$\overline{{\left(\Delta H\right)}^2}=\frac{1}{N}{\sum }_{i=1}^N\left[⟨{\psi }_i\left|H_i^2\right|{\psi }_i⟩-{⟨{\psi }_i\left|H_i\right|{\psi }_i⟩}^2\right]$