Ground state spectroscopic constants of isothiocyanic acid,HNCS, from its microwave and millimeter wave spectra combined with far infrared data

The microwave and millimeter wave spectra of isothiocyanic acid, HNCS, in the ground vibrational state have been investigated in the frequency region 8–300 GHz. The a-type R-branch transitions have been assigned up to J = 25 and K_a = 4, and the a-type ^qQ₁ branch transitions up to J = 45. No b-type transitions could be identified in the frequency region covered. The far infrared data reported by Krakow, Lord, and Neely [J. Mol. Spectrosc., 27, 148 (1968)] were combined with our millimeter wave data in order to determine reliable spectroscopic constants. The rotational Hamiltonian, Watson's formalism with S reduction, has been extended empirically to higher order to facilitate the fitting of the large centrifugal distortion effects. The obtained constants are:

$\text{A = 1357.3 GHz; B = 5883.4627 MHz; C = 5845.6113 MHz; D}{}_{\mathrm{J}}\text{= 1.19393 kHz; D}{}_{\mathrm{JK}}\text{= ?1025.37 kHz; D}{}_{\mathrm{K}}\text{= 51.57 GHz; d}{}_1\text{= ?13.781 Hz; d}{}_2\text{= ?4.59 Hz.}$

The ¹⁴N quadrupole coupling constant has also been determined: χ_aa = 1.114 MHz.     

The microwave spectrum of 1-phosphapropyne,CH3CP: Molecular structure,dipole moment,and vibration-rotation analysis

The J = 4 ← 3 and J = 3 ← 2 rotational transitions of 1-phosphapropyne, CH₃CP, between 26.5 and 40 GHz have been studied by microwave spectroscopy. The spectrum shows the characteristic vibration-rotation satellite patterns associated with a C_3v symmetric rotor. Apart from the most abundant isotope variant, the species ¹²CD₃¹²C³¹P, ¹²CD₂H¹²C³¹P, ¹²CH₂D¹²C³¹P, ¹³CH₃¹²C³¹P, ¹²CH₃¹³C³¹P, ¹³CD₃¹²C³¹P, and ¹²CD₃¹³C³¹P have also been studied. For ¹²CH₃¹²C³¹P the rotational constants B₀ = 4991.339 ± 0.003 MHz, D_J = 0.823 ± 0.092 kHz, D_JK = 66.59 ± 0.18 kHz have been determined. From these data the following structural parameters have been derived: $\text{r}{}_{\mathrm{s}}\text{(}\text{CH}\text{) = 1.107 ± 0.001}\text{A}\text{?}$, ∠_s(HCC) = 110.30 ± 0.09°, $\text{r}{}_{\mathrm{s}}\text{(}\text{CC}\text{) = 1.465 ± 0.003}\text{A}\text{?}$, $\text{r}{}_0\text{(}\text{CP}\text{) = 1.544 ± 0.004}\text{A}\text{?}$. The dipole moment has been determined as 1.499 ± 0.001 D by analysis of the Stark effect of the J = 3 ← 2, |K| = 1 line. The vibrational satellites (v_s = 1, 2, and 3) have been studied and various vibration-rotation parameters derived.     

The microwave spectrum of MnO3F

The microwave spectrum of MnO₃F has been remeasured and several corrections and new results have been obtained: B₀ = 4129.141 MHz, D_J = 1.12 kHz, D_JK = 1.87 kHz; $\text{α}{}_3{}^{\mathrm{B}}\text{= 8.622}$, $\text{α}{}_5{}^{\mathrm{B}}\text{= ? 11.994}$, $\text{α}{}_6{}^{\mathrm{B}}\text{= 6.042}$, |q₅| = 16.005, and |q₆| = 8.456 MHz.     

Laser magnetic resonance measurement of rotational transitions in the metastable a1Δg state of oxygen

Laser magnetic resonance (LMR) for five rotational transitions, J = 4 ← 3, 5 ← 4, 7 ← 6, 8 ← 7, 9 ← 8, of the oxygen molecule ¹⁶O¹⁶O in its metastable state, a¹Δ_g, v = 0, are observed using six fir laser lines. Taking the known values of the g factors, their zero-field frequencies are obtained as 340.0085(6), 424.9810(9), 594.870(1), 679.780(1), and 764.658(1) GHz, respectively. They are fit by $\text{(}\text{E}\text{h}\text{) = B}{}_0\text{[J(J + 1) ? 4] + D}{}_0\text{[J(J + 1) ? 4]}{}^2\text{+ (?1)}{}^{\mathrm{J}}\text{(}\text{1}\text{2}\text{)qJ (J + 1)[J(J + 1) ? 2]}$, where B₀ = 42.50457(10) GHz, D₀ = 153.14(110) kHz, and q = 0.050(90) kHz.     

