CISDT, CISD

Practical configuration interaction methods augment the Hartree-Fock by adding only a limited set of substitutions, truncating the Cl expansion at some level of substitution. For example, the CIS method adds single excitations to the Hartree-Fock determinant, CID adds double excitations, CISD adds singles and doubles, CISDT adds singles, doubles, and triples, and so on. 

It can clearly be seen that the CISD curve is worse than either of the other two, which are essentially identical out to a AR of 1.3 A. The size inconsistency of the CISD method also has consequences for the energy curve when the bond is only half broken. Figure 11.11 illustrates why the use of Cl methods has declined over the years, it normally gives less accurate results compared with MP or CC methods, but at a similar or Irigher computational cost. Furthermore, it is difficult to include the important triply excited configurations in Cl methods (CISDT scales as M ), but it is relatively easy to include them in MP or CC methods (MP4 and CCSD(T) scales as M ). 

R Energy (H) HE CISD CISDT CCSD CCSDT 2POS 2POS + T1T2 3POS... 

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. 

F f V. and Q = T4 -F T /2 + fXfiH + T1T3 -F T M etc. The inclusion of T ll in even the simplest CCD model explains why CCD is usually better than CID, CISD, or even CISDT. Once we have CISDTQ, this term is picked up along with several others showing that CISDTQ = CCSD(T) (e.g., as shown in Table 4). In operator form, the CISD equations in the canonical SCF case are... 

CISD. CISD (configuration interaction, single double) are LCAO expressions that treat configuration interactions by including one or two excited states. The designations CISDT and CISDTQ expand this to three and four excitations, respectively. 

The trial wavefunction can include the exchange of 1, 2 or 3 electrons from the valence band into unoccupied orbitals these are known as Cl singles (CIS), Cl doubles (CID) and Cl triples (CIT), respectively. CIS, CISD, and CISDT are methods configurational... 

Develop some procedure for selection of the most important con%urations. In its most general form this method is called GenCI. Frequently used are CIS, CID, CISD, CISDT etc. methods where 1-electron, 2-electron, 1+2-electron, 1+2+3-electron excitations of electrons from occupied HF states to virtual ones are taken into account. These methods can be called restricted Cl (RCI) methods. In some computer codes for molecular calculations automatic selection of the most important configurations is performed [119]. 

Fig. 5.16. The Cl dissociation curves of the C2v water molecule in the cc-pVDZ basis (atomic units) for a fixed HOH bond angle of 110.565. In the two uppermost figures, we have on the left plotted the dissociation curves for the CISD wave function (black line) and the FCl wave function (grey line) on the right, we have plotted the difference between the CISD and FCI energies. In the middle and lower figures, we have made similar plots for the CISDT and CISDTQ wave functions.

---