Centrifugal Distortion Coefficients Research Articles

The unusual symmetry of hexafluoro-o-xylene-A microwave spectroscopy and computational study.

The rotational constants and quartic centrifugal distortion coefficients of hexafluoro-o-xylene were precisely derived from the 8 GHz to 18 GHz gas phase microwave spectrum. In addition, the rotational constants of all singly substituted 13C isotopologues were determined. Instead of the intuitively expected symmetry of C2v, as in o-xylene, calculations with a variety of methods (B3LYP, CAM-B3LYP, ωB97XD, MP2, and coupled-cluster singles, doubles, and perturbative triples) predict a C2 symmetry structure in which the two CF3 groups rotate in opposite directions by about 16°. While the experimental results in this study are not capable of proving this unusual symmetry, they can support future microwave, gas phase electron diffraction or nuclear magnetic resonance studies. From the presented data, a preliminary r0 structure was determined, reproducing the experimental rotational constants with deviations of no more than 15 kHz. Analysis of the interactions between the two CF3 groups using an effective fragment potential approach identifies two major contributions to their interaction, due to exchange-repulsion and electrostatic repulsion, with electrostatic repulsion responsible for the barrier at the C2v geometry.

Coherent manipulation of the internal state of ultracold 87Rb133Cs molecules with multiple microwave fields.

We explore coherent multi-photon processes in 87Rb133Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of 87Rb133Cs up to N = 6, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient Dv = h × 207.3(2) Hz.

Thermal self polymerization investigated by microwave molecular spectroscopy – Rotational characterization of the methyl methacrylate dimer

Rotational constants, Watson’s S centrifugal distortion coefficients, and internal rotation parameters of the methyl methacrylate dimer were retrieved from the microwave spectrum of the dimer phase of methyl methacrylate, which was subjected to a thermal self-polymerization process. The dimer contains three methyl rotors. Coupling of the methyl internal rotation to the overall rotation causes a complicated splitting of the rotational spectrum. The fact that only the two methoxymethyl groups contributed resolvable (>5kHz) splittings simplified the spectral assignment somewhat and a fit of spectroscopic parameters to the experimental data was achieved to within experimental accuracy. The methyl methacrylate self-polymerization system is intended as an easily accessible model system for polymerization and the analysis of the dimer presented in this study contributes to the stepwise understanding by means of microwave spectroscopy and ab initio methods.

Transient chirality of anilides - The rotational spectrum of trans-benzanilide

The rotational spectrum of trans-benzanilide C13H11NO is reported for the most part of the cm-wave range (3–19 GHz). Heavy atom frame conversion between the two possible enantiomers surprisingly leads to significant tunnelling splittings in the observed spectrum. The large amplitude motion parameters for the occurring tunnelling as well as the nuclear quadrupole coupling constants for the 14N were determined in addition to the rotational constants and quartic centrifugal distortion coefficients. Contrary to other trans-anilides, calculations indicate the existence of a non planar amide group in trans-benzanilide.

Rotational characterization of methyl methacrylate: Internal dynamics and structure determination

Rotational constants, Watson’s S centrifugal distortion coefficients, and internal rotation parameters of the two most stable conformers of methyl methacrylate were retrieved from the microwave spectrum. Splittings of rotational energy levels were caused by two non equivalent methyl tops. Constraining the centrifugal distortion coefficients and internal rotation parameters to the values of the main isotopologues, the rotational constants of all single substituted 13C and 18O isotopologues were determined. From these rotational constants the substitution structures and semi-empirical zero point structures of both conformers were precisely determined.

Spectroscopic Study of N2(b1Πu, ν = 8) by Atmospheric-Pressure Resonant-Enhanced Multiphoton Ionization and Fluorescence Detection

A spectroscopic analysis of the strongly perturbed N2(b(1)Πu, ν = 8) state has been conducted, accounting for b(1)Πu(ν = 8) ← X (1)Σg(+)(ν = 0) transitions, for the first time, up to J' = 20. A novel laser spectroscopy technique, using a combination of resonant-enhanced multiphoton ionization and fluorescence detection at atmospheric pressure, avoids the severe effects of perturbation reported in past extreme vacuum ultraviolet absorption experiments that produced weak and unusable spectra for the ν = 8 level. The R, Q, and P branches of the three-photon absorption transition b(1)Πu(ν = 8) ← X(1)Σg(+)(ν = 0) were fit, allowing rotational term energy assignment up to J' = 20 and molecular constants to be determined. Evidence of the previously suspected perturbation in b(1)Πu(ν = 8) is clear in this data, with significant Λ-type doubling at higher J' along with an anomalous negative value determined for the centrifugal distortion coefficient.

High-Resolution Rotational Spectroscopy of a Cyclic Ether.

The conformational landscape of crown ethers has constituted a central topic in the development of host-guest supramolecular chemistry. We report a high-resolution rotational study of a crown ether, 1,4,7,10,13-pentaoxacyclopentadecane (15-crown-5), by means of molecular beam Fourier transform microwave spectroscopy. The considerable size and the broad range of conformations allowed by the flexibility of the cyclic backbone of this ether pose important challenges to spectroscopy approaches. In this investigation, three stable rotamers of the 15-crown-5 ether have been identified and characterized through their rotational constants and centrifugal distortion coefficients. Ab initio quantum calculations at the MP2 level predict these conformers as the most stable ones for the title system and reproduce accurately their distinct structural features. The results pave the ground for an extensive survey of the conformational landscape of the 15-crown-5 and related cyclic ethers in the near term.

Rotational spectroscopy and dynamics of carbonyl sulphide studied by terahertz free induction decays signals

A terahertz time domain spectroscopy experiment is used to study the coherent re-emission after exciting more than 60 energy rotational states of OCS molecules in gas phase. Due to the regular structure of the absorption spectrum of such linear molecules, a set of subsequent pulses separated by 82.6ps is re-radiated from the vapour and recorded up to 450ps. A model based on a linear response of the gas and by use of “Maxwell–Bloch” equations has permitted the re-emitted free induced decay to be investigated. Spectroscopic parameters, such as rotational constant, centrifugal distortion coefficient and relaxation times are responsible for the temporal shape and so can be evaluated. The influence of the optical thickness to access the relaxation times is discussed.

High resolution study of AsHD 2: Ground state and the three bending fundamental bands ν3, ν4, and ν6

For the first time the infrared spectrum of the AsHD 2 molecule has been measured in the region of the bending fundamental bands ν 3, ν 4, and ν 6 on a Fourier transform spectrometer with a resolution of 0.0024 cm −1 and analyzed. More than 5500 transitions with J max = 26 have been assigned and used both to obtain “ground state combination differences” and for the determination of upper state ro-vibrational energies of the triad (001000), (000100), and (000001). Rotational parameters including centrifugal distortion coefficients up to octic terms of the ground vibrational state were calculated by fitting more than 500 “ground state combination differences” with J max and K a max = 21 . The obtained set of 24 parameters provides a rms-deviation of 0.00011 cm −1. The upper energies were fitted with 52 parameters of an effective Hamiltonian which takes into account strong resonance interactions between all vibrational states of the triad (001000), (000100), and (000001). The rms-deviation for the energy levels considered in the fit is 0.00014 cm −1.

Rovibrational spectra of the N2–HF complex at the vHF=3 level

We report the analyses of the three intermolecular combination bands of the hydrogen-bonded N2-HF complex at vHF=3, observed by molecular beam intracavity laser induced fluorescence. The origin of the HF intermolecular bending combination band, (3001(1)0)<--(00000), is 11 548.45(3) cm(-1), 328.2 cm(-1) higher than that of the (30000)<--(00000) transition with an origin at 11 220.250(1) cm(-1). The average rotational constant of the (3001(1)0) level is 0.103 63(1) cm(-1), a 4.8% reduction from B(30000)=0.109 21(1) cm(-1). Perturbations are observed as line splittings, increased line widths, and reduced peak intensities of a number of lines of the e and f components of (3001(1)0). In addition, the centrifugal distortion coefficients of both components are large, negative, and different. The N2 intermolecular bend transition (30001(1))<--(00000) has an origin at 11 288.706(1) cm(-1), 68.456(2) cm(-1) above that of the (30000)<--(00000) transition. This is the lowest combination state at v(HF)=3 level. It is unperturbed, yielding B(30001(1))=0.110.10(1) cm(-1). The transition to the intermolecular stretching state, (30100)<--(00000), has an origin at 11 318.858(1) cm(-1) with B(30100)=0.105 84(1) cm(-1). Both the (30100) and (30000) levels show an isolated perturbation at J=4. The Lorentzian component of the line widths, which show considerable variation with soft mode, are GammaL(30000)=490(30) MHz, GammaL(30100)=630(30) MHz, GammaL(3001(1)0)=250(30) MHz, and GammaL(30001(1))=500(50) MHz.

