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Solids
Published in Elaine A. Moore, Lesley E. Smart, Solid State Chemistry, 2020
Neil Allan, Elaine A. Moore, Lesley E. Smart
Suppose we form a linear chain of hydrogen atoms. For N hydrogen atoms, there are N molecular orbitals. In the lowest energy orbital all the 1s orbitals combine constructively—all the interactions between neighbouring 1s orbitals are bonding. In contrast, in the highest energy orbital all the orbitals combine destructively and all the interactions between neighbouring 1s orbitals are antibonding. These are shown in Figure 4.7 for N = 4. Lying in between these two extremes are (N − 2) molecular orbitals, in which there are some bonding and some antibonding interactions between neighbouring orbitals. The more bonding than antibonding interactions in a given molecular orbital, then the lower in energy is this orbital.
Chemistry Foundations in Nanotechnology
Published in Wesley C. Sanders, Basic Principles of Nanotechnology, 2018
Molecular orbitals can be used to understand the basic operation of molecular electronics, which will be discussed in Chapter 5. Molecular orbitals have characteristics similar to atomic orbitals. For instance, molecular orbitals can hold a maximum of two electrons. Additional similarities include electrons occupying the same molecular orbital require opposite spins, and molecular orbitals have definite energies. Whenever two atomic orbitals overlap, two molecular orbitals are formed: one bonding, one antibonding, as shown in Figure 2.8 (Miessler, Fischer and Tar 2014).
Molecular Orbital Theory of Surfaces
Published in Arthur T. Hubbard, The Handbook of Surface Imaging and Visualization, 2022
Structure-influencing, adsorbate-surface bonding interactions are seen in several forms, which are exemplified by CO and unsaturated hydrocarbons and hydrocarbon radicals. Typically, hydrocarbon adsorbate a orbital levels beneath the d band and adsorbate π orbital levels lie near the top of the σ set. The π* levels lie just above the Fermi level, and the σ* levels lie well within the empty surface s + p band. The strength of an adsorbate a or tt stabilization depends on how well the adsorbate orbitals overlap the metal surface orbitals and on how close they are in energy. The larger the overlap and the closer in energy, the greater the orbital stabilization. For every bonding orbital there is an antibonding counterpart that is destabilized. Whether or not there is a net bonding interaction due to these interactions depends on whether the antibonding counterpart orbitals are occupied. If they are, these interactions amount to a closed-shell repulsion. Mixing in of empty d or s + p band orbitals stabilizes the antibonding counterparts, rendering the net result a weak repulsion or a weak attraction. Thus, benzene adsorbs weakly by π donation stabilization, and water and ammonia bind fairly weakly by lone-pair a donation stabilization.11 The latter is true even when a orbital stabilizations are several eV in molecular orbital calculations or photoemission measurements. Empty π* orbitals in adsorbate molecules stabilize surface valence band orbitals, especially when overlap with them is high and they are close in energy. These back-bonding interactions are relatively strong because there are never any occupied antibonding counterpart orbitals to lower the bond order. These ideas are illustrated schematically in Figure 33.1 for ethylene chemisorbed on a metal and in Figure 33.2 for adsorbed CO.
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.
Syntheses, characterization and DFT studies of two new (π-allyl) palladium(II) complexes of β-8,9-dihydrohimachalene
Published in Journal of Coordination Chemistry, 2023
Abdelmajid Faris, Youssef Edder, Ismail Hdoufane, Intissar Ait Lahcen, Mohamed Saadi, Lahcen EL Ammari, Moha Berraho, Driss Cherqaoui, Brahim Boualy, Abdallah Karim
Figure 6 reveals the distribution and localization of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO), which are related to the electron-donating and the antibonding characters of the orbitals, respectively. For 5, the HOMO is observed in the bridge formed by Pd and Cl due to the π-bonding orbitals in this area. On the contrary, the LUMO is well distributed in the bond with Pd, Cl and the organic moieties, responsible for π*-bonding orbitals, but not localized in the alkyl skeleton. For 6, the π-bonding orbitals of the HOMO reside in bonds formed by Pd with P, Cl and the cycloheptane of the himachalene moiety, whereas the electron density on the LUMO is localized in the same area with an extension to the cyclohexane moiety and one of the benzyl groups attached to P. The energy gap between HOMO and LUMO for 5 and 6 is 4.72 and 4.44 eV, respectively, which confirms the stability of 5 and 6 [44]. For 6, the LUMO orbitals are concentrated around Pd, so a nucleophilic substitution appears feasible via these orbitals.
Synthesis, thermodynamic, photophysical and DFT studies of some trivalent metal chelates of a hexadentate tripodal hydroxyquinolinate-based ligand
Published in Journal of Coordination Chemistry, 2018
Rifat Akbar, Minati Baral, B. K. Kanungo
The ample way to study intra- and inter-molecular bonding and interaction among bonds, NBO analysis was carried out on TMOM5OX and its metal complexes. According to the NBO analysis, the weaker hydrogen bond interaction was found between the nitrogen and hydroxyl of the quinoline group with 2.87 kcal/mol of stabilization energy. It is evident that the electron density (ED) in O42-H75 antibonding σ* orbital was significantly increased (0.00818e) by the strong hydrogen bond between hydroxyl group (O42-H75) and nitrogen (N35) in the molecule. The interaction between N35 and H42-O75 leads to an increase in electron density (ED) of O-H antibonding orbital. The increase of population in O-H antibonding orbital weakens the O-H bond, which event in bond elongation and arrive red-shift of stretching frequency in IR spectrum.