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Orbitals and Bonding
Published in Michael B. Smith, A Q&A Approach to Organic Chemistry, 2020
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. If certain simplifying assumptions are made, it is possible to use the Schrödinger equation to generate a different wavefunction for electrons with differing energies relative to the nucleus. A particular solution to the so-called Schrödinger wave equation, for a given type of electron, is determined from the Schrödinger equation, and a solution for various values of ψ that correspond to different energies shows the relationship between orbitals and the energy of an electron. The wavefunction is described by spatial coordinates ψ(x,y,z), and using Cartesian coordinates a point is defined that describes the position of the electron in space. What is a node?
General Chemistry
Published in Steven L. Hoenig, Basic Chemical Concepts and Tables, 2019
The following is a summary in which the quantum numbers are used to fill the atomic orbitals with electrons:No two electrons can have the same four quantum numbers. This is the Pauli exclusion principle.Orbitals are filled in the order of increasing energy.Each orbital can only be occupied by a maximum of two electrons and must have different spin quantum numbers (opposite spins).The most stable arrangement of electrons in orbitals is the one that has the greatest number of equal spin quantum numbers (parallel spins). This is referred to as Hund’s rule.Figure 1.3 shows the completed energy level diagram for oxygen. The arrow notation is used to signify the different spin quantum numbers, ms, of the electrons in the orbital
Symbols, Terminology, and Nomenclature
Published in W. M. Haynes, David R. Lide, Thomas J. Bruno, CRC Handbook of Chemistry and Physics, 2016
W. M. Haynes, David R. Lide, Thomas J. Bruno
Octanol-water partition coefficient (P)* - A measure of the way in which a compound will partition itself between the octanol and water phases in the two-phase octanol-water system, and thus an indicator of certain types of biological activity. Specifically, P is the ratio of the concentration (in moles per liter) of the compound in the octanol phase to that in the water phase at infinite dilution. The quantity normally reported is log P. Oersted (Oe) - A non-SI unit of magnetic field (H), equal to 79.57747 A/m. Ohm ()* - The SI unit of electric resistance, equal to V/A. [1] Ohm's law - A relation among electric current I, potential difference V, and resistance R, viz., I = V/R. At constant temperature the resistance for many materials is constant to high precision. Olefins - Acyclic and cyclic hydrocarbons having one or more carbon-carbon double bonds, apart from the formal ones in aromatic compounds. The class olefins subsumes alkenes and cycloalkenes and the corresponding polyenes. [5] Oligomer - A substance consisting of molecules of intermediate relative molecular mass (molecular weight), the structure of which essentially comprises the multiple repetition of units derived, actually or conceptually, from molecules of low relative molecular mass. In contrast to a polymer, the properties of an oligomer can vary significantly with the removal of one or a few of its units. [8] Oligopeptides - Peptides containing from three to nine amino groups. [5] Onsager relations - An important set of equations in the thermodynamics of irreversible processes. They express the symmetry between the transport coefficients describing reciprocal processes in systems with a linear dependence of flux on driving forces. Optical rotary power - Angle by which the plane of polarization of a light beam is rotated by an optically active medium, divided by path length and by concentration of the active constituent. Depending on whether mass or molar concentration is used, the modifier "specific" or "molar" is attached. [2] Orbital - A one-electron wavefunction. Atomic orbitals are classified as s-, p-, d-, or f-orbitals according to whether the angular momentum quantum number l = 0, 1, 2, or 3. Molecular orbitals, which are usually constructed as linear combinations of atomic orbitals, describe the distribution of electrons over the entire molecule. Oscillator strength (f) - A measure of the intensity of a spectroscopic transition, defined by f= 8 2 me v 3he
The CNDOL Fockian with the configuration interaction of single excited wave functions to model the exciton properties of large molecular systems for photovoltaic devices
Published in Molecular Physics, 2023
Yoana Pérez-Badell, Luis A. Montero-Cabrera
The meanings of the terms are PA and PB are the total electron densities of valence orbitals in atoms A and B, respectively as pμν is the one-electron density involving atomic orbitals μand ν.Z is the Coulomb electron interaction term corresponding to atomic orbitals of azimuthal quantum numbers l and k in atoms A and B, respectively.− Iμ and Aμ are the valence state ionisation potential and electron affinities, respectively, of the μ Slater atomic orbital as taken from Hinze and Jaffe [41]. − ZA is the number of valence electrons or ‘core charge’ of atom A.− Z is the interaction energy of an electron in an l atomic orbital of atom A with respect to the core charge of atom B.− Z depends on the Sμν overlap integral of μ and ν Slater atomic orbitals.
Bio-conjugated N-(2-hydroxy-1-naphthaldehyde)-glucosamine Cu(II) complex: Bacterial sensitivity and superoxide dismutase-like activity
Published in Journal of Coordination Chemistry, 2018
Jan Mohammad Mir, Deepak Kumar Rajak, Ram Charitra Maurya
The natural atomic charge is based on the theory of the natural population analysis. The analysis is carried out with NBOs. They are linear combinations of the natural atomic orbitals. The derivation of a valence-shell atomic orbital (NAO) involves diagonalization of the localized block of the full density matrix of a given molecule associated with basic functions on that atom. A distinguishing feature of NAOs is that they meet the simultaneous requirement of orthonormality and maximum occupancy. In a polyatomic molecule, the NAOs mostly retain one-center character, and, thus, they are optimal for describing the molecular electron density around each atomic center. NBOs are linear combinations of the NAOs of two bonded atoms. Moreover, Koopman’s theorem helps to depict a hardness-softness including absolute electronegativity (χabs), absolute hardness (η) from the energy of the frontier orbitals in term of ionization energies (I.E.) and electron affinities (E.A). The respective data for (2-hnd-glsH2) and its complex may be arrived by following the theorem and are given in Table 4. Hard molecules have a large HOMO-LUMO gap, and soft molecules have a small HOMO-LUMO gap. The absolute electronegativity (χabs), absolute hardness (η) can be used to establish the biological relation of a compound.
Photoinduced relaxation dynamics of nitrogen-capped silicon nanoclusters: a TD-DFT study
Published in Molecular Physics, 2018
Xiang-Yang Liu, Xiao-Ying Xie, Wei-Hai Fang, Ganglong Cui
There are several different analysis methods having already been used to examine excited-state characters, intramolecular and intermolecular electron or energy transfers of complex systems in particular those donor-acceptor and dendrimers systems. One of the most popular methods is analysing the one-electron transition density matrices, which can be implemented in different atomic orbital (AO) representations. For example, Lischka and Plasser use the common nonorthogonal AOs [80]. Differently, Lan and co-workers use the orthogonalised Löwdin's AOs [101]. In this work, we have implemented the analysis method by Lan et al. [101].