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Multi-configurational Self-consistent Field
Multi-configurational self-consistent field (MCSCF) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground states which are quasi-degenerate with low-lying excited states or in bond-breaking situations). It uses a linear combination of configuration state functions (CSF), or configuration determinants, to approximate the exact electronic wavefunction of an atom or molecule. In an MCSCF calculation, the set of coefficients of both the CSFs or determinants and the basis functions in the molecular orbitals are varied to obtain the total electronic wavefunction with the lowest possible energy. This method can be considered a combination between configuration interaction (where the molecular orbitals are not varied but the expansion of the wave function is) and Hartree–Fock (where there is only one determinant, but the molecular orbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of Molecule, molecules, Material, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed Wave function, wave functions as well as to observable properties such as structures, spectra, and Thermodynamics, thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics. Chemists rely heavily on spectroscopy through which information regarding the Quantization (physics), quantization of energy on a molecular scale can be obtained ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Bond
A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds, or some combination of these effects. Chemical bonds are described as having different strengths: there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force, and hydrogen bonding. Since opposite electric charges attract, the negatively charged electrons surrounding the nucleus and the positively charged protons within a nucleus attract each other. Electrons shared between two nuclei will be attracted to both of them. "Constructive quantum mechanical wavefunction interference" stabilizes the paired nuclei (see Theories of chemical bonding). Bonded nuclei maintain an optima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hartree–Fock Method
In computational physics and chemistry, the Hartree–Fock (HF) method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system in a stationary state. The method is named after Douglas Hartree and Vladimir Fock. The Hartree–Fock method often assumes that the exact ''N''-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of ''N'' spin-orbitals. By invoking the variational method, one can derive a set of ''N''-coupled equations for the ''N'' spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system. Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations in order parameter allows interaction terms to be replaced with quadratic terms, obtaining exactly solvable Hamiltonians. Especially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yakov Frenkel
__NOTOC__ Yakov Il'ich Frenkel (; 10 February 1894 – 23 January 1952) was a Soviet physicist renowned for his works in the field of condensed-matter physics. He is also known as Jacob Frenkel, frequently using the name J. Frenkel in publications in English. Early years He was born to a Jewish family in Rostov on Don, in the Don Host Oblast of the Russian Empire on 10 February 1894. His father was involved in revolutionary activities and spent some time in internal exile to Siberia; after the danger of pogroms started looming in 1905, the family spent some time in Switzerland, where Yakov Frenkel began his education. In 1912, while studying in the Karl May Gymnasium in St. Petersburg, he completed his first physics work on the Earth's magnetic field and atmospheric electricity. This work attracted Abram Ioffe's attention and later led to collaboration with him. He considered moving to the USA (which he visited in the summer of 1913, supported by money hard-earned by tutoring ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Fock
Vladimir Aleksandrovich Fock (or Fok; ) (December 22, 1898 – December 27, 1974) was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics. Biography He was born in St. Petersburg, Russia. In 1922 he graduated from Petrograd University, then continued postgraduate studies there. He became a professor there in 1932. In 1919–1923 and 1928–1941 he collaborated with the Vavilov State Optical Institute, in 1924–1936 with the Leningrad Institute of Physics and Technology, in 1934–1941 and 1944–1953 with the Lebedev Physical Institute. Scientific work His primary scientific contribution lies in the development of quantum physics and the theory of gravitation, although he also contributed significantly to the fields of mechanics, theoretical optics, and physics of continuous media. In 1926, he derived the Klein–Gordon equation. He gave his name to Fock space, the Fock representation and Fock st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Hartree
Douglas Rayner Hartree (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree–Fock equations of atomic physics and the construction of a differential analyser using Meccano. Early life and education Douglas Hartree was born in Cambridge, England. His father, William, was a lecturer in engineering at the University of Cambridge. His mother, Eva Rayner, was president of the National Council of Women of Great Britain and first woman to be mayor of the city of Cambridge. One of his great-grandfathers was Samuel Smiles; another was the marine engineer William Hartree, partner of John Penn. Douglas Hartree was the oldest of three sons who survived infancy. A brother and sister died in infancy when he was still a child, but his two brothers would later also die. Hartree's 7-year-old brother John Edwin died when Hartree was 17, and Hartree's 22-year-old broth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charlotte Froese Fischer
Charlotte Froese Fischer (September 21, 1929 – February 8, 2024) was a Canadian-American applied mathematician, computer scientist and physicist noted for the development and implementation of the Multi-Configurational Hartree–Fock (MCHF) approach to atomic-structure calculations and its application to the description of atomic structure and spectra. The experimental discovery of the negative ion of calcium was motivated by her theoretical prediction of its existence. This was the first known anion of a Group 2 element. Its discovery was cited in Froese Fischer's election to Fellow of the American Physical Society. Early life Charlotte Froese was born on September 21, 1929, in the village of Stara Mykolaivka (formerly Pravdivka, and Nikolayevka), in the Donetsk region, in the present-day Ukraine, to parents of Mennonite descent. Her parents immigrated to Germany in 1929 on the last train allowed to cross the border before its closure by Soviet authorities. After a few mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Cost
A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computation are mathematical equation solving and the execution of computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. Computer science is an academic field that involves the study of computation. Introduction The notion that mathematical statements should be 'well-defined' had been argued by mathematicians since at least the 1600s, but agreement on a suitable definition proved elusive. A candidate definition was proposed independently by several mathematicians in the 1930s. The best-known variant was formalised by the mathematician Alan Turing, who defined a well-defined statement or calculation as any statement that could be expressed in terms of the initialisation parameters of a Turing machine. Other (mathematically equivalent) definitions include Alonzo Church's '' lambda-definabil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nitric Oxide
Nitric oxide (nitrogen oxide, nitrogen monooxide, or nitrogen monoxide) is a colorless gas with the formula . It is one of the principal oxides of nitrogen. Nitric oxide is a free radical: it has an unpaired electron, which is sometimes denoted by a dot in its chemical formula (•N=O or •NO). Nitric oxide is also a heteronuclear diatomic molecule, a class of molecules whose study spawned early modern theories of chemical bonding. An important intermediate in industrial chemistry, nitric oxide forms in combustion systems and can be generated by lightning in thunderstorms. In mammals, including humans, nitric oxide is a signaling molecule in many physiological and pathological processes. It was proclaimed the " Molecule of the Year" in 1992. The 1998 Nobel Prize in Physiology or Medicine was awarded for discovering nitric oxide's role as a cardiovascular signalling molecule. Its impact extends beyond biology, with applications in medicine, such as the development of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Active Space
In quantum chemistry, a complete active space is a type of classification of molecular orbitals. Spatial orbitals are classified as belonging to three classes: * ''core'', always hold two electrons * ''active'', partially occupied orbitals * ''virtual'', always hold zero electrons This classification allows one to develop a set of Slater determinants for the description of the wavefunction as a linear combination of these determinants. Based on the freedom left for the occupation in the active orbitals, a certain number of electrons are allowed to populate all the active orbitals in appropriate combinations, developing a finite-size space of determinants. The resulting wavefunction is of multireference nature, and is blessed by additional properties if compared to other selection schemes. The active classification can theoretically be extended to all the molecular orbitals, to obtain a full CI treatment. In practice, this choice is limited, due to the high computational cost ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Coulson
Charles Alfred Coulson (13 December 1910 – 7 January 1974) was a British applied mathematician and theoretical chemist. Coulson's major scientific work was as a pioneer of the application of the quantum theory of valency to problems of molecular structure, dynamics and reactivity. He was also a Methodist lay preacher, served on the World Council of Churches from 1962 to 1968, and was chairman of Oxfam from 1965 to 1971. Early life The parents of Charles Coulson and his younger twin brother John Metcalfe Coulson were educators who hailed from the Midlands. The twins were born when their father, Alfred, was principal of Dudley Technical College and superintendent of the Methodist Sunday School, and their mother Annie Sincere Hancock was Headmistress of Tipton Elementary School, close by. Coulson's parents maintained a religious Methodist home. When the Coulson brothers were 10, their father was appointed Superintendent of Technical Colleges for the South-West of Engla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Set (chemistry)
In theoretical chemistry, theoretical and computational chemistry, a basis set is a set of Function (mathematics), functions (called basis functions) that is used to represent the Wave function, electronic wave function in the Hartree–Fock method or Density functional theory, density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer. The use of basis sets is equivalent to the use of an approximate resolution of the identity: the Atomic orbital, orbitals , \psi_i\rangle are expanded within the basis set as a linear combination of the basis functions , \psi_i\rangle \approx \sum_\mu c_ , \mu\rangle, where the expansion coefficients c_ are given by c_ = \sum_\nu \langle \mu, \nu \rangle^ \langle \nu , \psi_i \rangle. The basis set can either be composed of atomic orbitals (yielding the linear combination of atomic orbitals approach), which is the usual choice within the qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
