Quantitative millimetre wavelength spectrometry at pressures approaching atmospheric: II. Determination of oxygen at atmospheric pressure

A millimetre wavelength (MMW) Fabry-Perot cavity spectrometer described in earlier work has been applied to the measurement of oxygen absorption at 60 GHz and atmospheric pressure in a gas matrix of nitrogen. The spectrometer has also been modified such that the MMW source is stabilised by a sub-harmonic microwave signal transmitted by an infrared carrier on a single mode telecommunications fibre optic. This is a step towards developing an instrument comprising minimal electronic components that can perform MMW spectrometry remotely. Oxygen determinations were achieved by monitoring the change in the quality factor (Q) of a resonant Fabry-Perot cavity due to the presence of an absorbing sample. The MMW absorption of the sample was determined by incrementing the frequency modulation (FM) deviation of the source frequency scanning the cavity resonance profile. The response curve of absorption signal versus fraction of oxygen in nitrogen was found to be linear throughout the working range of 1-100% O₂ (v/v) in N₂ with a slope of (1.407±0.007)×10⁻⁴ m⁻¹ (% O₂)⁻¹. The detection limit (3× standard deviation of the background) was found to be ∼0.8% (v/v). The MMW technique employed is advantageous since, unlike common MMW techniques, there is no vacuum requirement. Application of this method, to the monitoring of oxygen in gas mixtures of practical importance, is proposed. Values of the oxygen spectral absorption coefficients of lines between 55 and 60 GHz were measured at reduced pressure and found to be within ±2% of previous literature values. A pressure correction coefficient for O₂ absorption at 60 GHz in the 45-121 kPa range was obtained and found to be (1.354±0.014)×10⁻⁴ m⁻¹ kPa⁻¹.     

Density functional theory study of nine-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to the germanium clusters Ge(9)(z) clusters (z = -6, -4, -3, -2, 0, +2, and +4) starting from three different initial configurations. Double-zeta quality LANL2DZ basis functions extended by adding one set of polarization (d) and one set of diffuse (p) functions were used. The global minimum for Ge(9)(2)(-) is the tricapped trigonal prism expected by Wade's rules for a 2n + 2 skeletal electron structure. An elongated tricapped trigonal prism is the global minimum for Ge(9)(4)(-) similar to the experimentally found structure for the isoelectronic Bi(9)(5+). However, the capped square antiprism predicted by Wade's rules for a 2n + 4 skeletal electron structure is only 0.21 kcal/mol above this global minimum indicating that these two nine-vertex polyhedra have very similar energies in this system. Tricapped trigonal prismatic structures are found for both singlet and triplet Ge(9)(6)(-), with the latter being lower in energy by 3.66 kcal/mol and far less distorted. The global minimum for the hypoelectronic Ge(9) is a bicapped pentagonal bipyramid. However, a second structure for Ge(9) only 4.54 kcal/mol above this global minimum is the C(2)(v)() flattened tricapped trigonal prism structure found experimentally for the isoelectronic Tl(9)(9)(-). For the even more hypoelectronic Ge(9)(2+), the lowest energy structure consists of an octahedron fused to two trigonal bipyramids. For Ge(9)(4+), the global minimum is an oblate (squashed) pentagonal bipyramid with two pendant Ge vertices.