Configuration interaction 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. 

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.

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... 

First we focus on the mechanisms that arise from interactions among the configurations in the active space, restricting ourselves to the role played by the two Cu + ions. For this centro-symmetric system, the active orbitals g = (a + b)l and u = a — b) pi shown in Fig. 5.1 define four different determinants... 

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. 

This calculation is typically performed in some form of a restricted configuration interaction (Cl) expansion (CASSCF [complete active space self consistent field], MRCI [multireference configuration interaction]). The perturbation V is represented by the operators and The perturbed wave function F and energy E satisfy the equation... 

T. Fleig, J. Olsen, C. M. Marian. The Generalized Active Space Concept for the Relativistic Treatment of Electron Correlation I. Kramers-restricted two-component configuration interaction. /. Chem. Phys., 114(11) (2001) 4775 790. 

The electronic states and the relevant matrix elements have been determined using the Restricted Open-shell Hartree-Fock (ROHF) method, [337] followed by a configuration interaction (Cl) calculation with double excitations. The active space is hmited to 10 molecular orbitals (MO), consisting of 2 occupied, 1 singly-occupied, and 7 unoccupied MOs. Excitations to the higher MOs are neglected. The total munber of configuration state functions (CSFs) in the active space amounts to 479. 

Bloch-equation-based multistate PT formulations, termed quasidegenerate PT (QDPT) [22], largely assume an orthonormal set of vectors in the configuration interaction (Cl) space that is partitioned for a model space and its complement. This restricts applicability to model spaces easily separable from the rest, e.g., formed by simple determinants. While determinants facilitate a transparent derivation of many-body QDPT formulae [23, 24], identifying the determinants that need to be included in the model space is not always trivial. Though complete active space (CAS) appears a simple way out, CAS-based QDPT is unfortunately prone to the so-called intruder problem, especially for large active spaces. 

MC approaches [30] involve the optimization of molecular orbitals within a restricted subspace of electronic occupations provided such active space is appropriately chosen, they allow for an accurate description of static electron correlation effects. Dynamical correlation effects can also be introduced either at the perturbation theory level [complete active space with second-order perturbation theory (CASPT2), and multireference Mpller-Plesset (MR-MP2) methods] [31] or via configuration interaction (MR-CI). 

---