-Cross, M. Rotger, A. A. Ruth, S. S. Yu, K. Sung, S. A. Tashkun,
  J. Tennyson, V. G. Tyuterev, J. Vander Auwera, B. A. Voronin, A. Makie,
  The 2015 edition of the GEISA spectroscopic database, J. Mol. Spectrosc.
  327 (2016) 31–72.
http://dx.doi.org/10.1016/j.jms.2016.06.007
  doi:10.1016/j.jms.2016.06.007.

17NoHaFa
A. Noelle, G. K. Hartmann, A. Fahr, D. Lary, Y.-P. Lee, P. Limao-Vieira,
  R. Locht, F. J. Martin-Torres, K. McNeill, J. J. Orlando, F. Salama, A.-C.
  Vandaele, R. P. Wayne, M. Brunger, UV/Vis+ Spectra Data Base, 11th Edition
  (2017).

03FlPiCa
J.-M. Flaud, C. Piccolo, B. Carli, A. Perrin, L. H. Coudert, J.-L. Teffo, L. R.
  Brown, Molecular line parameters for the MIPAS (Michelson Interferometer for
  Passive Atmospheric Sounding) experiment, Atmos. Oceanic Opt. 16 (2003)
  172–182.

smpo
Y. Babikov, S. N. Mikhailenko, A. Barbe, V. G. Tyuterev,  S&MPO - An
  information system for ozone spectroscopy on the WEB, J. Quant. Spectrosc.
  Radiat. Transf. 145 (2014) 169–180.

03OrChxx.O3
J. Orphal, K. Chance, Ultraviolet and visible absorption cross-sections for
  HITRAN, J. Quant. Spectrosc. Radiat. Transf. 82 (2003) 491–504.
http://dx.doi.org/10.1016/S0022-4073(03)00173-0
  doi:10.1016/S0022-4073(03)00173-0.

16OrStTa.O3
J. Orphal, J. Staehelin, J. Tamminen, G. Braathen, M. R. De Backer, A. Bais,
  D. Balis, A. Barbe, P. K. Bhartia, M. Birk, J. B. Burkholder, K. Chance,
  T. von Clarmann, A. Cox, D. Degenstein, R. Evans, J.-M. Flaud, D. Flittner,
  S. Godin-Beekmann, V. Gorshelev, A. Gratien, E. Hare, C. Janssen, E. Kyrola,
  T. McElroy, R. McPeters, M. Pastel, M. Petersen, I. Petropavlovskikh,
  B. Picquet-Varrault, M. Pitts, G. Labow, M. Rotger-Languereau, T. Leblanc,
  C. Lerot, X. Liu, P. Moussay, A. Redondas, M. Van Roozendael, S. P. Sander,
  M. Schneider, A. Serdyuchenko, P. Veefkind, J. Viallon, C. Viatte, G. Wagner,
  M. Weber, R. I. Wielgosz, C. Zehner, Absorption cross-sections of ozone in
  the ultraviolet and visible spectral regions: Status report 2015, J. Mol.
  Spectrosc. 327 (2016) 105–121.
http://dx.doi.org/10.1016/j.jms.2016.07.007
  doi:10.1016/j.jms.2016.07.007.

03Orphal.O3
J. Orphal, A critical review of the absorption cross-sections of O_3 and
  NO_2 in the ultraviolet and visible, J. Quant. Spectrosc. Radiat. Transf.
  157 (2003) 185–209.
http://dx.doi.org/10.1016/S1010-6030(03)00061-3
  doi:10.1016/S1010-6030(03)00061-3.

12SmDeBe.O3
M. A. H. Smith, A. M. Devi, D. C. Benner, The quest for ozone intensities in
  the 9-11 μm region: A retrospective, J. Quant. Spectrosc. Radiat. Transf.
  113 (2012) 825–828.

16JaBoJe.O3
C. Janssen, C. Boursier, P. Jeseck, Y. Te, Line parameter study of ozone at 5
  and 10 μm using atmospheric FTIR spectra from the ground: A spectroscopic
  database and wavelength region comparison, J. Mol. Spectrosc. 326 (2016)
  48–59.

10ThVoDe.O3
X. Thomas, P. Von Der Heyden, M. R. De Backer-Barilly, M. T. Bourgeois,
  A. Barbe, Infrared absolute intensities of ozone in the 10 and 5 μm
  spectral range: New investigations, J. Quant. Spectrosc. Radiat. Transf. 111
  (2010) 1080–1088.

