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Dyall's Hamiltonian
In quantum chemistry, the Dyall Hamiltonian is a modified Hamiltonian with two-electron nature. It can be written as follows: :\hat^ = \hat^_i + \hat^_v + C :\hat^_i = \sum_^ \varepsilon_i E_ + \sum_r^ \varepsilon_r E_ :\hat^_v = \sum_^ h_^ E_ + \frac \sum_^ \left\langle ab \left.\ cd \right\rangle \left(E_ E_ - \delta_ E_ \right) :C = 2 \sum_^ h_ + \sum_^ \left( 2 \left\langle ij \left.\ ij\right\rangle - \left \langle ij \left.\ ji\right\rangle \right) - 2 \sum_^ \varepsilon_i :h_^ = h_ + \sum_j \left( 2 \left\langle aj \left.\ bj \right\rangle - \left\langle aj \left.\ jb \right\rangle \right) where labels i,j,\ldots, a,b,\ldots, r,s,\ldots denote core, active and virtual orbitals (see 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 * ''vi ...) respectively, \var ... [...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 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. Common metho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian (quantum Mechanics)
Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian with two-electron nature ** Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule * Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system * Hamiltonian path, a path in a graph that visits each vertex exactly once * Hamiltonian group, a non-abelian group the subgroups of which are all normal * Hamiltonian economic program, the economic policies advocated by Alexander Hamilton, the first United States Secretary of the Treasury See also * Alexander Hamilton (1755 or 1757–1804), American statesman and one of the Founding Fathers of the US * Hamilton (other) Hamilton may refer to: People * Hamilton (name), a common ... [...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] |