Microwave spectrum and structure of cyanamide: Semirigid bender treatment

An extensive study of the microwave spectrum of cyanamide has been undertaken, the analysis being based in part on semirigidbender calculations by the methods of Bunker and Szalay. Inversion lines of NH₂CN, $\text{K}{}_{\mathrm{?1}}\text{= 2}{}^{\mathrm{a}}\text{Q}$ branches and a number of vibrational satellites of the J = 2?1 transition were observed. A two-vibrational-state Hamiltonian was used to fit simultaneously the 0⁺ and 0^? microwave data and yielded rotational constants X, Y, Z, D_J, D_JK, d₁, H_JK as well as the inversion splitting and the μ_yz-connecting matrix element. Vibrational satellite data of seven isotopic species and infrared frequencies of NH₂CN were included in the semirigid bender calculations: The NCN spine is nonlinear by ca. 5° in the equilibrium structure of the molecule. Also, $\text{r}{}_{\mathrm{<mtext>NH</mtext>}}\text{A}\text{?}\text{= 0.9994 + 0.0144?}{}^2$; <HNH/2 = 60.39° ? 0.1134?²; $\text{r}{}_{\mathrm{<mtext>NC</mtext>}}\text{A}\text{?}\text{= 1.3301 + 0.0327?}{}^2$ (? is the inversion angle in rad); $\text{r}{}_{\mathrm{<mtext>CN</mtext>}}\text{= 1.1645}\text{A}\text{?}$ fixed. The inclusion of the NC bond flexing was necessary in order to reproduce the observed vibrational satellite patterns of NH₂CN, NHDCN, and ND₂CN. The barrier to inversion of the amino group is 510 ± 6 cm^?1 with minima at ±45.0 ±0.2°. The inversion dipole moment is 0.91 ± 0.02 Debye.     

Measurements of rotational transitions and hyperfine structure in PH2D

New rotational transition frequencies and measurements of hyperfine structure on two transitions are reported for PH₂D. All observed transitions are Q branch (ΔJ = 0) so only two independent rotational constants are obtained. These are A-C = 46 593.44 ± 0.67 MHz and κ(A-C) = 2B-A-C = ?34 545.9 ± 1.3 MHz. Nine transitions were fit to these parameters and the distortion parameter D_JK to obtain D_JK = 4.30 ± 0.04 MHz. Hyperfine structure due to spin-rotation interactions was observed on the 1₁₀ ← 1₁₁ transition at 6 024.645 MHz and on the 4₁₄ ← 4₀₄ transition at 20 815.334 MHz. Spin-rotation tensor components obtained are $\text{(M}{}_{\mathrm{aa}}\text{+ M}{}_{\mathrm{bb}}\text{)}\text{2}\text{=}\text{(M}{}_{\mathrm{aa}}\text{+ M}{}_{\mathrm{cc}}\text{)}\text{2}\text{= ?98 ± 3}\text{kHz}$.     

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.     

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.     

Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

The microwave spectrum,substitution structure,and dipole moment of thioketen,H2CCS

The microwave spectrum of the unstable thiocarbonyl thioketen, H₂CCS, has been investigated in the region 26.5–40 GHz. All singly substituted species as well as D₂CCS have been studied and the derived rotational constants yield the following structural parameters: $\text{r}{}_{\mathrm{<mtext>s</mtext>}}\text{(CS) = 1.554 ± 0.003}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>s</mtext>}}\text{(CC) = 1.314 ± 0.003}\text{A}\text{?}$, $\text{r}{}_{\mathrm{<mtext>s</mtext>}}\text{(CH) = 1.090 ± 0.006}\text{A}\text{?}$, ∠_s(HCH) = 120.3 ± 0.5°. The dipole moment is μ = 1.02 ± 0.01 D. Four low frequency vibrational modes have been observed and their assignments are discussed.     

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 far-infrared Laser Magnetic Resonance Spectrum of the OH radical

The far-infrared Laser Magnetic Resonance (LMR) Spectrum of the OH radical in the v = 0 level of the X²Π state has been studied in detail. All transitions that are accessible with currently available laser lines have been recorded. The measurements have been analyzed and subjected to a single least-squares fit using an effective Hamiltonian. The data provide primary information on the rotational and fine-structure intervals between the lowest rotational levels and the parameter values determined in the fit are $\text{A}\text{?}{}_0\text{= ?4168.63913(78)}\text{GHz}$, $\text{γ}\text{?}{}_0\text{= ?3.57488(49)}\text{GHz}$, B₀ = 555.66097(11) GHz, D₀ = 0.0571785(86) GHz.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

The microwave spectrum,substitution structure and dipole moment of cyanobutadiyne,HCCCCCN

