Centrifugal distortion analysis of the rotational spectrum of aziridine: Comparison of different Hamiltonians

Previous measurements of rotational spectrum of aziridine up to 1.85 THz have been supplemented by new data in 225-660 GHz frequency range. A total of 1465 transitions (915 of them are newly assigned ones) with maximum values of J = 59 and K_c = 50 were fit to a standard Watson Hamiltonian using the S- and A-reductions and the representations I^r and III^r. Although aziridine is an asymmetric oblate top, the combination (A, III^r) gives the worst results. From the point of view of the convergence of the Hamiltonian, the best results are obtained with the combination (S, III^r). It is explained that the failure of the combination (A, III^r) is due to the large value of the parameter σ=(2C-A-B)/(A-B) which makes some sextic centrifugal distortion constants much too large impeding the convergence of the Hamiltonian. It is also shown that the calculation of the centrifugal distortion constants from a force field is sometimes an ill-conditioned operation. Finally, the use of a non-reduced Hamiltonian (with six quartic centrifugal distortion constants) was successful in the particular case thanks to the method of predicate observations.     

A theoretical study of BrCN in the Π electronic ground state: Large amplitude bending motion

We have calculated the three-dimensional potential energy surfaces for the 1 ²A′ and 1 ²A″ states of BrCN⁺ at the MR-SDCI_DK+Q/[QZP-ANO-RCC (Br, C, N)] level of theory, where MR-SDCI_DK means ‘multi-reference single and double excitation configuration interaction calculation with Douglas-Kroll Hamiltonian.’ These ab initio potential energy surfaces have a common minimum (corresponding to the state) at a linear equilibrium structure with r_e(Br-C) = 1.735 Å and r_e(C-N) = 1.199 Å. Variational RENNER calculations yield a zero-point averaged structure (with the structural parameters calculated as expectation values over rovibrational wavefunctions) with 〈r(Br-C)〉₀ = 1.739 Å, 〈r(C-N)〉₀ = 1.204 Å, and 〈∠(Br-C-N)〉₀ = 172(4)°. A severe Fermi resonance between 2ν₂ and ν₃ has been found theoretically for the ²A″ potential energy surface. Comparing the ab initio zero-point averaged structure with a recent, experimentally derived r₀ structure, it is concluded that the effects of large-amplitude bending motion should be taken into account explicitly in the process of deriving the r₀ structure from the experimental values of the rotational constants. The electronic structure of BrCN⁺ has also been discussed.     

High resolution study of the 3ν1 band of SO2

The second overtone band 3ν₁ of sulfur dioxide has been studied for the first time with high resolution rotation-vibration spectroscopy. About 3000 transitions involving about 900 upper state energy levels with have been assigned to the 3ν₁ band. In the analysis, an effective Hamiltonian taking into account accidental interactions between the vibrational states (3 0 0), (2 2 0), and (0 4 1) was used. The Watson operator in A-reduction and I^r representation was used in the diagonal blocks of the Hamiltonian. As the result of analysis a set of parameters reproducing the initial experimental data with the rms = 0.00028 cm⁻¹ was obtained.     

High-resolution infrared study of collisionally cooled trans-1,2-dichloroethylene

A recently constructed long-path enclosive flow cooling apparatus is employed to obtain the Fourier transform gas-phase infrared absorption spectrum of natural isotopic trans-1,2-dichloroethylene with a resolution of 0.00190 cm⁻¹ in the 800-1000 cm⁻¹ spectral region. The rotational structure of the out-of-plane CH flapping fundamental has been analyzed for the isotopic analogues ³⁵Cl₂ and ³⁵Cl³⁷Cl using the Watson A-reduced Hamiltonian model and I^r-representation. A ground-state combination difference analysis for the ³⁵Cl³⁷Cl isotopomer based on 1402 assigned transitions belonging to the ν₆ band yields a band origin of 897.94493(10) cm⁻¹ and values for the ground-state rotational constants: A₀ = 1.7466454(44) cm⁻¹, B₀ = 0.05019643(82) cm⁻¹ and C₀ = 0.04877977(82) cm⁻¹ together with quartic centrifugal distortion constants. The red-shift of 0.00444(10) cm⁻¹ observed for the ν₆ band origin of ³⁵Cl³⁷Cl relative to the ³⁵Cl₂ band origin is now consistent with the Rayleigh rule.     

Fourier transform microwave spectroscopy of isotopically substituted diacetylenes: rs-structure, quadrupole coupling, and anisotropic nuclear spin-spin interaction

Monodeuterated diacetylene (HCCCCD) and its ¹³C-substituted species H¹³CCCCD, HC¹³CCCD, HCC¹³CCD, and HCCC¹³CD were investigated by Fourier transform microwave spectroscopy. The D nuclear quadrupole splittings were almost completely resolved. For H¹³CCCCD hyperfine splittings caused by the anisotropic nuclear spin-spin interaction between the H and ¹³C nuclei were also observed. The analysis yielded rotational constants, centrifugal distortion constants, and the constants for the nuclear quadrupole coupling and anisotropic nuclear spin-spin interaction. The substitution structure of HCCCCD was calculated as follows: r_s(C-H) = 1.056054(39) Å, r_s(CC) = 1.208631(4) Å, r_s(C-C) = 1.374117(6) Å, r_s(CC) = 1.208116(4) Å, and r_s(C-D) = 1.056231(17) Å, in the order of the arrangement of the bonds. A rough estimate of the equilibrium structure is also presented. The eQq constant for the deuterium nucleus is 0.2061(4) MHz. The anisotropic ¹³C-H spin-spin interaction constant was experimentally determined for the first time as b = −29.2(15) kHz, which is defined as the coefficient of (3I_2zI_3z − I₂ · I₃), where I₂ and I₃ denote the H and ¹³C nuclear spins, respectively, and I_2z and I_3z their components along the molecular axis. The observed b constant is not accounted for by the direct magnetic dipole-dipole interaction only, suggesting a significant contribution from indirect anisotropic interaction.     

High-resolution FTIR measurement and analysis of the ν3 band of C2H3D

The Fourier transform infrared (FTIR) spectrum of the ν₃ band of C₂H₃D was measured at an unapodized resolution of 0.0063 cm⁻¹ in the 1240-1340 cm⁻¹ region. Rovibrational constants for the upper state (ν₃ = 1) up to five quartic and two sextic centrifugal distortion terms had been obtained by assigning and fitting a total of 1037 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00051 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 674 combination differences together with 21 microwave frequencies from the present infrared measurements with a root-mean-square deviation of 0.00040 cm⁻¹. The upper state (ν₃ = 1) and ground state rovibrational constants of C₂H₃D represent the most accurate values obtained so far. The A-type ν₃ band, centred at 1288.788826 ± 0.000044 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₃ = 1 rovibrational constants obtained, the inertial defect Δ₃ was 0.1619724 ± 0.0000001 μŲ.     

High-resolution FTIR spectrum of the ν12 band of ethylene-d (C2H3D)

The infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) has been recorded with an unapodized resolution of 0.004 cm⁻¹ in the wavenumber range of 1340-1460 cm⁻¹ using the Fourier transform technique. By assigning and fitting a total of 870 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation, three rotational and five quartic centrifugal distortion constants for the upper state (v₁₂ = 1) were determined for the first time. The rms deviation of the fit was 0.00044 cm⁻¹ which is close to the experimental precision of the absorption lines. The A-type ν₁₂ band centred at 1400.762811 ± 0.000041 cm⁻¹was found to be relatively free from local frequency perturbations. The inertial defect Δ₁₂ was found to be 0.20928 ±  0.00002 μŲ.     

High-resolution infrared analysis of the ν7 band of cis-ethylene-d2 (cis-C2H2D2)

The spectrum of the ν₇ band of cis-ethylene-d₂ (cis-C₂H₂D₂) has been recorded with an unapodized resolution of 0.0063 cm⁻¹ in the 740-950 cm⁻¹ region using a Bruker IFS 125 HR Fourier transform infrared spectrometer. By fitting 2186 infrared transitions of ν₇ with a standard deviation of 0.00060 cm⁻¹ using a Watson’s A-reduced Hamiltonian in the I^r representation, accurate rovibrational constants for ν₇ = 1 state have been derived. The band center of ν₇ has been found to be 842.20957 ± 0.00004 cm⁻¹. In a simultaneous fit of 1331 infrared ground state combination differences from the present ν₇ transitions, together with 22 microwave frequencies, ground state constants have been improved. The rms deviation of the ground state fit was 0.00027 cm⁻¹.     

Improved rovibrational constants for the ν12 band of C2H3D

The Fourier transform infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) was recorded at an unapodized resolution of 0.0063 cm⁻¹ in the 1330-1475 cm⁻¹ region. Upper state (ν₁₂ = 1) rovibrational constants inclusive of three rotational, five quartic, and four sextic centrifugal distortion constants were improved by assigning and fitting 1444 infrared transitions using Watson’s A-reduced Hamiltonian in the I^r representation. The present analysis yielded more higher-order upper state constants than previously reported. The rms deviation of the fit is 0.00055 cm⁻¹. Improved ground state rovibrational constants were also determined from the combined fit of 2026 ground state combination differences (GSCD) from the assigned infrared transitions of the ν₁₂, ν₃ and ν₆ bands and 21 microwave frequencies of C₂H₃D. The rms deviation of the GSCD fit is 0.00047 cm⁻¹. The A-type ν₁₂ band is centered at 1400.76262 ± 0.00004 cm⁻¹. Local frequency perturbations were not detected in the analysis. The calculated inertial defect Δ₁₂ is 0.20809 ± 0.00003 μŲ.     

Ground state parameters of BiH3 from infrared and millimeter-wave spectra: ground state and equilibrium structures

Unstable, short-lived BiH₃ has been synthesized and investigated by rotational spectroscopy in the range 158 (J=1-0) to 1280 GHz (J=8-7). Quadrupole and spin-rotation hyperfine structures (eQq=584.676(96) MHz), and the A₁A₂ splitting of the K=3 ground state level, have been resolved. By merging the pure rotational data with 1764 ground state combination differences obtained from the analysis of high resolution Fourier transform infrared spectra of the ν₁-ν₄ bands [J. Mol. Spectrosc. (2004) (in press)] spanning J and K values up to 16 and 14, respectively, with 0?ΔK?9, the ground state rotational and centrifugal distortion constants up to octic and sextic terms for reductions A and B, respectively, have been determined. Of the reductions of the ground state rovibrational Hamiltonian, reduction B including ε rather than h₃ as off-diagonal element is clearly favored. An experimental r₀ structure of the very-near spherical oblate symmetric top BiH₃, r(BiH)=178.82 pm and α(HBiH)=90.320°, has been deduced from the rotational constants B₀=2.64160172(18) and C₀=2.6010403(31) cm⁻¹. The derived experimental r_e structure, r_e(BiH)=177.834(50) pm and α_e(HBiH)=90.321(10)°, was determined. This is in excellent agreement with the most recent ab initio structure, r_e(BiH)=177.84 pm, and α_e(HBiH)=90.12°.     

The ν12 band of ethylene-1-C (CCH4) by high-resolution FTIR spectroscopy

The Fourier transform infrared (FTIR) spectrum of the ν₁₂ fundamental band of ethylene-1-¹³C (or ¹³C¹²CH₄) was recorded with an unapodized resolution of 0.0063 cm⁻¹ in the wavenumber region of 1360-1520 cm⁻¹. Rovibrational constants for the upper state (ν₁₂ = 1) up to five quartic and two sextic centrifugal distortion terms were derived for the first time by assigning and fitting a total of 879 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00066 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 523 combination-differences from the present infrared measurements, with a rms deviation of 0.00090 cm⁻¹. The A-type ν₁₂ band which is centred at 1439.34607 ± 0.00004 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₁₂ = 1 rovibrational constants obtained, the inertial defect Δ₁₂ was found to be 0.242826 ± 0.000002 μŲ.     

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.     

Laser spectroscopy of holmium monosulphide: Electronic, vibrational and rotational structure of the A[14.79]8.5-X8.5, A[14.79]8.5-W[0.25]7.5 and A[14.79]8.5-V[0.98]7.5 transitions

Laser induced fluorescence spectra of HoS have been obtained using a Broida oven and a ring dye laser. Dispersed fluorescence spectra showed transitions from a common upper state, A[14.79]8.5 to the v = 0 and 1 vibrational levels of three low lying states, labelled X8.5, W[0.25]7.5 and V[0.98]7.5 (the states are labelled [10⁻³T₀]Ω according to their energy and Ω assignment). High resolution excitation spectra were obtained for all six transitions and a rotational analysis yielded the following principal constants, in cm⁻¹, for the X, W and V states, respectively: T₀ = 0, 251.8713(31), 980.6969(37); B_e = 0.121903(42), 0.121729(37), 0.122561(34); ΔG_1/2 = 463.8811(46), 462.9411(45), 461.2084(127). For the A state, T₀ = 14794.6987(28) cm⁻¹ and B₀ = 0.112596(29) cm⁻¹. The three low lying states are shown to arise from the Ho²⁺[4f¹⁰(⁵I₈)6s]S²⁻ configuration in accord with Ligand Field Theory predictions. The atomic origin of each of the three low lying electronic states was determined from the observed resolved hyperfine structure.     

Microwave spectra, molecular structure and theoretical calculation of two isotopic species of acetyl isocyanate CD3C(O)NCO and CH3C(O)NCO

The microwave spectra of two isotopic species of acetyl isocyanate, ¹³CH₃C(O)NCO and CD₃C(O)NCO, were observed in order to determine the r_o structure and confirmation of the molecular conformation. These isotopic species were prepared by reacting acetyl-2-¹³C-chloride or acetyl-d₃ chloride with sliver cyanate. The rotational spectra of A-level in 26.5-60.0 GHz region have been observed by Stark-modulated microwave spectrometer. Some absorption lines in E-level were observed in ¹³CH₃C(O)NCO. The rotational constants in the ground vibrational state were determined to be A = 10654.8(18), B = 2177.32(2), and C = 1827.65(2) MHz for ¹³CH₃C(O)NCO, and A = 9713.90(6), B = 2042.04(2), and C = 1722.78(2) MHz for CD₃C(O)NCO, respectively. The values of ΔI (= I_c − I_a − I_b) of the ¹³C species (−3.024(13) uŲ) and the d₃ species (−6.163(3) uŲ) indicate that the molecule has C_s symmetry. The r_s coordinates of the carbon atom in the methyl group were determined to be |a| = 2.183(3), |b| = 0.706(9), and |c| = 0.080(87) Å. The determined coordinates were in agreement with those calculated for the cis form, in which the carbonyl group is eclipsed by the NCO group. The six structural parameters of the cis form were adjusted by fitting to the observed rotational constants. The observed rotational constants of the cis form were in better agreement with those calculated using the QCISD/6-31G (d, p) level rather than those calculated using the MP2/6-31G (d, p) level. The barrier of internal rotation of the methyl group was determined as 4.283(16) kJ mol⁻¹ in ¹³CH₃C(O)NCO. The structural tendencies and the relationship between ∠RNC and ¹⁴N quadrupole coupling constants (χ_cc) were discussed.     

Single crystal EPR and optical absorption study of Cr doped l-histidine hydrochloride monohydrate

EPR study of the Cr³⁺ ion doped l-histidine hydrochloride monohydrate single crystal is done at room temperature. Two magnetically inequivalent interstitial sites are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The zero field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations and the parameters are: D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.9108±0.0002, g_y=1.9791±0.0002, g_z=2.0389±0.0002, A_x=(252±2)×10⁻⁴ cm⁻¹, A_y=(254±2)×10⁻⁴ cm⁻¹, A_z=(304±2)×10⁻⁴ cm⁻¹ for site I and D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.8543±0.0002, g_y=1.9897±0.0002, g_z=2.0793±0.0002, A_x=(251±2)×10⁻⁴ cm⁻¹, A_y=(257±2)×10⁻⁴ cm⁻¹, A_z=(309±2)×10⁻⁴ cm⁻¹ for site II, respectively. The optical absorption studies of single crystals are also carried out at room temperature in the wavelength range 195-925 nm. Using EPR and optical data, different bonding parameters are calculated and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are: B=636, C=3123, Dq=2039 cm⁻¹, h=1.46 and k=0.21, respectively.     

The pure rotational spectrum of TiS (XΔr) at submillimeter wavelengths

The pure rotational spectrum of TiS in its X³Δ_r ground state has been measured using millimeter-wave direct-absorption techniques in the frequency range of 313-425 GHz. This free radical was created by the reaction of titanium vapor, produced in a high-temperature Broida-type oven, with H₂S. Eight to ten rotational transitions were recorded for the main titanium isotopologue, ⁴⁸TiS, in the v = 0 and v = 1 levels, as well as for the v = 0 state of ⁴⁶TiS, observed in natural abundance (⁴⁸Ti:⁴⁶Ti = 74:8). All three Ω components were observed in almost every recorded transition, with no evidence for lambda-doubling. The data were fit with a Hund’s case(a) Hamiltonian, and rotational, spin-orbit, and spin-spin constants were determined, as well as equilibrium parameters for ⁴⁸TiS. Relatively few fine structure parameters were needed for the analysis of TiS (A, A_D, and λ), unlike other 3d metal species. The rotational pattern of the three fine structure components suggests the presence of a nearby excited ¹Δ state, lying ∼3000 cm⁻¹ higher in energy. From the equilibrium parameters, the dissociation energy for TiS was estimated to be ∼5.1 eV, in reasonable agreement with past thermochemical data.     

The high-resolution FTIR spectrum of the ν6 band of C2H3D

The absorption spectrum of the ν₆ band of C₂H₃D centered near 1125.27674 cm⁻¹ in the 1100-1250 cm⁻¹ region was recorded with an unapodized resolution of 0.0063 cm⁻¹ using a Fourier transform infrared (FTIR) spectrometer. A total of 947 infrared transitions of the A-B hybrid-type band were assigned and fitted to upper-state (ν₆ = 1) rovibrational constants using a Watson’s A-reduced Hamiltonian in the I^r representation up to eighth-order centrifugal distortion terms. The b-type infrared transitions of the band were analyzed for the first time. The root-mean-square deviation of the fit was 0.00062 cm⁻¹. The ground-state rovibrational constants up to eighth-order terms were also obtained by a fit of 617 combination differences from the present infrared measurements, simultaneously with 21 microwave frequencies with a root-mean-square deviation of 0.00055 cm⁻¹. From this work, the upper-state (ν₆ = 1) and ground-state constants of C₂H₃D were derived with the highest accuracy, so far. The a- and b-type transitions of the hybrid ν₆ band were found to be relatively free from local frequency perturbations. The ratio of the a- to b-type vibrational dipole transition moments (μ_a/μ_b) was found to be 1.05 ± 0.10. From the ν₆ = 1 rovibrational constants obtained, the inertial defect Δ₆ was calculated to be 0.3570 ± 0.0008 μŲ.     

The high-resolution infrared spectrum of pyrrole between 900 and 1500 cm revisited

The Fourier transform gas-phase infrared spectrum of pyrrole, C₄H₅N, has been recorded with a resolution of ca. 0.003 cm⁻¹ in the 900-1500 cm⁻¹ spectral region. Four fundamental bands, ν₈(A₁; 1016.9 cm⁻¹), ν₂₃(B₂; 1049.1 cm⁻¹), ν₇(A₁; 1074.6 cm⁻¹), ν₂₀(B₂; 1424.4 cm⁻¹) and the overtone band 2ν₁₆(A₁; 962.7 cm⁻¹) have been analysed using the Watson model. The ν₈ and 2ν₁₆ bands are unperturbed; the ν₇ and ν₂₃ bands are locally perturbed, while the ν₂₀ band is globally perturbed by weak c-Coriolis resonance. Upper state vibrational term values, and rotational and centrifugal distortion constants, have been obtained from fits using S-reduction and I^r-representation as well as A-reduction and III^r-representation. A set of ground state rotational and centrifugal distortion constants using A-reduction was obtained from a simultaneous fit of ground state combination differences from all five bands and previous microwave and millimetre-wave data.     

High-resolution infrared and microwave study of the ν20 and ν21 levels near 300 cm in 1,2,4-triazine

The gas phase far-IR spectrum of the ν₂₀ (A″, 367.88 cm⁻¹) and ν₂₁ (A″, 311.28 cm⁻¹) bands of 1,2,4-triazine, a five membered ring having the point group C_s, has been studied at a resolution ranging from 0.002 to 0.003 cm⁻¹. From the MW spectrum 58 transitions in the ν₂₀ level and 64 in the ν₂₁ level have been assigned. The ν₂₀ and ν₂₁ modes which are due to non-planar motions of the ring system are found to be nearly unperturbed. From a simultaneous analysis of IR and MW transitions band centers, rotational constants, and the quartic centrifugal distortion constants , and δ_K have been obtained using the Watson Hamiltonian, A-reduction, III^r-representation.     

Velocity modulation spectroscopy of molecular ions I: The pure rotational spectrum of TiCl (XΦr)

The pure rotational spectrum of the TiCl⁺ ion in its X³Φ_r ground state has been measured in the frequency range 323-424 GHz, using a combination of direct absorption and velocity modulation techniques. The ion was created in an AC discharge of TiCl₄ and argon. Ten, eleven, and nine rotational transitions were recorded for the ⁴⁸Ti³⁵Cl⁺, ⁴⁸Ti³⁷Cl⁺, and ⁴⁶Ti³⁵Cl⁺ isotopomers, respectively; fine structure splittings were resolved in every transition. The rotational fine structure pattern was irregular with the Ω = 4 component lying in between the Ω = 2 and 3 lines. This result is consistent with the presence of a nearby ³Δ_r state, which perturbs the Ω = 2 and 3 sub-levels, shifting their energies relative to the Ω = 4 component. The data for each isotopomer were analyzed in a global fit, and rotational and fine structure parameters were determined. The value of the spin-spin constant was comparable to that of the spin-orbit parameter, indicating a large second-order spin-orbit contribution to this interaction. The bond length established for TiCl⁺, r₀ = 2.18879 (7) Å, is significantly shorter than that of TiCl, which has r₀ = 2.26749 (4) Å. The shorter bond length likely results from a Ti²⁺Cl⁻ structure in the ion relative to the neutral, which is thought to be represented by a Ti⁺Cl⁻ configuration. The higher charge on the titanium atom shortens the bond.