|
Modern Valence Bond Theory
Modern valence bond theory is the application of valence bond theory VBT with computer programs that are competitive in accuracy and economy with programs for the Hartree–Fock or post-Hartree-Fock methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997); Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004) While Molecular Orbital Theory OTdescribes the electronic wavefunction as a linear combination of basis functions that are centered on the various atoms in a species (Linear combination of atomic orbitals), VBT describes the electronic wavefunction as a linear combination of several valence bond struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valence Bond Theory
In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule. History Lothar Meyer in his 1864 book, ''Die modernen Theorien der Chemie'', contained an early version of the periodic table containing 28 elements, classified elements into six families by their valence—for the first time, elements had been grouped according to their valence. Works on organizing the elements by atomic weight, until then had been stymied by the widespread use of equivalent weights for the elements, rather than atomic weights. In 1916, G. N. Lewis proposed that a chemical bond forms by the interaction of two shared bonding electrons, with the repr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Configuration Interaction
Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a quantum chemical multi-electron system. Mathematically, ''configuration'' simply describes the linear combination of Slater determinants used for the wave function. In terms of a specification of orbital occupation (for instance, (1s)2(2s)2(2p)1...), ''interaction'' means the mixing (interaction) of different electronic configurations (states). Due to the long CPU time and large memory required for CI calculations, the method is limited to relatively small systems. In contrast to the Hartree–Fock method, in order to account for electron correlation, CI uses a variational wave function that is a linear combination of configuration state functions (CSFs) built from spin orbitals (denoted by the superscript ''SO''), : \Psi = \sum_ c_ \Phi_^ = c_0\Phi_0^ + c_1\Phi_1^ + where Ψ is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valence Bond Programs
Valence bond (VB) computer programs for modern valence bond calculations:- * CRUNCH, by Gordon A. Gallup and his group. * GAMESS (UK), includes calculation of VB wave functions by the TURTLE code, due to J.H. van Lenthe. * GAMESS (US), has links to interface VB2000, and XMVB. * MOLPRO and MOLCAS include code by David L. Cooper for generating Spin Coupled VB wave functions from CASSCF calculations. * VB2000 version 2.7 (released, 2014), by Jiabo Li, Brian Duke and Roy McWeeny allows the use of Group Function theory, whereby different groups can be handled by different methods (VB or Hartree–Fock). Many types of VB, including spin-coupled VB, and CASVB calculations are possible. It is part of the GAMESS (US) release and can be compiled into the GAMESS(US) executable. There is a more limited stand-alone program. Earlier versions were interfaced to GAUSSIAN. * XMVB (previously known as XIAMEN), by Lingchun Song, Yirong Mo, Qianer Zhang and Wei Wu. This allows several VB methods, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Method
The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as '' geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi, respectively). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin Function
Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally biased portrayal of something Spin, spinning or spinnin may also refer to: Physics and mathematics * Spin, the rotation of an object around a central axis * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin group, a particular double cover of the special orthogonal group SO(''n'') * Spin tensor, a tensor quantity for describing spinning motion in special relativity and general relativity * Spin (aerodynamics), autorotation of an aerodynamically stalled aeroplane * SPIN bibliographic database, an indexing and abstracting service focusing on physics research Textile arts * Spinning (polymers), a process for creating polymer fibres * Spinning (textiles), the creation of yarn or thread by twisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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) and Hartree–Fock (where there is only one determinant, but the molecular orbitals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Methane Ionization
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Earth makes it an economically attractive fuel, although capturing and storing it poses technical challenges due to its gaseous state under normal conditions for temperature and pressure. Naturally occurring methane is found both below ground and under the seafloor and is formed by both geological and biological processes. The largest reservoir of methane is under the seafloor in the form of methane clathrates. When methane reaches the surface and the atmosphere, it is known as atmospheric methane. The Earth's atmospheric methane concentration has increased by about 150% since 1750, and it accounts for 20% of the total radiative forcing from all of the long-lived and globally mixed greenhouse gases. It has also been detected on other pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koopmans' Theorem
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934. Koopmans' theorem is exact in the context of restricted Hartree–Fock theory if it is assumed that the orbitals of the ion are identical to those of the neutral molecule (the ''frozen orbital'' approximation). Ionization energies calculated this way are in qualitative agreement with experiment – the first ionization energy of small molecules is often calculated with an error of less than two electron volts. Therefore, the validity of Koopmans' theorem is intimately tied to the accuracy of the underlying Hartree–Fock wavefunction. The two main sources of error are orbital relaxation, which refers to the changes in the Fock operator and Hartree–Fock orbitals when cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photoemission Spectroscopy
Photoemission spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in the substance. The term refers to various techniques, depending on whether the ionization energy is provided by X-ray, XUV or UV photons. Regardless of the incident photon beam, however, all photoelectron spectroscopy revolves around the general theme of surface analysis by measuring the ejected electrons. Types X-ray photoelectron spectroscopy (XPS) was developed by Kai Siegbahn starting in 1957 and is used to study the energy levels of atomic core electrons, primarily in solids. Siegbahn referred to the technique as "electron spectroscopy for chemical analysis" (ESCA), since the core levels have small chemical shifts depending on the chemical environment of the atom that is ionized, allowing chemical structure to be determined. Siegbahn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Structure
Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the chemical bonding, bonding between atoms of a molecule, as well as the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as complex (chemistry), coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article ''The Atom and the Molecule.'' Lewis structures extend the concept of the electron dot diagram by adding lines between atoms to represent shared pairs in a chemical bond. Lewis structures show each atom and its position in the structure of the molecule using its chemical symbol. Lines are drawn between atoms that are bonded to one another (pairs of dots can be used instead of lines). Excess electrons that form lone pairs are represented as pairs of dots, and are placed next to the at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triplet Oxygen
Triplet oxygen, 3O2, refers to the ''S'' = 1 electronic ground state of molecular oxygen (dioxygen). It is the most stable and common allotrope of oxygen. Molecules of triplet oxygen contain two unpaired electrons, making triplet oxygen an unusual example of a stable and commonly encountered diradical: it is more stable as a triplet than a singlet. According to molecular orbital theory, the electron configuration of triplet oxygen has two electrons occupying two π molecular orbitals (MOs) of equal energy (that is, degenerate MOs). In accordance with Hund's rules, they remain unpaired and spin-parallel and account for the paramagnetism of molecular oxygen. These half-filled orbitals are antibonding in character, reducing the overall bond order of the molecule to 2 from a maximum value of 3 (e.g., dinitrogen), which occurs when these antibonding orbitals remain fully unoccupied. The molecular term symbol for triplet oxygen is 3Σ. Spin The ''s'' = spins of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
