Restricted active space self-consistent field method

Instead of optimization of all the orbitals, only the active orbitals will be varied within the Complete Active Space Self-Consistent Field approximation (CASSCF). In the acronym of this method, the number of active orbitals and active electrons are also provided for the given system. For instance, CASSCF(6,4) denotes the calculations with the expansion including all the possible exchanges of the four electrons within the six active orbitals. The CASSCF approach leads to all possible exchanges in the given active space, and for a moderately sized system, the size of the active spaces can quickly exceed the computational resources. In such a case, the solution can be the Restricted Active Space Self-Consistent Field method (RASSCF), which supplies a way of limiting the size of the active space. 

Malmqvist, P.-A., Rendell, A., 8c Roos, B. O. (1990). The restricted active space self-consistent-field method, implemented with a split graph unitary group approach. The Journal of Physical Chemistry, 94, 5477-5482. 

Malmqvist P-A, Rendell A, Roos BO. The Restricted Active Space Self-Consistent-Field Method, Implemented with a Split Graph Unitary Group Approach. J Phys Chem. 1990 (4). Ma D, Li Manni G, Gagliardi L. The generalized active space concept in multiconfigurational self-consistent field methods. J Chem Phys [Internet]. 2011 Jul 28 [cited 2012 Mar 1] 135(4) 044128. Available from http //www.ncbi.nlm.nih.gov/pubmed/21806111. 

As for any full Cl expansion, the CASSCF becomes unmanageably large even for quite small active spaces. A variation of the CASSCF procedure is the Restricted Active Space Self-consistent Field (RASSCF) method. Here the active MOs are further divided into three sections, RASl, RAS2 and RAS3, each having restrictions on the... 

Empirical equilibrium coupling constants can be compared as a benchmark with calculated equilibrium coupling constants obtained with various methods. A comparison of these empirical equilibrium constants with calculated equilibrium constants suggested that the restricted-active-space self-consistent field (RASSCF) method is the best approach for calculating the indirect nuclear spin-spin coupling constants of small molecules, and that the second-order polarization propagator approximation (SOPPA) and DFT are similar in performance. 

Y. S. Kim, Y. S. Lee. The Kramers restricted complete active space self-consistent-field method for two-component molecular spinors and relativistic effective core potentials including spin-orbit interactions. /. Chem. Phys., 119 (2003) 12169. 

More precisely, a set of active orbitals and a number of active electrons are defined. All the configurations that can be built by excitations ofthe active electrons among the active orbitals are included into the wavefunction. Other, more flexible approaches for the selection of the conflgurations included in the MSCSF wavefunction exist, such as the Restricted Active Space Self-Consistent Field [23, 24] (RASSCF) and the Occupation Restricted Multiple Active Space (ORMAS) [25] methods. 

On the other hand, the Restricted Active Space Self-Consistent Field (RASSCF) method is a more general extension of the CASSCF method. Now, there are three subspaces within the active orbitals RASl (orbitals that are doubly occupied except for a maximum number of holes allowed in this orbital subspace), RAS2 (in these orbitals, all possible occupations are allowed), and RAS3 (orbitals that are unoccupied except for a maximum number of electrons allowed in this subspace). CASSCF calculations can be performed by allowing orbitals only in the RAS2 space. A single reference SDCl wave function is obtained by allowing a maximum of two holes... 

Reaction coordinate, 296, 314, 365, 368 Reaction Path (RP) methods, 390 Reaction surface, 390 Reaction volume, 390 Redundant variables, 34, 327 Relaxation time, in simulations, 380 Renormalized Davidson correction, 137 Resonance, resonance structures, 200 Response, wave function, 242 Restricted Active Space Self-Consistent Field (RASSCF) method, 119 Restricted Hartree-Fock (RHF) method, 70 Restricted Open-shell Hartree-Fock (ROHF) method, 70... 

This procedure suffers from a high degree of arbitrariness in the choice of just which configurations are deemed important. The calculation can be made somewhat more objective by including all excitations between a subset of occupied MOs and a subset of vacant orbitals. (These excitations are subject to certain restrictions as to multiplicity or order of excitation.) The orbitals chosen for the excitations are referred to as the active space , and the method is dubbed Complete Active Space Self Consistent Field (CASSCF) - ". Both MCSCF and CASSCF provide a certain fraction of the correlation energy, relative to a single configuration, Hartree-Fock, calculation. 

For the construction of spin eigenfunctions see, for example, Ref. [22], There are obviously many parallels to the multiconfiguration self-consistent field (MCSCF) methods of MO theory, such as the restriction to a relatively small active space describing the chemically most interesting features of the electronic structure. The core wavefunction for the inactive electrons, 4>core, may be taken from prior SCF or complete active space self-consistent field (CASSCF) calculations, or may be optimised simultaneously with the and cat. 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

---