Accurate Rotational Rest Frequencies for Ammonium Ion Isotopologues

Abstract

We report rest frequencies for rotational transitions of the deuterated ammonium isotopologues NH₃D⁺, ${\text{NH}}_2{\text{D}}_2^{+}$ and $\text{NHD}{\text{D}}_3^{+}$, measured in a cryogenic ion trap machine. For the symmetric tops NH₃D⁺ and ${\text{NHD}}_3^{+}$ one and three transitions are detected, respectively, and five transitions are detected for the asymmetric top ${\text{NH}}_2{\text{D}}_2^{+}$. While the lowest frequency transition of NH₃D⁺ was already known in the laboratory and space, this work enables the future radio astronomical detection of the two other isotopologues.

1. Introduction

Nitrogen is one of the most abundant elements in the local universe, and has a notably rich chemistry, with more than seventy nitrogen-containing molecules identified in space to date (CDMS 2018). Two of the most abundant nitrogen-bearing molecules in the interstellar medium (ISM) are N₂ and NH₃, which are predicted to be present in many different media, from cold dark clouds (see, e.g., Nejad et al. (1990)) or protostellar cores (see, e.g., Aikawa et al. (2008)) to active galactic nuclei (see, e.g., Harada et al. (2010)). N₂, being a homonuclear diatomic molecule, can not be observed through its (electric-dipole) rotation or vibration transitions. It can be observed, however, through electronic transitions in the far-ultraviolet, with only one direct observation reported by Knauth et al. (2004), or by its frequently used proxy, the diazenylium ion (N₂H⁺). Ammonia, in turn, is the first polyatomic molecule identified in space (Cheung et al. 1968), and since then has been observed in many environments. To date, all deuterated isotopologues of ammonia, NH₂D, NHD₂ and ND₃ have been observed (see e.g. Harju et al. (2017) for a recent account), as well as ¹⁵NH₃ and ¹⁵NH₂D (Gerin et al. 2009).

The astrophysical relevance of the ammonium ion, $\text{NH}{D}_4^{+}$, stems from its role as gas phase forebear of the ammonia molecule through its dissociative recombination. The full family of nitrogen hydrides is initiated by the reaction N⁺+H₂ → NH⁺ + H (Zymak et al. 2013). Subsequent exothermic H₂ abstraction reactions lead to the formation of ${\text{NH}}_2^{+}$, ${\text{NH}}_3^{+}$ and ${\text{NH}}_4^{+}$, and their recombination with electrons form the neutral hydrides NH, NH₂ and NH₃. Ammonia is supposed to be mainly depleted onto grains at the temperatures of cold dark clouds (T ~ 10 K). On the other hand, the grains can free NH₃ molecules upon heating by shocks or in irradiated regions, increasing its gas-phase concentration, and leading to appreciable quantities of ${\text{NH}}_4^{+}$, formed by the proton transfer from $H_3^{+}$ to NH₃. Actually, NH₃ has one of the highest proton affinities (PA) of simple interstellar molecules (PA[NH₃]=8.85 eV) including H₂ (which has PA[H₂]=4.39 eV), so ${\text{NH}}_4^{+}$, once formed, remains stable against further collisions with H₂.

${\text{NH}}_4^{+}$ has tetrahedral symmetry with no permanent electric dipole moment. Therefore, it is untraceable by radio astronomy through its rotational transitions. On the other hand, the deuterated isotopologues NH₃D⁺, ${\text{NH}}_2{\text{D}}_2^{+}$ and ${\text{NHD}}_3^{+}$ have sizeable permanent electric dipole moments (approximately 0.26 D, 0.29 D and 0.24 D, respectively) due to the separation between the center of charge (which remains centered on the central N atom) and the center of mass (which is displaced towards the D atoms), thus making their detection feasible. Indeed, the detection of ammonium in space was claimed through the assignment of an emission line centered at 262817 GHz (observed both in Orion IRc2 and in Barnard B1-bS) to the 1₀ − 0₀ transition of NH₃D⁺ (Cernicharo et al. 2013). The laboratory rest frequency was derived from the analysis of the high resolution infrared spectrum of the v₄ band, originally made by Nakanaga & Amano (1986) and considerably improved by Doménech et al. (2013). The rest frequency was later confirmed, and its uncertainty substantially decreased, by the direct measurement of the rotational transition by Stoffels et al. (2016).

