The D state of I2: a case study of statistical error propagation in the computation of RKR potential curves, spectroscopic constants, and Franck-Condon factors

Existing spectroscopic data for the ion-pair state of I₂ are reanalyzed with the primary goal of improving and extending to higher υ the rotational constants B_υ. To this end, data for several precisely known (υ,J) levels in the υ=203-207 region are analyzed together with vibrational and rotational data from a number of sources. The lack of rotational data for the υ=130-200 region makes the structure of this data set unusual, and has prompted a thorough study of the propagated statistical error in the directly fitted spectroscopic constants, T_υ and B_υ, and in the RKR potential curve calculated therefrom. For the first time, such error propagation computations have been extended to properties computed by numerical solution of the Schrödinger equation for the state in question: the quantum vibrational energy G_υ and rotational constant B_υ, centrifugal distortion constants D_υ and H_υ, and Franck-Condon factors for the D-X transition.     

Determination of the spin-spin centrifugal distortion parameters for deuterated selenoformaldehyde in its first excited triplet state

Recently-formulated centrifugal distortion corrections to the spin-spin Hamiltonian have been used to analyse the first excited triplet state (ã³A₂) of deuterated selenoformaldehyde. By including six spin-spin centrifugal distortion parameters, it is possible to account for the energy levels of this state using a single set of three rotational constants, A, B, and C, where previously nine spin-dependent parameters were required.     

Use of calculated centrifugal distortion constants (Dν, Hν, Lν and Mν) in the analysis of the B ← X system of I2

Fourier spectroscopy measurements of 14 703 lines from the B-X band system of I₂ are analyzed using centrifugal distortion constants calculated from RKR curves by the perturbation theory method of Hutson [J. Phys. B14, 851–857 (1981)]. Only vibrational and rotational constants are varied in the least-squares fits, with the centrifugal distortion constants fixed at the calculated values. The fit obtained in the present work is as good as when the centrifugal distortion constants are treated as independent parameters, but the molecular constants obtained are physically more meaningful because the statistical correlation between parameters is reduced. The analysis includes B-state vibrational levels up to v′ = 72, which is bound by only 0.5% of the well depth; the method used for calculating centrifugal distortion constants remains reliable even this close to dissociation. It is found that centrifugal distortion constants up to fifth order make significant contributions to the observed line positions.     

The υ1 fundamental bands of trans- and cis-DONO studied by high-resolution Fourier-transform spectroscopy

The absorption spectrum of deuterated nitrous acid DONO in the region from 2350 to 3000 cm⁻¹ has been recorded at a resolution of 0.003 cm⁻¹ using a Fourier-transform spectrometer. For the first time, 1366 a- and b-type transitions in the υ₁ fundamental band of trans-DONO and 741 b-type transitions in the υ₁ fundamental band of cis-DONO have been assigned. Rotational and centrifugal distortion constants up to sextic order were determined for the v₁ = 1 states of trans- and cis-DONO using non-linear least-squares calculations. Synthetic spectra calculated using the new rovibrational constants obtained for both species reproduce the observed spectra very well. In addition, the infrared transitions of this study were used, together with previously published pure rotational transitions, to determine improved rotational and centrifugal distortion constants of the ground states of trans- and cis-DONO.     

Upper and lower bounds of quartic centrifugal distortion constants

Expressions are obtained for the maximum and minimum possible values of the equilibrium centrifugal distortion constants τ_αβγδ for a molecule with given structure and vibrational frequencies. The method of calculation, based on Lagrangian multipliers, is also applied to the empirical centrifugal constants (such as D_J, D_JK, D_K, or Δ_J, Δ_JK, Δ_K, δ_J, δ_K) employed in fitting the rotational structure of spectra. These formulas make it possible to test whether a set of observed centrifugal constants is consistent with the rotational constants and vibrational frequencies. When inconsistencies arise, they are probably due to zero-point vibrational effects. By means of a second method employing inequalities, simpler formulas are derived for wider bounds. These are useful in calculating approximate values of the constants, as a preliminary to deciding which terms to include in the rotational Hamiltonian of any particular molecule.     

The harmonic force field and rz structure of HNCO

The presently available microwave, millimeter wave, and far-infrared data of five isotopic species of isocyanic acid, namely, HNCO, H¹⁵NCO, HN¹³CO, HNC¹⁸O, and DNCO, have been used to obtain improved values of the ground-state rotational constants, the five quartic distortion constants, and some higher-order distortion constants in the I^rS reduced Hamiltonian of Watson. The appropriate planarity relation among the quartic centrifugal distortion constants has been imposed in the fitting procedure. The general harmonic force field of isocyanic acid has been determined using all existing data, and assuming a trans bent equilibrium geometry of the molecule with an NCO angle of 170°. Finally an r_z structure has been obtained using the A_z, B_z, and C_z rotational constants of five isotopic species. The bending of the NCO chain is found to be 8° in the trans configuration.     

A planarity relation for sextic centrifugal distortion constants

The relations between the molecular parameters of a planar molecule are used to derive a planarity relation for the sextic centrifugal distortion constants from the recently published expressions [Aliev and Watson, J. Mol. Spectrosc.61, 29 (1976)]. This relation, which contains only the rotational constants and the quartic and sextic distortion constants, is strictly valid only for the equilibrium constants, but will be useful as a constraint in the fitting of rotational energies if the experimental error is larger than the vibrational defect. The planarity relation is compared with the observed constants for the SO₂, O₃, NO₂, H₂O, and H₂S molecules. There appears to be a significant defect for SO₂ and for H₂O and its isotopes. The defect for SO₂ may be too large to be genuine, and possibly results from truncation of the Hamiltonian at the sextic terms.     

Centrifugal distortion constants and force field of HClCO

Measurement of the a- and b-type rotational transitions of formyl chloride, HClCO, was extended up to J = 50 and k_a = 5 ← 4 in the frequency range of 8 to 200 GHz. Accurate rotational parameters including the sextic centrifugal distortion constants were determined from the observed spectrum for the ³⁵Cl and ³⁷Cl species. The τ defect in the planarity relations of the quartic centrifugal distortion constants was found to be negligibly small. From the quartic centrifugal distortion constants and the previously reported fundamental vibrational frequencies, force constants of formyl chloride were calculated by assuming the Urey-Bradley force field.     

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.     

The rotational spectra of the 79, 69, and 7 vibrational states of nitric acid

The rotational spectra of the first three vibrational states of nitric acid above 1000 cm⁻¹, 7¹9¹, 6¹9¹, and 7², have been measured and analyzed. The 7² state, along with the previously published 7¹ state, show the rotational and centrifugal distortional constants have a near linear dependence on the υ₇ vibrational quantum number. Large changes for several centrifugal distortion constants of the υ₇ = n series of states are attributed to a c-type Coriolis resonance manifold between the ν₇ and ν₆ vibrational modes and the Hamiltonian reduction and representation used to fit the spectra. The 7¹9¹ and 6¹9¹ states have torsional splittings of 12.361(8) and 22.47(1) MHz, respectively. These splittings are large compared to 2.340(8) MHz of the 9¹ state and can be explained by a ∼1-2% mixing through anharmonic Fermi resonances with the 9³ state, which has a large torsional splitting of ∼1760 MHz. The millimeter/submillimeter-wave spectrum of each state was fit separately to the experimental uncertainty of the measurements. The resultant rotational constants, distortional constants and inertial defects agree well with DFT calculations.     

The microwave spectrum of trioxaadamantane

The microwave spectrum of 2,8,9-trioxaadamantane has been investigated in the region from 12.4 to 26.5 GHz. The observed spectrum exhibited the expected symmetric top pattern, with the rotational constant B₀ = 1848.64 MHz. Numerous weaker lines were observed and were attributed to vibrational satellites of the main rotational transition. The transitions from J = 3 → 4 through J = 6 → 7 were studied and no centrifugal distortion effects were observed.A structure is derived that is consistent with the observed rotational constants of the normal and one isotopic species by use of the method of diagnostic-least-squares.The second order stark effect for the K = 0 state yielded a dipole moment of 3.01 ± 0.03 D.     

Pure rotational spectra of allene-1, 1-d2 and allene-d1 observed by microwave Fourier transform spectroscopy

Pure rotational transitions of allene-1, 1-d₂ and allene-d₁ in their vibronic ground state have been observed with a pulsed microwave Fourier transform spectrometer for the 8- to 18-GHz frequency range. Thirteen new transitions of allene-1, 1-d₂ with J up to 32 have been assigned. The measured transition frequencies have been combined with earlier measurements of Hirota and Matsumura [J. Chem. Phys. 59, 3038–3042 (1973)] in a least-squares fit of the rotational constants B and C and the centrifugal distortion constants Δ_J, Δ_JK, δ_J, and δ_K. Fifteen transition of allene-d₁ with J up to 34 have been assigned. The rotational constants A, B, and C, and the quartic centrifugal distortion constants Δ_J, Δ_JK, Δ_K, δ_J, and δ_K have been determined from the measured frequencies in a least-squares fit.     

Two conformers of ethyl pivalate studied by microwave spectroscopy

The rotational spectra of two conformers of ethyl pivalate, (CH₃)₃C-COO-C₂H₅ have been recorded by molecular beam FT microwave spectroscopy. The analysis yielded a set of three rotational constants and five quartic centrifugal distortion constants for each conformer. The conformers were identified by comparing the experimental rotational constants with those obtained by ab initio calculations at MP2/6-311++G∗∗ level. One conformer has C_s symmetry, the other one forms a pair of enantiomers with C₁ symmetry. Additionally, the torsional potentials of the tert-butyl group and of the methyl groups were obtained by ab initio methods.     

The microwave spectrum of o-benzyne measured in a novel Stark modulated spectrometer for transient molecules

A set of 36 new microwave transitions have been measured for o-benzyne, generated by pyrolysis of phthalic anhydride. All 50 known rotational transitions have been fitted to give an improved set of rotational and centrifugal distortion constants. A short waveguide based microwave spectrometer designed specifically for short lived species is described.     

Submillimeterwave spectrum of CH2PH and equilibrium structures of CH2PH and CH2NH

The rotational spectrum of phosphaethene (CH₂PH) was reinvestigated. One hundred and nineteen new lines were measured in the submillimeter range from 500 to 650 GHz. The determination of the centrifugal distortion constants is significantly improved. As the molecule is close to symmetric prolate top, both reduction A and S were compared. The equilibrium structure has been derived from experimental ground state rotational constants and ab initio rovibrational interaction parameters. This semi-experimental structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of quintuple-zeta quality and a core correlation correction. The structure of CH₂PH was compared to that of CH₂NH which was also determined for this goal. It is found that the semi-experimental structure of CH₂NH is less accurate than the ab initio structure. It is also found that the methylene group is much more asymmetric in CH₂NH than in CH₂PH.     

Centrifugal distortion analysis of difluoramine

The microwave rotational spectrum of difluoramine (NF₂H) has been analyzed in the frequency region 15–36 GHz involving rotational levels up to J = 19. The analysis gives refined rotational constants and all quartic centrifugal distortion constants. These constants have been used to predict additional Q-branch transitions of the molecule in the frequency region 5–95 GHz.     

The force field and rz structure of Ketene

Recently determined Coriolis coupling constants for H₂ and D₂ Ketene, centrifugal distortion constants for H₂, HD, and D₂ Ketene have enabled 16 of the 19 parameters in the general force field of Ketene to be determined with significance, the ambiguity between the choice of two sets of A₁ and B₁ species force constants being removed. The r₀ structure has been redetermined using the latest values of the rotational constants of H₂, HD, and D₂ Ketene and an r_z structure has been determined for the first time.     

Microwave spectra of SiH2DF and SiHD2F: Harmonic force field and molecular structure

The ground vibrational state rotational spectrum of SiH₂DF and SiHD₂F has been studied in the frequency region 24–58 GHz. The observed transitions have been used to obtain the A, B, C rotational constants and three of the five quartic distortion constants present in the reduced Hamiltonian of Watson.The A, B, C rotational constants obtained in this work in combination with the B constants of the six symmetric isotopes were used to determine accurate substitution and average structures. An approximate equilibrium structure is also estimated.The general harmonic force field of silyl fluoride has been redetermined using all existing data.     

Microwave spectrum of 3,4-epoxy-1-butene

The microwave spectrum of 3,4-epoxy-1-butene has been studied in the region 26.5–40 GHz. For the ground-state molecule, 170 lines have been assigned up to J = 34. From these the rotational constants and the centrifugal distortion constants were determined by least-squares fitting. The rotational constants are (in MHz): A = 17367.284 ± 0.011, B = 3138.186 ± 0.004, C = 3043.697 ± 0.004. The dipole moment has been determined from the Stark effect as (in Debye): μ_a = 0.72 ± 0.01, μ_b = 1.688 ± 0.003, μ_c = 0.39 ± 0.02, μ = 1.875 ± 0.005. The rotational constants and dipole moment components indicate that the assigned conformer is the s-trans form. A rotational assignment has also been made for the first excited state of the torsional mode. The fundamental frequency of the torsional mode has been estimated as 142 ± 20 cm^?1 from relative intensity measurement.     

Microwave spectrum of nitroxyl

The microwave spectrum of HNO has been observed and analyzed. Both a-type and b-type transitions have been measured. The rotational constants obtained are A = 553903.0 ± 2.7 MHz, B = 42308.52 ± 0.10 MHz, and C = 39169.46 ± 0.10 MHz. In the analysis of the spectrum, centrifugal distortion corrections are tentatively taken into account by using the centrifugal distortion constants determined by Dalby. The quadrupole coupling constants for nitrogen in HNO are determined to be χ_aa = 0.36 ± 0.56 MHz, χ_bb = ? 5.46 ± 0.30 MHz, and χ_cc = 5.10 ± 0.26 MHz. The dipole moment and its components determined from the Stark effect measurement are μ_total = 1.67 ± 0.03 D, μ_a = 1.03 ± 0.01 D, and μ_b = 1.31 ± 0.02 D. The microwave spectrum of DNO has been reanalyzed by taking into account the centrifugal distortion effect. The inertia defects for HNO and DNO have been calculated. The results are limited in precision by the lack of reliable force constants.