The spectrum of radioactive water vapor: the H₂¹⁹O radio-isotopologue

Abstract

The absorption spectrum of H₂¹⁹O, a radioactive isotopologue of the water molecule, is predicted using variational nuclear motion calculated based on a high precision potential energy function and ab initio dipole moment surface. Vibrational - rotational energy levels and wave functions, line centers and Einstein coefficients for dipole transitions are calculated. Predicted transition wavenumbers are improved by extrapolating known empirical energy levels of the stable H₂¹⁶O, H₂¹⁷O and H₂¹⁸O isotopologues to H₂¹⁹O. A line list for possible atmospheric application is presented which includes air line broadening coefficients. The calculations span a wide spectral range covering infrared and visible wavelengths, and are appropriate for temperatures up to 1000 K. Windows suitable for observing absorption by H₂¹⁹O are identified and comparisons made with the infrared spectra of water vapor in natural abundance, H₂¹⁵O and H₂¹⁴O.

Introduction

Water is one of the most important substances for humanity and its environment. Therefore, there are a large number of scientific works studying water and, in particular, the water molecule, its properties, reactivity, spectra, and isotopic composition.

Measurements and calculations of the absorption, emission, or scattering spectra of radioactive water isotopologues (radio-isotopologues) are of interest for many reasons. Radio-isotopologues of atmospheric gases, including H$_2$O, are formed in the atmosphere when the Earth is irradiated by cosmic rays. The interaction of atmospheric molecules with cosmic rays leads, for example, to the accumulation in the atmosphere of triterated water, HT$^{16}$O, and the carbon dioxide radio-isotopologue $^{14}$CO$_2$ [11]. It has been shown that various radio-isotopes of beryllium, carbon, nitrogen, and oxygen can be produced by lightning discharges [3, 29], which also leads to the appearance of radio-isotopologues such as $^{16}$O$^{15}$O and H₂¹⁵O in the atmosphere. We [51] previously showed that radio-isotopologue H₂¹⁵O is apparently present in trace amounts in the atmosphere during thunderstorms. Radioactivity occurring during a thunderstorm front is discussed by Bordonskiy [4].

Oxygen-19 is also found in the cooling circuits of nuclear reactors [8, 55], Nemoto et al. [28] discovered that radio-isotopologues of water are formed when a target containing deuterium is irradiated with femtosecond laser pulses, and the mechanism of production of these isotopologues is similar to their production in lightning discharges. Other radio-isotopologues of water, H₂¹⁹O and H$_2^{\ 20}$O, are produced in the primary cooling circuits of nuclear reactors [43]. The contribution of these isotopic modifications to radioactivity fields at nuclear power plants should be taken into account. Inside water-cooled fusion reactors, water is irradiated by neutrons when it passes the reactor core. This causes higher doses around the primary coolant: the main observed nuclides are $^{16}$N and $^{19}$O [19]. Similarly, these radioisotopes are also found in pressurized water reactors (PWRs) [43, 55] which has raised safety concerns [12, 17]. So far, only nuclear spectra (decay of the $^{19}$O atom) have been recorded [8]. It is clear that $^{19}$O lives long enough to form water molecules; however, the spectrum if H₂¹⁹O has yet to be investigated.

In the 1970 abstract review [1] there is mention of work on $^{19}$O and H₂¹⁹O (Investigation of the recoil chemistry of $^{19}$O and of radiolysis of water by reactor radiation. Blaser W. 1970. 79p. Dep. SFSTI (in German)). This abstract discussed the energies of $^{19}$O and some molecules such as H₂¹⁹O, H$^{16}$O$^{19}$OH, $^{16}$O$^{19}$OH and $^{16}$O$^{19}$O. A number of monographs discussing $^{19}$O species, including water, are available [2, 15, 20, 21, 23, 25, 30, 34, 36,37,38,39, 44]. In addition, there are a large number of monographs that consider the 6 main isotopes of oxygen from H₂¹⁴O to H₂¹⁹O.

