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Perturbative triples corrections:

To achieve ground state energies a high accuracy which systematically surpasses the acccuracy MP2 and DFT calculations for reaction and binding energies, the CCSD model should be combined with a perturbative correction for connected triples. The recommended approach for the correction is the CCSD(T) model

ECCSD(T) = ECCSD + E(4)DT + E(5)ST (10.18)

which includes the following two terms:
E(4)DT = $\displaystyle \sum_{{\mu_2}}^{}$tμ2CCSDμ2|[H, T3(2)]| HF〉 (10.19)
E(5)ST = $\displaystyle \sum_{{\mu_1}}^{}$tμ1CCSDμ2|[H, T3(2)]| HF〉 (10.20)

where the approximate triples amplitudes evaluated as:
t(2)aibjck = - $\displaystyle {\frac{{\langle {{ijk}\atop{abc}}\vert[\hat{H},T_2]\vert\mathrm{H...
... }}{{ \epsilon_a-\epsilon_i + \epsilon_b-\epsilon_j + \epsilon_c-\epsilon_k }}}$     (10.21)

In the literature one also finds sometimes the approximate triples model CCSD[T] (also denoted as CCSD+T(CCSD)), which is obtained by adding only E(4)DT to the CCSD energy. Usually CCSD(T) is slightly more accurate than CCSD[T], although for closed-shell or spin-unrestricted open-shell reference wavefunctions the energies of both models, CCSD(T) and CCSD[T] model, are correct through 4.th order perturbation theory. For a ROHF reference, however, E(5)ST contributes already in 4.th order and only the CCSD(T) model is correct through 4.th order perturbation theory.


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Next: Integral-direct implementation and resolution-of-the-identity Up: Characteristics of the Implementation Previous: CC calculations with restricted   Contents   Index
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