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Materials for Nanosensors
Published in Vinod Kumar Khanna, Nanosensors, 2021
First, let us briefly review molecular orbital concepts and theory. Molecular orbitals (MOs) are the solutions of the Schrӧdinger’s equation for molecules in the same way as atomic orbitals are solutions of this equation for atoms. Two atomic orbitals overlap to give two MOs: the molecular orbital at a lower energy than the overlapping atomic orbitals is called a bonding molecular orbital, whereas the molecular orbital at a higher energy than the overlapping orbitals is known as an antibonding molecular orbital.
Introduction to Computational Methods in Organic Materials
Published in Sam-Shajing Sun, Larry R. Dalton, Introduction to Organic Electronic and Optoelectronic Materials and Devices, 2016
A schematic diagram of the electron energy levels and corresponding wave functions in hydrogen molecule is shown in Figure 33.1. Two equivalent noninteracting hydrogen atoms have the same energy corresponding to the 1s-electron orbital in isolated atom. Creation of the hydrogen molecule is due to an interaction between two atoms that results in a characteristic change of the energy diagram according to Equation 33.11. One molecular orbital (σ1s) corresponding to the two overlapped 1s-atomic orbitals from the interacting atoms has an energy lower than that in an isolated atom (E0) by β (see Equation 33.11). This orbital can be occupied by two electrons from the interacting atoms having opposite spins, as shown in Figure 33.1. In addition, the energy structure of the hydrogen molecule represents another state characterized by an energy higher than that in an isolated atom (E0) by β (see Equation 33.11). This antibonding molecular orbital (σ1s*) is characterized by nonoverlapping 1s-atomic orbitals, as shown in Figure 33.1.
A DFT study on selective adsorption of NH3 from ammonia synthesis tail gas with typical aliphatic boranes
Published in Molecular Physics, 2023
Qingyu Zhang, Jin Mao, Wencai Peng, Han Li, Liqiang Qian, Wanxi Yang, Jichang Liu
Figure 1 also presents the HOMO and LUMO orbital shapes of NH3, N2, H2 and CH4, and Table 2 lists the corresponding orbital energies as well as Mulliken charges, dipole moments (μ) and polarizabilities (α) of adsorbates. According to the orbital shape in Figure 1, the HOMO orbital of NH3 is composed with in phase combination of N 2p atom orbital collinear with principal rotation axis and three H 1s atom orbitals, and is mainly contributed by the lone pair electrons of N atom. The LUMO orbital of NH3 is composed with out of phase combination of N 2s atom orbital and three H 1s atom orbitals, and can be regarded as three σ-antibonding orbitals of N and H. The HOMO of N2 is a bonding σ-molecular orbital composed of two N 2p atom orbitals approaching ‘head-to-head’, and the LUMO is a π anti-bonding molecular orbital composed of two N 2p atoms approaching ‘shoulder by shoulder’. The HOMO orbital of H2 is a σ-bonding molecular orbital composed of the in phase combination of two 1s orbitals of two H atoms, and LUMO is a σ-antibonding molecular orbital composed by the out of phase combination of two 1s orbitals of two H atoms. The HOMO of CH4 is provided by the in phase combination of C 2p atom orbital and four H 1s atom orbitals, and the LUMO is an anti-bonding orbital composed of C 2s atom orbital and four H 1s atom orbitals.
Calculation of the energy of a two-dimensional hydrogen molecule
Published in Molecular Physics, 2023
Nataliia Kashirina, Yaroslavna Kashyrina, Oleksandr Korol, Oleksandr Roik
The WF of the triplet term was chosen in the form: where A1 is the normalisation factor, σ*(i) is the sigma antibonding molecular orbital in 2DH2.