Accurate rotational spectroscopy of sulfur dioxide, SO2, in its ground vibrational and first excited bending states, v2 = 0, 1, up to 2 THz

Approximately 150 pure rotational transitions each have been recorded for SO₂, v₂ = 0 and 1, in selected frequency regions up to 2 THz. The J and K_a quantum numbers reach very high values: 92 and 23, respectively, for the ground vibrational state and 81 and 21, respectively, for the first excited bending state. The highest levels accessed are almost 3000 cm⁻¹ above ground. The relative experimental uncertainties Δν/ν are about 10⁻⁸ for several medium to strong, isolated lines, and generally better than 2.5 × 10⁻⁷. Improved spectroscopic parameters have been obtained for both states, particularly for the excited bending state. In fact, the accuracies with which the energy levels of the v₂ = 1 state are known depend essentially only on the accuracy with which the vibrational spacing is known from infrared spectroscopy.     

Observation of hot bands in the infrared spectrum of H2CO

Two hot bands in the infrared spectrum of formaldehyde (H₂CO) have been identified by means of tunable infrared laser spectroscopy using a jet-cooled sample. One band falls in the region 2760-2800 cm⁻¹; it follows a-type selection rules and it has been assigned as the ν₁ + ν₄ − ν₄ hot band. The other band falls in the region 2800-2860 cm⁻¹; it follows b-type selection rules and it has been assigned as the ν₅ + ν₄ − ν₄ hot band. The observations are restricted to low J and K_a levels. It has consequently been possible to ignore the effects of the extensive Coriolis couplings involving these levels in the analysis of the spectra and to model the rotational structure as that of a simple asymmetric top. Least-squares fits of the data have provided values for the band origins: 2774.2706(11) cm⁻¹ for the ν₁ + ν₄ − ν₄ and 2829.2621(8) cm⁻¹ for the ν₅ + ν₄ − ν₄ band. Term values for the upper vibrational levels involved in the transitions have been determined by use of the previously reported term values for the v₄ = 1 level.     

Rotational spectrum of trans-trans diethyl ether in the ground and three excited vibrational states

We report the results of a comprehensive reinvestigation of the rotational spectrum of diethyl ether based on broadband millimetre-wave spectra recently recorded at The Ohio State University and in Warsaw, covering the frequency region 108-366 GHz. The data set for the ground vibrational state of trans-trans diethyl ether has been extended to over 2000 lines and improved spectroscopic constants have been determined. Rotational spectra in the first excited vibrational states of the three lowest vibrational modes of trans-trans-diethyl ether, ν₂₀, ν₃₉, and ν₁₂ have been assigned. The v₂₀ = 1 and v₃₉ = 1 states are near 100 cm⁻¹ in vibrational term value and are coupled by a strong c-axis Coriolis interaction, which gives rise to many spectacular manifestations in the rotational spectrum. All of these effects have been successfully fitted for a dataset comprising over 3000 transitions, leading to precise determination of the energy difference between these states, (ΔE/hc)=10.400222(5) cm⁻¹. A newly developed software package for assignment and analysis of broadband spectra is described and made available.     

Infrared emission studies of the AΣ-XΠ electronic transition of the SiC radical

The gas phase infrared emission spectrum of the A³Σ⁻-X³Π electronic transition of SiC has been observed using a high resolution Fourier transform spectrometer. Three bands ν′ − ν″ = 0-1, 0-0, and 1-0 have been observed in the 2770, 3723, and 4578 cm⁻¹ regions, where the 0-1 and 0-0 bands were observed for the first time. The SiC radical was generated by a dc discharge in a flowing mixture of hexamethyl disilane [(CH₃)₆Si₂] and He. A total of 1074 rotational transitions assigned to the 0-1, 0-0, and 1-0 bands have been combined in a simultaneous analysis with previously reported pure rotational data to determine the molecular constants for SiC in the two electronic states. The principal equilibrium molecular constants for the A³Σ⁻ state are: B_e = 0.6181195(18) cm⁻¹, α_e = 0.0051921(20) cm⁻¹, r_e = 1.8020884(26) Å, and T_e = 3773.31(17) cm⁻¹, with one standard deviation given in parentheses. The effect of a perturbation was recognized between the ν = 4 level of X³Π and the ν = 0 level of A³Σ, and the analysis was carried out to determine the interaction parameter between the two states.     

