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: $\theta$

$\cos \theta =\frac{{\overrightarrow{r}}_{21}\cdot {\overrightarrow{r}}_{23}}{\left|{\overrightarrow{r}}_{21}\right|\left|{\overrightarrow{r}}_{23}\right|}$

Two typical forms are used to model the bending potential:

$V_{bend}(\theta )=\frac{1}{2}{k}_{\theta }{(\theta -{\theta }_0)}^2$

$V_{bend}(\cos \theta )=\frac{1}{2}{k}_c{(\cos \theta -c_0)}^2$

Dihedral angles. Internal Rotation

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