Thermodynamic Properties for Applications in Chemical Industry via Classical Force Fields - Multiscale Molecular Methods in Applied Chemistry - page 210

Hydrogen bonds can also be explicitly modeled, replacing the LJ 12-6 term
between hydrogen bonding atoms by an empirical hydrogen bonding potential
function that reproduces the hydrogen bonding distance and energy [ 19 ]. An
example is a modification of the LJ 10-12 potential:

12 10

C ij
r ij

D ij
r ij

u HB

cos 4

ð r ij ; y BHA Þ¼ ðy BHA Þ;

(19)

where C ij and D ij are the repulsive and attractive parameters and y BHA is the angle

between the atoms of the hydrogen bond (A-H···B).

2.2 Intramolecular Interactions

There are several types of intramolecular interactions, also called bonded or
valence interactions, which contribute to the potential energy, i.e., bond stretching,
bond angle bending, dihedral angle motion, improper angle bending, etc. These are
not exclusively pair interactions, but include three- and four-body interactions as
well. The parameters of the intramolecular potentials are typically fitted to repro-
duce geometries, vibrational frequencies, and energy profiles from ab initio calcu-
lations [ 9 ].

2.2.1 Bond Stretching

Bond stretching potentials describe the change in potential energy with the bond
distance between two neighboring sites. Bond stretching is frequently represented
by a harmonic potential. Thereby, analogously to Hook's law,

the sites are

connected by an ideal spring:

1
2 k ij ð

u har
bond

2

ð r ij Þ¼ r ij r 0 Þ ; (20)

where k ij is the bond stretching force constant and r 0 is a reference bond length. This
reference value is not the equilibrium length, but the bond length reached when all
the other force field terms are set to zero [ 19 ]. However, physically, bond stretching
does not exhibit a harmonic potential. Thus, anharmonic bond stretching potentials
are also used, the simplest one adding a cubic term to (20). Other examples of
anharmonic potentials are the Simon-Parr-Finland potential [ 51 ] or the Morse
potential [ 52 ]:

2

u Mor
bond

ð r ij Þ¼ D ½ 1 exp ða r ij Þ ; (21)