On the Kirkwood theory of natural optical activity

Vibration-rotation intensities have been calculated for transitions between states of arbitrary vibrational symmetries, for tetrahedral molecules. For this purpose eigenfunctions of first order Coriolis interactions, which are assumed to be much smaller than anharmonic splittings, have been used. While some bands, among which fundamentals and overtones, follow the ΔR = 0 selection rule, for others the most intense vibration-rotation lines are those with ΔR maximum, in agreement with our double-resonance investigations of stretching levels of methane. One such investigation is presented here, in which the lower (3v₃, F ₂) level of CH₄ has been found at 8906·78 cm^-1, in close agreement with local-mode predictions. Several I.R. lines in this region have been assigned, the effective rotational constants being 5·214 and 5·24 cm^-1 for R = J and R ≠ J Coriolis sublevels respectively.     

Geometry,strength of binding and Br2 charge redistribution in the complex OC ··· Br2 determined by rotational spectroscopy

The ground-state rotational spectra of the six isotopomers ¹⁶O¹²C ··· ⁷⁹Br⁷⁹Br, ¹⁶O¹²C ··· ⁸¹Br⁷⁹Br, ¹⁶O¹²C ··· ⁸¹Br⁸¹Br, ¹⁶O¹²C ··· ⁷⁹Br⁸¹Br, ¹⁶O¹³C ··· ⁷⁹Br⁷⁹Br, ¹⁶O¹³C ··· ⁸¹Br⁷⁹Br, were observed by pulsed-nozzle, Fourier-transform microwave spectroscopy. The spectroscopic constants B _O, D _J, χ _aa (Br_i), χ _aa (Br_o), M_bb (Br_i) and M _bb (Br_o), where i = inner and o = outer, were determined for each isotopomer. The complex is linear, with the weak bond between the C atom of CO and Br_i. The rotational constants were used to determine the distance r(C ··· Br_i) = 3.1058Å and to show that the Br—Br bond lengthens by ～0.005–0.01Å on complex formation. The intermolecular stretching force constant kσ = 5.0 Nm^?1 was obtained from D_J and the Br nuclear quadrupole coupling constants were interpreted to reveal that a fraction δ = 0.02 of an electronic charge is transferred from Br_i to Br_o when Br₂ is subsumed into the complex. Properties of the two series OC ··· XY and H₃N ··· XY, where XY = C1₂, Br₂ and BrC1, are compared.     

The millimeterwave spectrum of germyl fluoride: Determination and comparison of the effective, substitution, and equilibrium structures

The ground state rotational spectrum of germyl fluoride was measured up to 1273 GHz (J ≤ 63). The rotational constants and quartic and sextic centrifugal distortion constants have been determined accurately for five isotopic species in natural abundance (^{70/72/73/74/76}Ge). The high accuracy of the rotational constants of these five isotopomers allowed us to study the mass dependence of the substitution coordinate of Ge. Equilibrium rotational constants of ⁷⁴GeH₃F were deduced with the help of the axial rotational constant and the rotation-vibration interaction constants determined by high resolution infrared spectroscopy. The r₀, r_,I, and r_e structures of GeH₃F were determined.     

Microwave spectrum ofcis 3-fluorophenol

The microwave spectrum ofcis 3-fluorophenol involving rotational states up toJ=28 has been observed and analysed in the frequency range 23–25 GHz in the ground vibrational state at room temperature. Analysis yields three rotational and five quartic centrifugal distortion constants. A tentativer ₀ structure has been proposed satisfying the observed rotational constants. The small value of the inertia defect Δ=0·07 confirms the planarity of the conformer.     

Far-infrared rotational spectra of some freons; chlorotrifluoromethane,dichlorodifluoromethane, and trichlorofluoromethane

The far-infrared rotational spectra of chlorotrifluoromethane, dichlorodifluoromethane, and trichlorofluoromethane have been observed with an interferometric (Fourier transform) spectrometer in the region 10–40 cm^?1 at a resolution of 0.07 cm^?1. CCl₂F₂ exhibits a continuum spectrum at this resolution, but symmetric top rotational fine structure is observed for CClF₃ and CCl₃F. Isotope splitting is also observed in CClF₃, and analysis yields the rotational constants for C³⁵ClF₃ of B₀ = 0.11112 cm^?1, D_J = 1.6 × 10^?8cm^?1; and for C³⁷ClF₃, B₀ = 0.10835 cm^?1, D_J = 1.5 · 10^?8cm^?1. Isotopic shifts can be allowed for in CCl₃F to yield constants for C³⁵Cl₃F of B₀ = 0.0821 cm^?1, D_J = 1 × 10^?8cm^?1. These values are all in agreement with those deduced from microwave studies of the low J transitions apart from B₀ for C³⁵ClF₃, where the difference is outside the expected experimental error.     