Besides their importance as tracers of ${\text{NH}}_4^{+}$, the deuterated isotopologues are also relevant regarding the subject of deuterium fractionation. In cold dark clouds, when CO freezes onto grains and its abundance falls below that of HD, deuteration of other species becomes efficient. It can be explained by the exothermicity (~ 230 K) of the reaction ${\text{H}}_3^{+}+\text{HD}\to {\text{H}}_2{\text{D}}^{+}+{\text{H}}_2$ and subsequent deuteron transfer to other molecules. Similarly, the exothermic reactions of H₂D⁺ and ${\text{HD}}_2^{+}$ with HD efficiently produce ${\text{HD}}_2^{+}$ and ${\text{D}}_3^{+}$ (Hugo et al. 2009) in case of extreme depletion, and subsequent deuteron transfer to ammonia, e.g. ${\text{NH}}_3+{\text{H}}_2{\text{D}}^{+}\to {\text{NH}}_3{\text{D}}^{+}+{\text{H}}_2$, lead to the deuterated forms of ${\text{NH}}_4^{+}$. Furthermore, the zero point energy differences of other reactions involving H or D atoms at temperatures of cold dark clouds (T ~ 10 K) also enhance deuteration (Millar 2003). For the case of nitrogen, the reaction N⁺ + HD → ND⁺ + H has a lower endothermicity than the corresponding reaction with H₂ mentioned above (Grozdanov et al. 2016), leading to an enrichment in deuterated ammonium and ammonia isotopologues. The detected abundances of deuterated variants of ammonia are orders of magnitude higher compared to what is expected based on the [D]/[H] abundance ratio (2.35 ×10⁻⁵ in the local universe (Linsky et al. 2006)). Detection of other deuterated ammonium isotopologues besides NH₃D⁺ will clearly help to constrain and understand the conditions of formation and distribution of ammonia molecules, and, possibly, other nitrogen-containing prebiotic species.

The only previous spectroscopic laboratory data on the doubly and triply deuterated species (${\text{NH}}_2{\text{D}}_2^{+}$and ${\text{NHD}}_3^{+}$) that we are aware of are the recent publication of the analysis of the v₁ and v₆ infrared bands of ${\text{NH}}_2{\text{D}}_2^{+}$ (Chang & Nesbitt 2018), and the communication of preliminary results on the analysis of the v₁ band of ${\text{NHD}}_3^{+}$ (Chang & Nesbitt 2013), both recorded at high resolution in a supersonic slit-jet discharge with an infrared difference-frequency laser spectrometer. In this work, we present direct and accurate laboratory measurements of the lowest frequency rotational transitions of NH₃D⁺, ${\text{NH}}_2{\text{D}}_2^{+}$ and ${\text{NHD}}_3^{+}$. The fundamental rotational frequency for NH₃D⁺ has already been published previously, and we only confirm its value, while our reported values for the other two isotopologues represent the first available sub-mm wave data.

2. Experimental Methods

The rotational transitions of the deuterated ammonium isotopologues have been measured in the Köln laboratories exploiting the rotational state dependence of the attachment of He atoms to cations (Brünken et al. (2014, 2017); Jusko et al. (2017); Doménech et al. (2017, 2018)). The experiment was performed in the 4 K trapping machine COLTRAP described by Asvany et al. (2010, 2014). The ions were generated in a storage ion source by bombarding the precursor gas mixture with electrons (energy 30-40 eV). For generating NH₃D⁺ and ${\text{NH}}_2{\text{D}}_2^{+}$, NH₃ (Messer, 99.8 % purity) and a 1:5 mixture of D₂ (Linde, 99.8 %) and He (Linde 99.999 %) were admitted to the ion source via two separate leakage valves. The approximate proportions were 1:1:5 for NH₃D⁺ and 1:2:10 for ${\text{NH}}_2{\text{D}}_2^{+}$. For ${\text{NHD}}_3^{+}$ we applied a similar mixture using ND₃ (Campro Scientific, 99 % atom D) and H₂ (Linde, 99.9999%). A pulse of several ten thousand mass-selected parent ions was injected into the 4 K cold 22-pole ion trap filled with about 10¹⁴ cm⁻³ He. During the trapping time of 750 ms, cation-helium complexes formed by three-body collisions. The detection of the resonant absorption of the admitted cw (sub)millimeter radiation by the trapped cold parent cations was achieved by observing the decrease of the number of cation-helium complexes formed. For example, for recording a rotational transition of ${\text{NH}}_2{\text{D}}_2^{+}$, the ${\text{NH}}_2{\text{D}}_2^{+}$ − He complexes are counted (typical counts are on the order of 2000) as a function of the (sub)millimeter-wave frequency. The (sub)millimeter-wave radiation was supplied by a rubidium atomic clock-referenced synthesizer (Rohde&Schwarz SMF100A) driving a multiplier chain source (Virginia Diodes, Inc.), covering the range 80-1100 GHz.