Calculated octic centrifugal distortion coefficients of non-linear molecules

The equilibrium octic centrifugal distortion coefficients of a molecule are coefficients of terms of the type H ˜ 08 in the expansion of the effective Hamiltonian. They depend on the quartic potential constants k k l m n ′ for the vibrational modes that have non-zero inertial derivatives, and therefore give information on these constants additional to that given by the other terms that depend on the quartic potential, H ˜ 24 and H ˜ 40 . The present work describes the calculation of these H ˜ 08 terms from a given potential by perturbation theory, using a computer program that calculates the coefficients in the successive contact transformations. Results are presented for the SO 2, ClO 2, O 3, and H 2O molecules.

Intramolecular hydrogen bonding in chiral alcohols: The microwave spectrum of the chloropropanols

The microwave Fourier transform spectrum of a mixture of 1-chloropropan-2-ol and 2-chloropropan-1-ol has been recorded in the range 5–18 GHz. The spectrum is extremely dense, as a result of both the large number of species present in the supersonic expansion, and the splitting of rotational transitions due to quadrupole coupling. Two conformational isomers of each molecule have been identified, and both the 35Cl and 37Cl isotopomers have been observed for both conformations of 1-chloropropan-2-ol and the most abundant conformation of 2-chloropropan-1-ol. All four observed conformations have weak intramolecular hydrogen bonds between the hydroxyl hydrogen and the chlorine atom. The basis of our assignment is a series of ab initio calculations, performed using the GAUSSIAN package, good agreement being observed between theoretical and experimental values of the rotational constants. Analysis of isotopic substitution and quadrupole coupling effects has reinforced this assignment. First-order centrifugal distortion coefficients, as well as diagonal and (in some cases) off-diagonal quadrupole tensor components have also been extracted. Diagonalisation of the quadrupole tensors for the 35Cl isotopomers results in a near-cylindrical quadrupole tensor, distorted in the C–Cl–H plane. This distortion, which is somewhat larger than in several comparable systems, supports the assertion that the most prevalent conformations are stabilised by an intramolecular hydrogen bond.

Jet-cooled diode laser spectra of CF3Br in the 9.2 μm region and rovibrational analysis of symmetric CF3stretching mode

Pulsed slit-jet high resolution (up to 0.0009 cm(-1) FWHM) infrared diode laser spectra of CF(3)Br, with natural isotopic abundance, were obtained in the region around 9.2 microm at the rotational temperature of about 50 K. In addition, diode laser spectra at reduced temperature (200 K) were recorded. We present here the rovibrational analysis of the nu(1) fundamental in the range 1075-1090 cm(-1). The fine structure of many P(J) and R(J) clusters has been well resolved for the first time. The assignment of rovibrational transitions has been accomplished up to K = 27, J = 63 for CFBr and K = 33, J = 62 for CFBr. A total of 636 (CFBr) and 880 (CFBr) lines were used in the final fit and a very accurate set of molecular constants, including the quartic centrifugal distortion coefficients for the v(1) = 1 state of both the bromine isotopologues, was obtained. In addition, spectral features belonging to the nu(1) + nu(6)-nu(6) hot band were unambiguously identified and a set of spectroscopic parameters were determined.

High-precision frequency measurements of the ν1 + ν3 combination band of 12C 2H 2 in the 1.5 μm region

A pair of 1.5 μm semiconductor laser frequency standards have been developed for optical telecommunications use, stabilised to transitions of 12C 2H 2 and 13C 2H 2, using cavity-enhanced Doppler-free saturation absorption spectroscopy. The absolute frequencies of 41 lines of the ν 1 + ν 3 band of 12C 2H 2, covering the spectral region 1520–1545 nm, have been measured by use of a passive optical frequency comb generator, referenced to 13C 2H 2 transitions of known frequency. The mean experimental uncertainties (coverage factor k = 1) of the frequency values are 3.0 kHz (type A) and 10 kHz (type B). Improved values of the band origin ν 0, rotational constants B′ and B″, and centrifugal distortion coefficients D′, D″, H′, and H″ are presented.

High-accuracy frequency atlas of 13C2H2 in the 1.5 μm region

A pair of 1.5 μm semiconductor laser frequency standards have been developed for optical telecommunications use, stabilised to Doppler-free transitions of the ν1 + ν3 and ν1 + ν2 + ν4 + ν5 combination bands of 13C2H2. The Allan deviation σ/f for a laser locked to line P(10) of the former band follows a slope of 1.6 × 10−12τ−1/2, reaching a minimum of 5.7 × 10−14 at τ = 4000 s. The absolute frequencies of 61 lines of the ν1 + ν3 band and 43 lines of the ν1 + ν2 + ν4 + ν5 band, covering the spectral region 1520 nm to 1552 nm, have been measured by use of a combined frequency chain and femtosecond comb, together with a passive optical frequency comb generator. The mean uncertainties for the line frequencies within each band are 1.4 kHz for the ν1 + ν3 band and 1.9 kHz for the ν1 + ν2 + ν4 + ν5 band, representing improvements on the precision of previously published data by factors of 100 and 104, respectively. Improved values of the rotational constant B″ and centrifugal distortion coefficients D″, H″ and L″ of the vibrational ground state are presented.