CW-cavity ring down spectroscopy of the ozone molecule in the 6625-6830 cm region

The absorption spectrum of ozone, ¹⁶O₃, has been recorded by CW-cavity ring down spectroscopy in the 6625-6830 cm⁻¹ region. The typical sensitivity of these recordings (α_min ∼ 3 × 10⁻¹⁰ cm⁻¹) allows observing very weak transitions with intensity down to 2 × 10⁻²⁸ cm/molecule. 483 and 299 transitions have been assigned to the 2ν₁ + 3ν₂ + 3ν₃A-type band and to the 2ν₁ + 4ν₂ + 2ν₃B-type band, respectively, which are the highest frequency bands of ozone recorded so far under high resolution. Rovibrational transitions with J and K_a values up to 46 and 12, respectively, could be assigned. Despite well-known difficulties to correctly reproduce the energy levels not far from the dissociation limit, it was possible to determine the parameters of an effective Hamiltonian which includes six vibrational states, four of them being dark states. The line positions analysis led to an rms deviation of 8.5 × 10⁻³ cm⁻¹ while the experimental line intensities could be satisfactorily reproduced. Additional experiments in the 5970-6021 cm⁻¹ region allows detecting the (233) ← (010) hot band reaching the same upper state as the preceding cold band. From the effective parameters of the (233) state just determined and those of the (010) level available in the literature, 329 transitions could be assigned and used for a further refinement of the rovibrational parameters of the effective Hamiltonian leading to a value of 7.6 × 10⁻³ cm⁻¹ for the global rms deviation. The complete list of the experimentally determined rovibrational energy levels of the (233), (242), and (520) states is given. The determined effective Hamiltonian and transition moment operators allowed calculating a line list (intensity cut off of 10⁻²⁸ cm/molecule at 296 K), available as Supplementary material for the 6590-6860 and 5916-6021 cm⁻¹ regions. The integrated band strength values are 1.75 × 10⁻²⁴ and 4.78 × 10⁻²⁵ cm/molecule at 296 K for the 2ν₁ + 3ν₂ + 3ν₃A-type band and to the 2ν₁ + 4ν₂ + 2ν₃B-type band, respectively, while the band intensity value of the (233) ← (010) is estimated to be 1.03 × 10⁻²⁴ cm/molecule.     

Vibrational and rotational analyses of bands between 636 and 660 nm in the red system of CuCl2

The long wavelength end of the electronic spectrum of CuCl₂, between 636 and 660 nm, has been recorded in the gas phase by laser-excitation spectroscopy using a sample prepared at low temperatures (ca. 10 K) in a free-jet expansion. Under these conditions, it is possible to resolve vibrational, rotational, and even Cu hyperfine structure. The (0, 0) band of the E²Π_u-X²Π_g transition has been identified with an origin at 15546.286(3) cm⁻¹ for ⁶³Cu³⁵Cl₂. The observation and analysis of bands involving vibrationally excited levels has allowed the determination of all three vibrational intervals for the E²Π_u state (ν₁ = 335.88 cm⁻¹, ν₂ = 112.42 cm⁻¹, and ν₃ = 482.17 cm⁻¹, ⁶³Cu³⁵Cl₂). In addition, two other, unrelated transitions have been identified in the same narrow wavelength region. This, combined with the observation of local perturbations of the rotational structure in various bands, reveals the presence of other closely lying electronic states in the same energy region.     

High resolution infrared spectrum and global analysis of ν5, ν12, and ν12 + ν6 − ν6 in CH3SiH3

