In this paper, an ultra-wideband dielectric resonator antenna (DRA) is investigated. It basically covers the bandwidth from 6 GHz to 16 GHz and achieves a relative bandwidth of 90.9%. It is found that a wide bandwidth can be reached with a small DRA by adopting multilayer form. Thus, the dimension of the designed DRA element which is composed of nine-element phased-scanning linear array is as small as 6.9mm x 8.2mm x 11 mm. While the maximum stable zenith gain is 6.2dB, the lobe width is 3 dB. The operating frequency range of the antenna array is from 5.42GHz to 16.5GHz, achieving a 101.1% relative bandwidth. A large scanning angle of ±60° is realized within the operating frequency band, with good scanning pattern and cross polarization. To verify the design and simulation, a 1 × 9 DRA array is fabricated, and measurements are carried out.
We characterized the stationary points along the nucleophilic substitution (SN2), oxidative insertion (OI), halogen abstraction (XA), and proton transfer (PT) product channels of M− + CH3X (M = Cu, Ag, Au; X = F, Cl, Br, I) reactions using the CCSD(T)/aug-cc-pVTZ level of theory. In general, the reaction energies follow the order of PT > XA > SN2 > OI. The OI channel that results in oxidative insertion complex [CH3–M–X]− is most exothermic, and can be formed through a front-side attack of M on the C-X bond via a high transition state OxTS or through a SN2-mediated halogen rearrangement path via a much lower transition state invTS. The order of OxTS > invTS is inverted when changing M− to Pd, a d10 metal, because the symmetry of their HOMO orbital is different. The back-side attack SN2 pathway proceeds via typical Walden-inversion transition state that connects to pre- and post-reaction complexes. For X = Cl/Br/I, the invSN2-TS’s are, in general, submerged. The shape of this M− + CH3X SN2 PES is flatter as compared to that of a main-group base like F− + CH3X, whose PES has a double-well shape. When X = Br/I, a linear halogen-bonded complex [CH3−X∙··M]− can be formed as an intermediate upon the front-side attachment of M on the halogen atom X, and it either dissociates to CH3 + MX− through halogen abstraction or bends the C-X-M angle to continue the back-side SN2 path. Natural bond orbital analysis shows a polar covalent M−X bond is formed within oxidative insertion complex [CH3–M–X]−, whereas a noncovalent M–X halogen-bond interaction exists for the [CH3–X∙··M]− complex. This work explores competing channels of the M− + CH3X reaction in the gas phase and the potential energy surface is useful in understanding the dynamic behavior of the title and analogous reactions.
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