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.     

Millimeter-wave spectrum of the C4v molecule iodine oxygen pentafluoride IOF5: K-doubling of the |k| = 2 transitions in the ground state spectrum

Measurements are reported for the rotational spectrum of the C_4v molecule IOF₅ in the ground vibrational state in the range 30–75 GHz (J7 ← 6 to J17 ← 16). The K-doubling of |k| = 2 transitions due to an off-diagonal centrifugal distortion interaction of the type (Δl, Δk) = (0, ±4) has been observed. The centrifugal distortion constants D_J, D_JK, and R₆ have been determined as 0.139(2) kHz, 0.107(4) kHz, and 21(2) Hz, respectively.     

The microwave spectra and structures of epihalohydrins: Epichlorohydrin

The microwave spectrum of the two chlorine isotopic species of epichlorohydrin ($\text{CH}{}_2\text{OCH}$CH₂Cl) is reported. The structure is a gauche conformation with the Cl atom twisted toward the oxygen side of the ring. The observed rotational constants (in MHz) and centrifugal distortion constants (in kHz) are: C₂H₃OCH₂³⁵Cl; A = 13 373.02, B = 2080.353, C = 1932.469, Δ_JK = ? 6, Δ_K = 2400, δ_J = ? 0.43, δ_K = 17, H_KJ = ? 0.13, H_K = 570, h_JK = 0.061, h_K = ? 5.1: C₂H₃OCH₂³⁷Cl; A = 13 361.24, B = 2028.853, C = 1887.990, Δ_JK = 0.31, Δ_K = 1669., δ_J = ? 0.16, δ_K = 54.1.     

ΔK = 2 transitions in H2CO and D2CO

Weak transitions of the type ΔJ = ± 1, $\text{Δ}\text{K}{}_{\mathrm{a}}\text{= ? 2}$, ΔK_c = ± 3 have been observed in H₂CO and D₂CO by the millimeterwave double resonance method and also by direct absorption with a Stark modulated spectrometer. The addition of these new transitions in a least-squares analysis, in which all previously known microwave and millimeterwave data are also included, results in an improved set of rotational and distortion constants.     

Nuclear Quadrupole Coupling Constants of Chlorine and Microwave Spectrum, Structure, and ab Initio Calculation of 1-Chloro-1,1,2-trifluoroethane

The microwave spectrum of the ³⁵Cl and ³⁷Cl isotopic species of 1-chloro-1,1,2-trifluoroethane (HCFC-133b) has been investigated in the frequency region 10 to 50 GHz using a Stark modulation microwave spectrometer. A pulsed jet Fourier transform microwave spectrometer was also used for the measurement of hyperfine splittings. A least-squares analysis of the observed b-type Q- and R-branch transition frequencies gave rotational and centrifugal distortion constants and components of the chlorine nuclear quadrupole coupling constant tensors in the principal axes system as follows: A=4625.161 (3) MHz, B=2004.127 (2) MHz, C=1875.813 (2) MHz, Δ_J=0.144 (9) kHz, Δ_JK=1.0748 (8) kHz, Δ_K=1.57 (1) kHz, δ_J=0.01376 (4) kHz, δ_K=−0.146 (4) kHz, χ_aa=−57.958 (10) MHz, χ_bb=21.231 (11) MHz, and χ_cc=36.727 (11) MHz for ³⁵ClCF₂CH₂F species, and A=4607.684 (6) MHz, B=1960.565 (2) MHz, C=1834.823 (2) MHz, Δ_J=0.106 (7) kHz, Δ_JK=1.022 (3) kHz, Δ_K=1.48 (1) kHz, δ_J=0.0142 (2) kHz, δ_K=−0.18 (2) kHz, χ_aa=−46.268 (11) MHz, χ_bb=17.319 (13) MHz, and χ_cc=28.950 (13) MHz for ³⁷ClCF₂CH₂F species. The structural parameters are calculated from the observed six rotational constants by assuming the partial structure of ab initio calculation. The electronic properties of the C-Cl bond are evaluated from the observed nuclear quadrupole constants of chlorine. These molecular properties are compared with those of other related molecules.     

