Spin-restricted triple-excitation corrections

The presence of /,/ and components requires an iterative solution of this equation—an approach that necessitates storage of the T3 amplitudes in each iteration This scheme is unreasonable because the number of such amplitudes would rapidly become the computational bottleneck as the size of the molecular system increased. This problem may be circumvented, however, by utilizing the so-called semicanonical molecular orbital basis in which the occupied-occupied and virtual-virtual blocks of the Fock matrix are diagonal. In this basis, the two final terms in the T3 equation above vanish, and the conventional noniterative computational procedure described earlier in the chapter may be employed. 

The use of semicanonical orbitals does have a drawback, however, in that one is necessarily forced to use a computational procedure comparable to that 

This problem can be avoided, however, if an appropriate open-shell perturbation theory is defined such that the zeroth-order Hamiltonian is diagonal in the truly spin-restricted molecular orbital basis. The Z-averaged perturbation theory (ZAPT) defined by Lee and Jayatilaka fulfills this requirement. ZAPT takes advantage of the symmetric spin orbital basis. For each doubly occupied spatial orbital and each unoccupied spatial orbital, the usual a and P spin functions are used, but for the singly occupied orbitals, new spin functions. 

The performance of the (zT) correction is essentially identical to that of the conventional ROHF-CCSD(T) method. Application of both to a series of diatomic molecules in ground and excited states indicates insignificant differences between the two in the prediction of bond lengths, harmonic vibrational frequencies, anharmonic constants, and so on. Unfortunately, the complicated equations associated with the (zT) correction have thus far precluded its large scale implementation and, as a result, further systematic studies involving larger basis sets have not yet been carried out. 

---

T. D. Crawford, T.. Lee, and H. F. Schaefer,/. Chem. Phys., 107, 7943 (1997). A New Spin-Restricted Triple Excitation Correction for Coupled Cluster Theory. 

---