Thermodynamic Properties for Applications in Chemical Industry via Classical Force Fields - Multiscale Molecular Methods in Applied Chemistry - page 211

where D is the energy well-depth and is related to the stretching force constant of

the bond. The Morse potential is more suitable to describe bond stretching than the
simple harmonic potential [ 53 ]. Note that (20) is a good approximation of (21) in
the case of small r ij .

a

2.2.2 Angle Bending

Angle bending interactions occur when an angle formed by three consecutive sites
is perturbed from its equilibrium value. Several potentials are employed to describe
this energy contribution. However, the majority of force fields is based on the
harmonic potential [ 54 ]

1
2 k y ðy y 0 Þ

2

u har

angle ðyÞ¼

(22)

or the trigonometric potential

1
2 k y ð

2

u cos

angle ðyÞ¼

cos ðyÞ cos ðy 0 ÞÞ ; (23)

where y 0 is its

equilibrium value. The bending force constant k y is typically smaller than the bond
force constant k ij , because the energy required to distort an angle from its equilib-
rium value is lower than that required to stretch a bond [ 19 ].

y is the angle formed by three consecutive sites; cf. Fig. 2 , and

2.2.3 Torsional Rotation Terms

Many of the major changes in molecular conformations are due to bond rotations.
The torsion interactions account for the rotation around bonds of four adjacent sites
or the motion of dihedral angles. The torsional potentials are 2

p -periodic and

symmetric at 0 and p . For alkanes, the Ryckaert and Belleman [ 55 ] torsional

potential is often used:

r

ϕ

ψ

θ

Fig. 2 Schematic representation of the intramolecular coordinates: bond length r , bending angle
y , torsional dihedral angle ' , and improper dihedral angle c