Methyl group tunnelling and torsion in 2,4-hexadiyne

The tunnelling splitting of the ground torsional level of solid 2,4-hexadiyne and transitions to excited torsional states have been measured at low temperatures using neutron inelastic scattering. At 4 K the tunnelling splitting is 1·060 μeV (0·0086 cm^-1). It decreases as the temperature is raised, to 0·834 μeV (0·0067 cm^-1) at 35 K, and to less than 0·6 μeV at 50 K. A V-2←V=0 transition in the torsional vibration has been observed at 222 cm^-1 which shifts to 160 cm^-1 in the fully deuterated compound.

The values of the torsional frequencies, tunnelling frequency, and the change of tunnelling splitting with temperature have been fitted exactly to a potential energy for rotation of a methyl group given by

with a barrier to rotation of 432 cm^-1.

Changes in the tunnelling transitions as the temperature increases are compared with existing theories of the mechanism.     

Zeeman spectroscopy of the 4 Eu → 2 B 1g phosphorescence of copper porphin in an n-alkane single crystal

The phosphorescence spectrum of the metastable ⁴ E_u state of copper porphin in single crystals of n-octane (C₈) and n-decane (C₁₀) has been studied between 2·3 and 35 K, with and without a magnetic field B. The crystal field splitting between the orbital components observed at 35 K is δ = 30·3 ± 0·3 (C₈), 13·8 ± 0·2 cm^-1 (C₁₀). From the Zeeman shifts we derive the effective orbital angular momentum Λ′ = 0·8 ± 0·2 (C₁₀), the spin-orbit coupling parameter |Z′| = 1·5 ± 1·0 cm^-1 (C₁₀), the spin-spin dipolar interaction parameters D = -0·1 ± 0·2 cm^-1 (C₈, C₁₀) and |E| = 0·31 ± 0·03 cm^-1 (C₈, C₁₀), and the g-factors g _∥ = 2·14 ± 0·04 (C₈, C₁₀) and g _⊥ = 2·00 ± 0·03 (C₈, C₁₀).     

High-resolution infrared spectrum of acetylene in the region of the bending fundamental v 5

The infrared spectrum of C₂H₂ in the region of the bending fundamental v ₅ has been studied at a resolution of about 0·015 cm^-1. The molecular constants G ₀(v ₅=1) = 730·3341 (1) cm^-1 and B ₀ = 1·176641 (2) cm^-1 have been derived. In addition to the fundamental, all the hot bands starting from the levels v ₄ and v ₅ have been investigated. The vibrational, vibration-rotation coupling and centrifugal constants for the excited vibrational states v ₅ = 2 and v ₄ = v ₅ = 1 have been derived using the vibration-rotation energy matrix.     

Ground-state constants A 0 and DK 0 of 12CH3I from perturbation-allowed transitions

The upper levels of the bands v ₅ and v ₃ + v ₆ of CH₃I are coupled through a Fermi and an l(2, -1) resonance. This gives rise to perturbation-allowed transitions. Altogether, more than 200 such lines corresponding to three different K-value pairs have been observed between 1320 cm^-1 and 1520 cm^-1. By fixing the sextic constant H^K ₀ equal to zero, the following values were obtained: A ₀ = 5·173931(2) cm^-1 and D^K ₀ = 87·36(6) × 10^-6 cm^-1. The possible values of H^K ₀ and their effects on the results are 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.     

High resolution study of the v 7 + v 8 band of ethylene (C2H4) at 1889 cm-1

The v ₇ + v ₈ A-type band of C₂H₄ has been recorded between 1932 and 1847 cm^-1 with a resolution of 0·06 cm^-1. The transitions with K _-1 ? 8> and J ? 2>5 have been assigned. Although slight Coriolis resonances perturb the band, the analysis has been made easy through the use of an elaborate set of asymmetric top computer programmes. The band centre and a set of upper state constants have been obtained. With these constants, 288 observed upper state energy levels have been fitted with a standard deviation of 0·021 cm^-1.

Using very simple expressions, we have predicted all the resonance effects perturbing the levels of ethylene near 2000 cm^-1. This led us to the identification of the v ₄ + v ₈ and v ₈ + v ₁₀ combination bands in low resolution spectra.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

Pair exchange interaction in a crystalline nitroxide radical ESR study of dimers in the triplet state

The dimerization of the 9-aza-bicyclo (3,3,1) nonan-3-one-9-oxyl in the solid state is investigated by use of ESR spectroscopy. The ESR spectrum of a single crystal is characteristic of symmetric pairs of exchange-coupled radicals in a thermally accessible triplet state. The presence of well-resolved hyperfine structure is evidence for strongly localized excitations with a jumping rate lower than 10⁷ Hz.

