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Volumes and surface areas of common solids
Published in John Bird, Bird's Basic Engineering Mathematics, 2021
A square-based pyramid is shown in Fig. 28.9 with base dimensions x by x and the perpendicular height of the pyramid h. For the square-base pyramid shown, volume=13x2hProblem 9. A square pyramid has a perpendicular height of 16 cm. If a side of the base is 6 cm, determine the volume of the pyramid
Volumes and surface areas of common solids
Published in John Bird, Basic Engineering Mathematics, 2017
A square pyramid has a perpendicular height of 4cm $ 4\,\,\text{ cm} $ . If a side of the base is 2.4cm $ 2.4\,\,\text{ cm} $ long, find the volume and total surface area of the pyramid.
Three new zinc(II) 4′-chloro-2,2′:6′,2ʺ-terpyridine (4′-Cltpy)-based complexes: synthesis, spectroscopic and structural studies, thermal behavior, and Hirshfeld surface analysis
Published in Journal of Coordination Chemistry, 2023
Farzin Marandi, Aidin Bahrami, Nahideh Mahmoum-Gonbadi, Harald Krautscheid
Three new Zn(II) complexes with 4′-chloro-2,2′:6′,2ʺ-terpyridine (4′-Cltpy), [Zn(4′-Cltpy)(N3)2], 1, and [Zn(4′-Cltpy)(NCS)2], 2 (two 1:1 metal/ligand complexes), and a 1:2 metal/ligand complex, [Zn(4′-Cltpy)2](NO3)2·2H2O, 3, have been synthesized and characterized by elemental analysis, IR, 1H NMR spectroscopy and single-crystal X-ray diffraction. The Zn2+ in 1 is in a distorted square pyramid, in 2 intermediate between square pyramidal and trigonal bipyramidal environment, with τ index of 0.12 for 1 and 0.48 for 2. The coordination mode of ZnII in 3 is distorted octahedral. In this structure, two free nitrate anions as counterions and two non-coordinating solvent water molecules with hydrogen bonding interactions form anionic chains. For these structures, intermolecular interactions were studied, as well as thermal behavior. The Hirshfeld surface analysis has been used for more detailed investigation of intermolecular interactions and the role of C–H···π interactions as driving force for crystal structure formation has been demonstrated.
Vanadium(IV) coordination complexes with excellent biological activities: a synthetic, characterization, and density functional theory approach
Published in Journal of Coordination Chemistry, 2022
Sonika Sharma, Debasish Das, Biswajit Sadhu, Neeraj Sharma
The new bis(4-nitrocinnamohydroxamato)oxidovanadium(IV) complexes have been synthesized and characterized by various physicochemical and spectroscopic techniques. The bidentate chelating bonding of the hydroxamate ligand through carbonyl (C = O) oxygen and hydroxylamine (–NHO) oxygen atom has been inferred. A square-pyramidal geometry around vanadium was supported by DFT calculations. The thermal decomposition study of the complex has yielded VO2 as the sole decomposition product. The 1:1 coordination compounds of 1 with 2-cyanopyridine and 4-aminobenzonitrile have also been synthesized and characterized. Bonding through pyridine ring nitrogen of 2-CNpy in 2 and through N-atom of CN of 4-CNAn in 3 with vanadium has been inferred. Complexes 1-3 exhibited promising biological activity against tested pathogenic fungi and bacteria and in vitro cytotoxic activities towards Hep2C cell line. The coordination of nitrogen bases played a pivotal role in cytotoxic activity in 2 and 3 being more active than the parent complex. DFT analysis along with calculation of global reactivity descriptors demonstrated the thermodynamic stability of the complexes and identified the role of ligand to metal charge transfer in the studied complexes. TD-DFT analyses further decipher the involvement of molecular orbitals into the UV–vis transition, which is in good correlation with the experimental electronic spectra.
Crystal structure, magnetic properties, and structural prediction for an oxidovanadium(IV) complex [VO(dmf)5][PF6]2
Published in Journal of Coordination Chemistry, 2021
Shohei Yamamoto, Ryoji Mitsuhashi, Masahiro Mikuriya, Masayuki Koikawa, Hiroshi Sakiyama
Oxidovanadium(IV) complexes have simple d1 electronic configuration and are popular for studying not only fundamental physicochemical properties but also for physiological activities [1–9]. In particular, oxidovanadium(IV) complexes have received considerable attention as potential therapeutic agents for the treatment of diabetes, and their physiological and biochemical compatibility have been extensively studied. The symmetry of the basic skeletal structure of the oxidovanadium(IV) complex is also interesting. The vanadium(IV) ion has a very high affinity for the oxido ligand and forms octahedral and square-pyramidal oxidovanadium(IV) complexes with coordination geometry of C4v symmetry. In this study, one of our interests is the structural prediction for a complex of this symmetry.