China 
Africa 
Explore chapters and articles related to this topic
X-ray-excited Auger and Photoelectron Spectroscopy
Published in M. Prutton, Electronic Properties of Surfaces, 2018
where ϵi, is the eigenvalue found for the one-electron Schrödinger equation for orbital i in the SCF calculation for the N-electron atom. Tabulations of ϵi have been published by several authors (Froese Fischer 1972b, Mann and Waber 1973, Desclaux 1973). Koopmans’ theorem presupposes the frozen orbital approximation whereby the wavefunctions of the N − 1 ‘spectator’ electrons are assumed to be unchanged by the removal of electron i. Alternatively, the wavefunctions of the spectator electrons may be considered to respond to the change in potential consequent upon ionisation with the requirement that EB(i) be determined from the difference of two SCF calculations, one giving the total energy of the N-electron atom, Eatom(N), and the other the total energy of the (N − 1)-electron ion, Eion(N − 1). This is termed the ∆SCF approach and () EΔSCF(i)=Eion(N−1)−Eatom(N).
K
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[chemistry, computational, solid-state] In a one-dimensional, one-electron atomic model the eigenvalues for the energy for the free electron exchange energy are given as the one-electron ionization energy, making this a limited binary system. Koopmans’ theorem in particular describes the removal of an electron from any of the available molecular electron orbits, hence forming a positive ion and can define the ionization energy for the process. In most other approximations the energy is defined by transition states, pertaining to the electron shell model. Named after Tjalling Charles Koopmans (1910–1985) from the Netherlands, who introduced the concept in 1934 and received the Nobel Prize in Physics in 1975.
KOH ratio effect, characterization, and kinetic modeling of methylene blue from aqueous medium using activated carbon from Thevetia peruviana shell
Published in Chemical Engineering Communications, 2021
Ndifreke Etuk Williams, Nur Pasaoglulari Aydinlik
The HyperChem® software was used to model the sub-atomic structure of MB with activated carbon, and the compound quantum structure arrangement/composition was then determined based on the spatial sub-atomic structure of MB. The full geometry of MB was optimized by means of semi-empirical parameterization method 3 (PM3) using a 0.1 kcal/(Ǻ mol) root mean square (RMS) gradient of the Polar-Ribiere algorithm. In all calculations, the Restricted Hartree-Fock (RHF) method was utilized while determining the energy of the highest occupied molecular orbital (EHOMO) and the lowest unoccupied molecular orbital (ELUMO) as well as the energy gap (ΔE = ELUMO — EHOMO) (Youssef and Ahmed 2019). Quantum chemical descriptors were used considering Koopmans’ theorem, which states that in closed-shell molecules, certain quantum parameters, such as ionization potential (I), chemical/compound hardness (α), electronegativity (χ), global chemical softness (μ), and nucleophilicity (ε), can be correlated with frontier orbital energies (Eduok et al. 2016). Hence, Equations (1)–(5):
DFT study of stability and electronic properties of cyclic tetramer involving dinucleobase monomers, comprising acetylene central block substituted at both edges with guanine and cytosine nucleobases
Published in Molecular Physics, 2022
Hamid Reza Masoodi, Sotoodeh Bagheri, Alireza Gholipour, Masoud Rohani Moghadam, Alireza Bazmandegan-Shamili
Due to molecular interactions, the HOMO donates electrons and its energy corresponds to the first ionisation energy while LUMO represents electron acceptors and its energy is associated with the electron affinity. Koopmans theorem [31] states that the first ionisation energy (I) and electron affinity (A) are respectively equal to I = −EHOMO and A = −ELUMO. As can be seen from Table 3, I and A values of H-bonded tetrameric arrangement are amplified when the dielectric constant of solvent increases. These relations can be shown as:
A Computational Screening on Inhibitability of Piper Betle Essential Oil Chemical Structures against Spike Proteins of Mutated SARS-CoV-2-variants D614G, N501Y, and S477N
Published in Smart Science, 2022
Phan Tu Quy, Tran Thi Ai My, Nguyen Thi Thanh Hai, Thanh Q. Bui, Duong Tuan Quang, Nguyen Thanh Triet, Phan Phuoc Hien, Nguyen Thi Ai Nhung
Quantum properties of the studied compounds were investigated based on density functional theory (DFT). Geometry optimization of the molecules was conducted without symmetry constraints using Gaussian 09 [30] at the level of theory M052X/6-311++G(d,p) [31]. Calculation of vibrational frequencies on the molecules was for confirmation that their structures are in global minimum on the potential energy surface (PES). Single-point energies at the M052X/6-311++G(d,p)-level-optimized geometries were calculated with the frozen-core approximation for non-valence-shell electrons by a larger basis set def2-TZVPP [32]. The resolution-of-identity (RI) approximation was applied for each run of structural optimization. The appropriate auxiliary basis sets were applied. Frontier orbital analysis was performed at the level of theory M052X/def2-TZVPP, which had been proposed for plotting of the localized molecular orbitals and orbital energy. These were achieved using NBO 5.1 [31] available in Gaussian 09. Moreover, electron density distributions were revealed by bonding analysis. Highest occupied molecular orbital (HOMO) energy, EHOMO, presents the tendency of a molecule to donate electrons; meanwhile, the value ELUMO (for lowest unoccupied molecular orbital – LUMO) of a molecule infers electron-accepting ability. Energy gap ΔE = ELUMO – EHOMO is considered as a parameter for intermolecular reactivity since it exhibits the capability of forming excited-state electrons toward the surface of a molecule. Ionization potential (I) and electron affinity (A) of inhibitory molecules were calculated by the application of Koopmans’ theorem [33] related to HOMO and LUMO energy as I = -EHOMO and A = -ELUMO. The obtained ionization potential and electron affinity values were used to yield the electronegativity (χ) of a molecule, calculated by the following equation: χ = (I + A)/2. Regarding an N electron system with total electronic energy (E) and external potential ν(r), electronegativity (χ) is defined as the negative of chemical potential (μ): χ = – μ = – (∂E/∂N)ν(r) [34,35].