Multireference configuration interaction
Encyclopedia
In quantum chemistry
, the multireference configuration interaction method consists in a configuration interaction
expansion of the eigenstates of the electronic molecular Hamiltonian in a set of Slater determinant
s which correspond to excitations of the ground state
electronic configuration but also of some excited state
s. The Slater determinants from which the excitations are performed are called reference determinants. The higher excited derterminants (also called configuration state function
s (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 taking more references.
As a result of a MRCI calculation one gets a more balanced correlation
of the ground and excited state
s. For quantitative good energy differences (excitation energies) one has to be careful in selecting the references. Taking only the dominant configuration of an excited state into the reference space leads to a correlated (lower) energy of the excited state. The generally too high excitation energies of CIS or CISD are lowered. But usually excited states have more than one dominant configuration and so the ground state is more correlated (due to a) now including some configurations with higher excitations (triply and quadruply in MRCISD) b) the neglect of other dominant configurations of the excited states which are still uncorrelated).
Selecting the references can be done manually (
), automatically (all possible configurations within an active space of some orbitals) or semiautomatically (taking all configurations as references that have been shown to be important in a previous CI or MRCI calculation)
This method has been implemented first by Robert Buenker and Sigrid D. Peyerimhoff
in the seventies under the name Multi-Reference single and Double Configuration Interaction (MRDCI).
The MRCI method can also be implemented in semi-empirical methods. An example for this is the OM2/MRCI method developed by Walter Thiel's
group.
Quantum chemistry
Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...
, the multireference configuration interaction method consists in a configuration interaction
Configuration interaction
Configuration interaction 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...
expansion of the eigenstates of the electronic molecular Hamiltonian in a set of Slater determinant
Slater determinant
In quantum mechanics, a Slater determinant is an expression that describes the wavefunction of a multi-fermionic system that satisfies anti-symmetry requirements and consequently the Pauli exclusion principle by changing sign upon exchange of fermions . It is named for its discoverer, John C...
s which correspond to excitations of the ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
electronic configuration but also of some excited state
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
s. The Slater determinants from which the excitations are performed are called reference determinants. The higher excited derterminants (also called configuration state function
Configuration state function
In quantum chemistry, a configuration state function , is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration.-Definition:...
s (CSFs) or shortly configurations) are then chosen either by the program according to some perturbation theoretical
Perturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
ansatz
Ansatz
Ansatz is a German noun with several meanings in the English language.It is widely encountered in physics and mathematics literature.Since ansatz is a noun, in German texts the initial a of this word is always capitalised.-Definition:...
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
Electronic correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.- Atomic and molecular systems :...
and so a lower energy. The problem of size inconsistency
Size consistency
In quantum chemistry, size consistency is a property that guarantees the consistency of the energy behavior when interaction between the involved molecular system is nullified ....
of truncated CI-methods is not solved by taking more references.
As a result of a MRCI calculation one gets a more balanced correlation
Electronic correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system.- Atomic and molecular systems :...
of the ground and excited state
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
s. For quantitative good energy differences (excitation energies) one has to be careful in selecting the references. Taking only the dominant configuration of an excited state into the reference space leads to a correlated (lower) energy of the excited state. The generally too high excitation energies of CIS or CISD are lowered. But usually excited states have more than one dominant configuration and so the ground state is more correlated (due to a) now including some configurations with higher excitations (triply and quadruply in MRCISD) b) the neglect of other dominant configurations of the excited states which are still uncorrelated).
Selecting the references can be done manually (
), automatically (all possible configurations within an active space of some orbitals) or semiautomatically (taking all configurations as references that have been shown to be important in a previous CI or MRCI calculation)This method has been implemented first by Robert Buenker and Sigrid D. Peyerimhoff
Sigrid D. Peyerimhoff
Sigrid Doris Peyerimhoff is a theoretical chemist and Emeritus Professor at the Institute of Physical and Theoretical Chemistry, University of Bonn, Germany....
in the seventies under the name Multi-Reference single and Double Configuration Interaction (MRDCI).
The MRCI method can also be implemented in semi-empirical methods. An example for this is the OM2/MRCI method developed by Walter Thiel's
Walter Thiel (chemist)
Walter Thiel is a German theoretical chemist.- Academic career :Walter Thiel studied chemistry at the University of Marburg from 1966 to 1971, where he subsequently obtained his doctorate with A. Schweig in 1973. After a post-doctoral stint at the University of Texas at Austin with M. J. S...
group.
See also
- Configuration interactionConfiguration interactionConfiguration interaction 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...