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A Mo/ller–Plesset energy functional (Lagrangian) which is variational in all variables (the Lagrange multipliers, the orbital rotation parameters, and the orbital energies) is constructed. The variational property ensures that the responses of the orbitals and orbital energies to order n in geometrical perturbations determine the energy derivatives to order 2n+1. The Lagrange multipliers satisfy the somewhat stronger 2n+2 rule. The multipliers, orbital rotations, and orbital energy responses are determined from coupled perturbed Hartree–Fock-type equations using an exponential parametrization of the orbitals. This ensures that the orbital rotations and energy responses are treated in the same way and calculated from a single set of linear equations. Explicit expressions for energy derivatives up to third order are derived for the second-order Mo/ller–Plesset energy.

A suite of tools for the analysis of magnetically induced currents is introduced.These are applicable to both the weak-field regime, well described by linear response perturbation theory, and to the high-field regime, which is inaccessible to such methods.A disc-based quadrature scheme is proposed for the analysis of magnetically induced current susceptibilities, providing quadratures that are consistently defined between different molecular systems and applicable to both planar 2D and general 3D molecular systems in a black-box manner. The applicability of the approach is demonstrated for a range of planar ring systems, the ground and excited states of the benzene molecule and the ring, bowl and cage isomers of the C 20 molecule in the presence of a weak magnetic field. In the presence of a strong magnetic field, the para-to dia-magnetic transition of the BH molecule is studied, demonstrating that magnetically induced currents present a visual interpretation of this phenomenon, providing insight beyond that accessible using linear-response methods.