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The Schrödinger Wave Equation
Published in Daniel D. Pollock, PHYSICAL PROPERTIES of MATERIALS for ENGINEERS 2ND EDITION, 2020
The hydrogen atom has one electron. This can occupy any of the states n = 1, ℓ = 0, mℓ = 0, and ms = ±1/2. These are 1s states because ℓ = 0. The energy difference between these states is small. Either of these states, but not both, may be occupied in a given atom.
The Hydrogen Atom
Published in Vinod Kumar Khanna, Introductory Nanoelectronics, 2020
The hydrogen atom is the simplest atom comprising a nucleus containing a single proton and an electron revolving around the nucleus. The oppositely charged electron and the proton are held together by the Coulombic electrostatic attraction. The potential energy of the system is V(r)=−e24πε0r
Background theory
Published in Michael de Podesta, Understanding the Properties of Matter, 2020
The hydrogen atom is the simplest atom, consisting of just one electron and one proton. The electrostatic potential energy around the proton varies roughly as 1/r (Eq. 2.5), binding the electron to the proton. Figure 2.16 illustrates the nature of the potential and some of the wave functions. The web site for this book has some attractive colour images of the wave functions of hydrogen-like atoms.
Biological response of Schiff base metal complexes incorporating amino acids – a short review
Published in Journal of Coordination Chemistry, 2020
Alagarraj Arunadevi, Natarajan Raman
Salem et al. synthesized Co(II) and Ni(II) complexes using the Schiff base ((z)-2-(2methoxybenzylideneamino)-3-methylbutanoic acid) and co-ligand of anthranilic acid [49]. Synthetic route of the complexes is given in Scheme S11. The Schiff base and its chelates were tested for their antimicrobial and antioxidant properties. The antioxidant activity of the compounds was measured by the method of DPPH free radical assay. The antioxidant activity indicates that the free Schiff base and its Ni(II) complex have higher activity compared to the Co(II) complex. In this case the authors say that DPPH is able to accept an electron or hydrogen atom (proton) to become a stable diamagnetic molecule. Thus, the loss of the DPPH transition signal intensity in the presence of antioxidants is clearly directly proportional to the concentration (or number) of protons accepted. In the synthesized compounds, the ligand has higher antioxidant activity than its complexes, due to the presence of the carboxylic group which can dissociate easily and inhibits the working of the free radical. The antioxidant activity of Ni(II) complex is higher than the Co(II) complex. The authors suggest this higher reactivity is due to the easier proton dissociation of coordinated water in the case of Ni(II) complex due to its smaller size with increasing effective nuclear charge which facilitates the proton loss.
The role of guaiacyl moiety in free radical scavenging by 3,5-dihydroxy-4-methoxybenzyl alcohol: thermodynamics of 3H+/3e− mechanisms
Published in Molecular Physics, 2019
Ana Amić, Zoran Marković, Jasmina M. Dimitrić Marković, Dejan Milenković, Bono Lučić
All electronic calculations were performed using the Gaussian 09 program package [35]. The influence of solvents was calculated with an implicit continuum solvation model – SMD, which takes into account the full solute electron density in the estimation of the energy of solvation [36]. Spin unrestricted calculations were used for radical species. Since spin contamination can affect the accuracy of enthalpies of open-shell systems, the spin operator ⟨S2⟩ values for all of the open-shell species have been checked. Spin contamination can be considered negligible if the value of ⟨S2⟩ differs from the correct value (⟨S2⟩ = 0.75 for singlet and ⟨S2⟩ = 2.00 for triplet) by less than 10% [37]. To analyse the electronic structures and the distribution of the unpaired electron in the radical species, natural bond orbital (NBO) analysis was performed by using the NBO 5.9 software [38]. Enthalpies and energies were calculated at standard temperature and pressure. Published values of the gas-phase enthalpy of proton and electron as well as of the solvation enthalpy of a hydrogen atom, proton and electron were used [39-42].
Metamorphic degree of coal dependence of content and genesis of coal-bed methane in China
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2019
Wenping Jiang, Qun Zhang, Fangui Zeng
It is concluded that the binding energy of carbon-carbon bonds in condensation aromatic rings and aromatic hydrocarbons is much higher. The carbon-carbon bonds above cannot be broken by heating. Thus, the carbon atoms in methane are mainly derived from both the side chains of aromatic rings and aliphatic hydrocarbons in small molecular compounds. It is necessary to mention that the aforementioned carbon atoms partly participate in the reaction with oxygen to generate carbon dioxide and unsaturated aliphatic hydrocarbon, etc. The hydrogen atom in methane mainly stems from the condensation of aromatic rings, slippage of side chains and aliphatic hydrocarbons. Besides the formation of methane, hydrogen atoms can also participate in the formation of water and hydrogen. The formation of methane due to the combination between hydrogen atoms and carbon atoms is determined by the binding energy. The binding energy corresponding to carbon atom and hydrogen atom, hydrogen atom and hydrogen atom and hydrogen atom and oxygen atom are similar, which are 415. 4KJ/mol, 436KJ/mol, and 463KJ/mol, separately; however, the binding energy between carbon atom and oxygen atom is as high as 750KJ/mol (Vandenbroucke and Largeau 2007). At the initial stage of thermal simulation experiment, both hydrogen atoms and carbon atoms slipping from the aromatic rings and aliphatic hydrocarbons in small molecule compounds mainly form methane; at the subsequent high-temperature stage, many hydrogen atoms generated from the enhanced condensation of the aromatic rings, whereas the slipping carbon atoms are extremely lower and cannot combine with the hydrogen atoms. Consequently, the yield of methane decreases; nevertheless, the yield of hydrogen increases.