Restricted active space SCF

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. 

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 ... 

The choice of reference space for MRCI calculations is a complex problem. First, a multieonfigurational Hartree-Fock (MCSCF) approach must be chosen. Common among these are the generalized valence-bond method (GVB) and the complete active space SCF (CASSCF) method. The latter actually involves a full Cl calculation in a subspace of the MO space—the active space. As a consequence of this full Cl, the number of CSFs can become large, and this can create very long Cl expansions if all the CASSCF CSFs are used as reference CSFs. This problem is exacerbated when it becomes necessary to correlate valence electrons in the Cl that were excluded from the CASSCF active space. It is very common to select reference CSFs, usually by their weight in the CASSCF wave function. Even more elaborate than the use of a CASSCF wave function as the reference space is the seeond-order Cl, in which the only restriction on the CSFs is that no more than two electrons occupy orbitals empty in the CASSCF wave function. Such expansions are usually too long for practical calculations, and they seldom produce results different from a CAS reference space MRCI. 

Tsipis [73] gives extensive tabulations of M-L bond energies. The vast majority of post-HF calculations are restricted to simple ML or ML2 systems where L is monatomic (H, O or halide) or a small ligand such as CO, CH3, NH3, PH3 or C2H4. These molecules are small enough to facilitate the necessary correlation treatment. Multi Reference Cl and Complete Active Space SCF are the most popular correlated methods and appear capable of good accuracy (i.e. to within 5-10 kcal/mole). 

The number of active orbitals that can be used in a CASSCF calculation is limited. Some problems needs larger active spaces than can be used today. It is then possible to use a less general way to construct the wave function, for example, the restricted active space (RAS) SCF method [79]. Such methods can use larger active spaces, but there exist no corresponding RASPT2 program yet. Such a code would be of great value. 

The complexity of choosing the active space was clear already in the first application of the CASSCF/CASPT2 method to a transition metal [4], The problem was to describe the electronic spectrum of the Ni atom. We present in Table 5-3 the results obtained with different active spaces (from Ref. [4]). Calculations were performed for each state separately. We note first the large errors obtained with the SCF method (open shell restricted SCF). The results are improved with the... 

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. 

To make the NEGF-SCF step even more efficient, the restricted MO space idea is proposed. The idea is similar to the scheme of the complete active space (CAS)-SCF method in quantum chemistry [81, 82]. The MOs, whose occupation number should be determined by N EGF-SCF, are the only active MOs, and their energies cover the region dose to EF Vb/2. The inactive MOs, which are core orbitals, are always fully occupied. The MOs of much higher energy than EF are virtual MOs, and their electron occupations are always equal to zero. In typical cases, the applied bias is within a few volts, and the active MOs in the restricted MO space are only about 10% of the MOs in the whole MO space. Note that orbital relaxation is allowed for all MOs because the Hamiltonian is updated. The fixed values in the inactive and virtual MOs are only occupation numbers. 

As long as a satisfactory multireference coupled-cluster theory is missing, there are various options for states that need a zeroth-order multiconfiguration wave function. One possibility is to start from an MC-SCF calculation and to improve this by selected Cl. Since the MC-SCF part is basically extensive, while the Cl part is not, and since one can hardly go beyond external double excitations, one tends to include as many configurations in the MC-SCF part as possible. However, MC-SCF is usually of CAS (complete active space) [154] type, e.g. like full Cl, which restricts the possible size of the active space. Such multireference Cl scheme have been very popular for describing excited states, reaction barriers, dissociation processes etc. 

---