Determination of A 0 for CH3F from ground-state combination differences

The direct determination of the ground-state rotational constants A ₀ and D ₀ ^K of methyl fluoride has been accomplished through ground-state combination differences including perturbation-allowed transitions. The values found are A ₀ = 5·182009 ± 0·000012 and D ₀ ^K = (70·33 ± 0·25) × 10^-6 cm^-1. The ‘ normal ’ GSCD have also been used, in conjunction with microwave transitions, to yield improved values for the other rotational constants, including values for H ₀ ^{J K} and H ₀ ^KJ .     

The far infrared spectrum of 14N16O2

High resolution Fourier transform spectra in the 8–200 cm^-1 spectral region have been used to analyse the pure rotation spectrum of nitrogen dioxide. In this way, the spin rotation levels of the (000) state were accurately measured for K_a up to 14 and N up to 54. Using a hamiltonian which takes the spin-rotation and the hyperfine operators explicitly into account, it has been possible to derive a complete set of molecular parameters (rotational, spin-rotation and hyperfine constants) for the (000) state of ¹⁴N¹⁶O₂ from these experimental data and from the available microwave measurements. Numerous perturbations due to the hyperfine Fermi contact operator were analysed as well as a local resonance [42 0 42, J = 41·5] ? [41 2 40, J = 41·5] due to the electron spin-rotation interaction. Finally, a synthetic spectrum of the (000) ← (000) band of ¹⁴N¹⁶O₂ including all hyperfine transitions has been computed, covering the 0–235 cm^-1 spectral region.     

M-dependence of collisional transfer of rotational energy in OCS mixtures

Collision-induced transitions between rotational levels of OCS in the ground vibrational state have been investigated by steady-state microwave double resonance, with the M sublevels separated by a Stark field. The (2 ← 1)_P-(1 ← 0)_S, (3 ← 2)_P-(1 ← 0)_S, and (4 ← 3)_P-(1 ← 0)_S systems have been studied for pure OCS and for mixtures with excess CH₃OH, He, and H₂. For four-level systems having dipolar connections (ΔJ = 1; ΔM = 0, ± 1; parity ± ? ?) between pump and signal levels, it is found for OCS and the OCS-CH₃OH mixture that the dipole-type ΔJ = 1 transitions always dominate the collisional transfer, but for the OCS-He and OCS-H₂ mixtures that ΔJ = 2 quadrupole-type transitions are dominant. For all four collision partners, significant ΔJ = 2 and ΔJ = 3 collisional transfer is observed in some systems, indicating the presence of high-order terms in the collisional interaction.     

Internal rotation in methyl silane by avoided-crossing molecular-beam spectroscopy

The avoided-crossing molecular-beam electric-resonance technique was applied to methyl silane in the ground torsional state. A new type of anticrossing is introduced which breaks the torsional symmetry and obeys the selection rules ΔJ = 0, K = +1 /a3 ?1. For these “barrier” anticrossings, the values of the crossing fields E_c yield directly the internal rotation splittings; the E_c are independent of the difference (A-B) in the rotational constants. Such anticrossings were observed for J from 1 to 6. Studies were also conducted of several “rotational” anticrossings (J, K) = (1, ±1) /a3 (2, 0) for which E_c does depend on (A-B). The normal rotational transition (J, K) = (1, 0) ← (0, 0) was observed in the ground torsional state using the molecular beam spectrometer. The present data on CH₃²⁸SiH₃ were combined with Hirota's microwave spectra and analyzed with the torsion-rotation Hamiltonian including all quartic centrifugal distortion terms. In addition to evaluating B and several distortion constants, determinations were made of the moment of inertia of the methyl top I_α = 3.165(5) amu-Ų, the effective rotational constant A^eff = 56 189.449(32) MHz, and the effective height of the threefold barrier to internal rotation V₃^eff = 592.3359(73) cm^?1. The correlations leading to these two effective constants are discussed and the true values of A and V₃ are determined within certain approximations. For the isotopic species CH₃³⁰SiH₃, barrier and rotational anticrossings were observed. The isotopic changes in A and V₃ were determined, as well as an upper limit to the corresponding change in I_α.     

