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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] |
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] |
Molecular Orbitals
In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms ''atomic orbital'' and ''molecular orbital'' were introduced by Robert S. Mulliken in 1932 to mean ''one-electron orbital wave functions''. At an elementary level, they are used to describe the ''region'' of space in which a function has a significant amplitude. In an isolated atom, the orbital electrons' location is determined by functions called atomic orbitals. When multiple atoms combine chemically into a molecule, the electrons' locations are determined by the molecule as a whole, so the atomic orbitals combine to form molecular orbitals. The electrons from the constituent atoms occupy the molecular orbitals. Mathematically, molecular orbitals are an approximate solution to the Schrödin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slater Determinant
In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions).Molecular Quantum Mechanics Parts I and II: An Introduction to QUANTUM CHEMISTRY (Volume 1), P. W. Atkins, Oxford University Press, 1977, . Only a small subset of all possible fermionic wave functions can be written as a single Slater determinant, but those form an important and useful subset because of their simplicity. The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital \chi(\mathbf), where \mathbf denotes the position and spin of a single electron. A Slater determinant containing two electrons with the same spin orbital would correspond to a wave function that is zero everywhere. The Slater determinant is named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavefunction
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 trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrons
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multireference Configuration Interaction
In quantum chemistry, the multireference configuration interaction (MRCI) method consists of a configuration interaction expansion of the eigenstates of the electronic molecular Hamiltonian in a set of Slater determinants which correspond to excitations of the ground state electronic configuration but also of some excited states. The Slater determinants from which the excitations are performed are called reference determinants. The higher excited determinants (also called configuration state functions (CSFs) or shortly configurations) are then chosen either by the program according to some perturbation theoretical ansatz according to a threshold provided by the user or simply by truncating excitations from these references to singly, doubly, ... excitations resulting in MRCIS, MRCISD, etc. For the ground state using more than one reference configuration means a better correlation and so a lower energy. The problem of size inconsistency of truncated CI-methods is not solved by taki ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full CI
Full configuration interaction (or full CI) is a linear variational approach which provides numerically exact solutions (within the infinitely flexible complete basis set) to the electronic time-independent, non-relativistic Schrödinger equation. Explanation It is a special case of the configuration interaction method in which ''all'' Slater determinants (or configuration state functions, CSFs) of the proper symmetry are included in the variational procedure (i.e., all Slater determinants obtained by exciting all possible electrons to all possible virtual orbitals, orbitals which are unoccupied in the electronic ground state configuration). This method is equivalent to computing the eigenvalues of the electronic molecular Hamiltonian within the basis set of the above-mentioned configuration state functions. In a minimal basis set a full CI computation is very easy. But in larger basis sets this is usually just a limiting case which is not often attained. This is because exact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic 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 c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Active Space Perturbation Theory
Complete active space perturbation theory (CASPTn) is a multireference electron correlation method for computational investigation of molecular systems, especially for those with heavy atoms such as transition metals, lanthanides, and actinides. It can be used, for instance, to describe electronic states of a system, when single reference methods and density functional theory cannot be used, and for heavy atom systems for which quasi-relativistic approaches are not appropriate. Although perturbation methods such as CASPTn are successful in describing the molecular systems, they still need a Hartree-Fock wavefunction to provide a valid starting point. The perturbation theories cannot reach convergence if the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are degenerate. Therefore, the CASPTn method is usually used in conjunction with the Multi-configurational self-consistent field method (MCSCF) to avoid near-degeneracy correlation effe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NEVPT
In quantum chemistry, ''n''-electron valence state perturbation theory (NEVPT) is a perturbative treatment applicable to multireference CASCI-type wavefunctions. It can be considered as a generalization of the well-known second-order Møller–Plesset perturbation theory to multireference Complete Active Space cases. The theory is directly integrated into many quantum chemistry packages such as MOLCAS, Molpro, DALTON, PySCF and ORCA. The research performed into the development of this theory led to various implementations. The theory here presented refers to the deployment for the Single-State NEVPT, where the perturbative correction is applied to a single electronic state. Research implementations has been also developed for Quasi-Degenerate cases, where a set of electronic states undergo the perturbative correction at the same time, allowing interaction among themselves. The theory development makes use of the quasi-degenerate formalism by Lindgren and the Hamiltonian multipart ... [...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] |
