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Documento PDF - UniCA Eprints - Università degli studi di Cagliari.

Documento PDF - UniCA Eprints - Università degli studi di Cagliari.

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78 molecular dynamicsa.2.1Bonded interactionThe bondend interactions involved three contributions[62]:U bonded = U bonds + U angles + U <strong>di</strong>hedrals(A.19)U bonds = ∑ 1 2 K b(r − r 0 ) 2 describes the energy betweencovalently bonded atoms. K b is the constant of the force, r 0is the equilibrium <strong>di</strong>stance between two atoms and r is thelenght of the bond (Figure A.2 top left).U angle = ∑ 1 2 K a(θ − θ 0 ) 2 describes the energy due to thedeformation of the angle formed by the three particles. K ais the constant of the force and θ 0 is the equilibrium anglebetween the atoms and r is the lenght of the bond (FigureA.2 top right).U <strong>di</strong>hedral = ∑ 1 2 V φ(1 + cos(nφ − φ 0 ) represents the potentialdue to the torsion angles. The energy is linked at therotation around a bond. V φ is a constant that defines therotation barrier around the bond, φ 0 is the equilibrium <strong>di</strong>hedralangle and n is the multiplicity of the torsions (FigureA.2 bottom).Figure A.1.: Bon<strong>di</strong>ng (top left), angular (top right) and <strong>di</strong>hedral (bottom)interaction between two, three and four atoms.a.2.2Non-bonded interactionThe non-bonded interaction involves the atoms not chemicallybonded or separated by three o more bonds. It isthe sum between the Coulombic attraction and the van der

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