Coupled Cluster Methods
Restricted Active Space (RAS) Selection Schemes
The restricted active space (RAS) CI formalism is both a method of specifying the configurations to include in a truncated CI by dividing the orbitals into subsets and imposing restrictions on the allowed configurations based upon occupations within those subsets, and an efficient means of implementing the resulting CI calculation. The implementational details and advantages of the RAS CI method will not be discussed in this dissertation; instead, the reader is referred to the original RAS CI paper by Olsen and coworkers.[8] A valid RAS CI calculation may include any or all of the following 5 subsets of molecular orbitals (MOs) with the listed restrictions (Figure 2.1). The first subset consists of the lowest lying MOs, which interact only weakly with the other MOs, and are considered to be frozen, always doubly occupied, in any allowed configuration. The second subset, denoted RAS I, typically includes all the occupied MOs in some accepted reference, often the SCF wave function. Allowed configurations must contain a minimum of p electrons within RAS I. The third subset, denoted RAS II, includes MOs believed to be particularly important to the system under investigation.
Allowed configurations can have any combination of electrons in RAS II. The forth subset consists of high lying MOs which contribute only a little to the description of the system of interest. Any allowed configuration can only have a maximum of q electrons in RAS III. The final subset includes only the very highest MOs, counterparts to the frozen core orbitals, which contribute very weakly to the system and may safely be deleted from consideration. Any excitation based CI truncation scheme can be formulated using the RAS method. For example, a CISD with no frozen or deleted MOs performed on a system with 10 e- can be specified as having RAS I with a minimum of 8 e-, no RAS II, and RAS III with a maximum of 2 e-. A SOCI can be specified by requiring no electrons in RAS I, placing the virtual orbitals of the active space in RAS II, and allowing a maximum of two electrons into the remaining orbitals in RAS III.