The vibrational dependence of quartic centrifugal distortion

The dependence of the quartic centrifugal distortion coefficients of a molecule on the vibrational quantum number v k is of type H ˜ 24 in the expansion of the effective Hamiltonian. It gives information on the quartic potential constants of the type k ′ k k l m and is therefore additional to that provided by the anharmonicity constants x kl , which depend only on the quartic potential constants of the type k ′ k k l l . The present work describes the calculation of these H ˜ 24 terms from a given potential by perturbation theory, using a computer program which calculates the coefficients in the successive contact transformations. Results are presented, in terms of directional centrifugal distortion constants, for the SO 2, ClO 2, O 3, and H 2O molecules. Good agreement with observed coefficients is obtained for SO 2 and ClO 2. For O 3, the strong rotational resonance between the (100) and (001) states complicates the comparison, and the transformation to the effective Hamiltonian used empirically requires further study. For H 2O, poor agreement is obtained for the (010) level because of quasilinear behaviour. The effects of the resonance between (100) and (001) are less severe than for O 3, and the agreement with the observed is somewhat better.

Rovibrational analysis of the ν1fundamental of CF3Cl from diode laser spectra in a supersonic slit-jet expansion

Spectra of the ν1 fundamental band of CF3Cl (CFC-13), with natural isotopic abundance, were recorded with a tunable diode laser spectrometer in the range 1100–1116 cm−1 using a supersonic pulsed slit-jet expansion. A rotational temperature of about 50 K was reached and a significant simplification of the spectra was achieved. The reduced Doppler broadening obtained using the slit source led to a FWHM up to 0.0007 cm−1 and so it was possible to resolve almost completely the K-structure in the P(J) and R(J) clusters for the first time. From the final fit of the assigned transitions a reliable set of molecular constants including the quartic centrifugal distortion coefficients for the v1 = 1 state of CF335Cl and CF337Cl has been obtained.

A High-Resolution Microwave Study of the Butan-2-ol Argon Complex

The rotational spectrum of a weakly bound complex formed between the chiral secondary alcohol butan-2-ol and the rare gas argon has been observed using Fourier transform microwave spectroscopy. In the complex the butan-2-ol molecule adopts the “ga” or straight-chain conformation with the hydroxyl hydrogen opposite to the ethyl group. The argon is bonded to the hydroxyl hydrogen, and the H–Ar separation is calculated to be 2.97 Å. Our assignment is aided by a series of calculations performed using the GAUSSIAN 94 ab initio package. The agreement between experimental and calculated values for the rotational constants is good. It has also proved possible to extract quartic centrifugal distortion coefficients using the Watson A-reduction of the rotational Hamiltonian.

A High-Resolution Microwave Study of the Conformations of Butan-2-ol in a Supersonic Expansion

The microwave Fourier transform spectrum of the chiral, secondary alcohol butan-2-ol has been recorded in the range 6–18 GHz. The spectrum is relatively dense, due to the large number of species formed in the supersonic expansion used. Three conformational isomers of the butan-2-ol molecule have been identified and their spectra assigned using a semirigid, asymmetric-rotor model. They correspond to the three configurations that the central C–C bond can adopt. The basis of our assignment is a series of ab initio calculations, which have been performed using the GAUSSIAN 94 package, good agreement being observed between theoretical and experimental values of the rotational constants. First-order centrifugal distortion coefficients have also been extracted. It has proven possible, by examination of the relative strengths of a-, b-, and c-type transitions, to infer some further information about the position of the hydroxyl hydrogen atom within each conformer.

Microwave Torsional–Rotational Spectra of gauche CH3CD2OH and CH3CD2OD

The microwave torsional–rotational spectra of gauche CH3CD2OH and CH3CD2OD have been identified, assigned, and analyzed up to 70 GHz. From the observed a- and c-dipole transitions, it has been possible to determine the effective rotational coefficients and the gauche tunneling energy of the hydroxyl internal rotation. The product of inertia terms Ixy and Ixz were included in the analyses using the framework fixed axis method (FFAM) approach to the hydroxyl internal rotation. Further, the analyses were sensitive to selected effective centrifugal distortion coefficients. For CH3CD2OH, a-dipole lines were assigned for the first excited gauche state. As for CH3CH2OH, these lines were highly nonrigid rotor in behavior more than likely due to the resonance with the first excited state of the methyl torsion.