The vibration-torsion-rotation spectrum of CH₃SiH₃ has been measured from 470 to 725 cm⁻¹ at near-Doppler resolution. The full-width at half - maximum of the lines observed near 600 cm⁻¹ was 0.0011 cm⁻¹. The spectra were obtained using a Bruker IFS 125 HR Fourier transform spectrometer with the broadband source radiation being supplied from the synchrotron emission of the storage ring at the Canadian Light Source. Three vibrational bands were investigated: the lowest lying perpendicular fundamental ν₁₂ centred near 524 cm⁻¹, the lowest lying parallel fundamental ν₅ near 703 cm⁻¹, and the torsional hot band ν₁₂ + ν₆ − ν₆ near 534 cm⁻¹. For ν₁₂ and ν₅, the resolution and sensitivity are much improved over those in earlier studies, with many of the torsional multiplets now being resolved even in the cases where the upper levels are unperturbed. The primary motivation for the present work was the hot band, here reported for the first time, where the dependence of the silyl rock in ν₁₂ on the torsional motion is much more pronounced. In addition, for the vibrational ground state (gs), two “forbidden” high torsional overtones v₆ = 3 ← 0 and 5 ← 0 have been observed that become allowed through resonant mixing of the upper states with ν₁₂ and ν₅, respectively. In each case, two (K, σ) series have been measured where the mixing is largest. Here σ = 0, 1, −1 labels the torsional sub-levels. Using the Fourier transform waveguide spectrometer at E. T. H., the three σ-components of the (J = 1 ← 0) transition in ν₁₂ + ν₆ were observed, and a series of direct l-doubling transitions in ν₁₂ + ν₆ were measured for σ = 0. In a global fit, all the new data have been analysed along with the frequencies for other transitions obtained in earlier investigations. The analysis takes into account the relevant interactions among the torsional stacks of levels in the gs, ν₁₂, and ν₅. These include the previously known (gs, ν₁₂) Coriolis-like and (gs, ν₅) Fermi-like interactions along with a higher order (ν₁₂, ν₅) Coriolis-like coupling introduced here. This last is responsible for the strong perturbation of the ν₅ series with K = 10, 11, and 12, and of the corresponding hot band series. A good fit to 9282 frequencies including 7942 new measurements was obtained both with the Free Rotor model in which the torsion is classified as a rotation, and with the High Barrier model in which the torsion is classified as a vibration. The Hamiltonian is discussed with emphasis on the new terms required for treating ν₁₂ + ν₆ − ν₆.     

Joint ro-vibrational analysis of the HDS high resolution infrared data

High resolution Fourier transform spectra of the HDS molecule were recorded and analyzed for the first time in the region of the bands ν₁ + 2ν₂ (3938.6 cm⁻¹), ν₁ + ν₃ (4522.6 cm⁻¹), 2ν₂ + ν₃ (4638.8 cm⁻¹), 2ν₁ + ν₂ (4767.7 cm⁻¹), ν₁ + ν₂ + ν₃ (5525.2 cm⁻¹), 3ν₁ (5560.6 cm⁻¹), ν₁ + 2ν₃ (7047.2 cm⁻¹), and 2ν₂ + 2ν₃ (7123.9 cm⁻¹). The ro-vibrational energies of the upper vibrational states of these bands together with the ro-vibrational energies of 12 other bands already studied at high resolution were used as inputs in a Global Fit analysis firstly described in [O.N. Ulenikov, G.A. Onopenko, H. Lin, J.-H. Zhang, Z.-Y. Zhou, Q.-S. Zhu, R.N. Tolchenov, J. Mol. Spectrosc. 189 (1998) 29-39]. In this case, the resonance interactions between the states (v₁v₂v₃) and (v₁ ± 2 v₂ ? 1 v₃ ? 1) were taken into account. The resulting set of 143 parameters reproduces all the experimental data (2984 vibration-rotation energies of 20 vibrational states which correspond to about 9700 ro-vibrational transitions with J^max = 23) with accuracies comparable with the experimental uncertainties.     

The dipole moment of HOCl in vOH=4

Pulsed laser excitation and photofragment detection methods are used to observe the 17_0,17←16_1,16 pure rotational transition within the v_OH=4 vibrational state of HO³⁵Cl. Microwave frequency and Stark effect measurements give ν₀=27484.33(10) MHz and μ_b=1.562(9) D. The dependence of μ_b, which is approximately parallel to the OH bond, on the level of OH stretch excitation appears linear and is consistent with that of H₂O over the same 0-14 000 cm⁻¹ energy range.     

High-resolution laser spectroscopy of the potassium-argon molecule: The BΣ state

The absorption spectrum of the KAr molecule has been observed with high resolution between 13 032 and 13 077 cm⁻¹ using tunable laser diodes as light sources, a supersonic beam for production of the molecules, and laser-induced fluorescence for detection. In addition, optical-optical double resonance (OODR) experiments have been performed to simplify the spectrum and to get rotational assignment. Altogether, 670 lines due to the transition B²Σ⁺ ← X²Σ⁺ have successfully been assigned with vibrational levels of the B state ranging from v = 0 to v = 6. The corresponding energy values were fitted to the well-known Dunham expansion. In addition, we were able to analyse a local perturbation between the vibrational level v = 1 of the B state and v = 14 of the A²Π_3/2 state. Unexpected extra lines in the OODR spectra are most probably due to a collision-induced population of other levels. For the equilibrium distance and the well-depth of the B state we obtain from the Dunham expansion 7.03 (8) Å and 26.2 (8) cm⁻¹, respectively.     

