SQUARE45

Let

S = (b_1, b_2, \boldsymbol{\theta})

be a stack of

N

adjacent base pairs, where

b_i

is the

i

-th base pair and

\boldsymbol{\theta}

represents the relative orientation. The stacking interaction energy

E_{\text{stack}}

is modeled as a pairwise potential sum over adjacent bases: \n

E_{\text{stack}} = \frac{1}{2} \boldsymbol{\theta}^T \boldsymbol{K} \boldsymbol{\theta} + \frac{1}{N-1} \boldsymbol{\tau} \text{Tr}\big(\boldsymbol{R}_{i, i+1}\big)

\nwhere

\boldsymbol{K}

is the stiffness matrix governing torsional strain, and

\boldsymbol{R}_{i, i+1}

is the overlap matrix quantifying the

\pi

-electron overlap between

b_i

and

b_{i+1}

, typically approximated by a function of the distance

d_{i, i+1}

and the dihedral angle

\phi_{i, i+1}

Base Stacking Interactions