Analytic Energy Gradients and Hessians of Exact Two-Component Relativistic Methods: Efficient Implementation and Extensive Applications.

The algebraic exact two-component (X2C) relativistic Hamiltonian can be viewed as a matrix functional of the decoupling () and renormalization () matrices. It is precisely their responses to external perturbations that render X2C-based response theories different in form from the nonrelativistic counterparts. However, the situation is not really bad.