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B3LYP Functional
Hybrid functionals are a class of approximations to the exchange–correlation energy functional in density functional theory (DFT) that incorporate a portion of exact exchange from Hartree–Fock theory with the rest of the exchange–correlation energy from other sources ('' ab initio'' or empirical). The exact exchange energy functional is expressed in terms of the Kohn–Sham orbitals rather than the density, so is termed an ''implicit'' density functional. One of the most commonly used versions is B3LYP, which stands for " Becke, 3-parameter, Lee–Yang– Parr". Origin The hybrid approach to constructing density functional approximations was introduced by Axel Becke in 1993. Hybridization with Hartree–Fock (HF) exchange (also called exact exchange) provides a simple scheme for improving the calculation of many molecular properties, such as atomization energies, bond lengths and vibration frequencies, which tend to be poorly described with simple "ab initio" func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exchange Interaction
In chemistry and physics, the exchange interaction (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier. The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing sign (antisymmetric) when two particles are exchanged. Both bosons and fermions can experience the exchange interaction. For fermions, this interaction is sometimes called Pauli repulsion and is related to the Pauli exclusion principle. For bosons, the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation. The exchange interaction alters the expectation value of the distance when the wave functions of two or more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axel Becke
Axel Dieter Becke (born June 10, 1953) is a physical chemist and Professor of Chemistry at Dalhousie University, Canada. He is a leading researcher in the application of density functional theory (DFT) to molecules. Early life Becke was born in Esslingen, Germany. He graduated with a B.Sc. from Queen's University. He completed his M.Sc. and Ph.D. from McMaster University. Academic career From 1981 to 1983, Becke was a NSERC Postdoctoral Fellow at Dalhousie University. He took up his first faculty position at Queen's University in Kingston, Ontario in the 1980s. In 2006, he relocated to Dalhousie University to serve as the Killam Chair in Computational Science. Research Becke contributed in the development of non-LCAO, grid-based numerical methodologies for molecular orbital calculations. He was also contributed in the development and benchmarking of exchange-correlation functionals in Kohn-Sham density-functional theory. He is known for his highly cited work on the den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a complex function of a complex variable defined as: :\operatorname z = \frac\int_0^z e^\,\mathrm dt. This integral is a special (non-elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real. In statistics, for non-negative values of , the error function has the following interpretation: for a random variable that is normally distributed with mean 0 and standard deviation , is the probability that falls in the range . Two closely related functions are the complementary error function () defined as :\operatorname z = 1 - \operatorname z, and the imaginary error function () defined as :\operatorname z = -i\operatorname iz, where is the imaginary unit Name The name "error function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local-density Approximation
Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT) that depend solely upon the value of the electronic density at each point in space (and not, for example, derivatives of the density or the Kohn–Sham orbitals). Many approaches can yield local approximations to the XC energy. However, overwhelmingly successful local approximations are those that have been derived from the homogeneous electron gas (HEG) model. In this regard, LDA is generally synonymous with functionals based on the HEG approximation, which are then applied to realistic systems (molecules and solids). In general, for a spin-unpolarized system, a local-density approximation for the exchange-correlation energy is written as :E_^rho= \int \rho(\mathbf)\epsilon_(\rho(\mathbf))\ \mathrm\mathbf\ , where ''ρ'' is the electronic density and ''ε''xc is the exchange-correlation energy per particle of a homogeneous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Gradient Approximation
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. Compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infrared Spectroscopy
Infrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functional groups in solid, liquid, or gaseous forms. It can be used to characterize new materials or identify and verify known and unknown samples. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer (or spectrophotometer) which produces an infrared spectrum. An IR spectrum can be visualized in a graph of infrared light absorbance (or transmittance) on the vertical axis vs. frequency, wavenumber or wavelength on the horizontal axis. Typical units of wavenumber used in IR spectra are reciprocal centimeters, with the symbol cm−1. Units of IR wavelength are commonly given in micrometers (formerly called "microns"), symbol μm, which are related to the wavenumber in a reciprocal way. A com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bond Length
In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule. Explanation Bond length is related to bond order: when more electrons participate in bond formation the bond is shorter. Bond length is also inversely related to bond strength and the bond dissociation energy: all other factors being equal, a stronger bond will be shorter. In a bond between two identical atoms, half the bond distance is equal to the covalent radius. Bond lengths are measured in the solid phase by means of X-ray diffraction, or approximated in the gas phase by microwave spectroscopy. A bond between a given pair of atoms may vary between different molecules. For example, the carbon to hydrogen bonds in methane are different from those in methyl chloride. It is however possible to make generalizations when ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enthalpy Of Atomization
In chemistry, the enthalpy of atomization (also atomisation in British English) is the enthalpy change that accompanies the total separation of all atoms in a chemical substance (either an element or a compound). This is often represented by the symbol or All bonds in the compound are broken in atomization and none are formed, so enthalpies of atomization are always positive. The associated standard enthalpy is known as the standard enthalpy of atomization, /( kJ mol−1), at 298.15 K (or 25 degrees Celsius) and 100 kPa. Definition Enthalpy of atomization is the amount of enthalpy change when a compound's bonds are broken and the component atoms are separated into single atoms( or monoatom ). Enthalpy of atomization is denoted by the symbol Δat''H''. The enthalpy change of atomization of gaseous H2O is, for example, the sum of the HO–H and H–OH bond dissociation enthalpies. The enthalpy of atomization of an elemental solid is exactly the same as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Parr
Robert Ghormley Parr (September 22, 1921 – March 27, 2017) was an American theoretical chemist who was a Professor of Chemistry at the University of North Carolina at Chapel Hill. Career Parr received an A. B. degree ''magna cum laude'' from Brown University in 1942, and then entered the University of Minnesota, receiving a Ph.D. in physical chemistry in 1947. He joined the faculty at Minnesota upon receiving his Ph.D. and remained there one year. In 1948 he moved to the Carnegie Institute of Technology (now Carnegie Mellon University) in Pittsburgh, Pennsylvania, becoming a full professor in 1957. In 1962 he moved to Johns Hopkins University in Baltimore, Maryland, and in 1974 to the University of North Carolina at Chapel Hill, where he received appointment to an endowed professorship in 1990 and where he last taught. Achievements and awards Working with DuPont chemist Rudolph Pariser, Parr developed a method of computing approximate molecular orbitals for pi e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Atomic and molecular systems Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants. The single-determinant approximation does not take into account Coulomb correlation, leading to a total electronic energy different from the exact solution of the non-relativistic Schrödinger equation within the Born–Oppenheimer approximation. Therefore, the Hartree–Fock limit is always above this exact energy. The difference is called the ''correlation energy'', a term coined by Löwdin. The concept of the correlation energy was studied earlier by Wigner. A certain amount of electron cor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weitao Yang
Weitao Yang (; born March 31, 1961) is a Chinese-born American chemist who is the Philip Handler Professor of Chemistry at Duke University. His main contributions to chemistry include density functional theory development, and its applications to chemistry. Biography Yang was born in Chaozhou, Guangdong, China on March 31, 1961. He entered Peking University in 1978 as part of the first generation of college students after the Cultural Revolution. He received his BS in chemistry in 1982, after which he studied theoretical chemistry as a PhD student with Robert G. Parr at the University of North Carolina, Chapel Hill. He completed his PhD degree in 1986, and worked as a postdoc with Robert G. Parr (1986-1987) and William H. Miller (1988-1989). Yang currently works in the Department of Chemistry at Duke University since 1990, as Assistant Professor, Associate Professor, Professor, and Philip Handler Professor of Chemistry. Contributions Yang's main contributions to theoretical che ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