To address the various scientific and technical problems involved with the presence of radioactive water, detailed information is needed on the spectra of water radio-isotopologues. Since measuring the spectra of short-lived radioactive substances is costly and difficult due to both safety issues and the short lifetime of radio-isotope, the most convenient way to determine their spectrum is to calculate it using a high-precision methods benchmarked for the stable isotopologues against the extensive available experimental data. We have previously computed predicted spectra for H₂¹⁵O [51, 53] and H₂¹⁴O [52]. The present work is aimed at studying the vibrational and rotational states of the short-live radio-isotopologue of the water molecule H₂¹⁹O, and the associated spectrum at infrared (IR) and visible wavelengths. The calculations are carried out by combining two different techniques. The first of them uses a high-precision potential energy surface [6], which includes non-adiabatic and relativistic corrections, and the variational nuclear-motion code DVR3D [40]. The second step employs a simple quadratic approximation based on using the known empirical energy levels of three stable isotopologues H₂¹⁶O, H₂¹⁷O and H₂¹⁸O to improve the predicted transition frequencies. Calculations of vibrational energy levels of H₂¹⁹O as well as other isotopologues of water vapor (H$_2^{\ X}$O, where X =11,...,26) were early presented in Ref. [47].

Table 1 presents data on different oxygen isotopes. It can be seen that after $^{15}$O and $^{14}$O, $^{19}$O has the longest half-life. This also indicates the importance of predicting the spectrum H₂¹⁹O.

Table 1 Atomic mass and half-life for known isotpes of oxygen $^X$O, X=13,..,23 [27]

An key focus of our study is to show that at the current level of development of the theory, expensive and complex experiments can be replaced by calculations without loss of accuracy and reliability. Moreover, calculations within the framework of our semi-empirical approach allow not only the calculation of absorption spectra with high accuracy, but also thermodynamic functions such as the temperature-dependent entropy and heat capacity.

Calculated spectrum and of line list of H₂ ¹⁹O

The theoretical absorption spectrum of H₂¹⁹O is obtained via direct variational calculation of line centers and intensities for states with rotational levels with $J\le 20$ using a high accuracy potential energy surface (PES) [6], and an ab initio dipole moment surface (DMS) [22]. The calculations were carried out as follows. First, the vibrational-rotational (VR) energy levels and associated wavefunctions for H₂¹⁹O were computed using the DVR3D variational nuclear-motion package [40]. These calculations followed the same procedure used for other water radio-isotopologues [52, 53], but with mass of the oxygen atom set to 19.003577969 Da. The calculations were carried out on the “amun” cluster (UCL, London, UK). This procedure has been used to produce a number of line list for H$_2$O and it isotopologues including BT2, VTT [49], POKAZATEL [33], Conway [10], HotWat78 [32] and VoTe [50].

The line list for H₂¹⁹O, which we call VoTe-19, is designed for use at room temperature over a wide range of wavenumbers. It contains 72 920 states and 106 680 822 (more then one hundred million) transitions in total. The H₂¹⁹O (VoTe-19) line list is available from the ExoMol database www.exomol.com using ExoMol format [41]. Extracts from the States .states and Transition .trans files are shown in Tables 2 and 3, respectively. The H₂¹⁹O .trans files contain Einstein A coefficients (in s$^{-1}$) together with the upper and lower state ID numbers. The transitions are divided into twelve Transition files according the the following spectroscopic ranges: 0–500, 500–1000, 1000–1500, 1500–2000, 2000–2500, 2500–3500, 3500–4500, 4500–5500, 5500–7000, 7000–9000, 9000–14,000, 14,000–25,000 cm$^{-1}$.

The State file contains a list of ro-vibrational states of H₂¹⁹O with the state ID numbers, energy term values (in cm$^{-1}$), uncertainties (in cm$^{-1}$) and quantum numbers: the provision of which are discussed below. The exact quantum numbers are the total angular momentum J and the total symmetry $\Gamma = A_1, A_2, B_1, B_2$ in the Molecular Symmetry group C$_{2v}$(M). The total state degeneracy, $g_i$ is given by (2J+1) times the nuclear spin factor, $g_\textrm{ns}$. $^{19}$O has a nuclear spin of $I=\frac{5}{2}$ which for H₂¹⁹O leads to $g_\textrm{ns}=6$, 6, 18, and 18 for $\Gamma = A_1, A_2, B_1, B_2$, respectively.

