The isoelectronic molecules UN and UO+ are known to have Ω = 3.5 and Ω = 4.5 ground states, respectively (where Ω is the unsigned projection of the electronic angular momentum along the internuclear axis). A ligand field theory model has been proposed to account for the difference [Matthew and Morse, J. Chem. Phys. 138, 184303 (2013)]. The ground state of UO+ arises from the U3+(5f3(4I4.5))O2− configuration. Owing to the higher nominal charge of the N3− ligand, the U3+ ion in UN is stabilized by promoting one of the 5f electrons to the more polarizable 7s orbital, reducing the repulsive interaction with the ligand and rendering U3+(5f27s(4H3.5))N3− the lowest energy configuration. In the present work, we have advanced the characterization of the UN ground state through studies of two electronic transitions, [18.35]4.5-X(1)3.5 and [18.63]4.5-X(1)3.5, using sub-Doppler laser excitation techniques with fluorescence detection. Spectra were recorded under field-free conditions and in the presence of static electric or magnetic fields. The ground state electric dipole moment [μ = 4.30(2) D] and magnetic ge-factor [2.160(9)] were determined from these data. These values were both consistent with the 5f27s configurational assignment. Dispersed fluorescence measurements were used to determine vibrational constants for the ground and first electronically excited states. Electric dipole moments and magnetic ge-factors are also reported for the higher-energy electronically excited states.

The electronic structure of gas-phase UN has attracted attention, in part due to the interesting contrast with isoelectronic UO+. Previous studies1–3 have shown that the ground state of UO+ arises from the formal configuration U3+(5f3)O2−. The 5f electrons retain much of their atomic character, with the lowest energy distribution corresponding to the 5f3 4I4.5 atomic ion state.1 The electronic angular momentum (Ja = 4.5) is then quantized relative to the internuclear axis, producing states with Ω (the unsigned projection of Ja along the bond axis) = 4.5, 3.5, 2.5, 1.5, and 0.5, in ascending energy order. Hence, the electronic ground state is the Ω = 4.5 component. This pattern of energy levels is consistent with a ligand field theory (LFT) model of the low-energy electronic structure.1 

Given this background, it was surprising when Matthew and Morse2 discovered an Ω = 3.5 ground state for UN. Using an LFT model, they argued that the ground state was derived from the U3+(5f27s)N3− configuration. The difference, as compared to UO+, was attributed to the greater charge of the N3− ligand. This destabilizes the U 5f orbitals relative to the more polarizable 7s orbital, to the extent that the 5f27s configuration becomes energetically favored. This model was subsequently supported by high-level relativistic quantum chemistry calculations for UN (inclusive of spin–orbit coupling). The studies of Battey et al.4 and de Melo et al.5 yielded Ω = 3.5 ground state wavefunctions that had 5f27s fractional characters of 84% and 83%, respectively. Both studies also reported the molecular constants for many low-energy electronic states: 27 states below 10 000 cm−1 (Ref. 4) and 62 states below 20 000 cm−1 (Ref. 5).

Matthew and Morse2 examined the electronic transitions of UN in the spectral range from 19 200 to 23 900 cm−1 using mass-selected resonant two-photon (R2PI) ionization spectroscopy. They observed numerous bands, of which seven were investigated at the level of rotational resolution with the [18.35]4.5 ← X(1)3.5 band near 18 349 cm−1 being most relevant to the present study. Battey et al.4 also performed mass-selected R2PI spectroscopy as part of their experimental and theoretical effort to determine the ionization energy of UN. They detected and rotationally resolved the [18.63]4.5 ← X(1)3.5 band near 18 633 cm−1. More recently, de Melo et al.5 probed low energy electronic states of UN by means of UN anion photo-detachment spectroscopy. The threshold detachment peak defined an electron affinity for UN of 1.4 eV, and a cluster of excited states was evident, starting at an energy that was ∼0.6 eV above the ground state of UN. The congested structure of the photo-detachment spectrum was analyzed through comparison with the predictions of high-level electronic structure calculations.5 The only other spectroscopic data available for UN were obtained by Green and Reedy,6 who observed site dependent fundamental vibrational intervals of 1000.9, 995.5, and 991.9 cm−1 for matrix isolated UN.

Limited spectroscopic data are available for UN+. Battey et al.4 used two-color pulsed field ionization-zero kinetic (PFI-ZEKE) photoelectron spectroscopy to determine the UN ionization energy (6.2987 eV), UN+ ground state Ω value (=4), and the vibrational interval (1072 cm−1). The Ω = 4 value was consistent with the expectation that the first ionization limit would correspond to the removal of the 7s electron.

In the present study, we have used high-resolution electronic spectroscopy with laser-induced fluorescence (LIF) detection to examine the electric dipole moment and magnetic ge-factor for the [18.63]4.5, [18.35]4.5, and X(1)3.5 states of UN. For the ground state, the electric dipole moment is a particularly good benchmark for testing the predictions of relativistic electronic structure calculations.7 Further insights concerning the parent electronic configuration for the ground and excited electronic states are derived from an analysis of the magnetic ge-factors. As these measurements were conducted at a spectral resolution significantly higher than the previous R2PI measurments2,4 (a full-width at half maximum of ∼40 MHz as compared to ∼6 GHz), we also report improved field-free molecular constants for the [18.63]4.5, [18.35]4.5, and X(1)3.5 states. Finally, medium spectral resolution LIF spectroscopy was used to record the two-dimensional (2-D) (excitation and dispersed LIF) spectra. These measurements yielded the identification of the [0.47]4.5 low-lying excited state and the determination of the [0.47]4.5 and X(1)3.5 vibrational intervals.

The method used for the production of a cold (rotational temperature ∼ 10 K) supersonic molecular sample of UN was similar to that used in our previous studies of UO8 and UF.9 Specifically, UN was generated via 532 nm laser ablation of a depleted uranium rod in the presence of a pulsed supersonic expansion of a 5% NH3/95% argon mixture. Low-spectral resolution laser excitation survey spectral scans were recorded using a pulsed dye laser, probing a free-jet expansion of ∼10 cm downstream from the nozzle orifice. In the case of the high-resolution field-free, Stark and Zeeman measurements, the free-jet expansion was skimmed and the resulting collimated molecular beam probed ∼50 cm from the source. Laser-induced fluorescence (LIF) detection was used in both the high-resolution and low-resolution measurements.

The initial detection and characterization of UN were achieved using a two-dimensional (2-D) technique previously described.10–12 In this approach, the LIF is wavelength dispersed horizontally across the two-dimensional gated and intensified charge coupled device (ICCD) array, which is attached to the exit port of a 0.67 m monochromator. The camera software sums down the vertical arrays of the ICCD and returns a one-dimensional array of intensity vs dispersed fluorescence wavelength for a given laser excitation wavelength. The laser wavelength is then stepped, and the process is repeated, to produce a 2-D spectrum with one of the dimensions being the laser excitation wavelength and the other dimension being the dispersed fluorescence (DF). In the visible range, an ∼75 nm window of the DF spectrum is viewed at a given laser excitation. Typically, the entrance slits of the monochromator were set to produce a spectral resolution of ∼0.7 nm, the signal from 20 ablation pulses was summed, and the pulsed dye laser was stepped in 0.1 cm−1 increments.

The high-resolution field-free, Stark and Zeeman spectra were recorded using the spectrometer described in the previous investigations of UO8 and UF.9 The excitation radiation was generated by a single-mode, continuous wave (CW) ring dye laser. The absolute wavelength was calibrated by co-recording the sub-Doppler I2 spectrum13 and the relative wavelength by co-recording the transmission of an actively stabilized confocal etalon. Static electric fields were generated by the application of a voltage across a pair of highly transmitting, conducting neutral density filters. The field strength was calibrated by means of a voltmeter and mechanical measurement of the plate separation. For the Zeeman measurements, homogeneous magnetic fields were generated by a pair of rare earth magnets attached to an iron yoke. The molecular beam passed through 5.0 mm holes in the center of the magnet/yoke assembly. The field was calibrated using a commercial gauss meter. A polarization rotator was used to align the electric field vector of the linearly polarized laser light relative to the static magnetic or electric fields. Systematic errors of up to 2% are estimated for both the static electric and magnetic field strengths.

The two electronic transitions examined in this study, [18.35]4.5-X(1)3.5 and [18.63]Ω- X(1)3.5, had both been observed in earlier mass-selected R2PI experiments using pulsed dye laser excitation.2,4 We extended the characterization of these transitions by recording 2-D fluorescence excitation spectra. Figure 1 shows the result for excitation wavelengths that cover the range of the [18.63]Ω- X(1)3.5 origin band. The horizontal axis gives the photon energy of the excitation laser, and the vertical axis gives the difference between the energies of the emitted and exciting photons. The trace at the bottom of Fig. 1 shows the 1-D LIF spectrum obtained by summing the fluorescence intensities within the dashed-line box that is centered at zero energy offset (i.e., on-resonance). The vertical trace at the far right-hand side of the figure shows the 1-D dispersed fluorescence spectrum obtained by summing the fluorescence intensities contained in the dashed-line box that is centered at an excitation energy of 18 635 cm−1. An expanded version of the LIF trace is shown in Fig. 2, along with a simulation generated using the PGOPHER software package.14 The resolution of Fig. 2 is significantly better than the corresponding Fig. 1 of Ref. 4. In the earlier study, the upper state Ω value was tentatively assigned as Ω = 3.5, but the quality of the data was not sufficient to rule out the possibility of Ω = 4.5. Figure 2 and the high-resolution spectra definitively confirmed that the upper state is Ω = 4.5 [the Q(3.5) and P(4.5) lines were not present in the high-resolution spectra]. An error in the band origin previously reported for the [18.63]Ω-X(1)3.5 transition was also discovered. In re-examining the earlier data, we found that the uncalibrated wavenumber scale provided by the dye laser scanning program had been inadvertently used for both the display of this band (Fig. 1 of Ref. 4) and the fitting of the molecular constants. Hence, the T0 value reported here (18 630.064 cm−1) supersedes the earlier determination, which was in error by +5.6 cm−1. Note that we are using corrected labeling for this state as it was formerly designated as [18.64]3.5.

