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Post–Hartree–Fock
In computational chemistry Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of mol ..., post–Hartree–Fock (post-HF) methods are the set of methods developed to improve on the Hartree–Fock method, Hartree–Fock (HF), or self-consistent field (SCF), method. They add electronic correlation, electron correlation which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged. Details In general, the SCF procedure makes several assumptions about the nature of the multi-body Schrödinger equation and its set of solutions: * For molecules, the Born–Oppenheimer approximation is inherently assumed. The true wavefunction should also be a function of the coordinates of each of the nuclei. * Typically, special ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Chemistry
Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical chemistry incorporated into computer programs to calculate the structures and properties of molecules, groups of molecules, and solids. The importance of this subject stems from the fact that, with the exception of some relatively recent findings related to the hydrogen molecular ion (dihydrogen cation), achieving an accurate quantum mechanical depiction of chemical systems analytically, or in a closed form, is not feasible. The complexity inherent in the many-body problem exacerbates the challenge of providing detailed descriptions of quantum mechanical systems. While computational results normally complement information obtained by chemical experiments, it can occasionally predict unobserved chemical phenomena. Overview Computational chemistry differs from theoretical chemistry, which involves a mathematical description of chem ... [...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] |
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 ... [...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 � ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-electron Valence State Perturbation Theory
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 multi ... [...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 electronic correlation, correlation and so a lower energy. The problem of size consistency, size inconsistency ... [...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 is) and Hartree–Fock (where there is only one determinant, but the molecular orbit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chemistry Composite Methods
Quantum chemistry composite methods (also referred to as thermochemical recipes) are computational chemistry methods that aim for high accuracy by combining the results of several calculations. They combine methods with a high level of theory and a small basis set (chemistry), basis set with methods that employ lower levels of theory with larger basis sets. They are commonly used to calculate thermodynamic quantities such as enthalpies of formation, atomization energies, ionization energies and electron affinities. They aim for chemical accuracy which is usually defined as within 1 kcal/mol of the experimental value. The first systematic model chemistry of this type with broad applicability was called Gaussian-1 (G1) introduced by John Pople. This was quickly replaced by the Gaussian-2 (G2) which has been used extensively. The Gaussian-3 (G3) was introduced later. Gaussian-n theories Gaussian-2 (G2) The G2 uses seven calculations: # the molecular geometry is obtained by a Mølle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Configuration Interaction
Quadratic configuration interaction (QCI) is an extension of configuration interaction that corrects for size-consistency errors in single and double excitation CI methods (CISD). Size-consistency means that the energy of two non-interacting (i.e. at large distance apart) molecules calculated directly will be the sum of the energies of the two molecules calculated separately. This method called QCISD was developed in the group of John Pople. It gives results that are comparable to the coupled cluster Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used ... method, CCSD. QCISD can be improved by the same perturbative inclusion of unlinked triples to give QCISD(T). This gives similar results to CCSD(T). References Post-Hartree–Fock methods {{quantum-chemistry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Møller–Plesset Perturbation Theory
Møller–Plesset perturbation theory (MP) is one of several quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry. It improves on the Hartree–Fock method by adding electron correlation effects by means of Rayleigh–Schrödinger perturbation theory (RS-PT), usually to second (MP2), third (MP3) or fourth (MP4) order. Its main idea was published as early as 1934 by Christian Møller and Milton S. Plesset. Rayleigh–Schrödinger perturbation theory The MP perturbation theory is a special case of RS perturbation theory. In RS theory one considers an unperturbed Hamiltonian operator \hat_, to which a small (often external) perturbation \hat is added: :\hat = \hat_ + \lambda \hat. Here, ''λ'' is an arbitrary real parameter that controls the size of the perturbation. In MP theory the zeroth-order wave function is an exact eigenfunction of the Fock operator, which thus serves as the unperturbed operator. The perturbation is the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-configuration Time-dependent Hartree
Multi-configuration time-dependent Hartree (MCTDH) is a general algorithm to solve the time-dependent Schrödinger equation for multidimensional dynamical systems consisting of distinguishable particles. MCTDH can thus determine the quantal motion of the nuclei of a molecular system evolving on one or several coupled electronic potential energy surfaces. MCTDH by its very nature is an approximate method. However, it can be made as accurate as any competing method, but its numerical efficiency deteriorates with growing accuracy. MCTDH is designed for multi-dimensional problems, in particular for problems that are difficult or even impossible to attack in a conventional way. There is no or only little gain when treating systems with less than three degrees of freedom by MCTDH. MCTDH will in general be best suited for systems with 4 to 12 degrees of freedom. Because of hardware limitations it may in general not be possible to treat much larger systems. For a certain class of problems, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupled Cluster
Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in nuclear physics. Coupled cluster essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Some of the most accurate calculations for small to medium-sized molecules use this method. The method was initially developed by Fritz Coester and Hermann Kümmel in the 1950s for studying nuclear-physics phenomena, but became more frequently used when in 1966 Jiří Čížek (and later together with Josef Paldus) reformulated the method for electron correlation in atoms and molecules. It is now one of the most prevalent methods in quantum chemistry that includes electronic correlation. CC theory is simply the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
