Formulae which relate pressure,activity and potentials of mean force to sums of integrals over Ursell-Mayer correlation functions of the distribution functions

The pure rotational spectrum in the far-infrared between 30 and 170 cm^-1 and its absolute intensity has been measured for CH₂D₂ in the vibrational ground state by high-resolution interferometric Fourier transform techniques. The analysis of the integrated cross-sections in the essentially water-free spectrum results in an accurate value for the permanent, vibrationally induced ground state electric dipole moment of CH₂D₂|μ₀| = (6·40±0·33) x 10^-3D.The influence of centrifugal effects on intensities and on the determination of the permanent dipole moment was investigated. Although centrifugal effects are important for the explanation of single band profiles, they appear to be of little relevance for the resulting permanent dipole moment. A new, more general 9- dimensional dipole moment function for methane is derived from ab initio calculations and experimental band strength information of CHD₃. Quantum Monte Carlo calculations using this function and a new, more general 9- dimensional analytical, anharmonic potential function for methane yield a semi-theoretical estimate μ₀ ^z = – (7·8±0·5)x10^-3D for CH₂D₂.     

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,dipole moment,and conformation of 3,6-dioxabicyclo[3.1.0.]hexane

The microwave spectrum of 3,6-dioxabicyclo[3.1.0.]hexane has been obtained. The rotational lines of one ring conformation only have been observed and assigned. Ground state rotational constants are A₀ = 6287.302 ± 0.011 MHa, B₀ = 4683.546 ± 0.008 MHz, and C₀ = 3358.517 ± 0.089 MHz. The diploe moment components obtained from Stark effect measurements are μ_a = 0.276 ± 0.010 D and μ_c = 2.47 ± 0.04 giving μ = 2.485 ±0.040 for the dipole moment of the molecule. The rotational constants and dipole moment components obtained experimentally can be satisfactorily explained only if the boat form is the most stable ring conformation.     

Microwave spectrum of the SF radical

The lowest rotational transition of the SF radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state has been observed and analyzed to determine the effective rotational constant B_eff and a magnetic hyperfine constant h to be 16 553.76₀ ± 0.052 MHz and 428.6₀ ± 0.71 MHz, respectively. The dipole moment was calculated from the Stark effects to be 0.79₄ ± 0.012 D.     

Microwave spectrum of CH3OD

The microwave spectrum of CH₃OD has been observed in the frequency region between 14 and 92 GHz. All the ground-state transitions with J ≤ 8 and J = 2 ← 1, a-type transitions in the excited torsional states (v = 1 and v = 2) have been observed. The spectrum has been analyzed and rotational constants, torsional constants, torsion-vibration-rotation interaction constants, and centrifugal distortion constants have been evaluated. The Stark effect measurements have been made and the dipole moment components have been determined as μ_a = 0.833 ± 0.008 D and μ_b = 1.488 ± 0.015 D.     

Spectra and structure of small ring compounds. Microwave spectrum of cyanocyclobutane

The rotational spectrum of cyanocyclobutane has been investigated in the region 18.0–40.0 GHz. Only A-type transitions were observed. R-branch assignments have been made for the ground state and the first three excited states of the ring puckering mode as well as the first two excited states of the out-of-plane cyano-bending mode. The microwave data are consistent with a bent equilibrium ground state for the ring with the cyano-group in the equatorial position. The dipole moment components were determined to be μ_a = 4.04 ± 0.09 D and μ_c = 0.92 ± 0.03 D with the total dipole moment, μ, having a value of 4.14 ± 0.09 D.     

Microwave spectrum and dipole moment of pentafluorobenzene

With the idea of evaluating the dipole moment of pentafluorobenzene from a lowJ transition, its microwave spectrum was investigated in the frequency region of 8,000 to 12,400 MHz. The spectrum had been earlier observed by the authors in the 12,400 to 18,000 MHz region which needs reassignment in the light of present investigations. The rotational constants areA=1480·856±0·003 MHz,B=1030·066±0·003 MHz andC=607·496±0·002 MHz. The dipole moment is 1·44±0·05 D.     