FIG. 1.

The 2-D spectrum of the products of an ablated U/NH3 supersonic expansion in the 18 570–18 645 cm−1 spectral range. The horizontal axis is the laser excitation wavenumber, and the vertical axis is the dispersed laser-induced fluorescence (DF) wavenumber relative to the laser excitation. The spectral window of the DF is tracked with the laser excitation wavenumber. At the bottom is the medium resolution X(1)3.5 → [18.63]4.5 LIF excitation spectrum obtained by the vertical integration of the indicated horizontal slice centered on the laser wavenumber (i.e., on-resonance detection). On the right is the DF spectrum obtained by horizontal integration of the indicated vertical rectangular slice centered at the [18.63]4.5-X(1)3.5 bandhead (ν = 18 635 cm−1).

FIG. 1.

The 2-D spectrum of the products of an ablated U/NH3 supersonic expansion in the 18 570–18 645 cm−1 spectral range. The horizontal axis is the laser excitation wavenumber, and the vertical axis is the dispersed laser-induced fluorescence (DF) wavenumber relative to the laser excitation. The spectral window of the DF is tracked with the laser excitation wavenumber. At the bottom is the medium resolution X(1)3.5 → [18.63]4.5 LIF excitation spectrum obtained by the vertical integration of the indicated horizontal slice centered on the laser wavenumber (i.e., on-resonance detection). On the right is the DF spectrum obtained by horizontal integration of the indicated vertical rectangular slice centered at the [18.63]4.5-X(1)3.5 bandhead (ν = 18 635 cm−1).

Close modal
FIG. 2.

Rotationally resolved LIF spectrum of the UN [18.63]4.5-X(1)3.5 0-0 transition. The downward-going trace is a simulation generated using the PGOPHER software package. The rotational temperature for this simulation was 70 K.

FIG. 2.

Rotationally resolved LIF spectrum of the UN [18.63]4.5-X(1)3.5 0-0 transition. The downward-going trace is a simulation generated using the PGOPHER software package. The rotational temperature for this simulation was 70 K.

Close modal

A 2-D spectrum in the vicinity of the [18.35]4.5-X(1)3.5 transition is shown in Fig. 3. The trace at the bottom shows the 1-D LIF spectrum obtained by summing the fluorescence intensities within the dashed-line box that is centered at zero energy offset and exhibits the intense [18.35]4.5-X(1)3.5 band, as well as a weaker band with a red degraded bandhead near 18 400 cm−1. The latter is assigned as the [18.40]-X(1)3.5 transition (see below) of UN. Note that the [18.338]3-X(1)4 band2 of background UO, which has an R-branch head near 18 355 cm−1, overlapped the [18.35]4.5-X(1)3.5 band of UN. Fortunately, the [18.338]3 state of UO preferentially fluoresces off-resonant, whereas the [18.35]4.5 state of UN preferentially fluoresces on-resonant upon excitation, causing the 1-D LIF spectrum to be dominated by UN spectral features. The vertical traces marked “A–C” on the far right-hand side of Fig. 3 show the 1-D dispersed fluorescence spectra obtained by summing the fluorescence intensities contained in the dashed-line boxes centered at excitation energies of 18 345 cm−1 (box “A”), 18 355 cm−1 (box “B”), and 18 400 cm−1 (box “C”). DF spectrum “A” is dominated by off-resonance UO emission. DF spectrum “B” is predominately the on-resonance UN emission, while DF spectrum “C” exhibits both on-resonance and off-resonance UN emission. Evidently, the vibronic wavefunction for the [18.35]4.5 and [18.40] states of UN are significantly different causing the Franck–Condon factor for the [18.35]4.5-X(1)3.5 transition to be near unity (i.e., diagonal) and that for the [18.40]-X(1)3.5 transition to be significantly non-diagonal.

FIG. 3.

The 2-D spectrum of the products of an ablated U/NH3 supersonic expansion in the 18 310 to 18 405 cm−1 spectral range. At the bottom is the medium resolution excitation spectrum obtained by vertical integration of the indicated horizontal slice centered on the laser wavenumber (i.e., on-resonance detection), which is dominated by the [18.35]4.5-X(1)3.5 and the weaker [18.40]-X(1)3.5 bands of UN. On the right are the DF spectra obtained by the horizontal integration of the indicated vertical rectangular slice centered at the [18.35]4.5-X(1)3.5 bandhead (ν = 18 355 cm−1), a weaker band head at 18 345 cm−1, which is assigned as the [18.338]3-X(1)4 band of UO (Mathew and Morse2) and the bandhead near 18 400 cm−1.

FIG. 3.

The 2-D spectrum of the products of an ablated U/NH3 supersonic expansion in the 18 310 to 18 405 cm−1 spectral range. At the bottom is the medium resolution excitation spectrum obtained by vertical integration of the indicated horizontal slice centered on the laser wavenumber (i.e., on-resonance detection), which is dominated by the [18.35]4.5-X(1)3.5 and the weaker [18.40]-X(1)3.5 bands of UN. On the right are the DF spectra obtained by the horizontal integration of the indicated vertical rectangular slice centered at the [18.35]4.5-X(1)3.5 bandhead (ν = 18 355 cm−1), a weaker band head at 18 345 cm−1, which is assigned as the [18.338]3-X(1)4 band of UO (Mathew and Morse2) and the bandhead near 18 400 cm−1.

Close modal

The DF spectra extracted from the 2-D spectra in the region of R-branch heads of the [18.63]4.5-X(1)3.5 and weaker [18.40]-X(1)3.5 bands of UN are shown in Fig. 4. Also shown is the associated energy level diagram, with relevant assignments, for the DF spectrum for the [18.63]4.5-X(1)3.5 bandhead excitation. That DF spectrum exhibits emission at the v″ = 0, 1, and 2 levels of the X(1)3.5 state and the v″ = 0 and 1 levels of the [0.47](1)4.5 state. The measured ΔG1/2 and ΔG3/2 vibrational spacings for the X(1)3.5 state are 1010.5 ± 5.0 and 1001.0 ± 5.0 cm−1, respectively. These energy spacings yield the vibrational constants ωe = 1020 and ωexe = 4.2 cm−1. The measured ΔG1/2 for the [0.47](1)4.5 state is 1008 ± 5 cm−1. The vibrational shifts in the DF spectrum resulting from the excitation of the [18.40]-X(1)3.5 band are identical to those resulting from the excitation of the [18.63]4.5-X(1)3.5 band, which is the basis for the assignment. The upper energy state of the band is a new electronic state rather than an excited vibrational level of [18.63]4.5 state. The band 471.5 cm−1 below the laser excitation energy is consistent with emission down to the (1)4.5 first electronically excited state. The ab initio calculations of Battey et al.4 and de Melo et al.5 predict energies for this state of 441 and 452 cm−1, respectively.

FIG. 4.

The DF spectra extracted from the 2-D spectra in the region of R-branch heads of the [18.63]4.5-X(1)3.5 and weaker [18.40]-X(1)3.5 bands of UN. The inset shows the associated energy level diagram and assignment. The numbers above the peaks are the Stokes shifts in wavenumbers. The Stokes shifts of “A” and “a” features for the two bands are identical, supporting the assignment of the [18.40]-X(1)3.5 band.

FIG. 4.

The DF spectra extracted from the 2-D spectra in the region of R-branch heads of the [18.63]4.5-X(1)3.5 and weaker [18.40]-X(1)3.5 bands of UN. The inset shows the associated energy level diagram and assignment. The numbers above the peaks are the Stokes shifts in wavenumbers. The Stokes shifts of “A” and “a” features for the two bands are identical, supporting the assignment of the [18.40]-X(1)3.5 band.

Close modal
Measurements carried out using the cw-dye laser system achieved an effective resolution of 40 MHz FWHM. As the previous studies of UN were carried out at much lower resolution (around 6 GHz), we recorded the bands of interest at high-resolution, under field-free conditions. The spectra exhibited P, Q, and R lines that spanned the range of excited state rotational levels from Jʹ = 4.5 to 10.5 ([18.35]4.5) and Jʹ = 4.5 to 13.5 ([18.63]4.5). There was no evidence of a measurable Ω-doublet splitting for either transition. The line centers derived from these data are collected in Table I. Molecular constants were obtained by least-squares fitting of the line centers (υ) to the expression
υ=T0+BJJ+1D(JJ+1)2BJJ+1+D(JJ+1)2,
(1)
where T0 is the band origin and B′/B″ and D′/D″ are the upper/lower state rotational and centrifugal distortion constants, respectively. The resulting molecular constants are listed in Table II. The constants for the [18.35]4.5-X(1)3.5 band are in good agreement with those reported in Ref. 2, within the stated experimental uncertainties.
TABLE I.

