∇ 2 Ωs U inter,s is the second-derivative Hessian matrix of the intermolecular energy function with respect to the optimisation variables Ω s , while ∇ Ωs ∇ pU r/d,s is a vector of second-order cross derivatives of the repulsive/dispersive energy component with respect to optimisation variables Ω s and p. Once the lattice energy minimisation is complete, both of these matrices can be evaluated. The former is independent of the parameter derivatives and thus can be reused for all parameters in the set of variables p. Evaluation of the latter utilizes the first-derivatives and second-order cross derivatives with respect to the parameter values for each parameter variable. Crucially, analytical expressions for all of these derivative terms have been explicitly derived in . As such, these quantities are likely to be far cheaper to evaluate than using finite difference calculations around a lattice minimisation, and also benefit from less numerical noise than finite differences. Moreover, no additional lattice minimisations need to be carried out since all of the required quantities are defined at the optimal structure geometry obtained for the evaluation of the merit function. With the values of the matrices determined, ∇ pΩ * s can be obtained by solving the set of linear equations formed by Equation ( ).