3. Results

We started our measurements by optimizing the experimental conditions using the known 1₀ − 0₀ line of NH₃D⁺, which has been measured by Stoffels et al. (2016) with the same ion trap technique. We confirm their value for 1₀ − 0₀, as well as the inability of the applied setups to detect the 2₀ − 1₀ and 2₁ − 1₁ transitions. All experimental values of this work are summarized in Table 1.

Table 1.

Frequencies of pure rotational transitions (in MHz) of deuterated ammonium isotopologues. The final error is given in parentheses in units of the last digit.

NH3D+	$J_K^{\prime }\leftarrow J_K^{″}$	this work	former worka
	10 ← 00	262816.8864(8)	262816.904(15)
${\text{NH}}_2{\text{D}}_2^{+}$	$J_{K_a^{\prime }{K}_c^{\prime }}^{\prime }\leftarrow J_{K_a^{″}{K}_c^{″}}^{″}$	this work	former predictionb
	110 ← 101	42273.4715(47)c	42270(6)
	111 ← 000	248918.2760(8)	248924(6)
	202 ← 111	412755.5374(27)
	212 ← 101	455534.5852(16)	455540(12)
	221 ← 110	540046.0112(75)
	220 ← 111	560809.9582(37)
	303 ← 212	632874.2(17)c
	313 ← 202	656593.10(82)c
${\text{NHD}}_3^{+}$	$J_K^{\prime }\leftarrow J_K^{″}$	this work
	10 ← 00	222228.9432(7)
	20 ← 10	444415.7929(42)
	21 ← 11	444421.2980(18)

^aStoffels et al. (2016)

^bChang & Nesbitt (2018)

^cour prediction

For ${\text{NH}}_2{\text{D}}_2^{+}$, we based our search on the predictions from the high resolution infrared vibration-rotation spectra of the v₁ and v₆ bands recently published by Chang & Nesbitt (2018). In total, we searched for eight rotational lines of ${\text{NH}}_2{\text{D}}_2^{+}$ of which five were detected. All measured and predicted transitions are included in Table 1. Figure 1 shows two example measurements for ${\text{NH}}_2{\text{D}}_2^{+}$. All lines have been measured at least 7 times and fitted to Gaussian functions, from which line centers and widths were determined. The values quoted in Table 1 represent the combined mean and standard deviation of all measurements. During the measurements, care was taken to avoid power broadening. By this, the linewidths are determined only by the Doppler broadening due to the kinetic temperature of the ions in the trap (nominal temperature T = 4 K), and also by a small contribution from the unresolved hyperfine splitting due to the quadrupole moments of the ¹⁴N and ²H nuclei, both with spin I=1. Effectively, we measure linewidths corresponding to T =10 – 20 K for ${\text{NH}}_2{\text{D}}_2^{+}$, depending on the observed line. The 1₀ − 0₀ line of NH₃D⁺ seems to be more affected by hyperfine splitting, with an effective temperature T ≈ 30 K.

Figure 1.

Example measurements of the 1₀₁ − 0₀₀ and 2₁₂ − 1₀₁ rotational transitions of ${\text{NH}}_2{\text{D}}_2^{+}$, recorded as depletion signal of the normalized ${\text{NH}}_2{\text{D}}_2^{+}$ −He counts. Grey dots are single measurements, the blue line is the average binned in 25 kHz steps, and the black trace is a Gaussian fit.

For ${\text{NHD}}_3^{+}$, our search was guided by mass-scaling the rotational constants from the other isotopologues, as well as by an estimation based on the available IR-derived rotational constants from the Nesbitt group (Chang & Nesbitt (2013)). In contrast to NH₃D⁺, we were able to measure not only the fundamental 1₀ − 0₀ for ${\text{NHD}}_3^{+}$, but also detected the 2₀ − 1₀ and 2₁ − 1₁ transitions. The reason is a more advantageous partition function for ${\text{NHD}}_3^{+}$, as well as more available millimeter-wave power at the lower transition frequencies of the heavier ${\text{NHD}}_3^{+}$.

