Analytical Gradients of the Second-Order Moller-Plesset Energy Using Cholesky Decompositions

An algorithm for computing analytical gradients of the second-order MOller-Plesset (MP2) energy using density fitting (DF) is presented. The algorithm assumes that the underlying canonical Hartree-Fock reference is obtained with the same auxiliary basis set, which we obtain by Cholesky decomposition (CD) of atomic electron repulsion integrals. CD is also used for the negative semidefinite MP2 amplitude matrix. Test calculations on the weakly interacting dimers of the S22 test set (Jureka et al., Phys. Chem. Chem. Phys. 2006, 8, 1985) show that the geometry errors due to the auxiliary basis set are negligible. With double-zeta basis sets, the error due to the DF approximation in intermolecular bond lengths is better than 0.1 pm. The computational time is typically reduced by a factor of 6-7. (c) 2013 Wiley Periodicals, Inc.