In
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 ...
, the multireference configuration interaction (MRCI) method consists of a
configuration interaction expansion of the
eigenstate
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system re ...
s of the
electronic molecular Hamiltonian in a set of
Slater determinants which correspond to excitations of the
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; 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
In quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...
s. 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
In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural ansatzes or, from German, ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be ...
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
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
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
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics ...
of the ground and
excited state
In quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Add ...
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
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' () "fame, glory, honour, praise, reno ...
and
Sigrid D. Peyerimhoff in the seventies under the name Multi-Reference Single and Double Configuration Interaction (MRSDCI). MRCI was further streamlined in 1988 by Hans-Joachim Werner and Peter Knowles, which made previous MRCI procedures more generalizable.
The MRCI method can also be implemented in
semi-empirical
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how the ...
methods. An example for this is the OM2/MRCI method developed by
Walter Thiel's group.
See also
*
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. Mathemati ...
References
Quantum chemistry
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