A reevaluation of the assignment of the vibrational fundamentals and the rotational analysis of bands in the high-resolution infrared spectra of trans- and cis-1,3,5-hexatriene

Assignments of the vibrational fundamentals of cis- and trans-1,3,5-hexatriene are reevaluated with new infrared and Raman spectra and with quantum chemical predictions of intensities and anharmonic frequencies. The rotational structure is analyzed in the high-resolution (0.0013-0.0018 cm⁻¹) infrared spectra of three C-type bands of the trans isomer and two C-type bands of the cis isomer. The bands for the trans isomer are at 1010.96 cm⁻¹ (ν₁₄), 900.908 cm⁻¹ (ν₁₆), and 683.46 cm⁻¹ (ν₁₇). Ground state (GS) rotational constants have been fitted to the combined ground state combination differences (GSCDs) for the three bands of the trans isomer. The bands for the cis isomer are at 907.70 cm⁻¹ (ν₃₃) and 587.89 cm⁻¹ (ν₃₅). GS rotational constants have been fitted to the combined GSCDs for the two bands of the cis isomer and compared with those obtained from microwave spectroscopy. Small inertial defects in the GSs confirm that both molecules are planar. Upper state rotational constants were fitted for all five bands.     

High resolution fourier transform spectrum of PD3 in the region of the stretching overtone bands 2ν1 and ν1+ν3

The infrared spectrum of the PD₃ molecule has been measured in the region of the first stretching overtone bands on a Fourier transform spectrometer with a resolution of 0.0068 cm⁻¹ and analyzed for the first time. More than 800 transitions with J^max=15 have been assigned to the bands 2ν₁ and ν₁+ν₃. An effective Hamiltonian was used which takes into account both the presence of resonance interactions between the states (2 0 0 0) and (1 0 1 0), and interactions of these with the third stretching vibrational state of the v=2 polyad, (0 0 2 0). A set of 44 spectroscopic parameters is obtained from the fit. This reproduces the 305 initial “experimental” upper rovibrational energies with an rms=0.0015 cm⁻¹.     

The millimeter-wave rotational spectrum of fluorobenzene

The room-temperature rotational spectrum of fluorobenzene was studied in the frequency region 167-318 GHz. Rotational transitions were assigned and measured in the ground vibrational state, and all six excited vibrational states with energies below 600 cm⁻¹, i.e., v₁₁ = 1, v₁₁ = 2, v_18b = 1, v_16a = 1, v_16b = 1, and v_6a = 1. Accurate quartic-level spectroscopic constants were determined for all states, allowing spectral predictions well into the submillimeter region. The states v_18b = 1 and v_16a = 1 were found to be connected by a strong Coriolis interaction, which allowed precise determination of their energy separation, ΔE = 7.455088(3) cm⁻¹. Unambiguous assignment of vibrational modes was made on the basis of the calculated inertial defect and nuclear spin statistical weights. Rotational constants for the ¹³C₄ isotopomer have also been redetermined and two new least-squares determinations of the geometry of fluorobenzene, r₀ and are reported.     

The high-resolution infrared spectrum of BF3 from 400 to 1650 cm

High-resolution infrared spectra of boron trifluoride, enriched to 99.5 at. % ¹¹B, have been measured from 400 to 1650 cm⁻¹. In that region we have identified and analyzed 16 absorption bands attributed to the three fundamental bands, two combination bands, 10 hot bands, and one difference band. All possible states were accessed in this region through direct transitions either from the ground state or as hot bands from thermally populated levels. The spectral resolution of the measurements varied from 0.0015 to 0.0020 cm⁻¹. An improved set of ground state rotational constants and rovibrational constants for the infrared-active fundamental vibrations have been determined from over 32 000 assigned transitions. This study resulted in the first direct characterization of the infrared-inactive ν₁ state of ¹¹BF₃ leading to values for ν₁, , and of 885.843205(24), 0.000678548(53), and 0.000337564(66) cm⁻¹, respectively. The Fermi resonance perturbation between the E′ states ν₃ and 3ν₄ (l = ±1) was further elucidated by observation of hot band transitions to both the 3ν₄ (l = ±1) and 3ν₄ (l = ±3) states. Several other resonances were also found including the weak rotational interaction, between the state 2ν₂ and the E′ state of ν₁ + ν₄.     