Laser Stark spectroscopy of FCN

Using a CO₂ laser, Stark shifted resonances have been measured for the CF stretching fundamental (ν₃) of FCN near 9.3 μm, and for two nearby “hot” bands. The band centers measured are 1076.492007 ± 0.000013 cm^?1 for 00⁰1-00⁰0, 1085.741046 ± 0.000050 cm^?1 for 01¹1-01¹0, and 1091.16222 ± 0.00015 cm^?1 for 02⁰1-02⁰0. The ground state dipole moment of FCN is found to be 2.1203 ± 0.0010 D and dipole moments are also given for the other states observed. Values are given for the rotational constant and l-doubling constant for the 01¹1 state.     

The rotational Raman spectra and cross sections of H2O, D2O, and HDO

We report the experimental rotational Raman spectra of H₂O, and of a mixture of D₂O and HDO in the vapor phase at room temperature, and their interpretation in terms of rotational–vibrational energies, wavefunctions, and transition moments of the molecular polarizability. These transition moments are based on high-level ab initio calculations of the wavelength dependent polarizability surface, and on wavefunctions where the rotational–vibrational coupling is considered in detail. As a byproduct of this analysis several tables have been compiled including scattering strengths and assignments for individual rotational transitions of the three species. From these tables the rotational Raman spectra can be simulated over the range of temperatures up to 2000 K for H₂O, and up to 300 K for D₂O and HDO.     

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.     

Millimeter-wave spectrum of 3-butynenitrile: Dipole moment and centrifugal distortion constants

The molecular rotational spectrum of 3-butynenitrile (3BN, propargyl cyanide), HCCCH₂CN, has been investigated in the vibrational ground state. A total of 222 transitions up to J = 69 have been measured between 8 and 300 GHz. The Hamiltonian used for the spectral analysis was required to include all centrifugal terms of fourth and sixth orders and one term of eighth order in the angular momentum components in order to reproduce the transition frequencies within the experimental error. Significant values for the respective distortion coefficients could be determined. The molecular dipole moment components were calculated from measured Stark effect shifts as |μ_a| = (3.23 ± 0.05) D, |μ_b| = (2.34 ± 0.02) D; μ_tot = (3.99 ± 0.05) D.     

Measurement of the electric dipole moment of NO (X2 Π ν = 0,1) by mid-infrared laser magnetic resonance spectroscopy

A pair of parallel Stark plates are added to a CO laser magnetic resonance spectrometer to apply electric field in the absorption cell. This apparatus is used to measure the molecular electric dipole moment via Zeeman and Stark effects simultaneously. The saturated absorption spectra of NO (X²Π_3/2, ν = 1 ← 0) was observed and the electric dipole moments of NO were directly measured in the presence of an electric field. The dipole moments are determined as μ₀(ν = 0) = 0.1595(15) D, μ₁ (ν = 1) = 0.1425(16) D. The electric dipole moment of the vibrationally excited state (ν = 1) is determined for the first time. The dependence of the electric dipole moments on its nuclear distances is interpreted.     

Microwave spectrum,dipole moment,and conformation of 3-methylcyclopentanone

The rotational spectrum of 3-methylcyclopentanone has been observed in the frequency region from 18.0 to 26.5 GHz. Both a-type and b-type transitions in the ground vibrational state and a-type transitions in five excited states have been assigned. The ground state rotational constants are determined to be A = 5423.32 ± 0.18, B = 1949.51 ± 0.01, and C = 1529.59 ± 0.01 MHz. Analysis of the measured quadratic Stark effects gives the dipole moment components ∥μ_a∥ = 2.97 ± 0.02, ∥μ_b∥ = 1.00 ± 0.03, ∥μ_c∥ = 0.18 ± 0.06, and the total dipole moment ∥μ_t∥ = 3.14 ± 0.03 D. These data are consistent with a twisted-ring conformation with a methyl group in the equatorial position.     