In addition, for some of the levels, approximate quantum numbers are given using standard harmonic oscillator - rigid rotor designations: $v_{1},v_{2},v_{3},K_{a},K_{c}$; the provision of these is discussed below. Here $v_1, v_2, v_3$ are the normal mode vibrational quantum numbers, $K_a$ and $K_c$ are the oblate and prolate rotational quantum numbers (projection of the angular momentum on the a and c molecular axes, respectively).

DVR3D only supplies rigorous quantum numbers which for H$_2$O correspond to J, parity and whether the state is ortho or para. To provide the approximate rotation and vibration quantum labels, namely $v_{1}$, $v_{2}$, $v_{3}$, $K_{a}$ and $K_{c}$, we matched the H₂¹⁴O energies to the assigned states of the parent isotopologue H₂¹⁶O as provided in the VoTe line list [50], which was based on the calculations with the same PES [50]. Following VoTe, here we also provide the parity of the $K_{c}$ quantum number, which can be reconstructed from the (rigorous) values of J and the total symmetry $\Gamma$ as shown in [7]. ExoMol [41, 42] standard notation is adopted and the value “NaN” is to denote undetermined quantum numbers.

As an attempt to improve the energy levels, and hence transition wavenumbers, predicted for H₂¹⁹O, we apply pseudo-experimental corrections given by Eq. (1) below to the set of 3426 empirical energy levels identified as common to all three stable isotopologues of interest. These states are indicated with the label “IE” (isotopologue extrapolation [24]) in contrast to all other, calculated values, labelled with “Ca”. Following the pseudo-experimental extrapolation method proposed in [32, 33], we use the obs.-calc. residuals obtained for the parent isotopolgue to obtain empirical corrections to the ro-vibrational energy values of the minor isotopologues of water as follows:

$$\begin{aligned} E_{N}^\textrm{corr} = E_{N}^\textrm{calc} + E_{16}^\textrm{obs}-E_{16}^\textrm{calc}, \end{aligned}$$

(1)

where $E_{N}^\textrm{calc}$ is a DVR3D energy calculated for a isotopologue, $N=17,18, 19$, and $E_{16}^\textrm{obs}-E_{16}^\textrm{calc}$ is an empirical correction estimated as the difference between the calculated and experimental energies of H₂¹⁶O. The approach is based on the assumption that the main source of the error is from the inaccuracy of the Born-Oppenheimer PES of water, which should affect all four isotopologues similarly and was shown to work well for H₂¹⁸O and H₂¹⁷O [32, 33].

The provision of uncertainties in the energy levels is now a formal part of the ExoMol data structure [41, 42]. For the pseudo-experimental values, the uncertainties are estimated as the the obs.-calc. residuals of the H₂¹⁷O isotopologue obtained as the difference between the W2020 and DVR3D energy values. For the other levels, formula (2) was used:

$$\begin{aligned} \textrm{unc} = \Delta \xi \tilde{E} + \Delta B J(J+1), \end{aligned}$$

(2)

with $\Delta \xi$=1/35000 cm$^{-1}$ and $\Delta B$=0.0005 cm$^{-1}$. Formula (2) was obtained via correlation and auto-correlation methods [5] applied to the W2020 [14] data of the three isotopologues in conjunction with the method of Voronin et al. [52]. For H₂¹⁶O, we can use residuee for the 19225 empirical energy levels provided W2020, and calculate the errors using formula (2). For rotational-vibrational states, where the energies of all three H₂¹⁶O isotopologues were present in W2020, we used the double uncertainty of the main isotopologues, since it is very small.