jt557
L. S. Rothman, I. E. Gordon, Y. Babikov, A. Barbe, D. C. Benner, P. F. Bernath,
  M. Birk, L. Bizzocchi, V. Boudon, L. R. Brown, A. Campargue, K. Chance, E. A.
  Cohen, L. H. Coudert, V. M. Devi, B. J. Drouin, A. Fayt, J.-M. Flaud, R. R.
  Gamache, J. J. Harrison, J.-M. Hartmann, C. Hill, J. T. Hodges,
  D. Jacquemart, A. Jolly, J. Lamouroux, R. J. Le Roy, G. Li, D. A. Long,
  O. M. Lyulin, C. J. Mackie, S. T. Massie, S. Mikhailenko, H. S. P.
  Müller, O. V. Naumenko, A. V. Nikitin, J. Orphal, V. Perevalov,
  A. Perrin, E. R. Polovtseva, C. Richard, M. A. H. Smith, E. Starikova,
  K. Sung, S. Tashkun, J. Tennyson, G. C. Toon, V. G. Tyuterev, G. Wagner, The
  HITRAN 2012 molecular spectroscopic database, J. Quant. Spectrosc.
  Radiat. Transf. 130 (2013) 4 – 50.
http://dx.doi.org/10.1016/jqsrt.2013.07.002
  doi:10.1016/jqsrt.2013.07.002.

17DrCrYu.O3
B. J. Drouin, T. J. Crowford, S. Yu, Validation of ozone intensities at 10
  μm with THz spectrometry, J. Quant. Spectrosc. Radiat. Transf. 203
  (2017) 282–292.

95BoMiBa.O3
S. Bouazza, S. Mikhailenko, A. Barbe, L. Regalia, V. G. Tyuterev, J. J.
  Plateaux, The ν_1+ ν_2+ 2ν_3 and ν_2+ 3ν+3 Bands of
  ^16O_3, J. Mol. Spectrosc. 174 (1995) 510 – 519.
http://dx.doi.org/10.1006/jmsp.1995.0019
  doi:10.1006/jmsp.1995.0019.

toonoz
G. Toon,
  https://mark4sun.jpl.nasa.gov/report/o3_spectroscopy_evaluation_20170930.compressed.pdf Evaluation of HITRAN 2016 O_3
  linelist, (private communication) (2017).
<https://mark4sun.jpl.nasa.gov/report/o3_
spectroscopy_evaluation_20170930.compressed.pdf>

17TyKaTa.O3
V. G. Tyuterev, R. V. Kochanov, S. A. Tashkun, Accurate ab initio dipole
  moment surfaces of ozone: First principle intensity predictions for
  rotationally resolved spectra in a large range of overtone and combination
  bands, J. Chem. Phys. 146 (2017) 064304.

99TyKaTa.O3
V. G. Tyuterev, S. Tashkun, P. Jensen, A. Barbe, Determination of the
  effective ground state potential energy function of ozone from
  high-resolution infrared spectra, J. Mol. Spectrosc. 198 (1999) 57–67.

ozpesconf
V. G. Tyuterev, R. V. Kochanov, S. A. Tashkun, Analytical representation for
  the ozone electronic ground state potential function in the spectroscopically
  accessible range and extended vibration predictions, in: Proceedings of
  XVII International Symposium HighRus-2012, 2012, pp. 29–50.

jt156
A. E. Lynas-Gray, S. Miller, J. Tennyson, Infra red transition intensities
  for water: a comparison of ab initio and fitted dipole moment surfaces,
  J. Mol. Spectrosc. 169 (1995) 458–467.

jt573
J. Tennyson, Vibration-rotation transition intensities from first principles,
  J. Mol. Spectrosc. 298 (2014) 1–6.
http://dx.doi.org/10.1016/j.jms.2014.01.012
  doi:10.1016/j.jms.2014.01.012.

14TyKaCa.O3
V. G. Tyuterev, R. Kochanov, A. Campargue, S. Kassi, N. Mondelain, A. Barbe,
  E. Starikova, M. R. DeBacker, P. G. Szalay, S. Tashkun, Does the "Reef
  Structure" at the Ozone Transition State towards the Dissociation Exist? New
  Insight from Calculations and Ultrasensitive Spectroscopy Experiments, Phys.
  Rev. Lett. 113 (2014) 143002–143003.

Bubukina2011
I. I. Bubukina, O. . L. Polyansky, N. F. Zobov, S. Yurchenko, Accurate water
  potential energy surface, Optics and spectroscopy 277 (2011) 346–349.

03YuCaJe.PH3
S. N. Yurchenko, M. Carvajal, P. Jensen, F. Herregodts, T. R. Huet, Potential
  parameters of PH_3 obtained by simultaneous fitting of ab initio data and
  experimental vibrational band origins, Chem. Phys. 290 (2003) 59–67.

jt613
O. L. Polyansky, K. Bielska, M. Ghysels, L. Lodi, N. F. Zobov, J. T. Hodges,
  J. Tennyson, High accuracy CO_2 line intensities determined from theory
  and experiment, Phys. Rev. Lett. 114 (2015) 243001.
http://dx.doi.org/10.1103/PhysRevLett.114.243001
  doi:10.1103/PhysRevLett.114.243001.

05Hattig
C. Hattig, Optimization of auxiliary basis sets for RI-MP2 and RI-CC2
  calculations: Core-valence and quintuple-zeta basis sets for H to Ar and
  QZVPP basis sets for Li to Kr, Phys. Chem. Chem. Phys. 7 (2005) 59–66.
http://dx.doi.org/10.1039/b415208e
  doi:10.1039/b415208e.

molpro
MOLPRO (version 2002.1) is a package of  electronic structure programs
  designed by H.-J. Werner and P. J. Knowles.

00CeWexx.methods
P. Celani, H.-J. Werner, Multireference perturbation theory for large
  restricted and selected active space reference wave functions, J. Chem. Phys.
  112 (2000) 5546.

11ShKnWe.methods
K. R. Shamasundar, G. Knizia, H.-J. Werner, A new internally contracted
  multi-reference configuration interaction method, J. Chem. Phys. 135 (2011)
  054101.

jt509
L. Lodi, J. Tennyson, O. L. Polyansky, A global, high accuracy ab initio dipole
  moment surface for the electronic ground state of the water molecule, J.
  Chem. Phys. 135 (2011) 034113.
http://dx.doi.org/10.1063/1.3604934
  doi:10.1063/1.3604934.

jt714
I. I. Mizus, A. A. Kyuberis, N. F. Zobov, V. Y. Makhnev, O. L. Polyansky,
  J. Tennyson, High accuracy water potential energy surface for the
  calculation of infrared spectra, Phil. Trans. Royal Soc. London A 376 (2018)
  20170149.
http://dx.doi.org/10.1098/rsta.2017.0149
  doi:10.1098/rsta.2017.0149.

Grechko2008
M. Grechko, P. Maksytenko, N. F. Zobov, S. V. Shirin, O. L. Polyansky, T. R.
  Rizzo, O. V. Boyarkin, Collisionally assisted spectroscopy of water from
  27 000 to 34 000 cm^-1, J. Phys. Chem.A 112 (2008) 10539.

Maksytenko20071
P. Maksytenko, N. . Zobov, S. V. Shirin, O. L. Polyansky, J. S. Muenter, T. R.
  Rizzo, O. V. Boyarkin, Approaching the full set of energy levels of water, J.
  Chem. Phys. 126 (2007) 241101.

jt494
N. F. Zobov, S. V. Shirin, L. Lodi, B. C. Silva, J. Tennyson, A. G.
  Császár, O. L. Polyansky, First-principles rotation-vibration spectrum
  of water above dissociation, Chem. Phys. Lett. 507 (2011) 48–51.

jt338
J. Tennyson, M. A. Kostin, P. Barletta, G. J. Harris, O. L. Polyansky,
  J. Ramanlal, N. F. Zobov, DVR3D: a program suite for the calculation of
  rotation-vibration spectra of triatomic molecules, Comput. Phys. Commun. 163
  (2004) 85–116.

jt14
J. Tennyson, B. T. Sutcliffe, The ab initio calculation of the
  vibrational-rotational spectrum of triatomic systems in the close-coupling
  approach, with KCN and H_2Ne as examples, J. Chem. Phys. 77 (1982)
  4061–4072.
http://dx.doi.org/10.1063/1.444316
  doi:10.1063/1.444316.

04Watson.diatom
J. K. G. Watson, The inversion of diatomic born-oppenheimer-breakdown
  corrections, J. Mol. Spectrosc. 223 (2004) 39–50.
http://dx.doi.org/10.1016/j.jms.2003.09.007
  doi:10.1016/j.jms.2003.09.007.

jt522
L. Lodi, J. Tennyson, Line lists for H_2^18O and H_2^17O based on
  empirically-adjusted line positions and ab initio intensities, J. Quant.
  Spectrosc. Radiat. Transf. 113 (2012) 850–858.
http://dx.doi.org/10.1016/j.jqsrt.2012.02.023
  doi:10.1016/j.jqsrt.2012.02.023.

jt625
E. Zak, J. Tennyson, O. L. Polyansky, L. Lodi, S. A. Tashkun, V. I. Perevalov,
  A room temperature CO_2 line list with ab initio computed
  intensities, J. Quant. Spectrosc. Radiat. Transf. 177 (2016) 31–42.
http://dx.doi.org/10.1016/j.jqsrt.2015.12.022
  doi:10.1016/j.jqsrt.2015.12.022.

jt697
E. J. Zak, , J. Tennyson, Ro-vibronic transition intensities for triatomic
  molecules from the exact kinetic energy operator; electronic spectrum for the
  C̃ ^1B_2 ←X̃ ^1A_1 transition in SO_2, J. Chem.
  Phys. 147 (2017) 094305.
http://dx.doi.org/10.1063/1.4986943
  doi:10.1063/1.4986943.

10ScMcxx.O3
R. Schinke, G. McBane, Photodissociation of ozone in the hartley band:
  Potential energy surfaces, nonadiabatic couplings, and singlet/triplet
  branching ratio, J. Chem. Phys. 132 (2010) 044305.





