Modelling of internal degrees of freedom, usual techniques:
Bond distances
Atoms linked by a chemical bond (stretching):
However, this internal coordinates are very often kept constrained (fixed bond distances)
Bond Angles
Bond sequence: 1-2-3:
Bond Angle:
Two typical forms are used to model the bending potential:
Dihedral angles. Internal Rotation
Bond sequence: 1-2-3-4
Dihedral angle (
) definition:
Consider the following vectors:
; Unit vector in the direction of the 2-3 bond
; normalized component of
ortogonal to ![{\displaystyle {\vec {a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/546e6615827e17295718741fd0b86f639a947f16)
; normalized component of
ortogonal to ![{\displaystyle {\vec {a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/546e6615827e17295718741fd0b86f639a947f16)
![{\displaystyle {\vec {c}}={\vec {a}}\times {\vec {b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8717b5424d185ba2406d4b1165d43a74e47f80b)
![{\displaystyle e_{34}=(\cos \phi ){\vec {a}}+(\sin \phi ){\vec {c}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ba286d66dc8fe0b663a144adbbb2dc01d233780)
For molecules with internal rotation degrees of freedom (e.g. n-alkanes), a torsional potential is
usually modelled as:
![{\displaystyle \Phi _{tors}\left(\phi \right)=\sum _{i=0}^{n}a_{i}\left(\cos \phi \right)^{i}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56f948f4ab156bc4fbce2a7bdcbf3909d87b3df4)
or
![{\displaystyle \Phi _{tors}\left(\phi \right)=\sum _{i=0}^{n}b_{i}\cos \left(i\phi \right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7e74bf9978c2ac42ebba782070030036e9e5cbbd)
Van der Waals intramolecular interactions
For pairs of atoms (or sites) which are separated by a certain number of chemical bonds:
Pair interactions similar to the typical intermolecular potentials are frequently
used (e.g. Lennard-Jones potentials)