Restricted active space

In this section, we describe calculations of the P,T-odd interaction constant Wd for the ground (X2E, 2) states of YbF and BaF molecules using all-electron DF orbitals and a restricted active space (RAS) configuration interaction (Cl) treatment. 

The P,T-odd constant Wd and dipole moment p(. for the ground state of the BaF molecule are calculated using the restricted active space (RAS) configuration... 

Restricted active space self-consistent field (RASSCF) scheme, ab initio calculations, P,T-odd interactions, 253-259... 

The Restricted Active Space (RAS) State Interaction Approach With Spin-Orbit Coupling. 

The selection of configuration state functions to be included in MCSCF calculations is not a trivial task. Two approaches which can reduce the complexity of the problem are the complete active space self-consistent-field (CASSCF) [68] and the restricted active space self-consistent-field (RASSCF) [69] approach. Both are implemented in the Dalton program package [57] and are used in this study. Throughout the paper a CASSCF calculation is denoted by i active gactive RASSCF calculation by For the active spaces of HF, H2O, and CH4... 

Another means to reduce the scale of the problem is to shrink the size of the CAS calculation, but to allow a limited number of excitations from/to orbitals outside of the CAS space. This secondary space is called a restricted active space (RAS), and usually the excitation level is limited to one or two electrons. Thus, while all possible configurations of electrons in the CAS space are permitted, only a limited number of RAS configurations is possible. Remaining occupied and virtual orbitals, if any, are restricted to occupation numbers of exactly two and zero, respectively. 

Another extension of the CASSCF model, which has recently been developed, is to introduce several active spaces, and restrict the number of electrons in each subspace in some way. The Restricted Active Space (RAS) model employs five orbital subspaces instead of three ... 

The major problem with the CASSCF method is the limited number of active orbitals that can be used. However, one notes in many applications that some of these orbitals will have occupation numbers rather close to two for the whole process one is studying, while others keep low occupations numbers. The restricted Active Space (RAS) SCF method was developed to handle such cases [15, 24], Here, the active space is partitioned into three subspaces RAS1, RAS2, and RAS3 with the following properties ... 

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... 

Restricted Active Space Self-Consistent Field Sn2 reaction, 305, 367 —Variational Transition State Theory (VTST), 306... 

RASSCF see restricted-active-space selfconsistent field... 

In 1988, Olsen and co-workers46 presented the restricted active space (RAS) Cl, which specifies the Cl space in an a priori manner reminiscent of the second-order Cl (SOCI) and its derivatives. Olsen partitions the orbitals into three subspaces, labeled RAS I, RAS II, and RAS III. Typically, RAS I contains occupied and possibly very important virtual orbitals, RAS II contains the most important virtuals, and RAS III contains the less important virtuals. The Cl space includes all determinants with a minimum of p electrons in RAS I and a maximum of q electrons in RAS III. There is no restriction on RAS II, which is akin to the complete active space. Using this simple procedure, it is possible to formulate any Cl space truncated according to excitation level (e.g., CISD, CISDT, etc.) as well as excitation class selected MR-CI spaces, such as SOCI and CISD[TQ], The RAS Cl method is discussed more fully in section 4.8. 

A specialization of the full class Cl which uses only three orbital subspaces is the Restricted Active Space (RAS) Cl approach introduced by Olsen et al.i6 in 1988 along with the string-based full Cl algorithm already discussed (section 4.4). The three subspaces are labeled I, II, and III, and the Cl space is limited by requiring a minimum of p electrons in RAS I and a maximum of q electrons in RAS III (cf. Figure 14). There are no restrictions on the number of electrons in RAS II, and thus it is analogous to the complete active space... 

Figure 14 Orbital partitioning and configuration selection in the Restricted Active Space Configuration Interaction method. The Cl space includes all determinants in which at least p electrons are in RAS I and at most q electrons are in RAS III.

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