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The van der Waals interactions fall off as 1/r 6 , and
can be cut off at much shorter distances, for
example 10Å. This cut off speeds the computations
significantly, even for relatively small molecules.
NOTE: To precisely reproduce the energies obtained with
Allinger’s force field: set the van der Waals cutoff constants
to large values in the MM2 Constants table.
Electrostatic Energy
dipole/dipole contribution
E = 14.388
∑∑
i
j
µ i
µ j
D µ
r ij
3
( cos χ − 3cosα i
cosα j )
where the value 14.388 converts the result from
ergs/mole to kcal/mole, χ is the angle between the
two dipoles µ i and µ j , α i and α j are the angles the
dipoles form with the vector, r ij , connecting the two
at their midpoints, and D µ is the (effective)
dielectric constant.
E Electrostatic
=
∑
i
q i
q j
j
∑
Drij
The electrostatic energy is a function of the charge
on the non-bonded atoms, q, their interatomic
distance, r ij , and a molecular dielectric expression,
D, that accounts for the attenuation of electrostatic
interaction by the environment (solvent or the
molecule itself).
In Chem3D, the electrostatic energy is modeled
using atomic charges for charged molecules and
bond dipoles for neutral molecules.
There are three possible interactions accounted for
by Chem3D:
• charge/charge
• dipole/dipole
• dipole/charge.
Each type of interaction uses a different form of the
electrostatic equation as shown below:
charge/charge contribution
E = 332.05382
∑
i
q i
q j
j
∑
Dq r ij
where the value 332.05382 converts the result to
units of kcal/mole.
dipole/charge contribution
E = 69.120
∑ ∑
i
j
r ij
2
q i
µ j
D µ
D q
( cosα j )
where the value 69.120 converts the result to units
of kcal/mole.
Bond dipole parameters, µ, for each atom pair are
stored in the bond stretching parameter table. The
charge, q, is stored in the atom types table. The
molecular dielectric is set to a constant value
between 1.0 and 5.0 in the MM2 Atom types table.
NOTE: Chem3D does not use a distance-dependent
dielectric.
Cutoff Parameters for Electrostatic
Interactions
The use of cutoff distances for electrostatic terms,
as for van der Waals terms, greatly improves the
computational speed for large molecules by
eliminating long-range interactions from the
computation.
As in the van der Waals calculations, Chem3D
invokes a fifth-order polynomial switching function
in order to maintain second-order continuity in the
force-field. The switching function is invoked as
minimum values for charge/charge, charge/dipole,
136•Computation Concepts
CambridgeSoft
Molecular Mechanics Theory in Brief