|
Non-covalent Interactions Index
The Non-Covalent Interactions index, commonly referred to as simply Non-Covalent Interactions (NCI) is a visualization index based in the Electron density (ρ) and the reduced density gradient (s). It is based on the empirical observation that Non-covalent interactions can be associated with the regions of small reduced density gradient at low electronic densities. In quantum chemistry, the non-covalent interactions index is used to visualize non-covalent interactions in three-dimensional space. Its visual representation arises from the isosurfaces of the reduced density gradient colored by a scale of strength. The strength is usually estimated through the product of the electron density and the second eigenvalue (λ) of the Hessian of the electron density in each point of the isosurface, with the attractive or repulsive character being determined by the sign of λ. This allows for a direct representation and characterization of non-covalent interactions in three-dimensional spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Water Molecules Cluster
3 is a number, numeral, and glyph. 3, three, or III may also refer to: * AD 3, the third year of the AD era * 3 BC, the third year before the AD era * March, the third month Books * ''Three of Them'' (Russian: ', literally, "three"), a 1901 novel by Maksim Gorky * ''Three'', a 1946 novel by William Sansom * ''Three'', a 1970 novel by Sylvia Ashton-Warner * ''Three'' (novel), a 2003 suspense novel by Ted Dekker * ''Three'' (comics), a graphic novel by Kieron Gillen. * ''3'', a 2004 novel by Julie Hilden * ''Three'', a collection of three plays by Lillian Hellman * ''Three By Flannery O'Connor'', collection Flannery O'Connor bibliography Brands * 3 (telecommunications), a global telecommunications brand ** 3Arena, indoor amphitheatre in Ireland operating with the "3" brand ** 3 Hong Kong, telecommunications company operating in Hong Kong ** Three Australia, Australian telecommunications company ** Three Ireland, Irish telecommunications company ** Three UK, British telecom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Six Water Molecules Cluster
6 is a number, numeral, and glyph. 6 or six may also refer to: * AD 6, the sixth year of the AD era * 6 BC, the sixth year before the AD era * The month of June Science * Carbon, the element with atomic number 6 * 6 Hebe, an asteroid People * Alphonse Six (1890–1914), Belgian football player * Didier Six (born 1954), former French international footballer * Franz Six (1909–1975), Nazi official * Frederick N. Six (born 1929), Justice of the Kansas Supreme Court * James Six (1731–1793), British scientist * Jan Six (1616-1700), an important cultural figure in the Dutch Golden Age * Robert Six (1907–1986), Chief Executive Officer of Continental Airlines between 1936 and 1981 * Regine Sixt, German businessperson * Valérie Six (born 1963), French politician * Perri 6 (an extremely rare surname), social scientist * Six family, family of regents of Amsterdam, founded by Jan Six Music * Six (band), an Irish pop band created by a TV reality show * ''Six'' (musical), a musi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eight Water Molecules Cluster
8 is a number, numeral, and glyph. 8 or eight may also refer to: Years * AD 8, the eighth year of the AD era * 8 BC, the eighth year before the AD era Art *The Eight (Ashcan School), a group of twentieth century painters associated with the Ashcan School *The Eight (painters), an avant-garde art movement of Hungarian painters Motor vehicles *Bentley Eight, Bentley's "entry-level" offering from 1984 until 1992 *Leyland Eight, a luxury car produced by Leyland Motors from 1920 to 1923 *Mercury Eight, a first Post War Mercury car design *Morris Eight, a small car inspired by the Ford Model Y *Standard Eight, a small car produced by Standard Motor Company 1938–59 *Wolseley Eight, a four-door, light saloon car produced by Wolseley Motors Limited from 1946 to 1948 *Straight eight, automobile engine *Eight cylinder, automobile engine Sports *Eight (rowing), rowing boat used in the sport of competitive rowing *Figure 8 (belay device), rock climbing equipment also known as an "eight ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron 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 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 proportional to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-covalent Interactions
In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/ mol (1000–5000 calories per 6.02 molecules). Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects. Non-covalent interactions are critical in maintaining the three-dimensional structure of large molecules, such as proteins and nucleic acids. In addition, they are also involved in many biological processes in which large molecules bind specifically but transiently to one another (see the properties section of the DNA page). These interactions also heavily influence drug design, crystallinity and design of materials, particularly f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". Definitions and properties Suppose f : \R^n \to \R is a function taking as input a vector \mathbf \in \R^n and outputting a scalar f(\mathbf) \in \R. If all second-order partial derivatives of f exist, then the Hessian matrix \mathbf of f is a square n \times n matrix, usually defined and arranged as follows: \mathbf H_f= \begin \dfrac & \dfrac & \cdots & \dfrac \\ .2ex \dfrac & \dfrac & \cdots & \dfrac \\ .2ex \vdots & \vdots & \ddots & \vdots \\ .2ex \dfrac & \dfrac & \cdots & \dfrac \end, or, by stating an equation for the coefficients using indices i and j, (\mathbf H_f)_ = \fra ... [...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] |
X-ray Scattering Techniques
X-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystal structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing the scattered intensity of an X-ray beam hitting a sample as a function of incident and scattered angle, polarization, and wavelength or energy. Note that X-ray diffraction is now often considered a sub-set of X-ray scattering, where the scattering is elastic and the scattering object is crystalline, so that the resulting pattern contains sharp spots analyzed by X-ray crystallography (as in the Figure). However, both scattering and diffraction are related general phenomena and the distinction has not always existed. Thus Guinier's classic text from 1963 is titled "X-ray diffraction in Crystals, Imperfect Crystals and Amorphous Bodies" so 'diffraction' was clearly not restricted to crystals at that time. Scattering techniques Ela ... [...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] |
Fermi Energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band. The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi ''level'' (also called electrochemical potential).The use of the term "Fermi energy" as synonymous with Fermi level (a.k.a. electrochemical potential) is widespread in semiconductor physics. For example:''Electronics (fundamentals And Applications)''by D. Chattopadhyay''Semiconductor Physics and Applications''by Balkanski and Wallis. There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article: * The Fermi energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jellium
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 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 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 within density functional theory; the for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erin Johnson
Erin Johnson is a Canadian computational chemist. She holds the Herzberg–Becke Chair at Dalhousie University. She works on density functional theory and intermolecular interactions. Education and early career Johnson is from Ottawa, Canada. She completed her B.Sc. Hons. in Integrated Science (chemistry/mathematics) at Carleton University in 2004. She earned her PhD at Queen's University in 2007, working with Axel D. Becke. In 2006, they demonstrated a simple potential for exchange energies; the Becke–Johnson potential. She developed the exchange-hole dipole moment dispersion model (XDM), which describes intermolecular interactions. The model is a density functional model based on second-order perturbation theory, and uses the interaction of induced dipoles to model dispersion. Her PhD focussed on improving the accuracy and efficiency of computational chemistry. She was a Natural Sciences and Engineering Research Council postdoctoral fellow at Duke University with Yan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
