Complete active space

In quantum chemistry, a complete active space (CAS) is a systematic partitioning of molecular orbitals used to construct multireference wavefunctions. Orbitals are divided into inactive (or core), active, and virtual subspaces. A chosen number of electrons is distributed among all configurations of the active orbitals, while inactive orbitals remain doubly occupied and virtual orbitals unoccupied.

The complete-active-space self-consistent-field (CASSCF) method was introduced in 1980 by Björn O. Roos, Peter R. Taylor, and Per E. M. Siegbahn. It provides a variational multiconfigurational reference wavefunction in which both the configuration-interaction coefficients and molecular orbitals are optimized. A subsequent Newton–Raphson formulation enabled the treatment of substantially larger CAS expansions.

CAS wavefunctions capture the dominant static (nondynamic) correlation associated with bond dissociation, open-shell species, transition-metal complexes, and electronically excited states, for which a single Slater determinant can be qualitatively inadequate. In principle, making every orbital active gives a full configuration interaction treatment; in practice, the rapidly increasing size of the configuration space restricts CAS calculations to selected orbitals.

The remaining dynamic correlation is commonly recovered through post-CASSCF methods such as CASPT2 or NEVPT2.

Active-space selection

Selecting chemically appropriate active orbitals is a central practical challenge of CASSCF calculations. Christoph J. Stein and Markus Reiher at ETH Zürich proposed an automated procedure based on orbital-entanglement measures obtained from density-matrix renormalization group calculations. Related open-source software includes the Active Space Finder (ASF), which supports semi-automatic active-space selection for methods such as CASSCF.

See also

References

  1. 1 2 Roos, Björn O.; Taylor, Peter R.; Siegbahn, Per E. M. (1980). "A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach". Chemical Physics. 48 (2): 157–173. doi:10.1016/0301-0104(80)80045-0.
  2. ↑ Siegbahn, Per E. M.; Almlöf, Jan; Heiberg, Anders; Roos, Björn O. (1981). "The complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule". The Journal of Chemical Physics. 74 (4): 2384–2396. doi:10.1063/1.441359.
  3. ↑ Andersson, Kerstin; Malmqvist, Per-Åke; Roos, Björn O. (1992). "Second-order perturbation theory with a complete active space self-consistent field reference function". The Journal of Chemical Physics. 96 (2): 1218–1226. doi:10.1063/1.462209.
  4. ↑ Angeli, Celestino; Cimiraglia, Renzo; Malrieu, Jean-Paul (2001). "N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant". Chemical Physics Letters. 350 (3–4): 297–305. doi:10.1016/S0009-2614(01)01303-3.
  5. ↑ Stein, Christoph J.; Reiher, Markus (2016). "Automated selection of active orbital spaces". Journal of Chemical Theory and Computation. 12 (4): 1760–1771. arXiv:1602.03835. doi:10.1021/acs.jctc.6b00156.