CISDT

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 the specific case of the Cl-corrected MMCC(2,3) approach, very good results are obtained when the wave function in Eq. (67) is replaced by the wave function obtained in the active-space CISDt calculations, which... 

CISDt = CISDt (CCSD)gT(eesD) CISDt CISDt CISDt CISDt... 

Figure 2. Potential energy curves for the CH+ ion (energies in hartree and the C-H distance in bohr see Refs. [44,47] for the EOMCCSD and MMCC(2,3)/CI data see Refs. [45,103] for the full Cl data). The results include the ground state and the two lowest excited states of the symmetry (the full Cl curves are indicated by the dotted lines and other results are represented by ), the lowest two fl states (the full Cl curves are indicated by the dashed-dotted lines and other results are represented by 0)> the lowest state (the fuU Cl curve is indicated by the dashed hne and other results are indicated by A), (a) A comparison of the EOMCCSD and full Cl results, (b) A comparison of the CISDt and full Cl results, (c) A comparison of the MMCC(2,3)/CI and fuU Cl results. 

As shown in Table 2, the inexpensive MMCC(2,3)/CI approach is capable of providing the results of full EOMCCSDT quality. Indeed, the errors in the vertical excitation energies for the 2 S+, 1 A, 2 A, and 2 states of CH+ that have large double excitation components, obtained with the noniterative MMCC(2,3)/CI approximation, are 0.006-0.105 eV. This should be compared to the 0.327-0.924 eV errors in the EOMCCSD results, the 0.219-0.318 eV errors obtained with the CC3 method, and the 0.504-0.882 eV errors obtained with the CISDt approach used to construct wave functions T ) for the MMCC(2,3)/CI calculations [47,48]. For the remaining states shown in Table 2 (the third and fourth states and the lowest-energy state), the errors in the CISDt-corrected MMCC(2,3) results, relative to full Cl, are 0.000-0.015 eV. Again, the only standard EOMCC method that can compete with the MMCC(2,3)/CI approach is the expensive full EOMCCSDT approximation. 

The Cl-corrected MMCC methods provide us with an excellent description of excited states dominated by double excitations and excited-state potentials along bond breaking coordinates, but one may think of reducing the costs of the CISDt-corrected MMCC(2,3) and similar cal-... 

CISDT CI including single, double, and triple electronic excitations... 

---