“Forbidden” millimeter-wave transitions in arsine

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been used for observation of the “forbidden” transitions J → J, K = ±4 → ±1 and J → J, K = ±5 → ±2 in AsH₃. A comprehensive computer analysis was made of the frequencies measured in this work together with available microwave frequencies of other transitions. This analysis provides accurate values of the rotational constants, nuclear quadrupole couplings, and effective structural parameters of the molecule. The spectral constants B₀ and C₀ (in MHz) are 112 470.597 and 104 884.665, respectively.     

Far infrared spectrum and spectroscopic constants of AsH3 in the ground state

The far ir spectrum of arsine, AsH₃, was recorded in the range 25–100 cm^?1 with a resolution of approximately 0.004 cm^?1. ΔJ = +1, ΔK = 0 rotational transitions were measured and assigned up to J″ = 12. These transitions, together with the presently available microwave and submillimeter-wave data and ground state combination differences, were analyzed on the basis of a rotational Hamiltonian which includes Δk = ±3 and Δk = ±6 interaction terms. The derived ground state molecular parameters reproduced the transition frequencies of both allowed and “perturbation allowed” transitions within the accuracy of the measurements. The equilibrium structure was determined for the AsH₃ molecule.     

High resolution proton magnetic resonance of selenophene

The high resolution proton magnetic resonance of selenophene has been studied at 100 Mc/s. The spectrum was analysed as an A₂X₂ system and the following coupling constants were obtained: J ₂₃ = 5·35, J ₂₄ = 1·05, J ₃₄ = 3·56, J ₂₅ = 2·47 c.p.s. Coupling was also observed between ⁷⁷Se and the α and β protons and coupling constants of 48 c.p.s. (α) and 9·5 c.p.s. (β) were obtained. The τ values were 2·30 (α) and 2·88 (β). The results are compared with values available for furan, pyrrole and thiophene and the conclusion is drawn that selenophene is probably a planar molecule.     

An anharmonic force field for carbonyl sulphide

A 16-parameter force field for OCS based on curvilinear coordinates is presented in table 2 and the agreement between observed and calculated transitions and rotational constants is indicated in tables 4, 5 and 6. The computational approach differs from that of Morino and Nakagawa [2] and similar work on other molecules by other authors, in that perturbation theory is eschewed and the calculated vibrational transitions and rotational constants are derived via the numerical solution of a large matrix. The usual parameters x_ij , y_ijk , α _i ^B and γ _ij ^B are thereby rendered inappropriate intermediates. The approach also leads to estimates of B _e - B ₀ for each isotopic species and thence suggests equilibrium distances r _CO = 1·155386(21) Å and r _CS = 1·562021(17) Å.     

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

The force constants and equilibrium geometry of water were calculated ab initio from Hartree-Fock self-consistent field wavefunctions using the force method, and a 53/31, a 73/3 + 1 and a 95/41 + 2 gaussian lobe basis set. The force method proved to be very economic and numerically accurate.

The calculated values agree well with the experimental ones. Especially good is the agreement for the interaction constant F_rα . Calculated force constants for the 95/41 + 2 basis are: F_r = 9·158 mdyn/å, F_α = 0·8513 mdyn/å, F_rα = +0·3007, F_rr = -0·1724; the experimental values from isotope frequencies are: F_r = 8·456, F_α = 0·762, F_rα = +0·246, F_rr = -0·100 mdyn/å. The agreement in the geometry is also good for the 95/41 + 2 basis r _e = 0·9518 å, α = 107·49°, and the experimental r _e = 0·9572 å, α = 104·52°.

Force constants were found to be quite insensitive to variation in the basis functions, all three sets giving almost the same result. On the other hand, the dipole moment derivative is very sensitive.     

High-resolution,near-infrared CW-CRDS,and ab initio investigations of N2O–HDO

We have investigated the N₂O–HDO molecular complex using ab initio calculations at the CCSD(T)-F12a/aug-cc-pVTZ level of theory and using cavity ring-down spectroscopy to probe an HDO/N₂O/Ar supersonic jet around 1.58 μm. A single a-type vibrational band was observed, 13 cm^?1 redshifted compared to the OH+OD excited band in HDO, and 173 vibration-rotation lines were assigned (T_rot ≈ 20 K). A weighted fit of existing microwave and present near infrared (NIR) data was achieved using a standard Watson's Hamiltonian (σ = 1.26), producing ground and excited states rotational constants. The comparison of the former with those calculated ab initio suggests a planar geometry in which the OD rather than the OH bond in water is almost parallel to NNO. The equilibrium geometry and dissociation energy (D_e = –11.7 kJ/mol) of the water–nitrous oxide complex were calculated. The calculations further demonstrate and allow characterising another minimum, 404 cm^?1 (ΔE₀) higher in energy. Harmonic vibrational frequencies and dissociation energies, D₀, were calculated for various conformers and isotopic forms of the complex, in both minima. The absence of N₂O–D₂O from dedicated NIR experiments is reported and discussed.     