Observed and calculated line positions (cm−1) of the [18.35]4.5-X(1)3.5(v″ = 0) and [18.63]4.5-X(1)3.5(v = 0) bands of UN [18.35]4.5- X(1)3.5(v″ = 0) and [18.63]4.5-X(1)3.5(v″ = 0).

[18.35]4.5-X(1)3.5(v″ = 0)[18.63]4.5-X(1)3.5(v″ = 0)
LineJJObservedaObs-CalcLineJJObservedbObs-Calc
R(3.5) 4.5 3.5 52.1570 −0.0007 R(3.5) 4.5 3.5 33.2344 0.0013 
R(4.5) 5.5 4.5 52.6091 −0.0023 R(4.5) 5.5 4.5 33.8232 0.0013 
R(5.5) 6.5 5.5 52.9961 −0.0006 R(5.5) 6.5 5.5 34.3707 0.0021 
R(6.5) 7.5 6.5 53.3114 −0.0013 R(6.5) 7.5 6.5 34.8730 −0.0001 
R(7.5) 8.5 7.5 53.5569 −0.0013 R(7.5) 8.5 7.5 35.3363 0.0011 
R(8.5) 9.5 8.5 53.7335 0.0013 R(8.5) 9.5 8.5 35.7549 0.0001 
Q(4.5) 4.5 4.5 48.4716 −0.0009 R(9.5) 10.5 9.5 36.1325 0.0008 
Q(5.5) 5.5 5.5 48.1081 0.0006 R(10.5) 11.5 10.5 36.4634 −0.0023 
Q(6.5) 6.5 6.5 47.6753 0.001 R(11.5) 12.5 11.5 36.7559 −0.0007 
Q(7.5) 7.5 7.5 47.1732 0.0012 R(12.5) 13.5 12.5 37.0046 0.0003 
Q(8.5) 8.5 8.5 46.5986 −0.0008 R(13.5) 14.5 13.5 37.2093 0.0007 
Q(9.5) 9.5 9.5 45.9561 0.0006 Q(4.5) 4.5 4.5 29.5463 −0.0016 
Q(10.5) 10.5 10.5 45.2386 −0.0003 Q(5.5) 5.5 5.5 29.3185 0.0005 
P(5.5) 4.5 5.5 43.9693 0.0007 Q(6.5) 6.5 6.5 29.0475 0.0012 
P(6.5) 5.5 6.5 42.7872 0.0021 Q(7.5) 7.5 7.5 28.7313 −0.0011 
P(7.5) 6.5 7.5 41.5353 0.0017 Q(8.5) 8.5 8.5 28.3779 0.0015 
P(8.5) 7.5 8.5 40.2127 −0.0004 Q(9.5) 9.5 9.5 27.9773 −0.0008 
P(9.5) 8.5 9.5 38.8223 −0.0005 P(5.5) 4.5 5.5 25.0412 −0.0028 
     P(6.5) 5.5 6.5 23.9955 −0.0002 
     P(7.5) 6.5 7.5 22.9042 −0.0014 
Rms = 0.0012 cm−1 σ = 0.0014 cm-1 
[18.35]4.5-X(1)3.5(v″ = 0)[18.63]4.5-X(1)3.5(v″ = 0)
LineJJObservedaObs-CalcLineJJObservedbObs-Calc
R(3.5) 4.5 3.5 52.1570 −0.0007 R(3.5) 4.5 3.5 33.2344 0.0013 
R(4.5) 5.5 4.5 52.6091 −0.0023 R(4.5) 5.5 4.5 33.8232 0.0013 
R(5.5) 6.5 5.5 52.9961 −0.0006 R(5.5) 6.5 5.5 34.3707 0.0021 
R(6.5) 7.5 6.5 53.3114 −0.0013 R(6.5) 7.5 6.5 34.8730 −0.0001 
R(7.5) 8.5 7.5 53.5569 −0.0013 R(7.5) 8.5 7.5 35.3363 0.0011 
R(8.5) 9.5 8.5 53.7335 0.0013 R(8.5) 9.5 8.5 35.7549 0.0001 
Q(4.5) 4.5 4.5 48.4716 −0.0009 R(9.5) 10.5 9.5 36.1325 0.0008 
Q(5.5) 5.5 5.5 48.1081 0.0006 R(10.5) 11.5 10.5 36.4634 −0.0023 
Q(6.5) 6.5 6.5 47.6753 0.001 R(11.5) 12.5 11.5 36.7559 −0.0007 
Q(7.5) 7.5 7.5 47.1732 0.0012 R(12.5) 13.5 12.5 37.0046 0.0003 
Q(8.5) 8.5 8.5 46.5986 −0.0008 R(13.5) 14.5 13.5 37.2093 0.0007 
Q(9.5) 9.5 9.5 45.9561 0.0006 Q(4.5) 4.5 4.5 29.5463 −0.0016 
Q(10.5) 10.5 10.5 45.2386 −0.0003 Q(5.5) 5.5 5.5 29.3185 0.0005 
P(5.5) 4.5 5.5 43.9693 0.0007 Q(6.5) 6.5 6.5 29.0475 0.0012 
P(6.5) 5.5 6.5 42.7872 0.0021 Q(7.5) 7.5 7.5 28.7313 −0.0011 
P(7.5) 6.5 7.5 41.5353 0.0017 Q(8.5) 8.5 8.5 28.3779 0.0015 
P(8.5) 7.5 8.5 40.2127 −0.0004 Q(9.5) 9.5 9.5 27.9773 −0.0008 
P(9.5) 8.5 9.5 38.8223 −0.0005 P(5.5) 4.5 5.5 25.0412 −0.0028 
     P(6.5) 5.5 6.5 23.9955 −0.0002 
     P(7.5) 6.5 7.5 22.9042 −0.0014 
Rms = 0.0012 cm−1 σ = 0.0014 cm-1 
a

Line centers—18 300 cm−1.

b

Line centers—18 600 cm−1.

TABLE II.

Molecular constants for the X(1)3.5(v″ = 0), [18.35]4.5, and [18.63]4.5 states of UN. cm−1 units except for the dipole moments and the dimensionless g-factors.

ParameterX(1)3.5(v″ = 0)[18.35]4.5[18.63]4.5
B 0.40948(9) 0.3766(1) 0.38864(8) 
107D 10(7) 69(9) 17(6) 
μel (D) 4.30(2) 4.05(3) 4.32(2) 
g-factor 2.160(9) 3.93(1) 3.599(9) 
T0 18 349.289(3) 18 630.064(1) 
ParameterX(1)3.5(v″ = 0)[18.35]4.5[18.63]4.5
B 0.40948(9) 0.3766(1) 0.38864(8) 
107D 10(7) 69(9) 17(6) 
μel (D) 4.30(2) 4.05(3) 4.32(2) 
g-factor 2.160(9) 3.93(1) 3.599(9) 
T0 18 349.289(3) 18 630.064(1) 

Stark shift measurements were carried out for the R(3.5) and Q(4.5) rotational lines of the [18.63]4.5-X(1)3.5(v″ = 0) transition and the R(3.5) line of the [18.35]4.5-X(1)3.5(v″ = 0) transition. Spectra were recorded with the laser polarization oriented either parallel (//) or perpendicular (⊥) to the applied field direction. These conditions impose the selection rules ΔMJ = 0 or ΔMJ = ±1, respectively (where MJ is the field-axis projection of the total angular momentum). The applied electric fields ranged from 1533 to 2319 V/cm. Representative spectra for the [18.63]4.5-X(1)3.5 R(3.5) line, for field-free conditions and a field of 2626.8 V/cm, are shown in Fig. 5.

FIG. 5.

Stark-effect spectra for the [18.63]4.5-X(1)3.5 R(3.5) rotational line. Trace A was recorded under field-free conditions. Traces B and C show the line splittings resulting from the application of an electric field of 2626.8 V/cm.

FIG. 5.

Stark-effect spectra for the [18.63]4.5-X(1)3.5 R(3.5) rotational line. Trace A was recorded under field-free conditions. Traces B and C show the line splittings resulting from the application of an electric field of 2626.8 V/cm.

Close modal
The Stark Hamiltonian was defined by15 
ĤStark=μeE=μeEcos(θ),
(2)
where E is the electric field and μe is the molecular electric dipole moment. For the low applied electric field strengths used in these measurements, the Stark tuning of the degenerate Ω-doublet was adequately predicted by the first-order perturbation theory expression,15 
ΔνStarkMHz=Ψelec;JΩMJ±|ĤStark|Ψelec;JΩMJ=μeEMJΩJ(J+1)×0.50348,
(3)
where the electric dipole moment is in Debye units and E is the electric field strength in V/cm units. Note that the operator connects levels of opposite parity. A linear least-squares fitting program was used to analyze the data given in Tables III and IV. The Stark shifts of the two band systems were included in a simultaneous fit that yielded values for μe of 4.30(2), 4.05(3), and 4.32(2) D for the X(1)3.5, [18.35]4.5, and [18.63]4.5 states. The observed and calculated shifts are compared in Tables III and IV. The standard deviations for the fit were 20.0 and 42.3 MHz for the [18.35]4.5-X(1)3.5 and [18.63]4.5-X(1)3.5 band systems, respectively. These errors were commensurate with the estimated measurement uncertainty.
TABLE III.

Observed and calculated Stark splittings (MHz) for the R(3.5) line of the UN [18.35]4.5-X(1)3.5(v″ = 0) transition.

Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)
R(3.5)// 3.5 3.5 253.12 −108 −10 R(3.5)// 3.5 3.5 3037.97 −1212 −38 
 −3.5 −3.5 253.12 100  2.5 2.5 3037.97 −859 −21 
 3.5 3.5 506.33 −175 21  1.5 1.5 3037.97 −500 
 2.5 2.5 506.33 −112 28  0.5 0.5 3037.97 −160 
 1.5 1.5 506.33 −73 11  −0.5 −0.5 3037.97 186 18 
 0.5 0.5 506.33 −32 −4  −1.5 −1.5 3037.97 528 25 
 −0.5 −0.5 506.33 39 11  −2.5 −2.5 3037.97 858 20 
 −1.5 −1.5 506.33 86  −3.5 −3.5 3037.97 1201 27 
 −2.5 −2.5 506.33 131 −9 R(3.5)⊥ 4.5 3.5 3544.30 −20 39 
 −3.5 −3.5 506.33 199  −4.5 −3.5 3544.30 20 −39 
R(3.5)// 3.5 3.5 1012.66 −390  −3.5 −2.5 3544.30 −320 12 
 2.5 2.5 1012.66 −278  −2.5 −1.5 3544.30 −715 
 1.5 1.5 1012.66 −169 −2  −1.5 −0.5 3544.30 −1099 16 
 0.5 0.5 1012.66 −51  −0.5 0.5 3544.30 −1505 
 −0.5 −0.5 1012.66 51 −5  0.5 1.5 3544.30 −1920 −22 
 −1.5 −1.5 1012.66 173  3.5 2.5 3544.30 366 34 
 −2.5 −2.5 1012.66 289  2.5 1.5 3544.30 757 33 
 −3.5 −3.5 1012.66 404 13  1.5 0.5 3544.30 1145 30 
R(3.5)// 3.5 3.5 1533.16 −629 −36  0.5 −0.5 3544.30 1504 −2 
 2.5 2.5 1533.16 −437 −14       
 1.5 1.5 1533.16 −271 −17       
 0.5 0.5 1533.16 −76       
 −0.5 −0.5 1533.16 103 18       
 −1.5 −1.5 1533.16 281 27       
 −2.5 −2.5 1533.16 453 30       
 −3.5 −3.5 1533.16 630 37       
Rms = 19.36 MHz   σ = 20.04 MHz 
Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)
R(3.5)// 3.5 3.5 253.12 −108 −10 R(3.5)// 3.5 3.5 3037.97 −1212 −38 
 −3.5 −3.5 253.12 100  2.5 2.5 3037.97 −859 −21 
 3.5 3.5 506.33 −175 21  1.5 1.5 3037.97 −500 
 2.5 2.5 506.33 −112 28  0.5 0.5 3037.97 −160 
 1.5 1.5 506.33 −73 11  −0.5 −0.5 3037.97 186 18 
 0.5 0.5 506.33 −32 −4  −1.5 −1.5 3037.97 528 25 
 −0.5 −0.5 506.33 39 11  −2.5 −2.5 3037.97 858 20 
 −1.5 −1.5 506.33 86  −3.5 −3.5 3037.97 1201 27 
 −2.5 −2.5 506.33 131 −9 R(3.5)⊥ 4.5 3.5 3544.30 −20 39 
 −3.5 −3.5 506.33 199  −4.5 −3.5 3544.30 20 −39 
R(3.5)// 3.5 3.5 1012.66 −390  −3.5 −2.5 3544.30 −320 12 
 2.5 2.5 1012.66 −278  −2.5 −1.5 3544.30 −715 
 1.5 1.5 1012.66 −169 −2  −1.5 −0.5 3544.30 −1099 16 
 0.5 0.5 1012.66 −51  −0.5 0.5 3544.30 −1505 
 −0.5 −0.5 1012.66 51 −5  0.5 1.5 3544.30 −1920 −22 
 −1.5 −1.5 1012.66 173  3.5 2.5 3544.30 366 34 
 −2.5 −2.5 1012.66 289  2.5 1.5 3544.30 757 33 
 −3.5 −3.5 1012.66 404 13  1.5 0.5 3544.30 1145 30 
R(3.5)// 3.5 3.5 1533.16 −629 −36  0.5 −0.5 3544.30 1504 −2 
 2.5 2.5 1533.16 −437 −14       
 1.5 1.5 1533.16 −271 −17       
 0.5 0.5 1533.16 −76       
 −0.5 −0.5 1533.16 103 18       
 −1.5 −1.5 1533.16 281 27       
 −2.5 −2.5 1533.16 453 30       
 −3.5 −3.5 1533.16 630 37       
Rms = 19.36 MHz   σ = 20.04 MHz 
TABLE IV.

Observed and calculated Stark splittings (MHz) for the R(3.5) and Q(4.5) lines of the UN [18.63]4.5-X(1)3.5(v″ = 0) transition.

Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)
R(3.5)⊥ 4.5 3.5 1533.16 146 Q(4.5)// 4.5 4.5 1533.16 636 27 
−4.5 −3.5 1533.16 −133  3.5 3.5 1533.16 470 −3 
3.5 2.5 1533.16 305 32  2.5 2.5 1533.16 332 −6 
−3.5 −2.5 1533.16 −279 −6  1.5 1.5 1533.16 194 −9 
2.5 1.5 1533.16 438 33  0.5 0.5 1533.16 46 −22 
−2.5 −1.5 1533.16 −425 −20  −0.5 −0.5 1533.16 −37 31 
1.5 0.5 1533.16 584 46  −1.5 −1.5 1533.16 −221 −18 
−1.5 −0.5 1533.16 −558 −20  −2.5 −2.5 1533.16 −360 −22 
0.5 −0.5 1533.16 730 60  −3.5 −3.5 1533.16 −489 −16 
−0.5 0.5 1533.16 −704 −34  −4.5 −4.5 1533.16 −627 −18 
−0.5 −1.5 1533.16 863 61 Q(4.5)// 4.5 4.5 2626.80 1022 −21 
0.5 1.5 1533.16 −850 −48  3.5 3.5 2626.80 800 −11 
−1.5 −2.5 1533.16 996 61  2.5 2.5 2626.80 563 −16 
1.5 2.5 1533.16 −996 −61  1.5 1.5 2626.80 304 −44 
−2.5 −3.5 1533.16 1142 75  0.5 0.5 2626.80 111 −5 
2.5 3.5 1533.16 −1128 −61  −0.5 −0.5 2626.80 −111 
R(3.5)⊥ 4.5 3.5 2090.10 193  −1.5 −1.5 2626.80 −355 −7 
−4.5 −3.5 2090.10 −167 24  −2.5 −2.5 2626.80 −570 
3.5 2.5 2090.10 386 14  −3.5 −3.5 2626.80 −800 11 
−3.5 −2.5 2090.10 −348 24  −4.5 −4.5 2626.80 −962 81 
2.5 1.5 2090.10 567 15 Q(4.5)⊥ 4.5 3.5 1533.16 1145 68 
−2.5 −1.5 2090.10 −528 24  −4.5 −3.5 1533.16 −1158 −81 
1.5 0.5 2090.10 747 14  3.5 2.5 1533.16 1004 62 
−1.5 −0.5 2090.10 −708 25  −3.5 −2.5 1533.16 −1004 −62 
0.5 −0.5 2090.10 953 40  2.5 1.5 1533.16 849 42 
−0.5 0.5 2090.10 −889 24  −2.5 −1.5 1533.16 −862 −55 
−0.5 −1.5 2090.10 1121 27  1.5 0.5 1533.16 708 37 
0.5 1.5 2090.10 −1082 12  −1.5 −0.5 1533.16 −708 −37 
−1.5 −2.5 2090.10 1301 27  0.5 −0.5 1533.16 553 17 
1.5 2.5 2090.10 −1275 −1  −0.5 0.5 1533.16 −592 −56 
−2.5 −3.5 2090.10 1468 13  −0.5 −1.5 1533.16 425 24 
2.5 3.5 2090.10 −1443 12  0.5 1.5 1533.16 −437 −36 
R(3.5)⊥ 4.5 3.5 2626.80 241  −1.5 −2.5 1533.16 283 17 
−4.5 −3.5 2626.80 −203 37  1.5 2.5 1533.16 −296 −30 
3.5 2.5 2626.80 470  −2.5 −3.5 1533.16 142 12 
−3.5 −2.5 2626.80 −406 61  2.5 3.5 1533.16 −142 −12 
2.5 1.5 2626.80 685 −9 Q(4.5)⊥ 4.5 3.5 2090.10 1533 65 
−2.5 −1.5 2626.80 −622 72  −4.5 −3.5 2090.10 −1623 −155 
1.5 0.5 2626.80 914 −7  3.5 2.5 2090.10 1240 −44 
−1.5 −0.5 2626.80 −838 83  −3.5 −2.5 2090.10 −1406 −122 
0.5 −0.5 2626.80 1117 −31  2.5 1.5 2090.10 1061 −39 
−0.5 0.5 2626.80 −1079 69  −2.5 −1.5 2090.10 −1201 −101 
−0.5 −1.5 2626.80 1320 −55  1.5 0.5 2090.10 895 −20 
0.5 1.5 2626.80 −1295 80  −1.5 −0.5 2090.10 −984 −69 
−1.5 −2.5 2626.80 1536 −66  0.5 −0.5 2090.10 716 −15 
1.5 2.5 2626.80 −1510 92  −0.5 0.5 2090.10 −792 −61 
−2.5 −3.5 2626.80 1726 −102  −0.5 −1.5 2090.10 536 −10 
2.5 3.5 2626.80 −1764 64  0.5 1.5 2090.10 −588 −42 
R(3.5)// 3.5 3.5 1533.16 −432 31  −1.5 −2.5 2090.10 358 −4 
2.5 2.5 1533.16 −301 30  1.5 2.5 2090.10 −383 −21 
1.5 1.5 1533.16 −169 30  −2.5 −3.5 2090.10 192 14 
 0.5 0.5 1533.16 −47 19  2.5 3.5 2090.10 −204 −26 
 −0.5 −0.5 1533.16 84 18 Q(4.5) ⊥ 4.5 3.5 2319.00 1564 −65 
 −1.5 −1.5 1533.16 235 36  −4.5 −3.5 2319.00 −1628 
 −2.5 −2.5 1533.16 348 17  3.5 2.5 2319.00 1359 −66 
 −3.5 −3.5 1533.16 488 25  −3.5 −2.5 2319.00 −1410 15 
R(3.5)// 3.5 3.5 2090.10 −620 12  2.5 1.5 2319.00 1167 −53 
2.5 2.5 2090.10 −451  −2.5 −1.5 2319.00 −1205 15 
1.5 1.5 2090.10 −263  1.5 0.5 2319.00 975 −40 
0.5 0.5 2090.10 −75 15  −1.5 −0.5 2319.00 −1000 15 
−0.5 −0.5 2090.10 94  0.5 −0.5 2319.00 782 −29 
−1.5 −1.5 2090.10 291 20  −0.5 0.5 2319.00 −795 16 
−2.5 −2.5 2090.10 479 28  −0.5 −1.5 2319.00 577 −29 
−3.5 −3.5 2090.10 676 44  0.5 1.5 2319.00 −577 29 
R(3.5)// 3.5 3.5 2626.80 −789  −1.5 −2.5 2319.00 385 −17 
2.5 2.5 2626.80 −554 13  1.5 2.5 2319.00 −385 17 
1.5 1.5 2626.80 −329 11  −2.5 −3.5 2319.00 205 
0.5 0.5 2626.80 −113  2.5 3.5 2319.00 −180 17 
−0.5 −0.5 2626.80 131 18       
−1.5 −1.5 2626.80 357 17       
−2.5 −2.5 2626.80 592 25       
−3.5 −3.5 2626.80 827 33       
Rms = 41.80 MHz  σ = 42.25 MHz 
Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)Line, polMJMJField (V/cm)Shift (MHz)Δ (MHz)
R(3.5)⊥ 4.5 3.5 1533.16 146 Q(4.5)// 4.5 4.5 1533.16 636 27 
−4.5 −3.5 1533.16 −133  3.5 3.5 1533.16 470 −3 
3.5 2.5 1533.16 305 32  2.5 2.5 1533.16 332 −6 
−3.5 −2.5 1533.16 −279 −6  1.5 1.5 1533.16 194 −9 
2.5 1.5 1533.16 438 33  0.5 0.5 1533.16 46 −22 
−2.5 −1.5 1533.16 −425 −20  −0.5 −0.5 1533.16 −37 31 
1.5 0.5 1533.16 584 46  −1.5 −1.5 1533.16 −221 −18 
−1.5 −0.5 1533.16 −558 −20  −2.5 −2.5 1533.16 −360 −22 
0.5 −0.5 1533.16 730 60  −3.5 −3.5 1533.16 −489 −16 
−0.5 0.5 1533.16 −704 −34  −4.5 −4.5 1533.16 −627 −18 
−0.5 −1.5 1533.16 863 61 Q(4.5)// 4.5 4.5 2626.80 1022 −21 
0.5 1.5 1533.16 −850 −48  3.5 3.5 2626.80 800 −11 
−1.5 −2.5 1533.16 996 61  2.5 2.5 2626.80 563 −16 
1.5 2.5 1533.16 −996 −61  1.5 1.5 2626.80 304 −44 
−2.5 −3.5 1533.16 1142 75  0.5 0.5 2626.80 111 −5 
2.5 3.5 1533.16 −1128 −61  −0.5 −0.5 2626.80 −111 
R(3.5)⊥ 4.5 3.5 2090.10 193  −1.5 −1.5 2626.80 −355 −7 
−4.5 −3.5 2090.10 −167 24  −2.5 −2.5 2626.80 −570 
3.5 2.5 2090.10 386 14  −3.5 −3.5 2626.80 −800 11 
−3.5 −2.5 2090.10 −348 24  −4.5 −4.5 2626.80 −962 81 
2.5 1.5 2090.10 567 15 Q(4.5)⊥ 4.5 3.5 1533.16 1145 68 
−2.5 −1.5 2090.10 −528 24  −4.5 −3.5 1533.16 −1158 −81 
1.5 0.5 2090.10 747 14  3.5 2.5 1533.16 1004 62 
−1.5 −0.5 2090.10 −708 25  −3.5 −2.5 1533.16 −1004 −62 
0.5 −0.5 2090.10 953 40  2.5 1.5 1533.16 849 42 
−0.5 0.5 2090.10 −889 24  −2.5 −1.5 1533.16 −862 −55 
−0.5 −1.5 2090.10 1121 27  1.5 0.5 1533.16 708 37 
0.5 1.5 2090.10 −1082 12  −1.5 −0.5 1533.16 −708 −37 
−1.5 −2.5 2090.10 1301 27  0.5 −0.5 1533.16 553 17 
1.5 2.5 2090.10 −1275 −1  −0.5 0.5 1533.16 −592 −56 
−2.5 −3.5 2090.10 1468 13  −0.5 −1.5 1533.16 425 24 
2.5 3.5 2090.10 −1443 12  0.5 1.5 1533.16 −437 −36 
R(3.5)⊥ 4.5 3.5 2626.80 241  −1.5 −2.5 1533.16 283 17 
−4.5 −3.5 2626.80 −203 37  1.5 2.5 1533.16 −296 −30 
3.5 2.5 2626.80 470  −2.5 −3.5 1533.16 142 12 
−3.5 −2.5 2626.80 −406 61  2.5 3.5 1533.16 −142 −12 
2.5 1.5 2626.80 685 −9 Q(4.5)⊥ 4.5 3.5 2090.10 1533 65 
−2.5 −1.5 2626.80 −622 72  −4.5 −3.5 2090.10 −1623 −155 
1.5 0.5 2626.80 914 −7  3.5 2.5 2090.10 1240 −44 
−1.5 −0.5 2626.80 −838 83  −3.5 −2.5 2090.10 −1406 −122 
0.5 −0.5 2626.80 1117 −31  2.5 1.5 2090.10 1061 −39 
−0.5 0.5 2626.80 −1079 69  −2.5 −1.5 2090.10 −1201 −101 
−0.5 −1.5 2626.80 1320 −55  1.5 0.5 2090.10 895 −20 
0.5 1.5 2626.80 −1295 80  −1.5 −0.5 2090.10 −984 −69 
−1.5 −2.5 2626.80 1536 −66  0.5 −0.5 2090.10 716 −15 
1.5 2.5 2626.80 −1510 92  −0.5 0.5 2090.10 −792 −61 
−2.5 −3.5 2626.80 1726 −102  −0.5 −1.5 2090.10 536 −10 
2.5 3.5 2626.80 −1764 64  0.5 1.5 2090.10 −588 −42 
R(3.5)// 3.5 3.5 1533.16 −432 31  −1.5 −2.5 2090.10 358 −4 
2.5 2.5 1533.16 −301 30  1.5 2.5 2090.10 −383 −21 
1.5 1.5 1533.16 −169 30  −2.5 −3.5 2090.10 192 14 
 0.5 0.5 1533.16 −47 19  2.5 3.5 2090.10 −204 −26 
 −0.5 −0.5 1533.16 84 18 Q(4.5) ⊥ 4.5 3.5 2319.00 1564 −65 
 −1.5 −1.5 1533.16 235 36  −4.5 −3.5 2319.00 −1628 
 −2.5 −2.5 1533.16 348 17  3.5 2.5 2319.00 1359 −66 
 −3.5 −3.5 1533.16 488 25  −3.5 −2.5 2319.00 −1410 15 
R(3.5)// 3.5 3.5 2090.10 −620 12  2.5 1.5 2319.00 1167 −53 
2.5 2.5 2090.10 −451  −2.5 −1.5 2319.00 −1205 15 
1.5 1.5 2090.10 −263  1.5 0.5 2319.00 975 −40 
0.5 0.5 2090.10 −75 15  −1.5 −0.5 2319.00 −1000 15 
−0.5 −0.5 2090.10 94  0.5 −0.5 2319.00 782 −29 
−1.5 −1.5 2090.10 291 20  −0.5 0.5 2319.00 −795 16 
−2.5 −2.5 2090.10 479 28  −0.5 −1.5 2319.00 577 −29 
−3.5 −3.5 2090.10 676 44  0.5 1.5 2319.00 −577 29 
R(3.5)// 3.5 3.5 2626.80 −789  −1.5 −2.5 2319.00 385 −17 
2.5 2.5 2626.80 −554 13  1.5 2.5 2319.00 −385 17 
1.5 1.5 2626.80 −329 11  −2.5 −3.5 2319.00 205 
0.5 0.5 2626.80 −113  2.5 3.5 2319.00 −180 17 
−0.5 −0.5 2626.80 131 18       
−1.5 −1.5 2626.80 357 17       
−2.5 −2.5 2626.80 592 25       
−3.5 −3.5 2626.80 827 33       
Rms = 41.80 MHz  σ = 42.25 MHz 

Zeeman splittings were recorded for the R(3.5), R(4.5), Q(4.5), and Q(5.5) lines of the [18.63]4.5-X(1)3.5 transition and the R(3.5) and R(4.5) lines of the [18.35]4.5-X(1)3.5 transition. Magnetic fields of 470 and 1332 gauss were applied. Figure 6 shows the [18.63]4.5-X(1)3.5 R(3.5) line split by a magnetic field of 1332 gauss, with the laser polarization parallel and perpendicular to the field direction. The Zeeman splitting patterns were similar to those produced by the Stark effect, and the spectra were easily assigned. A total of 50 Zeeman shifts for the [18.35]4.5-X(1)3.5 lines and 104 shifts for the [18.63]4.5-X(1)3.5 lines were characterized. The data obtained from these measurements are collected in Tables V and VI.

