|
Electron Localization Function
In quantum chemistry, the electron localization function (ELF) is a measure of the likelihood of finding an electron in the neighborhood space of a reference electron located at a given point and with the same spin. Physically, this measures the extent of spatial localization of the reference electron and provides a method for the mapping of electron pair probability in multielectronic systems. ELF's usefulness stems from the observation that it allows electron localization to be analyzed in a chemically intuitive way. For example, the shell structure of heavy atoms is obvious when plotting ELF against the radial distance from the nucleus; the ELF for radon has six clear maxima, whereas the electronic density decreases monotonically and the radially weighted density fails to show all shells. When applied to molecules, an analysis of the ELF shows a clear separation between the core and valence electron, and also shows covalent bonds and lone pairs, in what has been called "a fai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Localization Function Of Kr (HF Cc-pV5Z)
The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's Invariant mass, mass is approximately Proton-to-electron mass ratio, 1/1836 that of the proton. Quantum mechanics, Quantum mechanical properties of the electron include an intrinsic angular momentum (spin (physics), spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of wave-particle duality, both particles and waves: They can collide with other particles and can be electron diffraction, diffracted like light. The #Quantum properties, wave ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Orbital
In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms ''atomic orbital'' and ''molecular orbital'' were introduced by Robert S. Mulliken in 1932 to mean ''one-electron orbital wave functions''. At an elementary level, they are used to describe the ''region'' of space in which a function has a significant amplitude. In an isolated atom, the orbital electrons' location is determined by functions called atomic orbitals. When multiple atoms combine chemically into a molecule, the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an approximate solution to the Schrödin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Bader
Richard F. W. Bader (October 15, 1931 – January 15, 2012) was a Canadian quantum chemist, noted for his work on the Atoms in molecules theory. This theory attempts to establish a physical basis for many of the working concepts of chemistry, such as atoms in molecules and bonding, in terms of the topology of the electron density function in three-dimensional space. Alongside the eminent chemist Ronald Gillespie, he had a significant influence on inorganic chemistry education in Canada. He was born in 1931 in Kitchener, Ontario, Canada. His parents were Albert Bader and Alvina Bader, who immigrated from Switzerland. His father was a butcher at Burns Pride of Canada and his mother was a housekeeper at Kitchener Hospital of Waterloo. He received a scholarship from McMaster University that allowed him to earn a BSC in 1953. His father was his best supporter who encouraged him and taught him to "never quit" his education and his dream. He finished his master's degree in science a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Topology
In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which concerns the ''geometric'' properties of smooth manifolds, including notions of size, distance, and rigid shape. By comparison differential topology is concerned with coarser properties, such as the number of holes in a manifold, its homotopy type, or the structure of its diffeomorphism group. Because many of these coarser properties may be captured algebraically, differential topology has strong links to algebraic topology. The central goal of the field of differential topology is the classification of all smooth manifolds up to diffeomorphism. Since dimension is an invariant of smooth manifolds up to diffeomorphism type, this classification is often studied by classifying the (connected) manifolds in each dimension separately: * In di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andreas Savin
Andreas ( el, Ἀνδρέας) is a name usually given to males in Austria, Greece, Cyprus, Denmark, Armenia, Estonia, Ethiopia, Eritrea, Finland, Flanders, Germany, Norway, Sweden, Switzerland, Romania, the Netherlands, and Indonesia. The name derives from the Greek language, Greek noun ἀνήρ ''anēr'', with genitive ἀνδρός ''andros'', which means "man". See the article on ''Andrew'' for more information. The Scandinavian name is earliest attested as antreos in a runestone from the 12th century. The name Andrea may be used as a feminine form, but is instead the main masculine form in Italy and the canton of Ticino in Switzerland. Given name Andreas is a common name, and this is not a comprehensive list of articles on people named Andreas. See instead . Surname * Alfred T. Andreas, American publisher and historian * Casper Andreas (born 1972), American actor and film director * Dwayne Andreas, a businessman * Harry Andreas * Lisa Andreas Places *Andreas, Isle of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Functional Theory
Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Electron Gas
Jellium, also known as the uniform electron gas (UEG) or homogeneous electron gas (HEG), is a quantum mechanical model of interacting electrons in a solid where the positive charges (i.e. atomic nuclei) are assumed to be uniformly distributed in space; the electron density is a uniform quantity as well in space. This model allows one to focus on the effects in solids that occur due to the quantum nature of electrons and their mutual repulsive interactions (due to like charge) without explicit introduction of the Crystal lattice, atomic lattice and structure making up a real material. Jellium is often used in solid-state physics as a simple model of delocalized electrons in a metal, where it can qualitatively reproduce features of real metals such as Electric-field screening, screening, plasmons, Wigner crystallization and Friedel oscillations. At zero temperature, the properties of jellium depend solely upon the constant electronic density. This property lends it to a treatment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin (,, ...). Every observed subatomic particle is either a boson or a fermion. Bosons are named after physicist Satyendra Nath Bose. Some bosons are elementary particles and occupy a special role in particle physics unlike that of fermions, which are sometimes described as the constituents of "ordinary matter". Some elementary bosons (for example, gluons) act as force carriers, which give rise to forces between other particles, while one (the Higgs boson) gives rise to the phenomenon of mass. Other bosons, such as mesons, are composite particles made up of smaller constituents. Outside the realm of particle physics, superfluidity arises because composite bosons (bose particles), such as low temperature helium-4 atoms, follow Bose–E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Density
In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either \rho(\textbf r) or n(\textbf r). The density is determined, through definition, by the normalised N-electron wavefunction which itself depends upon 4N variables (3N spatial and N Spin (physics), spin coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of density functional theory. According to quantum mechanics, due to the uncertainty principle on an atomic scale the exact location of an electron cannot be predicted, only the probability of its being at a given position; therefore electrons in atoms and molecules act as if they are "smeared out" in space. For one-electron systems, the electron density at any point is pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.png "Click for more on -> Electron Localization Function")
