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Ab Initio Quantum Chemistry Methods
''Ab initio'' quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. The background is described by Parr. ''Ab initio'' means "from first principles" or "from the beginning", implying that the only inputs into an ''ab initio'' calculation are physical constants. ''Ab initio'' quantum chemistry methods attempt to solve the electronic Schrödinger equation given the positions of the nuclei and the number of electrons in order to yield useful information such as electron densities, energies and other properties of the system. The ability to run these calculations has enabled theoretical chemists to solve a range of problems and their importance is highlighted by the awarding of the Nobel prize to John Pople and Walter Kohn. Accuracy and scaling ''Ab initio'' electronic structure method ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Chemistry
Computational chemistry is a branch of chemistry that uses computer simulation 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. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new drugs and materials. Examples of such properties are structure (i.e., the expected positions of the constituent atoms), absolute and relative (interaction) energies, electronic charge density distributions, dipoles and higher multipole moments, vi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Functional
Hybrid functionals are a class of approximations to the exchange–correlation energy functional in density functional theory (DFT) that incorporate a portion of exact exchange from Hartree–Fock theory with the rest of the exchange–correlation energy from other sources (''ab initio'' or empirical). The exact exchange energy functional is expressed in terms of the Kohn–Sham orbitals rather than the density, so is termed an ''implicit'' density functional. One of the most commonly used versions is B3LYP, which stands for " Becke, 3-parameter, Lee–Yang– Parr". Origin The hybrid approach to constructing density functional approximations was introduced by Axel Becke in 1993. Hybridization with Hartree–Fock (HF) exchange (also called exact exchange) provides a simple scheme for improving the calculation of many molecular properties, such as atomization energies, bond lengths and vibration frequencies, which tend to be poorly described with simple "ab initio" functiona ... [...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 multipart ... [...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] |
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] |
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 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 MP2 optimization using the ... [...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 in ... 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] |
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 pertur ... [...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] |
Unrestricted Hartree–Fock
Unrestricted Hartree–Fock (UHF) theory is the most common molecular orbital method for open shell molecules where the number of electrons of each spin are not equal. While restricted Hartree–Fock theory uses a single molecular orbital twice, one multiplied by the α spin function and the other multiplied by the β spin function in the Slater determinant, unrestricted Hartree–Fock theory uses different molecular orbitals for the α and β electrons. This has been called a ''different orbitals for different spins'' (DODS) method. The result is a pair of coupled Roothaan equations, known as the Pople–Nesbet–Berthier equations. :\mathbf^\alpha\ \mathbf^\alpha\ = \mathbf \mathbf^\alpha\ \mathbf^\alpha\ :\mathbf^\beta\ \mathbf^\beta\ = \mathbf \mathbf^\beta\ \mathbf^\beta\ Where \mathbf^\alpha\ and \mathbf^\beta\ are the Fock matrices for the \alpha\ and \beta\ orbitals, \mathbf^\alpha\ and \mathbf^\beta\ are the matrices of coefficients for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Restricted Open-shell Hartree–Fock
Restricted open-shell Hartree–Fock (ROHF) is a variant of Hartree–Fock method for open shell molecules. It uses doubly occupied molecular orbitals as far as possible and then singly occupied orbitals for the unpaired electrons. This is the simple picture for open shell molecules but it is difficult to implement. The foundations of the ROHF method were first formulated by Clemens C. J. Roothaan in a celebrated paper and then extended by various authors, see e.g. for in-depth discussions. As with restricted Hartree–Fock theory for closed shell molecules, it leads to Roothaan equations written in the form of a generalized eigenvalue problem :\mathbf \mathbf = \mathbf \mathbf \mathbf Where F is the so-called Fock matrix (which is a function of C), C is a matrix of coefficients, S is the overlap matrix of the basis functions, and \epsilon is the (diagonal, by convention) matrix of orbital energies. Unlike restricted Hartree–Fock theory for closed shell molecules, the form of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