ICLAS of weak transitions of water between 11 300 and 12 850 cm: Comparison with FTS databases

Very weak water vapor absorption lines have been investigated by intracavity laser absorption spectroscopy (ICLAS) in the 11 335-11 947 and 12 336-12 843 cm⁻¹ spectral regions dominated by the ν₁ + 3ν₂ + ν₃ and ν₂ + 3ν₃ bands, respectively. A detectivity on the order of α_min ∼ 10⁻⁹ cm⁻¹ was achieved with an ICLAS spectrometer based on a Ti: Sapphire laser. It allowed detecting transitions with an intensity down to 5 × 10⁻²⁸ cm/molecule which is about 10 times lower than the weakest line intensities previously detected in the considered region. A line list corresponding to 1281 transitions with intensity lower than 5 × 10⁻²⁶ cm/molecule has been generated. A detailed comparison with the line lists provided by the HITRAN database and by recent investigations by Fourier transform spectroscopy associated with very long multi pass cell is presented. The rovibrational assignment performed on the basis of the ab initio calculations of Schwenke and Partridge, has allowed for determining 176 new energy levels belonging to a total of 16 vibrational states.     

Rotational levels of the (0 0 0) and (0 1 0) states of D2O from hot emission spectra in the 320-860 cm region

The far-infrared emission spectra of deuterated water vapour were measured at different temperatures (1370, 1520, and 1950 K) in the range 320-860 cm⁻¹ at a resolution of 0.0055 cm⁻¹. The measurements were performed in an alumina cell with an effective length of hot gas of about 50 cm. More than 1150 new measured lines for the D₂¹⁶O molecule corresponding to transitions between highly excited rotational levels of the (0 0 0) and (0 1 0) vibrational states are reported. These new lines correspond to rotational states with higher values of the rotational quantum numbers compared to previously published determinations: J_max=26 and for the (0 0 0) ← (0 0 0) band, J_max=25 and for the (0 1 0) ← (0 1 0) band, and J_max=26 and for the (0 1 0) ← (0 0 0) band. The estimated accuracy of the measured line positions is 0.0005 cm⁻¹. To our knowledge no experimentally measured rotational transitions for D₂¹⁶O within an excited vibrational state have been available in the literature so far. An extended set of experimental rotational energy levels for (0 0 0) and (0 1 0) vibration states including all previously available data has been determined. For the data reduction we used the generating function model. The root mean square (RMS) deviation between observed and calculated values is 0.0012 cm⁻¹ for 692 rotational levels of the (0 0 0) state and 0.0010 cm⁻¹ for 639 rotational levels of the (0 1 0) vibrational state. A comparison of the observed energy levels with the best available values from the literature and with the global predictions from molecular electronic potential energy surface [J. Chem. Phys. 106 (1997) 4618] for the (0 0 0) and (0 1 0) states is discussed.     

Sub-Doppler and Doppler spectroscopy of DCN isotopomers in the terahertz region: ground and first excited bending states (v1v2v3)=(0 1 0)

The rotational spectra of the deuterium cyanide isotopic species DCN, D¹³CN, DC¹⁵N, and D¹³C¹⁵N were recorded in the vibrational ground and first excited bending state (v₂=1) up to 2 THz. The R-branch transitions from J=3←2 to J=13←12 were measured with sub-Doppler resolution. These very high resolution (∼70 kHz) and precise (±3-10 kHz) saturation dip measurements allowed for resolving the underlying hyperfine structure due to the ¹⁴N nucleus in DCN and D¹³CN for transitions as high as J=10←9. Additional high JR-branch (J=25←24 to J=28←27) transitions around 2 THz and direct l-type (ΔJ=0, J=19 to J=25) transitions from 66 to 118 GHz were recorded in Doppler-limited resolution. For the ground state of D¹³C¹⁵N, the J=1←0 transition was measured for the first time. The transition frequency accuracies for the other deuterated species were significantly improved. These new experimental data, together with the available infrared rovibrational data and previously measured direct l-type transitions, were subjected to a global least squares analysis for each isotopomer. This yielded precise sets of molecular constants for the ground and first excited vibrational states, including the nuclear quadrupole and magnetic spin-rotation coupling constants of the ¹⁴N nucleus for DCN and D¹³CN. The hyperfine structure due to the D, ¹³C, and ¹⁵N nuclei have not been resolved, but led to a broadening of the observed saturation dips.     