Microwave Spectrum,Nuclear Quadrupole Coupling Constants,and Structure of Bromodifluoromethane

The microwave spectrum of bromodifluoromethane, CHBrF₂(Halon 1201) has been studied for the first time from 7 to 40 GHz. A least-squares analysis of the observedc-type transition frequencies gave rotational and centrifugal distortion constants and components of the bromine nuclear quadrupole coupling constant tensor in the principal axes system as follows:A= 10199.7186(62) MHz,B= 2903.4150(26) MHz,C= 2360.1521(23) MHz, Δ_J= 0.660(14) kHz, Δ_JK= 2.87(11) kHz, Δ_K= 8.95 kHz, δ_J= 0.1344(24) kHz, δ_K= 3.22(15) kHz, χ_aa= 521.281(92) MHz, χ_bb− χ_cc= −38.32(9) MHz, and |χ_ac| = 187.1(26) MHz for the⁷⁹Br species;A= 10199.5567(54) MHz,B= 2876.5588(20) MHz,C= 2342.3796(18) MHz, Δ_J= 0.652(12) kHz, Δ_JK= 2.77(9) kHz, Δ_K= 8.21(61) kHz, δ_J= 0.1300(19) kHz, δ_K= 2.97(13) kHz, χ_aa= 435.61(10) MHz, χ_bb− χ_cc= −32.08(8) MHz, and |χ_ac| = 148.5(29) MHz for the⁸¹Br species. The structural parameters are calculated from all these rotational constants and the electronic properties of the carbon–bromine bond in bromodifluoromethane are evaluated from the observed nuclear quadrupole coupling constants. These molecular properties are compared with those of other related molecules.     

Microwave spectrum,centrifugal distortion constants,and quadrupole coupling constants of 3-chloropyridine

The microwave spectrum of 3-chloropyridine has been measured in the frequency region of 8.2 to 18 GHz. The rotational constants, centrifugal distortion constants, and the quadrupole coupling constants for the ³⁵Cl species are A = 5839.448 ± 0.027 MHz, B = 1604.152 ± 0.005 MHz, C = 1258.327 ± 0.004 MHz, Δ_J = 0.10 ± 0.01 KHz, Δ_JK = 0.36 ± 0.09 KHz, Δ_K = 1.18 ± 0.07 KHz, δ_J = ?0.008 ± 0.005 KHz, δ_K = 0.88 ± 0.20 KHz, χ_aa = ?70.04 ± 0.38 MHz, χ_bb = 36.68 ± 0.19 MHz. The values of rotational constants and quadrupole coupling constants for the ³⁷Cl species are A = 5840.052 ± 0.034 MHz, B = 1559.354 ± 0.01 MHz, C = 1230.739 ± 0.016 MHz, χ_aa = ?54.20 ± 1.26 MHz, χ_bb = 29.49 ± 0.48 MHz. The double bond character in the CCl bond is found to be 2%. The smaller than expected value of rotational constant A points to a “fattening” of the pyridine ring about the a-axis in contrast to 2-chloropyridine, where no such substitution effect was observed.     

The microwave spectrum and structure of chloromethyl cyclopropane

The microwave spectra of $\text{CH}{}_2\text{CH}{}_2\text{CH}$CH₂³⁵Cl and $\text{CH}{}_2\text{CH}{}_2\text{CH}$CH₂³⁷Cl have been observed and lines assigned to the gauche form. The rotational constants in MHz and distortion constants in KHz are: C₃H₅CH₂³⁵Cl, A = 11745.65, B = 2047.274, C = 1886.622, Δ_J = 0.85, Δ_JK = ? 0.9, Δ_K = 44., δ_J = ? 0.099, δ_K = 19.1, C₃H₅CH₂³⁷Cl, A = 11691.61B = 1997.664, C = 1842.823, Δ_J = 0.7, Δ_JK = ? 64.6, Δ_K = 2400, δ_J = 0.19, δ_K = ? 67.     

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.     

The infrared spectrum of isothiazole in the range 600–1500 cm−1, including a high-resolution study of the v 11(A′) band at 818 cm−1 and the v 16(A″) band at 727 cm−1, together with ab initio studies of the full spectrum

Abstract

The gas-phase high-resolution infrared spectrum of isothiazole in the range 600–1500 cm^?1 has been recorded, and revised band centres obtained for a number of vibrations. An analysis of the v ₁₁(A′) band at 818 cm^?1 and the v ₁₆(A″) band at 727 cm^?1 has been performed, using the Watson Hamiltonian, A-reduction, III^r representation. These were combined with previous microwave spectral data to provide combined analyses for rotational constants and quartic centrifugal distortion constants Δ _J , Δ _JK , Δ _K , δ _j and δ _K . These extend the knowledge derived from previous microwave and IR spectral studies. The equilibrium structures and the derived harmonic frequencies were calculated by ab initio methods, using a variety of basis sets with MP2, MP4 and CCSD(T) methods, and a comparison of these with experimental data is discussed. At a pragmatic level, the closest correlation of the rotational constants with experiment is not obtained with the most sophisticated methodology. Similarly, the vibration frequencies and intensities also vary strongly with the procedure. In particular, we found that the cc-pVTZ+MP2 results probably provide the best numerical comparison with experimental IR data for this molecule.     