Proton N.M.R. study of the dynamics of the ammonium ion in ferroelectric langbeinite, (NH4)2Cd2(SO4)3

The proton N.M.R. lineshape of polycrystalline Langbeinite, (NH₄)₂Cd₂(SO₄)₃, has been studied in the temperature range 300 K to 1·8 K. The resonance line is motionally narrowed over the entire temperature range, and the low temperature proton line shows clear evidence for tunnelling motion of the ammonium ion between spin-symmetry states. From a computer simulation of the lineshape, we obtain an estimate for the tunnelling splitting parameter, J, of the torsional ground state of the ammonium ion, as 375 ± 125 gauss. For an undistorted tetrahedral crystal field this corresponds to a tunnelling splitting Δ = 4J = 6·3 ± 2·1 MHz.

Pulsed proton N.M.R. studies have also been carried out on the above compound at 30·8 MHz and 48·2 MHz and the spin-lattice relaxation time (T ₁) has been measured by the π - t - π/2 pulse sequence as a function of temperature down to 77 K. At 30·8 MHz, a T ₁ minimum of 13 ms occurs at 105·8 K, and is ascribed to random reorientations of the NH₄ ⁺ ion. An activational energy barrier of 0·74 ± 0·1 kcal/mole and an associated pre-exponential factor of 8·0 × 10^-13 s are calculated for the above motional process, and the value of the activation energy is correlated with the tunnelling splitting of the torsional ground state.

An anomaly in T ₁ has been observed at the ferroelectric Curie point (95 K), indicating the order-disorder nature of the transition. This is the first experimental evidence relating to the nature of the transition in Langbeinite.     

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.     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.     

The pure rotational Raman spectrum of CS2 in the ground and 010 vibrational states

The pure rotational Raman spectra of CS₂ in the 00⁰0 and 01¹0 vibrational states have been observed using a low power HeNe laser (λ = 6328 Å) and a high resolution plane grating spectrograph. The ΔJ = 2 transitions with J = odd in the 01¹0 state are clearly resolved from the ground state transitions thus allowing the determination of some upper state rotational constants. The molecular constants determined in this work are for the 00⁰0 ground state, B_00⁰0 = 0.10912 ± 0.7 × 10⁻⁵ cm⁻¹, (D_J)_00⁰0 = (0.83 ± 0.18) × 10⁻⁸ cm⁻¹ and for the 01¹0 excited state B_01¹0^c = 0.10935 ± 0.00002 cm⁻¹ and (D_J)_01¹0^c = (1.5 ± 0.6) × 10⁻⁸ cm⁻¹.     

Resolved fluorescence spectra of NiH. Electronic structure,electronic energy transfer,and the Zeeman effect in low-lying states

Fourier transform spectra of collisionally induced fluorescence following isotopically selective laser excitation of NiH at ～550?nm have located an excited Ω?=?1/2 state of NiH lying 17900?cm^?1 above the electronic ground state. This is identified as v?=?0 of a ²Π_1/2 state originating from an Ni⁺ 3d⁸4s^{1 2}F configuration. Emission from this Ω′?=?1/2 state occurs predominantly to v″?=?0 and 1 of the ²Σ⁺ and W₂ ²Π_1/2 ligand field states, locating elusive f parity levels of W₂ ²Π_1/2 up to 5600?cm^?1 above the first rotational level of the electronic ground state, X ₁ ²Δ_5/2. Collisionally induced fluorescence following laser excitation at lower energies has also been recorded in the presence of a magnetic field (0.7–1?T), at Doppler limited resolution. Effective Landé factors g _J for rotational levels of the v?=?0 and 1 levels of the low-lying Ω″?=?5/2 and 3/2 components of the ²Δ and ²Π states of NiH have been derived from partially resolved Zeeman patterns. About 1600 transitions recorded in field-free conditions have been reduced to term energies relative to the lowest level of the ground state. They confirm strong spin-orbit mixing between the low-lying ligand-field states.