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This is because exact solution of the full CI determinant is NP-complete [citation needed], so the existence of a polynomial time algorithm is unlikely. The Davidson correction is a simple correction which allows one to estimate the value of the full CI energy from a limited configuration interaction expansion result. [citation needed]
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.
Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated. More specifically, given a confidence level γ {\displaystyle \gamma } (95% and 99% are typical values), a CI is a random interval which contains the parameter being estimated γ {\displaystyle ...
The term ab initio was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene. [ 2 ][ 3 ] The background is described by Parr. [ 4 ]Ab initio means "from first principles" or "from the beginning", implying that the only inputs into an ab initio calculation ...
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 ...
When taking all possible excited determinants, one speaks of Full-CI. In a Full-CI wavefunction all electrons are fully correlated. For non-small molecules, Full-CI is much too computationally expensive. One truncates the CI expansion and gets well-correlated wavefunctions and well-correlated energies according to the level of truncation.
The problem of size inconsistency of truncated CI-methods is not solved by taking more references. As a result of a MRCI calculation one gets a more balanced correlation of the ground and excited states. For quantitative good energy differences (excitation energies) one has to be careful in selecting the references.
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: 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 ...