Flexible molecules

Modelling of internal degrees of freedom, usual techniques:

Bond distances

• Atoms linked by a chemical bond (stretching):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{str} (r_{12}) = \frac{1}{2} K_{str} ( r_{12} - b_0 )^2 }

Bond Angles

Bond sequence: 1-2-3:

Bond Angle: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2 }

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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: