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Slater Orbitals
Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method. They are named after the physicist John C. Slater, who introduced them in 1930. They possess exponential decay at long range and Kato's cusp condition at short range (when combined as hydrogen-like atom functions, i.e. the analytical solutions of the stationary Schrödinger equation for one electron atoms). Unlike the hydrogen-like ("hydrogenic") Schrödinger orbitals, STOs have no radial nodes (neither do Gaussian-type orbitals). Definition STOs have the following radial part: : R(r) = N r^ e^\, where * is a natural number that plays the role of principal quantum number, = 1,2,..., * is a normalizing constant, * is the distance of the electron from the atomic nucleus, and * \zeta is a constant related to the effective charge of the nucleus, the nuclear charge being partly shielded by electrons. Historically, the effective nuclear charge was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Orbital
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. The term ''atomic orbital'' may also refer to the physical region or space where the electron can be calculated to be present, as predicted by the particular mathematical form of the orbital. Each orbital in an atom is characterized by a set of values of the three quantum numbers , , and , which respectively correspond to the electron's energy, angular momentum, and an angular momentum vector component (magnetic quantum number). Alternative to the magnetic quantum number, the orbitals are often labeled by the associated harmonic polynomials (e.g., ''xy'', ). Each such orbital can be occupied by a maximum of two electrons, each with its own projection of spin m_s. The simple names s orbital, p orb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - bi. The complex conjugate of z is often denoted as \overline or z^*. In polar form, the conjugate of r e^ is r e^. This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a^2 + b^2 (or r^2 in polar coordinates). If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root. Notation The complex conjugate of a complex number z is written as \overline z or z^*. The first notation, a vinculum, avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred in physics, where dagger (†) is used for the conjugate tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Physics B
The ''Journal of Physics B: Atomic, Molecular and Optical Physics'' is a biweekly peer-reviewed scientific journal published by IOP Publishing. It was established in 1968 from the division of the earlier title, ''Proceedings of the Physical Society''. In 2006, the '' Journal of Optics B: Quantum and Semiclassical Optics'' was merged with the ''Journal of Physics B''. The editor-in-chief is Marc Vrakking (Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy). Scope The journal covers research on atomic, molecular, and optical physics. Topics include atomic and molecular structure, spectra and collisions, ultracold matter, quantum optics and non linear optics, quantum information, laser physics, intense laser fields, ultrafast and x-ray physics and atomic and molecular physics in plasmas. The journal publishes research papers, fast track communications, topical reviews, tutorials, and invited articles. It occasionally publishes special issues on developing resea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Data And Nuclear Data Tables
''Atomic Data and Nuclear Data Tables'' is a quarterly peer-reviewed scientific journal covering nuclear physics. It is published by Elsevier and was established in 1969. The journal was established with the aid of Katharine Way, who later served as its editor until 1973. As of 2016, Boris Pritychenko is the journal's editor-in-chief. Abstracting and indexing The journal is abstracted and indexed in: *Chemical Abstracts Service *Current Contents/Physics, Chemical, & Earth Sciences *Energy Research Abstracts *Science Citation Index *Scopus According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 2.623. References ;Bibliography * External links * Elsevier academic journals Nuclear physics journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Chemical Physics
''The Journal of Chemical Physics'' is a scientific journal published by the American Institute of Physics that carries research papers on chemical physics."About the Journal" from the ''Journal of Chemical Physics'' website. Two volumes, each of 24 issues, are published annually. It was established in 1933 when '''' editors refused to publish theoretical works. The editors have been: *2019-present: Tim Lian *2008–2018: *2007–2008: [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basis Set (chemistry)
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or 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 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 quantum chemistry community; plane waves which are typically used within the solid state community, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GAUSSIAN