A total 3426 levels were replaced by the pseudo-experimental values. The maximum deviations of these changes do not exceed 0.1 cm$^{-1}$.

Table 2 Extract from the .states file of the H₂¹⁹O line list

Table 3 Extract from a .trans file of the H₂¹⁹O line list

Spectrum of H₂ ¹⁹O for applications

The line list produced was used to model spectra of H₂¹⁹O.

A 296 K, room temperature H₂¹⁹O line list was generated using the intensity threshold of >$10^{-30}$ cm/molecule for atmospheric applications containing 250 224 lines. The line list is provided as part of the supplementary material in a HITRAN-like format [16], see Table 4.

The HITRAN database provides data for seven isotopologues of water using the following isotopologue codes: 11(H₂¹⁶O), 12(H₂¹⁸O), 13(H₂¹⁷O), 14(HD$^{16}$O), 15(HD$^{18}$O), 16(HD$^{17}$O), 17(D$_2^{\ 16}$O). We adopted 18 as a code for H₂¹⁵O [53] and 10 for H₂¹⁴O [52]; here we use 19 for H$_2^{\ 19}$O. None of this number have yet to be adopted by HITRAN. The line list consists of the isotopologue code (19) (Molecule number 1 + Isotopologue number 9), line positions, 296 K intensities (cm/molecule), Einstein coefficients (s$^{-1}$), air-broadened widths ($\gamma _\textrm{air}$, cm$^{-1}$/atm), self-broadened widths ($\gamma _\textrm{self}$, cm$^{-1}$/atm), temperature dependence component of air $n_\textrm{air}$, line shifts (set to 0.0 cm$^{-1}$) and ro-vibrational quantum number. The line broadening parameters were evaluated using the J and ‘$JJ-$dependency’ methods [46, 48]. For the temperature-dependence exponent $n_{air}$ (unitless) we assumed the water vapor air-broadened half-widths from Table 7 of HITRAN2004 [35].

Table 4 Examples spectrum of H₂¹⁹O for applications

Partition function, Q(T), for H₂ ¹⁹O as a function of temperature, T(K).

Using vibrational-rotational energy levels, the partition function of H₂¹⁹O was calculated for different temperatures up to 1000 K using

$$\begin{aligned} Q(T)=\sum \limits _{i} g_i \text {exp}\bigg (-\dfrac{E_i}{kT}\bigg ). \end{aligned}$$

(3)

Fig. 1 shows a comparison of partition functions Q(T) of the H₂¹⁹O, H₂¹⁶O and H₂¹⁵O species for the temperature range from 1 to 1000 K. The main difference is the nuclear spin factor, which is 6 times larger for H₂¹⁹O than for H₂¹⁶O. Furthermore, the partition function of H₂¹⁶O is significantly more complete, with the levels from [50] covering the rotational excitations up to $J=50$.

Fig. 1

Partition function Q(T) for H₂¹⁹O, H₂¹⁶O and H₂¹⁵O water for temperature range from 1 to 1000 K

In principle, with a set of levels up to 25,000 cm$^{-1}$ and up to J = 20, our partition function of H₂¹⁹O should be appropriate for up to 800 K. Using our results for temperatures higher than this will lead to resulting spectra becoming increasingly incomplete, for more details about partition function see [18, 45]. Our partition function for H₂¹⁹O as in presented as a table in the Supplementary materials (Part-Fun-H219O-J20.dat).

Estimated possibility of detecting H₂ ¹⁹O in laboratory conditions

The isotopologues of H$_2$O have characteristic absorption fingerprints in the IR spectral region and can be analyzed quantitatively and qualitatively using spectroscopic methods. The advantage of high resolution spectroscopy is that it is a non-destructive and non-invasive method which allows simultaneous monitoring of several species in real time.

To reveal spectral windows in which H₂¹⁹O could be detected under laboratory conditions, we simulated the transmission of main isotopologues of H$_2$O (H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, HD$^{16}$O, HD$^{18}$O, HD$^{17}$O) in natural abundance with the addition H₂¹⁹O at high spectral resolution for $T=294$ K, atmospheric pressure of 1013 mbar, partial pressure of H$_2$O 18,800 ppm and path length of 100 m. The H₂¹⁹O/H$_2$O ratio was varied from 0.1 to 1%. Transmission was calculated using a line-by-line method [26] with a boxcar apparatus function.

The absorption line parameters, needed for the line-by-line transmission calculation, are the line intensity, S (cm$^{-1}$/molecule cm$^{-2}$), position of the line centre, $\nu ^*$ (cm$^{-1}$), lower-state energy, E (cm$^{-1}$), air- and self-broadened half-widths $\gamma _\textrm{air}$ and $\gamma _S$ (cm/atm), and temperature-dependence exponent for $\gamma _\textrm{air}$ - $n_\textrm{air}$. The H$_2$O absorption lines parameters of main isotopologues were taken from the HITRAN2020 spectroscopic database [16]; our calculated absorption line parameters were used to simulate the transmission by H₂¹⁹O. Laboratory spectrometers measure the intensity (radiance) of source I, attenuated by gaseous medium at the path length L with the transmission function T and apparatus function f with the spectral resolution $\Delta \nu$. The intensity at wavenumber $\nu$ is determined by

$$\begin{aligned} I(\nu )= & {} \int _{\Delta \nu } I_0(\nu ')T(\nu ')f(\nu '-\nu )d\nu '\nonumber \\= & {} \int _{\Delta \nu } I_0(\nu ') \exp (-K(\nu ')L)f(\nu '-\nu )d\nu '. \end{aligned}$$

(4)

The absorption coefficient, $K(\nu )$, includes the contributions of all spectral lines in the spectral interval considered and depends on pressure, p, and temperature, t:

$$\begin{aligned} K(\nu ,p,t) = \Sigma _{j=1}^M \Sigma _{i=1}^N S_{ij}(t) g(\nu _{ij}^*,\nu ,p,t) n_j, \end{aligned}$$

(5)

where $n_j$ is the concentration of the jth gas (isotopologue); M is the number of gases (isotopologues); N is the number of spectral lines belonging to the jth gas; and $g(\nu _{ij}^*,\nu ,p,t)$ is the absorption line profile function. A Voigt line profile [13, 31] is usually empolyed for atmospheric conditions. Line profiles were calculated using broadening line parameters $\gamma$ and the air temperature-dependence exponent, $n_{air}$. Transmission spectra of H$_2$O and H₂¹⁹O with a H₂¹⁹O/H$_2$O ratio of 0.5%, calculated with spectral resolution of 0.02 cm$^{-1}$ and 5 cm$^{-1}$ in the 0–15,000 cm$^{-1}$ spectral region, are shown in Fig. 2. It was found that use high spectral resolution of about 0.02 cm$^{-1}$ allows the H₂¹⁹O lines to be revealed against of the background H$_2$O lines at this H₂¹⁹O/H$_2$O concentration ratio.

Transmission spectra of H$_2$O and H₂¹⁹O with H₂¹⁹O/H$_2$O ratio of 0.5% are shown in Fig. 2.

By varying the H₂¹⁹O/H$_2$O ratio, spectral windows suitable for H₂¹⁹O detection under laboratory conditions were identified in regions from far to near IR. Examples of the windows are presented in Fig. 3, where one can observe a distinct contribution of the H₂¹⁹O lines against a background of H$_2$O absorption. The spectral lines for perspective H₂¹⁹O detection are located in the 411–414, 497–499, 1380–1383, 1902–1905, 1950–1954 and 7109–7112 cm$^{-1}$ wavenumber regions.