4. Spectroscopic Parameters

As accurate spectroscopic parameters and predictions for the ground state of NH₃D⁺ were already given by Stoffels et al. (2016) and Doménech et al. (2013), we treat here only the isotopologues ${\text{NH}}_2{\text{D}}_2^{+}$ and ${\text{NHD}}_3^{+}$. For ${\text{NH}}_2{\text{D}}_2^{+}$, the measured frequencies of the pure rotational lines collected in Table 1 were fit together with the ground state combination differences derived from Chang & Nesbitt (2018) (two duplicated entries had to be trimmed) using the program PGOPHER (Western 2017), rendering the final set of parameters for the ground state given in Table 2. Both sets of data were weighted according to their different uncertainties, in the kHz range for the present measurements, and ~ 7 MHz for the IR measurements, resulting in a weighted standard deviation of the fit σ_w = 1.02. The accuracy of the spectroscopic parameters of this work is marginally improved (a factor of ~ 2 − 3) with respect to the former work, since only five rotational lines could be recorded in high resolution but eight parameters are fit. It may be also noted that the δ_k parameter is not significantly different from zero in this fit.

Table 2.

Derived spectroscopic parameters (in MHz) from a fit to all measured transitions. Numbers in parentheses are one standard deviation in units of the last digit.

${\text{NH}}_2{\text{D}}_2^{+}$	Parameter	this work	former worka
	A	145600.69(33)	145601.7(12)
	B	118963.31(77)	118966.3(12)
	C	103324.30(63)	103328.6(18)
	ΔJ	1.698(46)	2.10(9)
	ΔJK	-0.85(24)	-1.9(4)
	ΔK	3.08(24)	3.87(3)
	δJ	0.371(15)	0.18(6)
	δK	0.01(20)	0.9(3)
${\text{NHD}}_3^{+}$	Parameter	this work	former workb
	B	111117.9794(6)	111120.9(8)
	DJ	1.7539(2)	2.01(7)
	DJK	-1.3763(11)	-2.0(2)

^aChang & Nesbitt (2018)

^bChang & Nesbitt (2013)

For ${\text{NHD}}_3^{+}$, we only have the three presently measured transition frequencies available therefore we cannot provide a least squares fit. Since, furthermore, the transitions obey ΔK = 0, we cannot determine C and D_K. With the three experimental frequencies we have determined B, D_J and D_JK, shown in Table 2 together with the values quoted by Chang & Nesbitt (2013). Our quoted errors are obtained propagating the experimental uncertainties through the closed linear relations existing between the three observed frequencies and the three retrieved constants. We have assumed that there is no correlation between the experimental frequencies, thus the uncertainties are just added in quadrature with the appropriate coefficients.

5. Conclusion and Outlook

We have measured, with kHz-level accuracies, rotational transitions originating from the lowest energy levels of the deuterated ammonium isotopologues NH₃D⁺, ${\text{NH}}_2{\text{D}}_2^{+}$ and ${\text{NHD}}_3^{+}$. Prior to this work, NH₃D⁺ was already identified in Orion IRc2 and Barnard B1b (Cernicharo et al. 2013). For the ${\text{NH}}_2{\text{D}}_2^{+}$ and ${\text{NHD}}_3^{+}$ isotopologues these rest frequencies will facilitate the search for these ions in the interstellar medium. Cold dark clouds, highly depleted in C and O are the kind of sources where high deuterium fractionation is expected. The cold protostellar core B1b is a source where the abundance of deuterated isotopologues of ammonia and the diazenylium ion (N₂H⁺) is quite remarkable, as is the presence of other multiply deuterated species, like D₂CS (Marcelino et al. 2005) or D₂S (Vastel et al. 2003). The chemical model used in the interpretation of NH₃D⁺ observations in B1b predicted that the abundance of ${\text{NH}}_2{\text{D}}_2^{+}$ could be just a factor of two lower than that of NH₃D⁺. Therefore, one could expect the detection of more deuterated species of the ammonium ion in this or other cold dark clouds. We note, however, that the partition function of ${\text{NH}}_2{\text{D}}_2^{+}$, being an asymmetric top, is more unfavorable, and, even at the low temperature of B1b (T ~ 12 K), spectral dilution is to be expected. The slightly higher electric dipole moment (0.29 D vs 0.26 D) just marginally improves this situation. Although the necessary sensitivity for this detection seems demanding, the ever increasing capabilities of receivers and observatories will likely make it possible in a not distant future. ${\text{NHD}}_3^{+}$ has a smaller abundance and dipole moment, but it has higher symmetry (it is a symmetric top, like NH₃D⁺) and, therefore, a more favorable partition function, so it may also be soon within the reach of observational radio astronomy. In any case the frequencies provided in this work will enable those detections.