High-resolution FTIR measurement of the ν4 band of methylene fluoride-d2

A high-resolution (0.002 cm⁻¹) infrared absorption spectrum of methylene fluoride-d₂ (CD₂F₂) of the lowest fundamental mode ν₄ in the region from 460 to 610 cm⁻¹ has been measured on a Bruker IFS 120-HR Fourier transform infrared spectrometer. More than 3500 transitions have been assigned in this B-type band centered at 521.9 cm⁻¹. The data have been combined with upper state pure rotational measurements in a weighted least-squares fit to obtain molecular constants for the upper state resulting in an overall standard deviation of 0.00018 cm⁻¹. Accurate value for the band origin (521.9578036 cm⁻¹) has been obtained and inclusion of transitions with very high J (?60) and K_a (?34) values has resulted in improved precision for sextic centrifugal distortion constants, in particular D_K, H_KJ, and H_K.     

The microwave spectrum,dipole moment,and molecular conformation of 2-cycloheptene-1-one

The microwave spectrum of 2-cycloheptene-1-one, an unsaturated cyclic ketone, has been studied in the regions 26.5–40 and 7.0–12.4 GHz. An analysis of the ground-state “a”-type transitions yielded the rotational constants (in MHz): A = 2997.27, B = 2049.24, C = 1399.76. The “a”-type transitions of an excited vibrational state were also assigned, giving A = 3000.51, B = 2046.65, C = 1398.88. The centrifugal distortion constants, D_J and D_JK, were needed to fit the data adequately. A study of the Stark effect yielded the dipole moment components (in debye) μ_a = 3.63 ± 0.023 and μ_c = 0.882 ± 0.040. The μ_b component could not be determined from the Stark effect data. These data are used to discuss the molecular conformation of cycloheptene-1-one.     

The Millimeter-Wave Spectrum of 2,3-Dihydrofuran

The millimeter-wave spectrum of 2,3-dihydrofuran in the ground and five ring-puckering excited states has been measured in the frequency range 100–250 GHz. The ground and first ring-puckering excited states have been fitted to a two-state Hamiltonian including Coriolis coupling interaction. The determined energy difference of 18.684(7) cm⁻¹between these states and theaandbtype coupling parameters are consistent with the ring-puckering potential function and the previously observed dependence of the centrifugal distortion constants Δ_JK, Δ_K, and δ_K. A small ring-puckering dependence of the quartic centrifugal distortion constants Δ_Jand δ_Jhas been also observed. This dependence is well accounted for in terms of the ring-puckering potential function and the vibrational dependence of the rotational constants.     

Vibration-rotation spectra of ethane and deuteroethanes: The ν2 band of CH3CD3

The ν₂ band of CH₃CD₃ has been measured under an effective resolution of 0.04 cm^?1. About 400 transitions observed in the region from 2130 to 2060 cm^?1 have been identified as due to the ν₂ fundamental band. The least-squares analysis of these transitions yields the band constants: ν₀ = 2089.957, B′ = 0.548937, D_J′ = 6.97 × 10^?7, D_JK′ = 1.92 × 10^?6, A′ - A″ = ?0.01158, and D_K′ - D_K″ = 1.30 × 10^?6 cm^?1. The ground-state constants B″, D_J″, and D_JK″ are fixed to the values obtained from microwave spectroscopy.     

Millimeter-wave spectrum of 2,3-difluorobenzonitrile and ab initio DFT calculations

The ground vibrational state rotational spectrum of 2,3-difluorobenzonitrile has been reinvestigated in the frequency range 40.0-99.0 GHz. High J and K₋₁ (J ? 62 and K₋₁ ? 20) transitions have been measured and analyzed to determine accurate rotational and centrifugal distortion constants. Finally, the experimental values were compared with the corresponding values computed at the DFT-B3PW91/6-31g(d,p) level of theory. A very good agreement has been found.     

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.     

High-resolution infrared spectrum and analysis of the ν1 band of CF337Cl

The rotational structure of CF₃³⁷Cl ν₁ band has been investigated using spectra of trifluorochloromethane in natural isotopic abundance, recorded with a tunable diode laser spectrometer. The spectra analyzed have been obtained by keeping the sample at low temperature (～200 K) to minimize the strong interference arising from “hot” band transitions. The K structure of many P(J) and R(J) multiplets has been resolved and positively identified: the maximum J value reached in the P and R branches was 38 and 40, respectively. About 650 unblended lines have been used for the least-squares fit to the energy expression including the quartic centrifugal distortion coefficients. Molecular constants for the ν₁ band of CF₃³⁷Cl have been derived. A weak perturbation affecting the rotational levels with K = 18 and J′ ≥ 36 has also been observed.     

Millimeter-wave spectrum of DCCCHO in the ground vibrational state

About 140 a- and b-type millimeter-wave transitions of propynal-d₁, DCCCHO, were measured in the ground vibrational state. The accurate rotational and centrifugal distortion constants were determined from the observed frequencies including the previous microwave measurements. Seven microwave transitions observed by infrared-microwave double resonance were also included in the analysis. The determined constants are A = 66778.016(12), B = 4463.8489(7), C = 4177.7950(7), Δ_J = 0.0015919(5), Δ_JK = −0.139214(13), Δ_K = 9.4328(18), δ_J = 0.0002885(4), δ_K = 0.03069(4), H_JK = −0.817(13) × 10⁻⁶, H_KJ = −9.62(4) × 10⁻⁶, H_K = 0.00255(8), h_J = 0.0047(3) × 10⁻⁶, in MHz.     

Centrifugal distortion effects in the microwave spectrum of methylene cyanide

The rotational spectrum of methylene cyanide has been measured up to J = 62 and a total of 82 b-type transitions have been obtained. These data have been analyzed with a semirigid rotor Hamiltonian to give accurate rotational and centrifugal distortion constants. The rotational constants are (in MHz) $\text{A}$ = 20882.7537 ≠ 0.017, $\text{B}$ = 2942.3003. ≠ 0.0031, $\text{C}$ = 2616.7225 ≠ 0.0031 The quartic centrifugal distortion constants are (in MHz)

$\text{Δ}{}_{\mathrm{J}}\text{(1.855455 ≠ 0.014) x 10}{}^{\mathrm{?3}}\text{Δ}{}_{\mathrm{JK}}\text{= (?6.79218 ≠ 0.027) x 10}{}^{\mathrm{?2}}$

$\text{Δ}{}_{\mathrm{K}}\text{(8.621628 ≠ 0.013) x 10}{}^{\mathrm{?1}}\text{δ}{}_{\mathrm{J}}\text{= (4.892607 ≠ 0.016) x 10}{}^{\mathrm{?4}}$

$\text{δ}{}_{\mathrm{K}}\text{= (6.7501 ≠ 0.29) x 10}{}^{\mathrm{?3}}$

The uncertainties are twice the standard deviations in the constants obtained from the least squares analysis, and represent approximately 95% confidence limits.     

The rotational levels of the ground vibrational state of formaldehyde

A variational procedure for rovibrational energy levels and wavefunctions of centrally connected tetra-atomic molecules is extended to include high rotational states, and in particular, J ? 10 levels for the vibrational ground state of formaldehyde. It is very important to do this because it has made possible the calculation of the usual rotational spectroscopic constants which correspond to the forcefield and geometry. A direct comparison with the ‘observed’ spectroscopic constants is therefore possible. The geometry and forcefield are refined against 65 J = 0 levels of H₂CO, 6 J = 0 levels of D₂CO, 42 J = 1, 70 J = 2 and 98 J = 3 levels of the ground and fundamentals of H₂CO and D₂CO, using an iterative scheme. The mean absolute error of the J = 0 levels is 1·10 cm^?1 and that for J ≠ 0 is 0·005 cm^?1, and the predicted geometry is CH = 1·10064 Å, CO = 1·20296 Å and HCO = 121·648°. Finally, the rotational constants A, B, and C for the ground state are 281956, 38846 and 34003 MHz, compared with the observed values 281971, 38836, and 34002 MHz. The centrifugal distortion constants Δ_J , Δ_JK , Δ_K and δ_J , are 77, 1275, 18113 and 11 kHz compared with 75, 1291, 19422 and 10 kHz. These results underline the accuracy of the new quartic forcefield.