Flexible molecules

Modelling of internal degrees of freedom, usual techniques:

Bond distances

• Atoms linked by a chemical bond (stretching):

$V_{str}(r_{12})={\frac {1}{2}}K_{str}(r_{12}-b_{0})^{2}$

Bond Angles

Bond sequence: 1-2-3:

Bond Angle: $\theta$

$\cos \theta ={\frac {{\vec {r}}_{21}\cdot {\vec {r}}_{23}}{|{\vec {r}}_{21}||{\vec {r}}_{23}|}}$

Two typical forms are used to model the bending potential:

$V_{bend}(\theta )={\frac {1}{2}}k_{\theta }\left(\theta -\theta _{0}\right)^{2}$

$V_{bend}(\cos \theta )={\frac {1}{2}}k_{c}\left(\cos \theta -c_{0}\right)^{2}$

Internal Rotation

For molecules with internal rotation degrees of freedom (e.g. n-alkanes), a torsional potential is usually modelled as: