Breakdown of the reduction of the rovibrational Hamiltonian: The case of SO2F2

The ground state rotational spectrum of the near-spherical top molecule S¹⁸O₂F₂ (sulfuryl fluoride) has been measured from 50 to 700 GHz. As for the parent isotopologue, S¹⁶O₂F₂ [K. Sarka, J. Demaison, L. Margulès, I. Merke, N. Heineking, H. Bürger, H. Ruland, J. Mol. Spectrosc. 200 (2000) 55-64], it was necessary to use a non-reduced Hamiltonian in order to obtain a satisfactory fit. It was possible to determine six quartic centrifugal distortion constants (instead of five for a standard asymmetric top) and five sextic constants (one of them not existing in the reduced Hamiltonian) could also be determined. This ground state level has also been analysed thanks to a tensorial formalism developed in Dijon. Only two tensorial sextic constants are fixed to zero, all others have been adjusted. Although S¹⁸O₂F₂ is less spherical than S¹⁶O₂F₂, the analysis was more difficult. It is partly due to the fact that S¹⁸O₂F₂ is oblate whereas S¹⁶O₂F₂ is prolate. The experimental quartic centrifugal distortion constants were found in good agreement with those calculated from the force field, confirming the correctness of the analysis.     

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 microwave spectrum and centrifugal distortion constants of vinyl fluoride

The rotational spectrum of vinyl fluoride up to J = 40 has been assigned and measured in the frequency region 8–37 GHz. Both a- and b-type transitions were observed. These measurements have been combined with those made in other frequency regions to calculate refined rotational constants and to obtain all quartic and some sextic centrifugal distortion constants. A comparison is made between the quartic centrifugal distortion constants measured here and those calculated from vibrational data.     

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.     

Millimeter-Wave Spectrum of CF(2)Cl(2), Taking into Account the Hyperfine Structure

A new investigation of the CF(2)(35)Cl(2) ground state rotational spectrum in the 50-100 GHz frequency range gave an opportunity to improve the accuracy of rotational and quartic distortion parameters by an order of magnitude and to determine values of six sextic centrifugal distortion parameters. A special technique was used to process line profiles of unresolved or partially resolved hyperfine structures of rotational transitions. It allowed us to improve significantly values for the diagonal parameters of quadrupole coupling chi(aa), (chi(bb)-chi(cc)) and to determine the off-diagonal parameter chi(ab). Copyright 2000 Academic Press.     

The Sextic Centrifugal Distortion Terms for an Open-Shell Complex Consisting of a Diatomic Molecule in a (2S+1)Sigma Electronic State and a Closed-Shell Partner

An effective Hamiltonian for calculating rotational energy levels of an open-shell diatomic molecule, in a (2S+1)Sigma electronic state, weakly bonded to a closed-shell partner was presented (W. M. Fawzy, J. Mol. Spectrosc. 191, 68-80 (1998)). The Hamiltonian was given as H = H(ev) + H(rot) + H(sr) + H(ss) + H(cd) + H(srcd) + H(sscd), where all the quartic centrifugal distortion correction terms were included in the Hamiltonian term H(cd) but the sextic centrifugal distortion terms were ignored. This Hamiltonian is useful in cases where the complex has a well-defined equilibrium geometry and if the barrier to large-amplitude motion is large compared to the rotational constant of both the closed-shell molecule and its paramagnetic partner; if the barrier to large-amplitude motion is small compared to the rotational constant of one or both of the fragments, then a different treatment is required. In this paper, we introduce the new Hamiltonian terms H(sex(A))(cd) and H(sex(S))(cd), which represent the sextic centrifugal distortion correction terms for an asymmetric rotor. We also introduce all the nonvanishing matrix elements of each of the H(sex(A))(cd) and H(sex(S))(cd) operators. These operators and their matrix elements are required for calculating the rotational energy levels of relatively high J values in the described type of weakly bonded open-shell complexes. The terms H(sex(A))(cd) and H(sex(S))(cd) and their matrix elements are also valid for any stable asymmetric rotor in a nondegenerate electronic state. A brief discussion of the new Hamiltonian terms and their matrix elements is given. Copyright 2000 Academic Press.     

The Forbidden RotationalQ-Branch of CH3CF3: Torsional Properties and (A1−A2) Splittings

The pure rotational spectrum driven by the small distortion dipole moment perpendicular to the symmetry axis has been investigated between 8 and 18 GHz for CH₃CF₃in the ground vibrational state using a pulsed Fourier transform waveguide spectrometer. This molecule has been selected as a prototype for the case of a symmetric top with small (∼500 kHz) torsional energy splittings in the ground torsional state (ν₆= 0). In this state, six (k± 3 ←k)Q-branch series have been measured for lower stateK= |k| between 3 and 8 with 27 ≤J≤ 75. For (ν₆= 1), three series with lower stateKbetween 5 and 7 with 49 ≤J≤ 66 have been observed. In two of these series, the torsional fine structure extending over ∼6.8 MHz has been fully resolved. The (A₁−A₂) splitting has been measured in the (ν₆= 0) series (K= 6 ← 3) for 37 ≤J≤ 74. The global data set of 443 frequencies included avoided-crossing molecular-beam splittings of Meerts and Ozier (1991.Chem. Phys.152, 241–259) and mm-waveR-branch measurements of Bocquetet al.(1994.J. Mol. Spectrosc.165, 494–499). In a weighted least-squares analysis, a good fit was obtained by varying 18 parameters in a Hamiltonian that represented both the torsional effects and the sextic splittings. Effective values have been determined for both rotational constants, eight torsional parameters including the barrier height, six diagonal centrifugal distortion constants, and two centrifugal distortion constants (? and ?_J) that characterize the (Δk= ±3) matrix elements. The difficulties are discussed that arise in defining a unique model for the torsional terms in the Hamiltonian when a high barrier symmetric top is investigated by distortion moment spectroscopy. The redundancies are investigated that exist in the quartic and sextic Hamiltonian for a near-spherical top such as CH₃CF₃.     

Centrifugal distortion constants of the NGLT form of allylamine from microwave spectrum analysis

The centrifugal distortion analysis of the microwave spectrum of the N-gauche lone-electron-pair trans (NGLT) rotameric form of allylamine has been carried out in the frequency region 5–40 GHz and up to J = 29 in its ground vibrational state. The analysis gives effective rotational constants and all the quartic centrifugal distortion constants.     

A new analysis of the ν2 fundamental band of H2O^＋＊

This paper reports that the absorption spectra of H2O^＋ have been measured by tunable mid-infrared diode laser spectroscopy in the spectral range of 1100-1380 cm^-1. The H2O＋ ions are generated in an AC glow discharge of the gaseous mixtures of H2O/He and detected with the velocity modulation technique. Forty new lines are assigned to the ν2 fundamental band of H2O^＋ （X^2B1）. The observed lines together with other data published previously are fitted to the standard effective Hamiltonian of an asymmetric top, yielding a set of improved rotational constants, spin-rotation constants and their quartic and sextic centrifugal distortion constants for the ν2=1 vibrational state of H2O＋.     

The microwave spectra of PH2D and PHD2, and the harmonic force field and structure of phosphine

Measurements of the pure rotational spectra of PH₂D and PHD₂ have been extended to include new Q-branch transitions and R-branch transitions. The rotational constants have been independently evaluated for the first time, along with some quartic and sextic centrifugal distortion constants. The spectrum of PD₃ has been reanalyzed to make the constants consistent with those reported for PH₃. The new results have been incorporated in a harmonic force field analysis. Both ground state average (r₂) and equilibrium (r_e) structures have been estimated.     

High-resolution rotational spectrum of methyl cyanide

The ground-state microwave spectrum of methyl cyanide is remeasured between 70 and 240 GHz with a molecular beam spectrometer and by use of the Lamb dip method. It allows us to determine with great accuracy the B rotational constant, the quartic and sextic centrifugal distortion constants, the nuclear quadrupole coupling constant, and the spin-rotation constants of nitrogen. The magnetic shielding constants of nitrogen are also determined.     

Microwave spectra and centrifugal distortion constants of formic acid containing 13C and 18O: Refinement of the harmonic force field and the molecular structure

Pure rotational spectra of H¹³COOH, HC¹⁸OOH, and HCO¹⁸OH have been measured in the frequency region 8–185 GHz. Analysis of the spectra has given improved rotational constants and quartic and sextic centrifugal distortion constants. The quartic distortion constants have been combined with previously published distortion constants of four other isotopic species, and with the vibrational wavenumbers of seven isotopic species, to produce a refined harmonic force field. An improved substitution structure and the ground state average structure have been obtained. Some unmeasured transition frequencies which may be of importance in radioastronomy are also presented.     

PO2自由基的光谱常数和非谐力场的理论研究

利用B3PW91、B3LYP和B3P86方法以及cc-pvQz和6-311++G(3df,3pd)基组计算了PO2自由基的光谱常数。先将计算的平衡几何结构、转动常数、谐频和基频、四次离心畸变常数和六次离心畸变常数与已有的相应实验或理论数据进行了比较。在此基础上,从理论上预测了非谐性常数、振转相互作用常数、科里奥利耦合常数、三次和四次力常数。计算结果表明,B3PW91/G理论水平得到的PO2自由基的光谱常数是可靠的。     

Analysis of the nu(12) Band of Ethylene-(13)C(2) by High-Resolution FTIR Spectroscopy

The Fourier transform infrared (FTIR) spectrum of the nu(12) fundamental band of ethylene-(13)C(2) ((13)C(2)H(4)) was recorded with an unapodized resolution of 0.004 cm(-1) in the frequency range from 1380 to 1500 cm(-1). Rovibrational constants for the upper state (nu(12)=1) up to five quartic and three sextic centrifugal distortion terms were derived for the first time by assigning and fitting a total of 1177 infrared transitions using a Watson's A-reduced Hamiltonian in the I(r) representation. The rms deviation of the fit was 0.00045 cm(-1). The ground state rovibrational constants were also determined for the first time by a fit of 738 combination differences from the present infrared measurements, with a rms deviation of 0.00060 cm(-1). The A-type nu(12) band with a band center at 1436.65411+/-0.00005 cm(-1) was found to be relatively free from local frequency perturbations. The inertial defect Delta(12) was found to be 0.24300+/-0.00002 u?(2). Copyright 2001 Academic Press.     

Van Vleck transformation as an alternative to the contact transformation: Non-linear molecules off resonance

The projector formulation for the Van Vleck transformation has been applied to the Wilson-Howard Hamiltonian (i.e., the Hamiltonian for the vibration-rotation energy of rigid molecules). Formal expressions are obtained for γ and q constants, for the linear vibrational dependence of quartic and for the sextic centrifugal distortion constants.     

The microwave spectrum and quadrupole coupling in tricarbonyl(methylcyclopentadienyl) manganese

The rotational spectrum of tricarbonyl(methylcyclopentadienyl) manganese has been recorded in the range from 1–23 GHz using an FTMW spectrometer working on a molecular beam. This spectrum is assigned for the first time, yielding the rotational constants of the molecule and quartic centrifugal distortion constants. The fine structure due to the quadrupole interaction of the ⁵⁵Mn nucleus could be solved and gave the quadrupole coupling tensor (which is compared with that of tricarbonyl(cyclopentadienyl)manganese, and the spin-rotation constants. An additional splitting of a few kHz, which could be observed for some transitions, is interpreted as arising from the internal rotation of the methyl group.     

A reduced form of the spin-rotation Hamiltonian for asymmetric-top molecules,with applications to HO2 and NH2

The spin-rotational Hamiltonian for an asymmetric-top molecule in a given vibrational level of an open-shell electronic state may contain more parameters than can be determined from the observed energy levels. This paper describes the reduction of the Hamiltonian by means of a unitary transformation to a form suitable for fitting to observed energies. It is shown that, for molecules of lower than orthorhombic symmetry, there are fewer determinable quadratic spin-rotation parameters than have been used previously. For example, for a molecule belonging to the group C₈, there are four, not five, determinable spin-rotation constants, ?_αβ. Similar indeterminacies exist among the quartic terms of the spin-rotation Hamiltonian. The case of a molecule of orthorhombic symmetry, for which there are six determinable quartic parameters, is considered in detail. The results are applied to the experimental data available on the spin-rotation splittings of the HO₂ and NH₂ radicals in their ground vibrational and electronic states.     

The far-infrared rotational spectrum of nitrous acid (HONO) and its deuterated species (DONO) studied by high-resolution Fourier-transform spectroscopy

In this paper, we present the first high-resolution (0.003 cm⁻¹) absorption measurements of the pure rotational spectra of nitrous acid (trans- and cis-HONO) and its deuterated species (trans- and cis-DONO) in the far-infrared region between 40 and 150 cm⁻¹. The spectra were first assigned based on rotational constants from previous studies in the microwave and mid-infrared regions. New rotational and centrifugal distortion constants were determined for all four species. The accuracy of the principal rotational constants was improved, and several quartic and sextic (and even a few octic) centrifugal distortion constants were obtained for the first time. Synthetic spectra calculated using the new constants of this study reproduce the observed spectra very well.     

Microwave spectroscopy of chlorine dioxide: Centrifugal distortion,spin-rotation interaction,and hyperfine interaction constants of 35ClO2 and 37ClO2

Forty-six and fifty-five ground-state rotational transitions of ³⁵ClO₂ and ³⁷ClO₂, respectively, were newly identified in the frequency region of 8–75 GHz. Most of the absorption lines previously reported were remeasured. Centrifugal distortion constants up to sextic ones were derived for both isotopic species. In order to reproduce the observed fine structures satisfactorily, an analysis with the spin-rotation interaction Hamiltonian which included quartic as well as quadratic terms in (electronic spin or rotational) angular momenta was necessary. More precise hyperfine constants were also determined.     

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.