FIG. 6.

Zeeman-effect spectra for the [18.63]4.5-X(1)3.5 R(3.5) rotational line. Trace A was recorded under field-free conditions. Traces B and C show the line splittings resulting from the application of a magnetic field of 1332 gauss.

FIG. 6.

Zeeman-effect spectra for the [18.63]4.5-X(1)3.5 R(3.5) rotational line. Trace A was recorded under field-free conditions. Traces B and C show the line splittings resulting from the application of a magnetic field of 1332 gauss.

Close modal
TABLE V.

Observed and calculated Zeeman shifts (MHz) for the UN [18.35]4.5-X(1)3.5(v″ = 0) R(3.5) and R(4.5) lines.

Line, polMJMJField (gauss)Obs (MHz)Obs-Calc (MHz)Line, polMJ′sMJField (gauss)Obs (MHz)Obs-Calc (MHz)
R(3.5)// 3.5 3.5 1332 1564 30 R(3.5) ⊥ 4.5 3.5 1332 2844 −24 
2.5 2.5 1332 1105  3.5 2.5 1332 2414 −15 
1.5 1.5 1332 662  2.5 1.5 1332 1985 −6 
0.5 0.5 1332 216 −3  1.5 0.5 1332 1532 −21 
−0.5 −0.5 1332 −231 −12  0.5 −0.5 1332 1102 −12 
−1.5 −1.5 1332 −680 −22  −0.5 −1.5 1332 650 −26 
−2.5 −2.5 1332 −1112 −16  −1.5 −2.5 1332 220 −17 
−3.5 −3.5 1332 −1571 −37  −4.5 −3.5 1332 −2880 −12 
R(4.5) ⊥ 5.5 4.5 1332 2485 −29  −3.5 −2.5 1332 −2410 19 
4.5 3.5 1332 2149 −12  −2.5 −1.5 1332 −1982 
3.5 2.5 1332 1794 −13  −1.5 −0.5 1332 −1575 −22 
2.5 1.5 1332 1443 −10  −0.5 0.5 1332 −1121 −7 
1.5 0.5 1332 1094 −6  0.5 1.5 1332 −688 −12 
0.5 −0.5 1332 765 19  1.5 2.5 1332 −223 14 
−0.5 −1.5 1332 396 R(4.5)// 4.5 4.5 1332 1578 −13 
−1.5 −2.5 1332 45  3.5 3.5 1332 1227 −10 
−2.5 −3.5 1332 −310  2.5 2.5 1332 877 −7 
−5.5 −4.5 1332 −2517 −3  1.5 1.5 1332 547 17 
−4.5 −3.5 1332 −2181 −20  0.5 0.5 1332 181 
−3.5 −2.5 1332 −1822 −15  −0.5 −0.5 1332 −168 
−2.5 −1.5 1332 −1479 −26  −1.5 −1.5 1332 −521 
−1.5 −0.5 1332 −1120 −20  −2.5 −2.5 1332 −874 10 
−0.5 0.5 1332 −766 −20  −3.5 −3.5 1332 −1224 13 
0.5 1.5 1332 −409 −16  −4.5 −4.5 1332 −1574 17 
1.5 2.5 1332 −54 −15       
2.5 3.5 1332 338 24       
Rms = 16.32 MHz,   σ = 16.83 MHz 
Line, polMJMJField (gauss)Obs (MHz)Obs-Calc (MHz)Line, polMJ′sMJField (gauss)Obs (MHz)Obs-Calc (MHz)
R(3.5)// 3.5 3.5 1332 1564 30 R(3.5) ⊥ 4.5 3.5 1332 2844 −24 
2.5 2.5 1332 1105  3.5 2.5 1332 2414 −15 
1.5 1.5 1332 662  2.5 1.5 1332 1985 −6 
0.5 0.5 1332 216 −3  1.5 0.5 1332 1532 −21 
−0.5 −0.5 1332 −231 −12  0.5 −0.5 1332 1102 −12 
−1.5 −1.5 1332 −680 −22  −0.5 −1.5 1332 650 −26 
−2.5 −2.5 1332 −1112 −16  −1.5 −2.5 1332 220 −17 
−3.5 −3.5 1332 −1571 −37  −4.5 −3.5 1332 −2880 −12 
R(4.5) ⊥ 5.5 4.5 1332 2485 −29  −3.5 −2.5 1332 −2410 19 
4.5 3.5 1332 2149 −12  −2.5 −1.5 1332 −1982 
3.5 2.5 1332 1794 −13  −1.5 −0.5 1332 −1575 −22 
2.5 1.5 1332 1443 −10  −0.5 0.5 1332 −1121 −7 
1.5 0.5 1332 1094 −6  0.5 1.5 1332 −688 −12 
0.5 −0.5 1332 765 19  1.5 2.5 1332 −223 14 
−0.5 −1.5 1332 396 R(4.5)// 4.5 4.5 1332 1578 −13 
−1.5 −2.5 1332 45  3.5 3.5 1332 1227 −10 
−2.5 −3.5 1332 −310  2.5 2.5 1332 877 −7 
−5.5 −4.5 1332 −2517 −3  1.5 1.5 1332 547 17 
−4.5 −3.5 1332 −2181 −20  0.5 0.5 1332 181 
−3.5 −2.5 1332 −1822 −15  −0.5 −0.5 1332 −168 
−2.5 −1.5 1332 −1479 −26  −1.5 −1.5 1332 −521 
−1.5 −0.5 1332 −1120 −20  −2.5 −2.5 1332 −874 10 
−0.5 0.5 1332 −766 −20  −3.5 −3.5 1332 −1224 13 
0.5 1.5 1332 −409 −16  −4.5 −4.5 1332 −1574 17 
1.5 2.5 1332 −54 −15       
2.5 3.5 1332 338 24       
Rms = 16.32 MHz,   σ = 16.83 MHz 
TABLE VI.

Observed and calculated Zeeman shifts in (MHz) for the UN [18.63]4.5-X(1)3.5(v″ = 0) R(3.5), R(4.5), Q(4.5), and Q(5.5) lines.

R(3.5)// 3.5 3.5 470 381 −21 Q(5.5)// 5.5 5.5 1332 2487 
 2.5 2.5 470 286 −1  4.5 4.5 1332 2017 −10 
 1.5 1.5 470 160 −12  3.5 3.5 1332 1566 −11 
 0.5 0.5 470 62  2.5 2.5 1332 1096 −30 
 −0.5 −0.5 470 −62 −5  1.5 1.5 1332 646 −30 
 −1.5 −1.5 470 −165  0.5 0.5 1332 196 −29 
 −2.5 −2.5 470 −278  −0.5 −0.5 1332 −235 −10 
 −3.5 −3.5 470 −376 26  −1.5 −1.5 1332 −705 −29 
R(3.5)⊥ 4.5 3.5 470 815 −17  −2.5 −2.5 1332 −1137 −11 
 3.5 2.5 470 704 −13  −3.5 −3.5 1332 −1606 −29 
 2.5 1.5 470 585 −18  −4.5 −4.5 1332 −2056 −29 
 1.5 0.5 470 482 −6  −5.5 −5.5 1332 −2506 −28 
 0.5 −0.5 470 372 −1 R(4.5)// 4.5 4.5 1332 1256 17 
 −0.5 −1.5 470 261  3.5 3.5 1332 978 15 
 −1.5 −2.5 470 150  2.5 2.5 1332 690 
 −2.5 −3.5 470 40 11  1.5 1.5 1332 412 −1 
 −4.5 −3.5 470 −830  0.5 0.5 1332 144 
 −3.5 −2.5 470 −720 −3  −0.5 −0.5 1332 −134 
 −2.5 −1.5 470 −593 10  −1.5 −1.5 1332 −424 −11 
 −1.5 −0.5 470 −490 −2  −2.5 −2.5 1332 −683 
 −0.5 0.5 470 −380 −7  −3.5 −3.5 1332 −972 −9 
 0.5 1.5 470 −269 −11  −4.5 −4.5 1332 −1252 −13 
 1.5 2.5 470 −150 −6 R(4.5)⊥ 5.5 4.5 1332 2063 −20 
 2.5 3.5 470 −47 −18  4.5 3.5 1332 1788 −20 
R(3.5)// 3.5 3.5 1332 1154 16  3.5 2.5 1332 1507 −26 
 2.5 2.5 1332 826 13  2.5 1.5 1332 1277 19 
 1.5 1.5 1332 488  1.5 0.5 1332 982 
 0.5 0.5 1332 149 −14  0.5 −0.5 1332 707 
 −0.5 −0.5 1332 −169 −6  −0.5 −1.5 1332 451 19 
 −1.5 −1.5 1332 −498 −10  −1.5 −2.5 1332 177 20 
 −2.5 −2.5 1332 −836 −23  −5.5 −4.5 1332 −2082 
 −3.5 −3.5 1332 −1164 −26  −4.5 −3.5 1332 −1807 
R(3.5)⊥ 4.5 3.5 1332 2354 −5  −3.5 −2.5 1332 −1510 23 
 3.5 2.5 1332 2021 −12  −2.5 −1.5 1332 −1257 
 2.5 1.5 1332 1704 −4  −1.5 −0.5 1332 −982 
 1.5 0.5 1332 1371 −12  −0.5 0.5 1332 −707 
 0.5 −0.5 1332 1055 −3  0.5 1.5 1332 −451 −19 
 −0.5 −1.5 1332 740  1.5 2.5 1332 −177 −20 
 −1.5 −2.5 1332 409 Q(4.5)// 4.5 4.5 470 1006 −27 
 −4.5 −3.5 1332 −2362 −3  3.5 3.5 470 784 −20 
 −3.5 −2.5 1332 −2048 −15  2.5 2.5 470 555 −19 
 −2.5 −1.5 1332 −1717 −9  1.5 1.5 470 339 −5 
 −1.5 −0.5 1332 −1375  0.5 0.5 470 124 
 −0.5 0.5 1332 −1066 −8  −0.5 −0.5 470 −124 −9 
 0.5 1.5 1332 −750 −18  −1.5 −1.5 470 −339 
 1.5 2.5 1332 −429 −22  −2.5 −2.5 470 −555 19 
Q(4.5)// 4.5 4.5 1332 2941 13  −3.5 −3.5 470 −784 20 
 3.5 3.5 1332 2295 18  −4.5 −4.5 470 −1006 27 
 2.5 2.5 1332 1631       
 1.5 1.5 1332 980       
 0.5 0.5 1332 334       
 −0.5 −0.5 1332 −311 14       
 −1.5 −1.5 1332 −957 19       
 −2.5 −2.5 1332 −1660 −33       
 −3.5 −3.5 1332 −2255 22       
 −4.5 −4.5 1332 −2923       
Rms = 15.20 MHz,   σ = 15.42 MHz 
R(3.5)// 3.5 3.5 470 381 −21 Q(5.5)// 5.5 5.5 1332 2487 
 2.5 2.5 470 286 −1  4.5 4.5 1332 2017 −10 
 1.5 1.5 470 160 −12  3.5 3.5 1332 1566 −11 
 0.5 0.5 470 62  2.5 2.5 1332 1096 −30 
 −0.5 −0.5 470 −62 −5  1.5 1.5 1332 646 −30 
 −1.5 −1.5 470 −165  0.5 0.5 1332 196 −29 
 −2.5 −2.5 470 −278  −0.5 −0.5 1332 −235 −10 
 −3.5 −3.5 470 −376 26  −1.5 −1.5 1332 −705 −29 
R(3.5)⊥ 4.5 3.5 470 815 −17  −2.5 −2.5 1332 −1137 −11 
 3.5 2.5 470 704 −13  −3.5 −3.5 1332 −1606 −29 
 2.5 1.5 470 585 −18  −4.5 −4.5 1332 −2056 −29 
 1.5 0.5 470 482 −6  −5.5 −5.5 1332 −2506 −28 
 0.5 −0.5 470 372 −1 R(4.5)// 4.5 4.5 1332 1256 17 
 −0.5 −1.5 470 261  3.5 3.5 1332 978 15 
 −1.5 −2.5 470 150  2.5 2.5 1332 690 
 −2.5 −3.5 470 40 11  1.5 1.5 1332 412 −1 
 −4.5 −3.5 470 −830  0.5 0.5 1332 144 
 −3.5 −2.5 470 −720 −3  −0.5 −0.5 1332 −134 
 −2.5 −1.5 470 −593 10  −1.5 −1.5 1332 −424 −11 
 −1.5 −0.5 470 −490 −2  −2.5 −2.5 1332 −683 
 −0.5 0.5 470 −380 −7  −3.5 −3.5 1332 −972 −9 
 0.5 1.5 470 −269 −11  −4.5 −4.5 1332 −1252 −13 
 1.5 2.5 470 −150 −6 R(4.5)⊥ 5.5 4.5 1332 2063 −20 
 2.5 3.5 470 −47 −18  4.5 3.5 1332 1788 −20 
R(3.5)// 3.5 3.5 1332 1154 16  3.5 2.5 1332 1507 −26 
 2.5 2.5 1332 826 13  2.5 1.5 1332 1277 19 
 1.5 1.5 1332 488  1.5 0.5 1332 982 
 0.5 0.5 1332 149 −14  0.5 −0.5 1332 707 
 −0.5 −0.5 1332 −169 −6  −0.5 −1.5 1332 451 19 
 −1.5 −1.5 1332 −498 −10  −1.5 −2.5 1332 177 20 
 −2.5 −2.5 1332 −836 −23  −5.5 −4.5 1332 −2082 
 −3.5 −3.5 1332 −1164 −26  −4.5 −3.5 1332 −1807 
R(3.5)⊥ 4.5 3.5 1332 2354 −5  −3.5 −2.5 1332 −1510 23 
 3.5 2.5 1332 2021 −12  −2.5 −1.5 1332 −1257 
 2.5 1.5 1332 1704 −4  −1.5 −0.5 1332 −982 
 1.5 0.5 1332 1371 −12  −0.5 0.5 1332 −707 
 0.5 −0.5 1332 1055 −3  0.5 1.5 1332 −451 −19 
 −0.5 −1.5 1332 740  1.5 2.5 1332 −177 −20 
 −1.5 −2.5 1332 409 Q(4.5)// 4.5 4.5 470 1006 −27 
 −4.5 −3.5 1332 −2362 −3  3.5 3.5 470 784 −20 
 −3.5 −2.5 1332 −2048 −15  2.5 2.5 470 555 −19 
 −2.5 −1.5 1332 −1717 −9  1.5 1.5 470 339 −5 
 −1.5 −0.5 1332 −1375  0.5 0.5 470 124 
 −0.5 0.5 1332 −1066 −8  −0.5 −0.5 470 −124 −9 
 0.5 1.5 1332 −750 −18  −1.5 −1.5 470 −339 
 1.5 2.5 1332 −429 −22  −2.5 −2.5 470 −555 19 
Q(4.5)// 4.5 4.5 1332 2941 13  −3.5 −3.5 470 −784 20 
 3.5 3.5 1332 2295 18  −4.5 −4.5 470 −1006 27 
 2.5 2.5 1332 1631       
 1.5 1.5 1332 980       
 0.5 0.5 1332 334       
 −0.5 −0.5 1332 −311 14       
 −1.5 −1.5 1332 −957 19       
 −2.5 −2.5 1332 −1660 −33       
 −3.5 −3.5 1332 −2255 22       
 −4.5 −4.5 1332 −2923       
Rms = 15.20 MHz,   σ = 15.42 MHz 
The Zeeman Hamiltonian was taken to be15 
ĤZeeman=μmB=μ0T1(B)iglT1li+gsT1(si),
(4)
where μ0 is the Bohr magneton, B is the magnetic flux density, and gl and gs are the electronic orbital and spin g-factors. For both the [18.35]4.5-X(1)3.5 and [18.63]4.5-X(1)3.5 band systems, the magnetic moment associated with the rotation of the molecule could be neglected for the low applied magnetic fields used in these measurements. Analogous to the Stark effect, the tuning was adequately predicted by the first-order perturbation theory expression,15 
ΔνZeeman=Ψelec;JΩMJ±|ĤZeeman|Ψelec;JΩMJ±=geμ0BMJΩJ(J+1).
(5)

Note that the Zeeman operator connects levels of the same parity. In Eq. (5), ge is the electronic expectation value of the operators in the square brackets in Eq. (4) and is used as the fitting parameter. The optimized ge values obtained by least-squares fitting of the data are given in Table II. The standard deviations of these fits were 16.8 and 15.4 MHz for the [18.35]4.5-X(1)3.5 and [18.63]4.5- X(1)3.5 band systems, respectively.

Ab initio computational predictions for the ground and low-lying excited states of UN were presented in Refs. 4 and 5. These studies reported high-level calculations that included scalar relativistic effects, configuration interactions, and spin–orbit coupling. Large basis sets were employed, with extrapolation to the complete basis set limit. Both studies used small core 60-electron effective core potentials (ECP60) for U. The published results did not report values for the electric dipole moment of ground state UN. In a previous study of ThN,16 it was found that BP86 density functional theory (DFT) calculations with a 60 electron ECP for Th yielded values for the ground state equilibrium distance, harmonic vibrational constant, and electric dipole moment that were in good agreement with the experimental values.