The forbidden (J → J + 1) spectrum of CH4 in the ground vibronic state

The pure rotational R-branch spectrum of CH₄ arising from the centrifugal distortion moment has been studied using a simple 12.10-m light-pipe cell and a conventional interferometer. Ten forbidden (J → J + 1) transitions for J = 7 to J = 16 have been observed in the spectral region 80–200 cm^?1 with a theoretical resolution of 0.5 cm^?1. The integrated intensity of the six strongest lines has been measured and was found to be of the order of twice that calculated from the distortion moment obtained earlier from a molecular beam study of the (J = 2) rotational level. In the approximation that frequency shifts due to this excess intensity are neglible, it has been determined that the rotational constant B₀ = (5.245 ± 0.004) cm^?1 and the scalar distortion constant D_S = (1.19 ± 0.09) × 10^?4 cm^?1. It is argued that the excess intensity is due to higher-order terms in the dipole moment operator and the validity of the frequency analysis is considered in this context.     

The Raman spectra and cross-sections of H2O, D2O, and HDO in the OH/OD stretching regions

We report the OH and OD stretching regions of the vapor phase Raman spectra of H₂O, and of a D₂O/HDO mixture, at room temperature. Also, the corresponding spectrum of H₂O at ∼2000 K in a methane/air flame is reported. These spectra are interpreted in terms of transition moments of the molecular polarizability, based on high-level ab initio calculations of the polarizability surface, and on variational wavefunctions considering the rotational-vibrational coupling in full. As a byproduct of this analysis several tables have been compiled including scattering strengths and assignments for individual rotational transitions of the three species. From these tables the Raman spectra in the OH/OD stretching regions can be simulated over the range of temperatures up to 2000 K for H₂O, and up to 300 K for D₂O and HDO.     

The molecular conformation and dipole moment of thiane from the microwave spectrum

The microwave spectrum of thiane, a heterocyclic analog of cyclohexane, has been studied in the region 26.5–40 GHz. The molecule is a highly asymmetric rotor (κ = 0.050154). From the analysis of both the a-type and c-type transitions, the rotational constants determined are (in MHz): A = 3992.719, B = 3005.812, and C = 1914.683. A study of the Stark effect has yielded the dipole moment components (in Debye units) μ_a = 1.684 ± 0.009, μ_c = 0.578 ± 0.002, which give a total dipole moment of μ = 1.781 ± 0.010. Comparison of the spectral data from tetrahydropyran, thiane, and 1,4-thioxane demonstrates the similarity in structure of these three compounds. It is found that a very reasonable set of structural parameters can be found which adequately fits the spectral data of all three molecules.     

Microwave spectrum,dipole moment,and structure of 3-aminopropanol

The microwave spectra of 3-aminopropanol and three of its deuterium substituted isotopic species have been investigated in the 26.5 to 40 GHz frequency region. The rotational spectrum of only one conformer has been assigned in which presumably a hydrogen bond of the OH---N type exists. The rotational spectra of a number of excited vibrational states have been observed and assignments made for some of these excited states. The average intensity ratio for the rotational transitions between the ground and excited vibrational states indicates that the first excited state is about 120 cm^?1 above the ground state.and the next higher state is roughly 200 cm^?1 above the ground vibrational state. The dipole moment was determined from the Stark effect measurements to be 3.13 ± 0.04 D with its principal axes components as |μ_a| = 2.88 ± 0.03 D, |μ_b| = 1.23 ± 0.04 D and |μ_c| = 0.06 ± 0.01 D. The possibility of another conformer where the hydrogen bond could be of NH---O type was explored, but the spectra of such a conformer could not be identified.     

The microwave spectrum of cyanoformamide

The spectrum of cyanoformamide, NCCONH₂, has been measured between 18 and 40 GHz using a Hewlett-Packard spectrometer with Stark modulation. The molecule is somewhat unstable and could most conveniently be measured in a flow system. The quadrupole hyperfine structure due to the two nitrogen nuclei has been analyzed for the ground state, and quadrupole coupling constants, rotational constants, and centrifugal distortion constants have been determined for the ground state. A rough determination of the components of the electric dipole moment was possible from the Stark shifts of suitable transitions.     

Laser stark spectroscopy of the ν2 fundamental band of 15NH3

The ν₂ fundamental band of ¹⁵NH₃ has been observed with a laser Stark spectrometer in Doppler-limited resolution. A set of 38 band constants including the electric dipole moment and its rotational dependence are determined from 416 Stark resonances observed in the present work and three submillimeter lines reported in the literature. The ν₂-band absorption line frequencies in the region 800–1160 cm⁻¹ and their relative absorption intensities are estimated from the band constants.