Improper Torsions and Out-of-plane Bending Motions

Fig 4 9 Without an out-cf-plane term, the oxygen atom in cyclobutane is predicted to lie out of the plane of the ring (left) rather than in the plane. 

A torsional potential of the following form is then used to maintain the improper torsion angle at 0° or 180°  

Of these three functional forms, the improper torsion definition is most widely used as it can then be easily included with the proper torsional terms in the force field. However, the 

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