Cyanobutadiyne (cyanodiacetylene), HCCCCCN, is sufficiently stable at low pressures to permit its rotational spectrum to be studied by microwave spectroscopy. The spectrum consists of a series of R-branch transitions typical of a linear molecule. The transitions with J = 9 to 14 which lie between 26.5 and 40.0 GHz have been measured for the vibrational ground state. Transitions have also been detected in natural abundance for all possible singly substituted ¹³C and ¹⁵N isotopic species. Deuteriated cyanobutadiyne, DCCCCCN, has also been synthesized and its ground state spectrum recorded. These measurements have enabled a complete substitution structure to be derived for the first time for a polyacetylene: r₈(HC_a) = 1.0569 ± 0.001, r₈(C_aC_b) = 1.2087 ± 0.001, r₈(C_bC_c) = 1.3623 ± 0.003, r₈(C_cC_d) = 1.2223 ± 0.004, r₈(C_dC_e) = 1.3636 ± 0.003, $\text{r}{}_8\text{(}\text{C}{}_{\mathrm{e}}\text{}\text{N}\text{) = 1.1606 ± 0.001}\text{A}\text{?}\text{(10}{}^{\mathrm{?10}}\text{m}\text{)}$. The spectroscopic parameters for the ground state are B₀ = 1331.3313 ± 0.001 MHz and D₀ = 0.0257 ± 0.002 KHz. The dipole moment, determined from the Stark effects of the J = 9 and 10 lines, is 4.33 ± 0.03 Debye.     

Microwave spectrum of the IO radical

The two lowest rotational transitions of the IO radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ ground electronic state have been observed by means of a Stark modulated spectrometer. The effective rotational constants in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state, the centrifugal distortion constant, the axial component of the magnetic hyperfine interaction, and the nuclear electric quadrupole coupling constant are determined accurately. It was necessary to take into account the second-order effects from the matrix elements off-diagonal in J for the analysis of the hyperfine structure. An equilibrium internuclear distance r_e is calculated to be 1.8677 ± 0.0028 Å from the effective rotational constant $\text{B}{}_0\text{(}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$, combined with α₃ from the A²Π → X²Π transition.     

Exact approach to equilibrium for the glauber model of a one-dimensional Ising system with random ±J bonds

The (discrete-time) Glauber model is considered for a one-dimensional system of spins s_j = ±1 with nearest-neighbor Ising interaction $\text{H}\text{= -Σ}{}_{\mathrm{j}}\text{J}{}_{\mathrm{j}}\text{s}{}_{\mathrm{j}}\text{s}{}_{\mathrm{j+1}}$. The J_j = ±J are treated as random variables with an arbitrary joint probability p(J). The exact time-dependent average 〈s_j〉_t is determined, and from it the “quenched” average $\text{〈〈s}{}_{\mathrm{j}}\text{〉}{}_{\mathrm{t}}\text{〉}{}_{\mathrm{<mtext>av</mtext>}}\text{=Σ}{}_{\mathrm{<mtext>J</mtext>}}\text{p}\text{(}\text{J}\text{)〈s}{}_{\mathrm{j}}\text{〉}{}_{\mathrm{t}}$ is explicitly found.     

Microwave spectra of deuterated ethylenes: Dipole moment and rz structure

The pure rotational spectra of three deuterated ethylenes, CH₂CD₂, CH₂CHD, and cis-CHDCHD, were observed by microwave spectroscopy, and the rotational and centrifugal distortion constants were determined precisely. The dipole moment of CH₂CD₂ was calculated from the Stark effects to be 0.0091 ± 0.0004 D. From the observed rotational constants the average structure was calculated to be $\text{r}{}_{\mathrm{z}}\text{(CC)}\text{= 1.3391 ± 0.0013}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{= 1.0869 ± 0.0013}\text{A}\text{?}$, θ_z(CCH) = 121.28 ± 0.10°, and $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{- r}{}_{\mathrm{z}}\text{(CD)}\text{= 0.00137 ± 0.00037}\text{A}\text{?}$, where the errors include one standard deviation in the fitting and errors due to an uncertainty (±0.03°) in θ_z(CCH) - θ_z(CCD).     

Modal content of noise generated by a coaxial jet in a pipe

The problem investigated was that of noise generated by air flow through a coaxial obstruction in a long, straight pipe of inside diameter, D = 97 mm. Downstream modal pressure spectra in the 200–6000 Hz frequency range were measured by a new technique [1] for orifices and nozzles of diameter d where $\text{0·03 ? (}\text{d}\text{D}\text{) ? 0·52}$. The Mach numbers of the flow through the restrictions ranged from 0·15 to choked conditions. The shape of the modal frequency spectrum was found to be determined by the frequency ratio $\text{f}{}_{\mathrm{r}}\text{=}\text{He}\text{St}\text{=}\text{U}{}_{\mathrm{i}}\text{D}\text{a}{}_0\text{d}$, where U_i is the jet velocity and a₀ is the speed of sound in the gas downstream of the restriction. This parameter is the ratio of two non-dimensional frequencies: namely, He, which controls acoustic propagation inside circular ducts, and St, which scales the jet noise spectrum shape. At low f_r(<3) the higher modes dominate the noise spectrum above their cut-off frequencies, while for higher f_r all modes are approximately of equal amplitude. The nature of large scale turbulence structures in the region of the jet near the nozzle exit may be used to explain these phenomena. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200–6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, depend strongly on the ratio of restriction diameter to pipe diameter ($\text{d}\text{D}$). Dividing the efficiency levels by the area ratio, $\text{(}\text{d}\text{D}\text{)}{}^2$, correlated the results over a moderate range of ($\text{d}\text{D}$).