Analytic evaluation of energy gradients for the singles and doubles coupled cluster method including perturbative triple excitations: Theory and applications to FOOF and Cr2

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Abstract
The analytic energy gradient for the singles and doubles coupled cluster method including a perturbative correction due to triple excitations [CCSD(T)] is formulated and computationally implemented. Encouraged by the recent success in reproducing the experimental equilibrium structure and vibrational frequencies of ozone, the new CCSD(T) gradient method is tested with two other ‘‘difficult’’ quantum chemistry problems: FOOF and Cr2. With the largest basis set employed in this work [triple zeta plus two sets of polarization functions (TZ2Pf)] at the CCSD(T) level of theory, the predictions for the O–O and O–F bond lengths in FOOF are 1.218 and 1.589 Å, respectively. These figures are in good agreement with the experimental values 1.216 and 1.575 Å. Based on CCSD calculations with even larger basis sets, it is concluded that the error of 0.014 Å in the O–F bond length at the TZ2Pf/CCSD(T) level of theory is due to the remaining basis set deficiency. On the other hand, the CCSD(T) prediction for the equilibrium bond length of Cr2 (1.604 Å), obtained with a large (10s8p3d2f1g) basis set capable of achieving the Hartree–Fock limit, is still 0.075 Å shorter than experiment, clearly indicating the importance of higher than connected triple excitations in a single‐reference treatment of this particular problem.