CW-cavity ring down spectroscopy of the ozone molecule in the 6220-6400 cm region

The absorption spectrum of ozone,¹⁶O₃, has been recorded in the 6220-6400 cm⁻¹ region by high sensitivity CW-cavity ring down spectroscopy (α_min ∼ 3 × 10⁻¹⁰ cm⁻¹). 1836 rovibrational transitions have been assigned to the 2ν₂ + 5ν₃, 5ν₁ + ν₃ and 2ν₁ +  2ν₂ + 3ν₃ A-type bands centred at 6305, 6355 and 6387 cm⁻¹, respectively. In addition, 99 lines of the very weak ν₁ + 2ν₂ +  4ν₃ and 4ν₁ + 3ν₂ B-type bands are identified. The modeling of the observed spectrum in the effective Hamiltonian approach was particularly laborious and complex as several rovibrational interactions of both Coriolis and anaharmonic type were found to be of importance, in particular for the (124) vibrational state. Nevertheless, it has finally been possible to fit the 990 experimentally determined energy levels with an rms deviation of 8.29 × 10⁻³ cm⁻¹ and to derive the transition moment parameters allowing a satisfactory reproduction of the observed intensities. As the differences in positions between the final calculations and observations are still larger than the experimental accuracy, we provide the list of all energy levels derived from the observation, in addition to their differences with the calculated ones. These experimental energy levels, with the transition moment parameters were used to generate a line-list of 2451 transitions, reproducing the observed spectrum. This list is given as Supplementary Material.     

The formaldehyde cation: Rovibrational energy level structure and Coriolis interaction near the adiabatic ionization threshold

Rotationally resolved pulsed-field-ionization zero-kinetic-energy photoelectron spectra of the 0⁰, 6¹ and 4¹ vibrational levels of the ground electronic state of the formaldehyde cation were recorded using a resonant three-color three-photon excitation scheme. The first adiabatic ionization energy of CH₂O (87793.33(1.30) cm⁻¹) and the rigid-rotor rotational constants (A⁺ = 8.874(8) cm⁻¹, B⁺ = 1.342(15) cm⁻¹, C⁺ = 1.148(18) cm⁻¹) of the vibronic ground state of CH₂O⁺ were derived. A strong a-type Coriolis interaction between the 6¹ and 4¹ vibrational levels was observed. The Coriolis coupling parameter and the deperturbed fundamental vibrational frequencies of the in-plane-rocking mode ν₆ and the out-of-plane bending mode ν₄ were determined to be 8.70(10) cm⁻¹, 823.67(30) cm⁻¹ and 1036.50(30) cm⁻¹, respectively. The intensity distribution of the photoelectron spectra was analyzed in the realm of a simple photoionization model.     

The ν1 + 3ν2 + 3ν3 and 4ν1 + ν2 + ν3 bands of ozone by CW-cavity ring down spectroscopy between 5900 and 5960 cm

The absorption spectrum of ozone, ¹⁶O₃, has been recorded in the 5903-5960 cm⁻¹ region by high sensitivity CW-cavity ring down spectroscopy (α_min ∼ 5 × 10⁻¹⁰ cm⁻¹). The ν₁ + 3ν₂ + 3ν₃ and 4ν₁ + ν₂ + ν₃ A-type bands centred at 5919.15 and 5947.07 cm⁻¹ were newly observed. A set of 173 and 168 energy levels could be experimentally determined for the (1 3 3) and (4 1 1) states, respectively. Except for a few K_a = 5 levels of the (4 1 1) state, the rotational structure of the two states was found mostly unperturbed. The spectroscopic parameters were determined from a fit of the corresponding line positions by considering the (1 3 3) and (4 1 1) states as isolated. The determined effective Hamiltonian and transition moment operators were used to generate a list of 785 transitions given as Supplementary Material.