Configuration interaction
Configuration interaction (CI) is a
In contrast to the
where Ψ is usually the electronic ground state of the system. If the expansion includes all possible
Truncating the CI-space is important to save computational time. For example, the method CID is limited to double excitations only. The method CISD is limited to single and double excitations. Single excitations on their own do not mix with the Hartree–Fock determinant. These methods, CID and CISD, are in many standard programs. The
The CI procedure leads to a
where c is the coefficient vector, e is the eigenvalue matrix, and the elements of the hamiltonian and overlap matrices are, respectively,
- ,
- .
Slater determinants are constructed from sets of orthonormal spin orbitals, so that , making the identity matrix and simplifying the above matrix equation.
The solution of the CI procedure are some eigenvalues and their corresponding eigenvectors .
The eigenvalues are the energies of the ground and some electronically excited states. By this it is possible to calculate energy differences (excitation energies) with CI methods. Excitation energies of truncated CI methods are generally too high, because the excited states are not that well correlated as the ground state is. For equally (balanced) correlation of ground and excited states (better excitation energies) one can use more than one reference determinant from which all singly, doubly, ... excited determinants are included (multireference configuration interaction).
MRCI also gives better correlation of the ground state which is important if it has more than one dominant determinant. This can be easily understood because some higher excited determinants are also taken into the CI-space.
For nearly degenerate determinants which build the ground state one should use the
See also
- Coupled cluster
- Electron correlation
- Multireference configuration interaction (MRCI)
- Multi-configurational self-consistent field (MCSCF)
- Post-Hartree–Fock
- Quadratic configuration interaction (QCI)
- Quantum chemistry
- Quantum chemistry computer programs
References
- Cramer, Christopher J. (2002). Essentials of Computational Chemistry. Chichester: John Wiley & Sons, Ltd. pp. 191–232. ISBN 0-471-48552-7.
- Sherrill, C. David; Schaefer III, Henry F. (1999). Löwdin, Per-Olov (ed.). The Configuration Interaction Method: Advances in Highly Correlated Approaches. Advances in Quantum Chemistry. Vol. 34. San Diego: Academic Press. pp. 143–269. ISBN 0-12-034834-9.