The ESR spectrum is well described by the spin hamiltonian

At 35 GHz the observed splitting of the m _s=+ 1?0 transition has been found to be slightly different from that of the m _s=0?-1 one; this anomaly is explained by the mixing of the m _s electronic states.

The parameters and the principal directions of the zero-field splitting, spectroscopic and hyperfine tensors are determined and discussed. The principal directions of the dipolar tensor indicate a nearly equal spin density on the nitrogen and oxygen atoms; from the fine structure parameters D and E, determined to be (-0·0723 ± 0·0005) cm^-1 and (-0·0044±0·0003) cm^-1 at T=293 K respectively, it is suggested that the unpaired electron is partly delocalized on the molecule.

The singlet-triplet energy gap (J) and the zero-field splitting parameters are shown to be linearly temperature-dependent. These variations with temperature are attributed to the thermal expansion of the crystal lattice.     

The ground-state rotational constants of silane

From thirty-nine combination difference equations we have determined three significant ground-vibronic state constants of silane: β ⁰/hc=2·85941 cm^-1, γ ⁰/hc=-3·82×10^-5 cm^-1 and ε ⁰/hc=-7·97×10^-7 cm^-1 or in Hecht's notation B ₀=2·85941 cm^-1, D _s=3·82×10^-5 cm^-1 and D _t=2·436×10^-6 cm^-1.     

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.     

Radiative decay of the metastable quartet state of copperporphin

In CuP the low temperature luminescence originates from eight transitions between a quartet (M = ±3/2, ±1/2) and a doublet (M′ = ±1/2) with M and M′ denoting the (approximate) eigenvalues of the spin angular momentum S_z along the fourfold axis. Here we report (1) the selection rules governing the polarizations of the transitions; (2) the zero-field splitting ξ between the ±3/2 and ±1/2 components of the quartet for CuP in an n-octane crystal (ξ = 1·1 ± 0·2 cm^-1); (3) a photo-selection experiment on CuP in an isopentane glass from which it is concluded that the ratio of in-plane to out-of-plane polarization in the 0-0 band at 2·1 K amounts to an intensity ratio I _‖/I _⊥ ≈ 2. The implications of these results for the different SOC pathways are analysed.     

An ab initio calculation of the rotational-vibrational energies in the electronic ground state of NH2

We have calculated ab initio the three-dimensional potential-energy surface of the NH₂ molecule at 145 nuclear geometries spanning energy ranges of about 18 000 cm^-1 for the NH stretch and 12 000 cm^-1 for the bend. The ab initio configuration-interaction calculations were done using the multireference MRD-CI method. The calculated equilibrium configuration has NH bond length r _e = 1·0207 Å and bond angle α = 103·1°. The rotational-vibrational energies for ¹⁴NH₂, ¹⁴NHD and ¹⁴ND₂ were calculated variationally using the Morse-oscillator rigid-bender internal-dynamics Hamiltonian. For ¹⁴NH₂ we calculate that υ₁ = 3267 (3219) cm^-1, υ₂ = 1462 (1497) cm^-1 and υ₃ = 3283 (3301) cm^-1, where experimental values are given in parentheses.     

MBPT studies of van der Waals molecules

The many-body perturbation theory is employed for the calculation of the interaction potential for the F^- … He system in the framework of the supermolecule method. A particular attention is paid to the choice of the basis set functions for the two subsystems and the related basis set superposition effects. It has been found that the main features of the interaction potential are recovered in the SCF approximation. The SCF potential has its minimum at the distance R = 6·4 a ₀ with the interaction energy of 53 cm^-1. The complete fourth-order MBPT method gives the potential minimum position and depth equal to 6·5 a ₀ and 64 cm^-1, respectively. The basis set superposition effects estimated by using the counterpoise technique are negligibly small for the SCF interaction potential, while at the correlated level their magnitude is comparable to the value of the total correlation contribution to the interaction energy. The basis set superposition effect in calculations of the electron correlation contribution to weak intermolecular interactions is found to be the major factor limiting the reliability of the corresponding theoretical data.     

Optical and Zeeman studies of the first excited singlet state of zinc porphin in a single crystal of n-octane: Evidence for Jahn-Teller instability

The absorption and fluorescence spectra of Zn porphin in an n-octane single crystal at 4·2 K are reported in the region between 17 400 and 18 500 cm^-1. A strong peak appears in both spectra at 17 961 cm^-1 and is assigned to the origin of one component (|x, 0>) of the nearly degenerate Q-band. In absorption a second strong line occurs at a frequency δ = 109 cm^-1 above the first; a corresponding line is almost totally absent in the emission spectrum at 4·2 K, but it appears as a hot band of appreciable intensity when the temperature is raised to 80 K. This feature is assigned to the origin of the other component (|y, 0>) of the Q-band. The lifting of the degeneracy of the Q-band is interpreted as a crystal field splitting of the Jahn-Teller unstable ¹ E_u state.