Fig. 2

Transmission spectra of H$_2$O and H₂¹⁹O, simulated with spectral resolution of (upper panel) 0.02 cm$^{-1}$ and (lower panel) 5 cm$^{-1}$; the H₂¹⁹O/H$_2$O ratio is 0.5%

Fig. 3

Spectral windows for the detection of H₂¹⁹O at different relative concentration of H₂¹⁹O. The H₂¹⁹O/H$_2$O ratio varies from 0.1 to 1%

In our previous studies [52, 53] the spectra of H₂¹⁵O and H₂¹⁴O radio-isotopologues were investigated, and the spectral windows, suitable for H₂¹⁴O and H₂¹⁵O detection, were identified. It is interesting to compare these results with ones obtained for H₂¹⁹O. This comparison reveals overlapping absorption lines of the radio-isotopologues and allows one to estimate how their interference might impact detections. The transmission spectra of H₂¹⁵O and H₂¹⁴O with the concentrations of 0.5% relative to H$_2$O content are shown in Fig. 4 in the spectral windows where the H₂¹⁹O can be detected.

As can see in Fig. 4, the H₂¹⁹O absorption lines overlap with H₂¹⁵O lines in the window of 1380–1383 cm$^{-1}$, that interfere with the H₂¹⁹O detection in this spectral range. Moreover, the H₂¹⁴O lines can influence on the H₂¹⁹O measurement in the 7109–7112 cm$^{-1}$ window. According to the transmissions comparisons, the most suitable spectral ranges for detecting H₂¹⁹O in laboratory conditions are 412–414 cm$^{-1}$ and 497–499 cm$^{-1}$.

Fig. 4

Transmission spectra of H$_2$O in natural abundance and radio-isotopogues: H₂¹⁴O, H₂¹⁵O and H₂¹⁹O at concentrations of 0.5% of H$_2$O

Conclusion

The first comprehensive calculation of vibrational-rotational spectrum of the water isotopologue H₂¹⁹O up to 25,000 cm$^{-1}$ is presented. An empirical line list for the H₂¹⁹O is created in the ExoMol-style using calculations based on a high-precision intramolecular potential energy surface which includes allowance for relativistic and non-adiabitic corrections, and ab initio dipole moment surfaces. The line list is computed using a spectroscopic model optimised for H₂¹⁶O and covers all transitions up to J=20, which means it should be valid for temperatures up to 800 K. The quality of the line list was improved through isotopologue extrapolation of the experimentally-determined energies of H₂¹⁶O, H₂¹⁷O and H₂¹⁸O. We hope that these theoretical prediction of H₂¹⁹O spectra will lead to experimental measurements.

Transmission spectra of H₂¹⁹O were simulated varying their concentration. A comparison of the simulated spectra of H₂¹⁹O with the transmission spectra of water vapor in natural abundance (H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, HD$^{16}$O, HD$^{18}$O, HD$^{17}$O), and H₂¹⁴O  H₂¹⁵O radio-isotopologues was carried out to find the spectral ranges are best suited for H₂¹⁹O detection in laboratory conditions. It was revealed that the spectral windows relevant for the H₂¹⁹O detection are placed in the regions of 411–414 cm$^{-1}$, 497–499 cm$^{-1}$, 1380–1383 cm$^{-1}$, 1902–1905 cm$^{-1}$, 1950–1954 cm$^{-1}$, and 7109–7112 cm$^{-1}$, with the two far infrared windows showing the least interference with the other radio-isotopologues. As $^{19}$O decays, the concentration of the H₂¹⁹O isotopologue will diminish, and its absorption will also decrease. The rate of decrease in absorption at a given wavelength, observed in real time, will provide additional evidence that it the absorptions are due to H₂¹⁹O.

Our predicted spectrum of H₂¹⁹O can be a useful tool for for astrophysics, plasma chemistry, nuclear reactor safety, medical procedures and aid the detection of this radio-isotopologue. It can be expect that H₂¹⁹O water plays a greater role in fast-paced complex chemical and nuclear processes than previously assumed. For example, it is possible that short-lived water vapor radio-isotopologues may be responsible for part of the anomalous radiation that is sometimes recorded during thunderstorms [9].

Vibrational-rotational spectroscopy is an effective, non-destructive tool for studying the properties of pollutants and radioactive substances in real time mode. Such studies can help to understand the physicochemical processes involved and to improve the safety of nuclear reactors.