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 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. Mathematical ...

expansion of the eigenstates of the

electronic molecular Hamiltonian In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation p ...

in a set of

Slater determinant In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system. It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two elect ...

s 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 In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals. For example, the electron configuration of the neon atom ...

but also of some

excited state In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to a ...

s. The Slater determinants from which the excitations are performed are called reference determinants. The higher excited determinants (also called

configuration state function In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. A CSF must not be confused with a configuration. In general, one configuration gives rise to several CSFs; all have the same ...

s (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 Ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the ...

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

of the ground and

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 (

\Phi_1, \Phi_2, \Phi_5, ...

), 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 (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 for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences an ...

methods. An example for this is the OM2/MRCI method developed by Walter Thiel's group.

References

Quantum chemistry {{quantum-chemistry-stub

See also

References