Analytic second derivatives, nuclear magnetic

Equations (49), (50) and (51) can be differentiated with respect to external perturbations (e. g. electric or magnetic fields) and with respect to nuclear coordinates, allowing for the analytical computation of free energy gradients [103,104] and second derivatives [106,110] they are used for geometry optimisations in solution, and for the calculation of force constants, polarizabilities etc. 

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