The Zeeman effect is investigated for the 0–0 transition of the phosphorescence spectrum and the |x, 0> and |y, 0> components of the Q-band absorption spectrum. From the phosphorescence experiment it is concluded that the great majority of the ZnP guests are oriented in the host with an angle of about 25° between the out-of-plane molecular axes and the crystal a-axis. The analysis of the Zeeman effect in absorption (H//crystal a-axis) is complicated by the Jahn-Teller instability which causes two additional unknowns to appear in the problem: the frequency ν and the nuclear displacement parameter α of the active mode. When not making an assumption about these parameters one can only derive a lower limit for the matrix element of the orbital angular momentum between the two electronic components: Λ > 4·6. If is identified with the low-frequency mode of 180 cm^-1 appearing in the absorption spectrum, then it follows that Λ = 6·1 ± 0·6 with α = 1·4 ± 0·1.     

Rotational analysis of the B-X band system of the SbO molecule

Rotational analyses of the two 0-0 bands of theB ²ΣX ²Π_reg system of SbO were carried out for the first time from spectrograms taken in the second order of a 21 ft. concave grating spectrograph having a dispersion of 1·25 Å/mm. The rotational constants of the ν=0 vibrational levels of the upper and lower states, and of the coupling constant A₀ of the lower²Π_reg state were deduced. These values are summarised below. v₀₀=25 334·93 cm^?1 B′₀=0·3190 cm^?1 B″₀=0·3490 cm^?1 A ₀=2276 cm^?1 r′₀=1·933 Å r″₀=1·848 Å.     

A rotationally-resolved Rydberg transition of I2

Rotationally-resolved bands leading to a Rydberg state R 0 _u ⁺ of molecular I₂ are observed in a two-stage, three-photon transition from the ground state. The R 0 _u ⁺ state interacts homogeneously with high vibrational levels, ν_F ≈ 200–250, of an ionic state F 0 _u ⁺, the perturbation being directed by the vibrational overlap integrals towards even-numbered vibrational levels of R. Spectral constants of R 0 _u ⁺ are (in cm^-1): T _e = 61665·15, ω_e = 209.29, ω_e x _e = 0·859, B _e = 0·03842 and α_e = 1·6 × 10^-4. The electronic matrix element for the R, F interaction (excluding one deviant result) is |W _e| = 107 ± 1 cm^-1; thus W _e/ω_e ≈ 0·5, corresponding to ‘intermediate’ coupling. Energy considerations indicate that R should be assigned to the 0 _u ⁺ state of either the configuration (2430 Π_1/2g )6pσ _u , or of (2421 ⁴Σ _u ^-)6sσ _g . This state is the first extra-valence state of I₂ to be rotationally analysed.     

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.     

Photoelectron spectra of halides

High resolution photoelectron spectra, obtained with He I (584 Å) resonance radiation, are reported for ClF, ClF₃, BrF₃ and BrF (partial spectrum). In some cases Ne I (736–744 Å) radiation has also been used. Spinorbit and vibrational fine structure is resolved for the ground ²II states of ClF⁺ and BrF⁺; values obtained for ClF⁺ and ζ = 630 cm^-1, v′ = 870 cm^-1, and for BrF⁺ ζ = 2600 cm^-1, v′ = 750 cm^-1. From the vibrational envelope of the X ²∏ states, a bond length change of δr _e (-)0·10 Å for ClF⁺ and BrF⁺ is estimated. Ab initio SCF-MO calculations for ClF and ClF₃ are used to aid in the interpretation of the spectra via Koopmans' theorem. A considerable amount of charge delocalization in the trifluorides is inferred from the photoelectron spectra, and this is borne out by the calculations.     

Higher ro-vibrational levels of H2O deduced from high resolution oxygen-hydrogen flame spectra between 6200 and 9100 cm-1

The spectra of hydrogen-oxygen and acetylene-oxygen flames have been recorded on a Fourier transform spectrometer in the region 6200–9100 cm^-1 with a resolution of 0·015 cm^-1. In this region, we have performed a detailed analysis of the 2v ₂ + v ₃, v ₁ + v ₃, v ₁ + v ₂ + v ₃ - v ₂ and v ₁ + v ₂ + v ₃ bands. A primary motive for this study was to obtain higher rotational energy levels for the (021), (101) and (111) vibrational states. Moreover an extensive set of rotational levels of the (010) vibrational state has been deduced from the combined study of hot bands involving the (011), (021) and (111) vibrational states. A room-temperature absorption spectrum of water recorded on a Fourier transform spectrometer in the region 1750–2300 cm^-1 (resolution 0·005 cm^-1) has also been used to confirm the analysis.