The generalized energy-based fragmentation(GEBF)approach[1] has been implemented for the analytic total energy gradients as follow,[2] δETot/δqA=∑n Cn〔δ(E)n/δqA-Fn.aQa-∑bfab〕+[〔M∑m Cm〕-1]∑b∈all fab,(1)where A denotes a real atom in a given subsystem,a,b denote the point-charge centers,n,a F is the electric field generated by the n-th subsystem on the center a(which can be calculated with some existing ab initio programs),and ab f represents the Coulomb force between charge on b and charge on a.The analytic energy gradients are shown to be more accurate than the approximate ones[3] and can be used for the geometry optimization and ab initio molecular dynamics(AIMD)for large systems.[2] A similar way is able to be applied to the second-order derivatives of the total energy with respect to nuclear displacements,i.e.Hessian matrix,which could be used for vibrational frequencies,intensities of normal modes,and various thermochemistry data(such as enthalpy,free energy,etc.).In additional,based on the multilevel GEBF approach for total energy,[4] a multilevel GEBF-MP2 method for energy gradients is developed.[5]