Ro-vibrational Energy Values Research Articles

High resolution analysis of the CD[formula omitted] deuterated methane: Extended investigation of the pentad region

A highly accurate rotational–vibrational analysis of Fourier transform infrared spectra of the 12CD4 molecule is presented. The high resolution infrared spectra were measured with a IFS125 HR Fourier transform interferometer from Bruker at an optical resolution of 0.003 cm−1 and analyzed in the 1750–2400 cm−1 region. Here the 2ν2, ν2+ν4, 2ν4, ν1 and ν3 bands (altogether, nine sub-bands of different symmetry) of the pentad are located. The number of 1213/1993/1576/77/1582 transitions with the Jmax = 23/23/23/14/32 were assigned to the 2ν2, ν2+ν4, 2ν4, ν1 and ν3 bands of 12CD4. The obtained experimental data were used for the determination of the upper ro-vibrational energy values. To provide more correct values of the upper energies, more than 7800 highly accurate “hot” transitions from the dyad region were additionally processed. In general, 4088 upper ro-vibrational energies of the pentad (for comparison, 2525 upper ro-vibrational energies with the value of Jmax=20 are known in the modern literature up to now) were determined, which were used then in the weighted fit procedure with a goal to determine the spectroscopic parameters (band centers, rotational, centrifugal distortion, tetrahedral splitting and resonance interaction parameters) of the effective Hamiltonian. The obtained drms value is 5.5×10−4 cm−1 which is almost one hundred times better than the reproduction of the same set of experimental data by the parameters known in the earlier literature.

The calculation of ro-vibrational energies, franck-condon factors and r-centroids for Yttrium/Scandium oxides in D-dimension

The spectroscopic data as ro-vibrational energy values, Franck-Condon Factors and r-centroids are obtained for Yttrium/Scandium oxides with (B 2Σ+, X 2Σ+) different electronic states. Ro-vibrational energy values are calculated by bound state solution of the Schrödinger equation for the general molecular potential by applying Pekeris-type approximation to the centrifugal term in D-dimensional. Using these solutions, the relation giving the bound state energy eigenvalues and the corresponding wave functions expression are derived. The Franck-Condon factors and r-centroids values are determined by using Fraser-Jarmain method for the B 2Σ+ → X 2Σ+ electronic transitions in both molecules. All the results obtained are given numerically in the tables. The obtained values are compared with the previously get data in the literature and it is seen that the results are consistent.

Effective Dipole Moment Model for Axially Symmetric C3v Molecules: Application to the Precise Study of Absolute Line Strengths of the ν6 Fundamental of CH335Cl.

The effective dipole moment model for molecules of axial C3v symmetry is derived on the basis of the symmetry properties of a molecule which, on the one hand, is of the same order of efficiency (but much simpler and clearer in applications) as the analogous models derived on the basis of the irreducible tensorial sets theory, and, on the other hand, mathematically more correct in comparison with concepts like the Herman-Walles function used in the models. As an application of the general results obtained, we discuss high-resolution infrared spectra of CH335Cl, recorded with the Zürich prototype ZP2001 (Bruker IFS125 HR) Fourier transform infrared spectrometer at a resolution of 0.001 cm-1 and analyzed in the region of 880-1190 cm-1 (ν6 bending fundamental centered at ν0 = 1018.070790 cm-1). Absolute strengths of more than 2800 transitions (2081 lines) were obtained from the fit of their shapes both with Voigt and Hartmann-Tran profiles, and parameters of the effective dipole moment of the ν6 band were determined by the computer code SYMTOMLIST (SYMmetric TOp Molecules: LIne STrengths), created on the basis of a derived theoretical model. As the first step of the analysis of the experimental data, assignments of the recorded lines were made. A total of 5124 transitions with Jmax = 68, Kmax = 21 were assigned to the ν6 band. The weighted fit of 2077 upper energy values obtained from the experimentally recorded transitions was made with a Hamiltonian which takes into account different types of ro-vibrational effects in doubly degenerate vibrational states of the C3v-symmetric molecule. As the result, a set of 25 fitted parameters was obtained which reproduces the initial 2077 upper "experimental" ro-vibrational energy values with a root mean square deviation drms=4.7×10-5 cm-1. At the second step of the analysis, the computer code SYMTOMLIST was used for determination of the parameters of the derived effective dipole moment model. Six effective dipole moment parameters were obtained from the weighted fit procedure which reproduces absolute experimental strengths of the 2804 initial experimental transitions with a relative drms=3.4%.

High resolution spectroscopy of asymmetric top molecules in nonsinglet electronic states: the ν3 fundamental of chlorine dioxide (16O35Cl16O) free radical in the X2B1 electronic ground state.

Highly resolved spectra of the 16O35Cl16O isotopologue of chlorine dioxide were recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer in the region of the ν3 band. The analysis was made in the frame of the spin-rotational effective Hamiltonian (in A-reduction and Ir-representation) taking into account spin-rotational coupling operators up to the sixth order and the corresponding reduction of the Hamiltonian. The mathematical description of the ro-vibrational spectra was implemented to the specially created computer program ROVDES. Under the present experimental conditions, we were able to assign more than 5200 spin-rotational transitions to the ν3 band. This number is 2.4 times higher compared to the previous studies available from the literature. The vibrational ground state parameters were improved, and the 2220 upper spin-rotation-vibration energy levels were determined and used as initial data in the inverse spectroscopic problem with the derived effective spin-rotational Hamiltonian. A total of 37 fitted parameters were determined (22 rotational and centrifugal parameters and 15 parameters of spin-rotation coupling). The appearance of strong Coriolis resonance interactions between the (001) and (100) vibrational states in the sets of (001)[N,Ka = 9], (001)[N,Ka = 17], (001)[N,Ka = 18] and (001)[N,Ka = 19] spin-rotation-vibration levels was experimentally observed for the first time and explained. The drms = 1.4 × 10-4 cm-1 reproduction of the initial "experimental" upper ro-vibrational energy values was achieved which is considerably better compared to the use of parameters from a previous study ([J. Ortigoso et al., J. Mol. Spectrosc., 1992, 155, 25-43]).

High–resolution spectroscopy of C2H3D: Line positions and energy structure of the strongly interacting [formula omitted] and [formula omitted] bands

High resolution infrared spectra of C2H3D were recorded in the region of 550–1950 cm−1 with a Bruker IFS125 HR Fourier transform infrared spectrometers and rotational structures of the five lowest strongly interacting ν10, ν7,ν8,ν4 and ν6 bands were analyzed. The number of about 28000 transitions (4200/6800/5600/5000/6400 for the bands ν10,ν7,ν8,ν4 and ν6) with Jmax = 40 and Kamax = 20 were assigned to these five bands. The weighted fit of 3990 upper energy values obtained from the experimentally recorded transitions was made with a Hamiltonian which takes into account resonance interactions between all studied bands as well as with the sixth ν3 band which was considered in this case as a “dark” one. As the result of analysis, a set of 279 fitted parameters was obtained which reproduces the initial 3990 upper “experimental” ro–vibrational energy values with the drms=1.7×10-4 cm−1; the initial nonsaturated, unblended and not very weak of 28000 assigned transitions are reproduced with the drms=2.2×10-4 cm−1. Ground state parameters of the C2H3D molecule were improved as well.

High–resolution re–investigation of the [formula omitted] and [formula omitted] bending bands of phosphine (PH[formula omitted

High resolution infrared spectra of PH3 were recorded with a Bruker IFS125 HR Fourier transform infrared spectrometer at an optical resolution of 0.0025 cm−1 and analyzed in the region of 600–1700 cm−1 where the ν2/ν4 bending dyad is located. The number of 2207 and 4564 transitions (in general, 3099 “allowed” and 3672 “forbidden”, which is about 2.5 times higher in comparison with the preceding studies) with Jmax = 29, Kmax = 28 (Jmax = Kmax = 24 in the earlier studies) were assigned to these two bands. Ground state parameters were improved on the basis of MW and IR data, known from the literature, and new IR data from the present study. The A1/A2 splittings for the states with the quantum number K=13 were experimentally recorded and theoretically explained for the first time. The weighted fit of 1284 upper energy values obtained from the experimentally recorded transitions was made with a Hamiltonian which takes into account resonance interaction between the (0100,A1) and (0001,E) vibrational states. As the result, a set of 86 fitted parameters was obtained which reproduces the initial 1284 upper “experimental”ro–vibrational energy values with the drms=9.8×10−5 cm−1.

First detection of the rare hydrogen sulfide isotopologue: The pure rotational and ν2 bands of HD33S

The high–resolution infrared spectrum of the HDS isotopologue was recorded and analyzed in the region of the ν2 fundamental band region (700–1400 cm−1) with a Bruker IFS 125HR Fourier transform infrared spectrometer (Zurich prototype ZP2001). Among the lines of the ν2 band of the HD32S and HD34S molecules, 801 transitions of HD33S were found in the spectrum and assigned for the first time (Jmax = 19 and Kamax = 12). Also for the first time, rotational energies of the ground vibrational state were determined from the 87 ground state combination differences obtained from the experimental data. Fits of parameters of the Watson hamiltonian with both ground state combination differences and ro–vibrational energy values (line positions) of the (010) vibrational state were made. Parameters of the effective dipole moments of the pure rotational transitions and of the ν2 band are obtained. Line lists (line positions and line strengths) of the pure rotational transitions and transitions belonging to the ν2 band are generated which can be useful for astrophysical and planetological applications.

Extended analysis of the high resolution FTIR spectra of H2MS ([formula omitted]) in the region of the bending fundamental band: The ν2 and [formula omitted] bands: Line positions, strengths, and pressure broadening widths

The high resolution infrared spectra of hydrogen sulfide, H2MS (M=32,33,34,36) in the natural abundance (95.041% of H232S, 0.748% of H233S, 4.196% of H234S and 0.015% of H236S), were recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer (Zürich prototype ZP2001) and analyzed in the ν2 fundamental band region (700 – 1800 cm−1). In the experimental spectra 1564, 1019, and 685 transitions were assigned to the ν2 bands of H232S, H234S and H233S (the maximum values of the quantum numbers are Jmax./Kamax. = 24/17, 20/14, 17/14). The subsequent weighted fits of experimentally assigned transitions were made with the Watson Hamiltonian and a set of parameters which reproduces the initial 333/249/216 infrared ro-vibrational energy values has been obtained from the assigned experimental line positions with the root mean square deviations of drms=2.2×10−4 cm−1,1.7×10−4 cm−1 and 1.5×10−4 cm−1 for the H232S, H234S and H233S isotopologues. Additionally, 703, 182 and 23 transitions with the values of quantum numbers Jmax./Kamax. = 18/14, 14/8 and 9/6 belonging to the 2ν2−ν2 hot bands of H232S, H234S and H233S (for the first time for the hot bands of the H234S and H233S species) were assigned in the experimental spectra. Rotational parameters of the ground vibrational state of H236S were re-determined, and, for the first time, 103 transitions (Jmax.=11,Kamax.=8) of the ν2 band of H236S were assigned in the experimental spectra. An analysis of ro-vibrational line strengths of 61 experimental isolated unsaturated and not too weak lines of the ν2 band of H232S was made (Jmax.=9,Kamax.=8), and five effective dipole moment parameters were obtained from the fit which reproduce the initial experimental line intensities with the drms = 1.4 %. An analogous analysis was performed for the H234S and H233S isotopologues. The half-widths analysis was made on the basis of the multi-spectrum fit with the Hartmann-Tran line profile, and self-pressure broadening coefficients were estimated for a few tens of lines for the three most abundant isotopologues.

High resolution FTIR spectroscopy of sulfur dioxide in the 1550–1950 cm−1 region: First analysis of the [formula omitted] bands of 32S16O18O and experimental line intensities of ro-vibrational transitions in the [formula omitted] bands of 32S16O2, 34S16O2, 32S18O2 and 32S16O18O

The high resolution infrared spectra of the 32S16O18O molecule were recorded for the first time with a Bruker IFS 120 HR Fourier transform interferometer and analysed in the region of 1550–1950cm−1 where the bands ν1+ν2 and ν2+ν3 are located. About 1050 and 1570 transitions were assigned in the experimental spectra with the maximum values of quantum numbers Jmax./Kamax. equal to 64/16 and 58/19 to the bands ν1+ν2 and ν2+ν3, respectively. The subsequent weighted fit of experimentally assigned transitions was made with the Hamiltonian model which takes into account the resonance interactions between the studied vibrational states. As the result, a set of 16 fitted parameters was obtained which reproduces the initial 1442 ro-vibrational energy values obtained from the assigned transitions with the drms=3.7×10−4cm−1. An analysis of more than 4050 experimental ro-vibrational line intensities of the ν1+ν2 and ν2+ν3 bands of 32S16O2 was made, and a set of 7 effective dipole moment parameters was obtained which reproduce the initial experimental line intensities with the drms=6.9%. Values of these parameters, being re-calculated to the values of corresponding parameters of the 34S16O2, 32S18O2 and 32S16O18O species were used for calculation of line intensities in the ν1+ν2 and ν2+ν3 bands of these three isotopologues. A list of transitions with their line intensities in the region of 1550–1950cm−1 for the four mentioned species is generated.

High resolution study of the rotational structure of doubly excited vibrational states of 32S16O18O: The first analysis of the 2ν1, [formula omitted], and 2ν3 bands

The high resolution infrared spectra of the 32S16O18O molecule were recorded with a Bruker IFS 120 HR Fourier transform interferometer for the first time in the region of 1800–2800cm−1 where the bands 2ν1, ν1+ν3, and 2ν3 are located. About 3970, 2960 and 3450 transitions were assigned in the experimental spectra with the maximum values of quantum numbers Jmax./Kamax. equal to 59/20, 68/25, and 43/18 to the bands 2ν1, ν1+ν3, and 2ν3, respectively. The subsequent weighted fit of experimentally assigned transitions was made with the Hamiltonian model which takes into account the resonance interactions between the studied vibrational states. As the result, a set of 39 fitted parameters was obtained which reproduces the initial 3213 ro-vibrational energy values obtained from the assigned transitions with the drms=2.4×10−4cm−1.

First study of the ro-vibrational structure of the g-symmetry vibrational states of [formula omitted] from the analysis of hot bands: The [formula omitted] and [formula omitted] bands

The two strongest absorption “hot” bands of C2D4, ν7+ν10−ν10 and ν10+ν12−ν10 were analyzed for the first time on the basis of high resolution infrared spectra recorded with a Bruker high resolution Fourier transform spectrometer. About 740 and 550 transitions (233 and 174 upper state ro-vibrational energy values) with Jmax.=25, Kamax=18 and Jmax.=20, Kamax.=10 for the bands ν7+ν10−ν10 and ν10+ν12−ν10 were assigned. The obtained upper ro-vibrational energies were used then in the weighted fit of parameters of the effective Hamiltonian which takes into account resonance interactions between the vibrational states (v7=v10=1) and (v10=v12=1), on the one hand, and eight other closely located vibrational states, on the other hand. A set of 46 varied parameters was obtained from the fit, which reproduces the initial experimental data with the rms deviation of 2.5×10−4cm−1 and which is close to experimental uncertainties.

High resolution analysis of C2D4 in the region of 600–1150 cm−1

High-accurate Fourier-transform infrared spectra of C2D4 were recorded and analyzed in the region of 600–1150cm−1 where the bands ν7(B1u), ν10(B2u), ν12(B3u) are located as well as the ν4(Au) band which is forbidden by the symmetry of the molecule. The ground state rotational structure was re-analyzed by the use of ground state combination differences obtained on the basis of infrared transitions of the ν12 and ν7 absorption bands. This gave us the possibility to considerably improve the rotational and centrifugal parameters of the ground vibrational state. The analysis of the experimental data and the subsequent weighted-fit procedure of the Hamiltonian parameters allowed us to reproduce the initial 4405 “experimental” ro-vibrational energy values with the drms=2.1×10−4cm−1.

Ro-vibrational analysis of the hot bands of 13C2H4: [formula omitted] and [formula omitted

Two “hot” absorption bands, ν7+ν10-ν10 and ν10+ν12-ν10, of 13C2H4 were recorded for the first time with a Bruker high resolution Fourier transform spectrometer and theoretically analyzed. About 640 and 270 transitions (168 and 136 upper state ro-vibrational energy values) with Jmax.=20,Kamax.=10 and Jmax.=23,Kamax.=9 for the bands ν7+ν10-ν10 and ν10+ν12-ν10, respectively, were assigned. For that purpose strong local resonance interactions with ten other closely located vibrational states were taken into account. A set of 36 varied parameters was obtained from the fit, which reproduces the initial experimental data with the rms deviation of 6.7×10-4cm and which is close to experimental uncertainties.

Study of the high resolution spectrum of 32S16O18O: The ν1 and ν3 bands

The high resolution infrared spectrum of the 32S16O18O molecule was recorded for the first time with a Bruker IFS 120 HR Fourier transform interferometer in the region of 930–1580cm−1 where the bands ν1 and ν3 are located. More than 3000 and about 2400 transitions were assigned in the experimental spectrum with the maximum values of quantum numbers Jmax./Kamax. equal to 58/23 and 68/23 to the bands ν1 and ν3, respectively. The further weighted fit of experimentally assigned transitions was made with the Hamiltonian model which takes into account Coriolis resonance interaction between the vibrational states (100) and (001). The 81 microwave transitions of the states (100) and (001) known from the literature also were taken into account. As the result, a set of 26 fitted parameters was obtained which reproduces the experiment-based 2690 ro-vibrational energy values of the two bands with the drms=1.8×10−4cm−1. Microwave transitions are also reproduced with the accuracy close to experimental uncertainty.

High resolution FTIR study of the [formula omitted] and [formula omitted] “hot” bands of C2H4

Two weak “hot” absorption bands, ν7+ν10−ν10 and ν10+ν12−ν10, of ethylene, C2H4, were analyzed for the first time with high resolution using the Fourier transform interferometer Bruker IFS-120 HR. As the result of analysis we assigned about 930 and 370 transitions (404 and 185 upper state ro-vibrational energy values) with Jmax.=27, Kamax.=14 and Jmax.=20, Kamax.=9 for the bands ν7+ν10−ν10 and ν10+ν12−ν10, respectively. Strong local resonance interactions of the vibrational state (v10=v12=1) with the five other states, and of the state (v7=v10=1) with the seven other states were taken into account, and a set of 77 varied parameters, which reproduce the initial experimental data with the rms deviation of 6.1×10−4cm−1 which is close to experimental uncertainties, was obtained.

Re-analysis of the (100), (001), and (020) rotational structure of SO2 on the basis of high resolution FTIR spectra

Three infrared spectra, weak (W), medium (M), and strong (S), of the 32SO2 molecule were recorded with high resolution in the 1000–1500cm−1 region. Spectra were recorded with the Fourier Transform interferometer Bruker IFS-120 HR in Oulu (Finland) with different pressures, absorption path lengths, and recording time. That allowed us to record not only the ν1 and ν3 bands with higher values of quantum numbers J and Ka than it was made earlier, but to record for the first time very weak 2ν2 band. In this case, transitions with the values Jmax./Kamax. equal to 89/37, 109/28, and 54/9 were assigned in the experimental spectra for the bands ν1, ν3, and 2ν2, respectively. As it became clear in the course of the analysis, the rotational parameters of the ground vibrational state, known in the literature, do not describe suitably the ground state combination differences (GSCD) for the states with the value Ka>26–27. As a consequence, the ground state rotational parameters were improved on the basis of our experimental data. The 12131 transitions assigned in the experimental spectrum (7618, 3952, and 561 transitions of the bands ν1, ν3, and 2ν2, respectively) were used for determination of ro-vibrational energy values of the vibrational states (100), (001), and (020). The lasts were used then in the fit procedure together with known in the literature high accurate sub-millimeter wave data. Resonance interactions between all three vibrational states have been taken into account in the Hamiltonian used for the fit. As a result, the 51 varied parameters, obtained from the fit, reproduce 4063 ro-vibrational energies of the states (100), (001), and (020) (12131 initial experimental transitions) with accuracies close to experimental uncertainties: the rms deviation is 6.1×10−5cm−1, 9.7×10−5cm−1, and 13.9×10−5cm−1 for our FTIR data (for the (100), (001), and (020) states, respectively), and comparable with experimental uncertainties for heterodyne data.

High resolution study of the [formula omitted] and [formula omitted] “hot” bands and ro-vibrational re-analysis of the [formula omitted] polyad of the 32SO 2 molecule

The weak “hot” absorption bands, ν 1 + 2 ν 2 − ν 2 and 2 ν 2 + ν 3 − ν 2 , were analysed with high resolution using the Fourier transform interferometer Bruker IFS-120 HR. In order to make possible an analysis of the ν 1 + 2 ν 2 − ν 2 and 2 ν 2 + ν 3 − ν 2 bands, as the first step, we re-analysed considerably the stronger “cold” bands, ν 1 + ν 2 and ν 2 + ν 3 , which are located in the same spectral regions. As the result of analysis we obtained about 2650 and 2050 transitions (1069 and 1001 upper state ro-vibrational energy values) with J max. = 78, K a max. = 27 and J max. = 68, K a max. = 24 for the bands ν 1 + ν 2 and ν 2 + ν 3 , respectively, that is considerably higher than in the earlier studies of corresponding bands ( J max. = 33, K a max. = 7 and J max. = 50, K a max. = 16 for the same bands, ν 1 + ν 2 and ν 2 + ν 3 , respectively). A strong local resonance interaction with the 3 ν 2 band was taken into account, and the set of parameters that reproduce the initial experimental data with an accuracy close to experimental uncertainties, was obtained. The weak ν 1 + 2 ν 2 − ν 2 and 2 ν 2 + ν 3 − ν 2 bands were assigned, and about 870 and 930 transitions (553 and 540 upper state ro-vibrational energy values) with J max. = 60 and K a max. = 20 and J max. = 59 and K a max. = 16 were assigned to the ν 1 + 2 ν 2 − ν 2 and 2 ν 2 + ν 3 − ν 2 bands, respectively. A complete list of assigned transitions is presented, and corresponding spectroscopic parameters are obtained from the fit of assigned transitions (upper energy values).