A note is in order on the physical interpretation of the σ and τ tensors in diamagnetic versus paramagnetic molecules. For diamagnetic molecules, the wavefunction has to change in response to the external magnetic field. This changed wavefunction creates an additional magnetic field ("induced field"). In the absence of the external field, the ground state wavefunction does not create a magnetic field, since there are no orbital currents and no unpaired spins. In contrast, if we e.g. treat a paramagnetic spin 1/2 system in the spin Hamiltonian approximation, then the two states are completely independent of the field strength and are equal to the states at zero field. The difference to the diamagnetic case is that already those states in zero field create a permanent magnetic field. It is just that at zero field, both states (creating opposite magnetic fields) have exactly equal populations, such that the created magnetic field averages to zero due to electronic fluctuations. If we apply an external field, we create a population difference (because of the energy splitting), meaning that the permanent magnetic fields of the two states will not exactly cancel, and there will be a net "induced field". At large enough fields, saturation effects will appear, until eventually (at room temperature for fields that are much larger than what can routinely be produced in the laboratory) only the lower-energy state is populated. For example, at room temperature (298 K) and 28.2 T (the magnetic induction inside a 1.2 GHz spectrometer), the lower Zeeman level of a spin 1/2 system with isotropic g-value (g ≈ 2) will have a population of around 53%, i.e., only slightly larger than the population of the upper level. In contrast, at 1000 T, the population of the lower level would reach around 99%. At this point, the "induced field" is constant, and no longer linear in the external field. Similar to the σ tensor, these saturation effects are the major origin of the τ tensor for paramagnetic molecules. It should be stressed that the formalism developed herein is a generalization of the diamagnetic case (since the Helmholtz free energy becomes equal to the ground state energy for diamagnetic molecules at reasonable temperatures), so the proper response of the wavefunction is also contained in the general equations for the fourth derivative of the Helmholtz free energy.