\begin{align}
    H_{I} =\sum_{i=a}^{b}H_i^{burial} + \sum_{i=a}^{b} \sum_{j=a}^{b}H_{ij}^{contact}  \\
    H_{C} =\sum_{i=a}^{b}H_i^{burial}  + \sum_{i=a}^{b} \sum_{j=1}^{L}H_{ij}^{contact},
\end{align}