Consequently, in the present work, we have used the ORCA program package17 to calculate the electric dipole moment and magnetic ge-factor for ground state UN. The all-electron SARC-DKH-TZVP basis set (with SARC/J auxiliary functions) was used for U, in combination with the aug-cc-pVTZ basis for N. Scalar relativistic effects were included using the second-order Douglas–Kroll Hamiltonian. Spin–orbit coupling was treated using the Breit–Pauli Hamiltonian with treatment of both one- and two-electron terms as described in Ref. 18 and section 9.29.2 of the Orca manual for version 4.0.1. Evaluation of the matrix elements of the spin–orbit Hamiltonian employed semi-numeric calculations of the Coulomb terms, exchange via one-center exact integrals, and spin–other orbit interactions. Most calculations used the mean-field/effective potential approximation.18 

Initially, the DFT/BP86 method was employed for spin-free calculations that were used to determine values for the equilibrium distance, vibrational constants, and dipole moment. To determine these properties, single-point calculations were carried out from R = 1.70 to 1.84 Å, in steps of 0.02 Å. These results were then fitted to a Morse potential. Calculations that included spin–orbit coupling were subsequently used to evaluate the ge-factor at the equilibrium distance. The BP86 functional yielded spin-free properties that were in good agreement with the experimental values (Re = 1.764 Å, ωe = 1002 cm−1, and μ = 4.37 D), but, with the inclusion of the spin–orbit coupling, the prediction of 1.27 for ge was far from the observed value. As BP86 is a pure generalized gradient approximation method, we also carried out calculations using the B3LYP hybrid functional (20% Hartree–Fock exchange) and the range-separated version CAM-B3LYP. The results are collected in Table VII.

TABLE VII.

Molecular Constants for UN X(1)3.5. Vibrational constants are in cm−1 units, electric dipoles are in Debye units, and the ge values are dimensionless.

MethodωeωexeDipolegeReference
SO-CASPT2 1010 ⋯ ⋯ 4  
SO-CASPT2 1007 ⋯ ⋯ 5  
BP86 1003 4.37 1.27 This work 
B3LYP 1211 20 3.65 2.07 This work 
CAM-B3LYP 1064 4.61 1.22 This work 
Experiment 1010.5(5.0) 4.2(2.5) 4.30(2) 2.16(1) This work 
MethodωeωexeDipolegeReference
SO-CASPT2 1010 ⋯ ⋯ 4  
SO-CASPT2 1007 ⋯ ⋯ 5  
BP86 1003 4.37 1.27 This work 
B3LYP 1211 20 3.65 2.07 This work 
CAM-B3LYP 1064 4.61 1.22 This work 
Experiment 1010.5(5.0) 4.2(2.5) 4.30(2) 2.16(1) This work 
The magnetic ge-value for the ground state of UN can be used to distinguish between different possible angular momentum coupling schemes and to evaluate previous predictions concerning the composition of the electronic wavefunction. The energy level pattern of UN is that of Hund’s case (c) because of the large spin–orbit interaction. The only electronic quantum number that can be extracted from the analysis of an individual vibronic state is Ω. However, as illustrated in a study of the lanthanide monoxide CeO,19 an interpretation of ge can be particularly valuable in identifying normally unspecified, approximately good Hund’s case (c) quantum numbers. As noted in the Introduction, the X(1)3.5 ground state wavefunction generated by ab initio calculations can be well represented by atomic ion basis functions arising predominantly from the U3+(5f27s)N3− configuration. Coupling between the spatially separated 5f and 7s orbitals is weak and best described by a j–j coupling scheme. The two interacting f-electrons couple to produce the sum of the orbital Lc, spin Sc, and total Jc electronic angular momenta for the 5f2 ionic core. The electronic angular momentum of the 7s electron, j, then couples with Jc to produce the total atomic ion angular momentum Ja. This electronic basis set is symbolically written as Ψelec=LcScJclsjJaΩ. The expectation value of the spin and orbital angular momenta operators of Eq. (4) (≡ge) was evaluated for this basis set in Ref. 19, and the resulting expression is reproduced here for convenience,
geLc,Sc,Jc:l,s,j:Ja,Ω=(A+B)Ω4Ja(Ja+1),
where
A=JaJa+1+JcJc+1j(j+1)Jc(Jc+1)3JcJc+1+ScSc+1LcLc+1
and
B=JaJa+1+jj+1JcJc+1j(j+1)[3jj+1+ss+1ll+1].
(6)

The quantum numbers for use in Eq. (6) are readily obtained using ligand field theory. Hund’s rules predict that the 3H4 term from the f2 configuration will be lowest in energy and, thus, most relevant for the Ω = 3.5 ground state of UN. The ab initio calculations of Refs. 4 and 5 predict that the ΛS composition for the U3+ ion in the ground state of UN is 83% 4H. Hence, the relevant quantum numbers for the basis set arising from the U3+(5f2(3H4)7s)N3− configuration are Lc = 5, Sc = 1, Jc = 4, l = 0, s = 0.5, j = 0.5, Ja = 3.5, and Ω = 3.5. Substitution into Eq. (6) gives ge = 2.33. The remaining atomic ion character is distributed as 8% 4Γ and 8% 2Γ, with ge values of 3.25 and 3.11, respectively. The weighted sum predicts a ge value of 2.47 for the X(1)3.5 ground state. The disagreement between this prediction and a measured value of 2.160 is not large enough to question the configurational parentage of the X(1)3.5 ground state, but it does suggest that the configuration interaction calculation has some deficiencies.

The ground state value for ΔG1/2 of 1010.5(5.0) cm−1 determined from the dispersed fluorescence data was consistent with the results obtained for UN trapped in a cryogenic Ar matrix. Green and Reedy6 observed three bands in the 991–1001 cm−1 range that were assigned to UN. The splitting into three components was attributed to the presence of three distinct matrix trapping sites. Based on the response of the spectrum to annealing of the matrix, the band at 1000.9 cm−1 was considered to originate from UN at the most stable trapping site.6 This frequency is just 9.6 cm−1 below the gas-phase value, which is entirely reasonable for the Ar matrix effect.

Recent computational predictions of the molecular constants for UN X(1)3.5 are compared to the experimental results in Table VII. Here, it can be seen that both ab initio (spin–orbit CASPT24,5) and DFT methods yielded results that were in good agreement with the measured values. The previous computational studies did not report predictions for the electric dipole moment or the magnetic ge-factor. Our DFT calculations yielded values for the electric dipole moment in the range of μe = 3.65 to 4.61 D at the equilibrium distance, in reasonable agreement with the measured value of μ0 = 4.30 D. Comparing the ground states of UN and ThN, we find that the electric dipole moment of ThN [5.11(9) D] is larger than that of UN. The zero-point vibrationally averaged bond length for ThN (R0 = 1.8222 Å) is slightly longer than that for UN (R0 = 1.7641 Å), but this difference alone is not sufficient to account for the difference in the dipole moments. Considered in terms of the formal charge separation, Mδ+Nδ−, the charge difference for ThN (δ = 0.57) is greater than that for UN (δ = 0.51).

The model-dependence of the ge values for ground state UN generated by the DFT calculations shows that the level of theory applied was insufficient for the recovery of this property. It is difficult to diagnose the root of this problem, but we note that the composition of the ΛS electronic wavefunction was, as expected, primarily 5f 27s. This is evident from the plots of the singly occupied orbitals shown in Fig. 7 (orbitals from the DFT/BP86 calculations). However, the Ω value for the spin–orbit coupled ground state was not defined. Note that changing how the electrons are distributed in the f-orbitals does not change the bonding significantly, so it is reasonable that the molecular constants and dipole moment would not be sensitive to f-orbital occupation details that markedly affect the ge-factor.

FIG. 7.

The singly occupied frontier orbitals of the ground state UN. The 7sσ orbital is viewed along an axis that is perpendicular to the bond axis. The 5fδ and 5fϕ orbitals are viewed along the bond axis in order to show the nodal planes. These orbitals are plotted on the same scale.

FIG. 7.

The singly occupied frontier orbitals of the ground state UN. The 7sσ orbital is viewed along an axis that is perpendicular to the bond axis. The 5fδ and 5fϕ orbitals are viewed along the bond axis in order to show the nodal planes. These orbitals are plotted on the same scale.

Close modal

The electric dipole moments obtained for the ground and excited states of UN were surprisingly similar. The most likely configurational assignments for the transitions reported here are that they are predominantly metal-centered 5f → 6d or 7s → 7p electron promotions.

The electronic structure of UN has been examined using high-resolution spectroscopy of vibronic transitions centered at 18 349 and 18 630 cm−1. External electric and magnetic fields were applied in order to measure electric dipole moments (from the Stark effect) and magnetic ge-factors (from the Zeeman effect). The primary focus was on the properties of the ground state. Both the ge-factor and the dipole moment were found to be consistent with previous studies that assigned the X(1)3.5 ground state to the formal U3+(5f27s)N3− electronic configuration. Dispersed fluorescence measurements defined ground state vibrational constants of ωe = 1010.5(5.0) and ωexe = 4.2(2.5) cm−1. The first electronically excited state, (1)4.5, was observed just 471.5(5) cm−1 above the ground state. DFT calculations yielded a reasonably good prediction for the ground state dipole moment, equilibrium bond length, and harmonic vibrational constant. However, the ground state magnetic ge-factor was greatly underestimated, indicative of problems with the details of the f-orbital occupations.

Electric dipole moment measurements for the excited states probed by direct laser excitation were close to the value obtained for the ground state. This suggests that the transitions were electron promotions that resulted in relatively small changes in the polarizability of the metal ion.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistry program under Award No. DE-FG02-01ER15153. We are most grateful to Prof. Thomas Varberg (Macalester College) for his careful reading of the manuscript and recognition that the Ω-assignment of the 18 630 cm-1 band should be changed from 3.5 to 4.5.

The authors have no conflicts to disclose.

Anh T. Le: Data curation (equal); Software (equal); Writing – review & editing (equal). Xi-lin Bai: Data curation (equal); Investigation (equal); Writing – review & editing (supporting). Michael C. Heaven: Formal analysis (equal); Funding acquisition (equal); Project administration (equal); Writing – original draft (equal); Writing – review & editing (equal). Timothy C. Steimle: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article.

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