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymous adjective ''Gaussian'' is pronounced . Mathematics Algebra and linear algebra Geometry and differential geometry Number theory Cyclotomic fields *Gaussian period *Gaussian rational *Gauss sum, an exponential sum over Dirichlet characters ** Elliptic Gauss sum, an analog of a Gauss sum **Quadratic Gauss sum Analysis, numerical analysis, vector calculus and calculus of variations Complex analysis and convex analysis *Gauss–Lucas theorem *Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions * Gauss's criterion – described oEncyclopedia of Mathematics* Gauss's hypergeometric theorem, an identity on hypergeometric series *Gauss plane Statistics *Gauss–Kuzmi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert F
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and '' berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warren
A warren is a network of wild rodent or lagomorph, typically rabbit burrows. Domestic warrens are artificial, enclosed establishment of animal husbandry dedicated to the raising of rabbits for meat and fur. The term evolved from the medieval Anglo-Norman concept of free warren, which had been, essentially, the equivalent of a hunting license for a given woodland. Architecture of the domestic warren The cunicularia of the monasteries may have more closely resembled hutches or pens, than the open enclosures with specialized structures which the domestic warren eventually became. Such an enclosure or ''close'' was called a ''cony-garth'', or sometimes ''conegar'', ''coneygree'' or "bury" (from "burrow"). Moat and pale To keep the rabbits from escaping, domestic warrens were usually provided with a fairly substantive moat, or ditch filled with water. Rabbits generally do not swim and avoid water. A ''pale'', or fence, was provided to exclude predators. Pillow mounds The most c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Pople
Sir John Anthony Pople (31 October 1925 – 15 March 2004) was a British theoretical chemist who was awarded the Nobel Prize in Chemistry with Walter Kohn in 1998 for his development of computational methods in quantum chemistry. Early life and education Pople was born in Burnham-on-Sea, Somerset, and attended the Bristol Grammar School. He won a scholarship to Trinity College, Cambridge, in 1943. He received his Bachelor of Arts degree in 1946. Between 1945 and 1947 he worked at the Bristol Aeroplane Company. He then returned to the University of Cambridge and was awarded his PhD in mathematics in 1951 on lone pair electrons. Career After obtaining his PhD, he was a research fellow at Trinity College, Cambridge and then from 1954 a lecturer in the mathematics faculty at Cambridge. In 1958, he moved to the National Physical Laboratory, near London as head of the new basics physics division. He moved to the United States of America in 1964, where he lived the rest of hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Journal Of Quantum Chemistry
The ''International Journal of Quantum Chemistry'' is a peer-reviewed scientific journal publishing original, primary research and review articles on all aspects of quantum chemistry, including an expanded scope focusing on aspects of materials science, biochemistry, biophysics, quantum physics, quantum information theory, etc. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 2.444. It was established in 1967 by Per-Olov Löwdin Per-Olov Löwdin (October 28, 1916 – October 6, 2000) was a Swedish physicist, professor at the University of Uppsala from 1960 to 1983, and in parallel at the University of Florida until 1993. A former graduate student under Ivar Waller, Löwd .... In 2011, the journal moved to an in-house editorial office model, in which a permanent team of full-time, professional editors is responsible for article scrutiny and editorial content. References External links * Chemistry journals Publications established ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1s Slater-type Function
A normalized 1s Slater-type function is a function which is used in the descriptions of atoms and in a broader way in the description of atoms in molecules. It is particularly important as the accurate quantum theory description of the smallest free atom, hydrogen. It has the form :\psi_(\zeta, \mathbf) = \left(\frac\right)^ \, e^. It is a particular case of a Slater-type orbital (STO) in which the principal quantum number n is 1. The parameter \zeta is called the Slater orbital exponent. Related sets of functions can be used to construct STO-nG basis sets which are used in quantum chemistry. Applications for hydrogen-like atomic systems A hydrogen-like atom or a hydrogenic atom is an atom with one electron. Except for the hydrogen atom itself (which is neutral) these atoms carry positive charge e(\mathbf Z-1), where \mathbf Z is the atomic number of the atom. Because hydrogen-like atoms are two-particle systems with an interaction depending only on the distance between t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
