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Analytical expressions for evaluating energy gradients for local coupled-cluster wavefunctions are derived, and relations between the conventional and local coupled-cluster theories are elaborated. In the more general local case additional terms arise from the geometry dependence of the localization transformation and the non-orthogonality of the projected atomic orbitals (PAOs) which are used to span the virtual space. Furthermore, if the excitations from a given orbital pair are restricted to subsets (domains) of PAOs, new terms arise from the geometry dependence of these subspaces. The gradient theory is also generalized to the case in which weakly correlated electron pairs are treated by local second-order Møller–Plesset theory (LMP2) while the contributions of strong pairs are computed at the coupled-cluster level. A number of test calculations are presented in which optimized equilibrium structures are compared for local and conventional calculations, and it is concluded that the local approximations hardly affect the accuracy.
Rauhut et al. (Mon,) studied this question.