General Energy Model

Because it is tedious to implement all the energy models that have been explored in the literature and impossible to anticipate all the energy models users may wish to explore, ChemTools allows users to define their own energy model. As this is a generic models, this model can reproduce the results of linear, quadratic, exponential, and rational energy models as special cases.

The energy expression should be specified symbolically through Sympy. ChemTools then takes the energies for the user-specified electron numbers and solves the (generally nonlinear) equations for parameters in the symbolically-defined energy model. The energy model is differentiated symbolically to determine the fundamental global reactivity indicators in the canonical and grand canonical ensemble. To define derived reactivity indicators, the maximum number of bound electrons, \(N_{\text{max}}\), is determined by numerical minimization,

\[N_{\text{max}} = \underbrace {\min }_N E(N)\]

The derived reactivity indicators are then defined using the usual formulas.