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Fundamentals of Semiconductor Photoelectrochemistry
Published in Anirban Das, Gyandshwar Kumar Rao, Kasinath Ojha, Photoelectrochemical Generation of Fuels, 2023
Mamta Devi Sharma, Mrinmoyee Basu
According to molecular orbital (MO) theory, the combination of several atomic orbitals results in bonding and antibonding atomic orbitals. The conduction (lowest unoccupied energy level, ECB) and valence bands (highest occupied energy level, VCB) are developed which correspond to the antibonding and bonding energy levels of semiconductors. The energy gap between the conduction (CB) and valence band (VB) is called bandgap (Eg) which is usually in the range of 1–4 eV. The VB is fully occupied with electrons and the CB is mostly empty at the zero K.
Conducting Polymers
Published in Ram K. Gupta, Conducting Polymers, 2022
Luis A. Camacho-Cruz, Marlene A. Velazco-Medel, José C. Lugo-González, Emilio Bucio
One intuitive first approach to explain the conductivity of these substrates is that electrons have free mobility on the bulk material like in metals. However, this is not the case, and the explanation relies on the understanding of some basic concepts of molecular orbital theory and band theory in solids. According to band theory and molecular orbital theory, in any chemical compound, valence atomic orbitals from all the atoms in the compound (mathematical wave functions for the behavior of electrons) combine through linear superimposition to form an equal number of molecular orbitals (again, mathematical wave functions for the behavior of electrons). The different linear combinations of the original atomic orbitals naturally form molecular orbitals with different energy between each other, in small molecules, these orbitals are divided between bonding and antibonding orbitals (Figure 1.3). It is important to note that the generation of linear combinations to form the molecular orbitals is governed by the symmetry of the system, and naturally that the combinations remain valid solutions to the constraints imposed by the Schrödinger equation for the system [20].
Quantum Confinement and Electronic Structure of Quantum Dots
Published in Vinod Kumar Khanna, Introductory Nanoelectronics, 2020
Hitherto, our attention has been focused on the top-down view of the band structure of crystals. Now we reverse our thinking. In the bottom-up approach, the nanocrystal is built up starting from individual atoms. Molecular orbital theory proposes that individual atomic orbitals combine to form molecular orbitals. The unification of atomic orbitals is accomplished by linearly conjoining the atomic orbitals. This approach is referred to as linear combination of atomic orbitals (LCAO). Suppose the atomic orbital of an atom A is described by the wave function ΨA while that of atom B is assigned the wave function ΨB. Let the electron clouds of the atoms A and B overlap. Then two molecular orbitals are formed: One molecular orbital is formed by the addition of wave functions of atoms A and B.Another molecular orbital is obtained by subtraction of these wave functions.
New architectures of supramolecular H-bonded liquid crystal complexes based on dipyridine derivatives
Published in Liquid Crystals, 2020
Sherif S. Nafee, Hoda A. Ahmed, Mohamed Hagar
Figures 7 and 8 show the estimated plots for frontier molecular orbitals HOMO (highest occupied) and LUMO (lowest unoccupied) of IB and IIA–E. From these figures, it is clear that the electron densities are mainly localised on the alkoxy acid for HOMO while it shifted to the dinitrogen base in case of LUMO. The energy difference between the frontier molecular orbitals (ΔE) could be used in the prediction of the capability of electron to transfer from HOMO to LUMO by any electrons excitation process. The global softness (S) = 1/ΔE is the parameter that predict the polarisability as well as the sensitivity of the compounds for the photoelectric effects. The higher global softness of the compounds enhanced their photoelectric sensitivity as well as their polarisability. Moreover, dynamic stability and optical absorption of H-bonded complex could be estimated from HOMO and LUMO studies. It is well known that the higher energy gap value between the frontier molecular orbitals enhances the stability in chemical nature. The calculated band gap energy of the H-bonded mixtures IB and IIB is 0.10832 and 0.10243 a.u., respectively, which is a clear evidence of the dynamic stability in all aspects [63]. As shown from Table 3 and Figure 8, the H-bonded complexes derived from the base I is less softer than those from of the base II, for the same length of the alkoxy chain in acid moiety. Moreover, the lower energy difference of IIB increases its polarisability to 662 instead of 657 for IB. On the other hand, the length of the alkoxy chain of the acid component highly affects the polarisability. Increasing the alkoxy chain length by two carbons enhances the polarisability by 40 units (Figure 9). It has been reported that the more is the polarisable compound the better characteristics of the liquid crystalline suitable for electro-optical applications [64–66]. Another important parameter that affects the type of the mesophase is the dipole moment. It obvious from Table 3 that the dipole moment of the V-shaped H-bonded complexes is higher by two folds than the linear shape derived from the base II. Obviously, the angular complexes (IA–E) have higher dipole moment than that of the linear one, IIA–E. These higher values of dipole moments enhance the lateral interactions with respect to the terminal one, and this could be another good explanation of the smectic C mesophase formation for the H-bonded complexes IA–E and the nematogenic phases observed for the other group IIA–E. Moreover, it is could be another reason on the higher entropies changes of smectic-Iso than nematic-Iso transitions. The arrangement of molecules due to the higher dipole moment leads to decrease in the internal entropy and so increases the entropies difference, while an opposite observation in case of the nematic mesophase.