Restricted active space configuration

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.

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... 

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. 

Configuration Interaction Density Functional Theory Equation of Motion CCSD Multiconfiguration-SCF Moller Plesset 2nd Order Multireference Cl Multistate CASPT2 Restricted Active Space SCF Restricted Hartree Fock Symmetry Adapted Cluster-CI Self Consistent Field Singlestate CASPT2... 

The deviation of the CASSCF curve from the FCI curve in Fig. 2 is caused by nonstatic or dynamical correlation [1]. Although dynamical correlation is usually less geometry-dependent than static correlation, it must be included for high accuracy (see Sec. 4). One might think that it is possible to include the effects of dynamical correlation simply by extending the active space. For small molecules, this is, to some extent true, in particular when using the techniques of restricted active space SCF (RASSCF) theory [46]. Nevertheless, because of the enormous number of determinants needed to recover dynamical correlation, the simultaneous optimization of orbitals and configuration coefficients as done in MCSCF theory is not a practical approach to the accurate description of electronic systems. 

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. 

Figrire 8 An overview of quantum chemical methods for excited states. Bold-italic entries indicate methods that are currently applicable to large molecules. Important abbreviations used Cl (configuration Interaction), TD (time-dependent), CC (coupled-cluster), HF (Hartree-Fock), CAS (complete active space), RAS (restricted active space), MP (Moller-Plesset perturbation theory), S (singles excitation), SD (singles and doubles excitation), MR (multireference). Geometry optimizations of excited states for larger molecules are now possible with CIS, CASSCF, CC2, and TDDFT methods. 

Applications to atoms are in most cases based on the publicly available programs using finite difference methods for integration in the solution of the (multi-configurational) Dirac-Hartree-Fock equations. The problem of introducing electron correlation in this framework is most successfully accomplished by employing complete active space (CAS) and restricted active space (RAS) techniques (see Ref. 84 for a recent application with further references to the literature) or coupled-cluster techniques. ... 

---