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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
We start by reminding the reader how to combine atomic orbitals for a very simple molecule, H2. For H2, the molecular orbitals (Figure 4.6) are formed by combining 1s orbitals on the two hydrogen atoms HA and HB. If we add these together, there is constructive interference between the two, forming a bonding orbital with enhanced probability of the electron being found in the internuclear region. If we subtract the two orbitals, there is destructive interference between the two 1s orbitals, forming an antibonding orbital in which the electron density in the internuclear region is reduced. The bonding orbital is lower in energy than the atomic 1s orbitals while the antibonding orbital is higher. The amount by which the energy is lowered for a bonding orbital depends on the extent of overlap between the 1s orbitals on the two hydrogens. If the hydrogen nuclei are pulled further apart, the overlap decreases and the decrease in energy is less. If the nuclei are pushed together, the overlap increases but the electrostatic repulsion of the two nuclei becomes important and counteracts the effect of the increased overlap.
Chemical Bond II: Molecular Orbitals
Published in Franco Battaglia, Thomas F. George, Understanding Molecules, 2018
Franco Battaglia, Thomas F. George
Likewise, the relative stability between a molecule and one of its ions can be predicted, depending on whether the electrons at play involve bonding or anti-bonding orbitals. For instance, the cation N2+ is predicted to be less stable than the neutral molecule, since from the latter the electron is taken off a bonding orbital. The cation O2+, instead, is predicted to be more stable than the neutral molecule because from this the electron is taken off an anti-bonding MO. These predictions are experimentally confirmed: the bond energies of N2 and N2+ are 9.9 and 7.9 eV, and those of O2 and O2+ are 5.2 and 6.8 eV. The bond energy sequence C2– (8.6)>C2(6.4)>C2+(5.3) is similarly justified (within parentheses are given the bond energies in eV).
Chemistry Foundations in Nanotechnology
Published in Wesley C. Sanders, Basic Principles of Nanotechnology, 2018
Bonding orbitals are constructive combinations of atomic orbitals. Antibonding orbitals are destructive combinations of atomic orbitals. They have a nodal plane where electron density equals zero, as illustrated in the molecular orbital diagram for hydrogen gas (H2) shown in Figure 2.9 (Miessler, Fischer and Tar 2014).
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 3 shows the structures of adsorbents as well as their HOMO and LUMO orbital shapes. Table 3 lists the frontier molecular orbital (FMO) energies, dipole moment (μ) and polarizability (α) of adsorbents. BH3 belongs to D3h point group and contains three identical σ bonds, and the geometry is trigonal planar with H–B–H bond angle of 120° (Figure 3). The bond length of B–H is 1.189 Å, which is consistent with previously reported experimental value of 1.190 Å [29]. The HOMO of BH3 is composed of in phase combination of B 2p atom orbital perpendicular to the principal rotation axis and two H 1s molecular orbitals (the third H 1s orbital cannot overlap with this B 2p orbital due to symmetry). Meanwhile, the LUMO of BH3 is solely contributed by B 2p molecular orbital collinear with the principal rotation axis, indicating that it is a non-bonding orbital. The HOMO and LUMO orbitals of other boranes are similar with BH3 except for mixing with some alkyl orbitals.
Quantum chemical study of tautomeric equilibriums, intramolecular hydrogen bonds, and π-electron delocalization in the first singlet and triplet excited states of 2-selenoformyl-3-thioxo-propionaldehyde
Published in Journal of Sulfur Chemistry, 2023
Ramin Rafat, Ebrahim Nakhaei, Farshid Zargari, Faezeh Gorgichi, Alireza Nowroozi
The NBO has been frequently used to analyze and interpret the mechanism of hydrogen bond formation [46]. In an X-H···Y hydrogen bond unit a definite quantity of electron density is shifted from the lone pair of proton acceptor (Y) to the anti-bonding orbital of the proton donor (σ*X–H) and a redisposition of electron density within the molecule occurs. The quantity of this interaction can be revealed by a second-order perturbation energy (E2), as presented in Table 6. By evaluating the values of E2, it can be concluded that the charge transfer energy for enol tautomers is more than for thiol and selenol conformers. For example, the sum of the charge transfer stabilization energies of enol, thiol, and selenol conformers in TD-DFT/singlet are about 134.61, 89.83, and 85.16 kcal/mol, respectively. These values indicate that the strength of hydrogen bonds of enol conformers is more than the other forms. Also, E2 values show that the strength of hydrogen bonds in the first singlet excited state is more than the corresponding triplet excited state, which is opposite to the results of excitation energies, hydrogen bond energies, and geometrical parameters. For instance, the sum of E2 for enol conformers in CIS/singlet, CIS/triplet, TD- DFT/singlet, and TD- DFT/triplet is around 207.16, 60.52, 134.61, and 115.03 kcal/mol, respectively. This duality may be assigned to the approximate nature of the NBO analysis, with respect to the other methods.
Quantum chemical computational studies of 1,3-diammonium propylarsenate: a semi organic crystalline salt
Published in Inorganic and Nano-Metal Chemistry, 2022
K. Senthilkumar, N. Kanagathara, V. Ragavendran, V. Natarajan, M.K. Marchewka
In the present study, a novel semi organic crystalline salt − 1,3–diammonium propylarsenate (1-3DAPAS) has been synthesized and established for the experimental and theoretical investigations. It is evident from single crystal X-ray diffraction that the structure of 1-3-DAPAS comprises diammonium propyl cations and arsenate anions. Also XRD study confirms the protonation of one proton from arsenic acid to 1,3 diamino propane molecule. Structure is optimized by using Gaussian 09 program with DFT/B3LYP-6-311++G(d,p) approach. Vibrational studies have also been carried out and correlated with the theoretical results. Besides these, the inter–intra molecular charge transfer interactions were confirmed by natural bonding orbital analysis and frontier molecular orbital investigation. The presence of reasonable inter and intra molecular stabilization energy influences the crystal packing of 1-3DAPAS molecule. The frontier orbital energy gap is calculated to be 1.96 eV and establishes the occurence of charge transfer within the molecule. The high dipole moment (15.235 Debye) of 1-3-DAPAS reveals the ionic nature of the obtained 1,3–diammonium propylarsenate. From the magnitude of first oder hyperpolarizabilty calculations which is 2.553 times that of urea, we believe that the synthesized compound 1-3-DAPAS may be potential candidate for the development of NLO materials.