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constant), while θ 0 defines the equilibrium angle.
This equation estimates the energy associated with
deformation about the equilibrium bond angle. The
constant, 0.02191418, is a conversion factor to
obtain the final units as kcal/mole.
Unique parameters for angle bending are assigned
to each bonded triplet of atoms based on their atom
types (C-C-C, C-O-C, C-C-H). For each triplet of
atoms, the equilibrium angle differs depending on
what other atoms the central atom is bonded to.
For each angle there are three possibilities: XR2,
XRH or XH2. For example, the XH2 parameter
would be used for a C-C-C angle in propane,
because the other atoms the central atom is bonded
to are both hydrogens. For isobutane, the XRH
parameter would be used, and for 2,2-
dimethylpropane, the XR2 parameter would be
used.
The effect of the K b and θ 0 parameters is to
broaden or steepen the slope of the parabola. The
larger the value of K b , the more energy is required
to deform an angle from its equilibrium value.
Shallow potentials are achieved with K b values less
than 1.0.
A sextic term is added to increase the energy of
angles with large deformations from their ideal
value. The sextic bending constant, SF, is defined in
the MM2 Constants table. With the addition of the
sextic term, the equation for angle bending
becomes:
E Bend
= 0.02191418 ∑ K [(θ −θ b o
) 2 + SF(θ −θ o
) 6 ]
Angles
NOTE: The default value of the sextic force constant
is 0.00000007. To precisely reproduce the energies
obtained with Allinger’s force field: set the sextic
bending constant to “0” in the MM2 Constants tables.
There are three parameter tables for the angle
bending parameters:
• Angle Bending parameters
• 3-Membered Ring Angle Bending parameters
• 4-Membered Ring Angle Bending parameters
There are three additional angle bending force
constants available in the MM2 Constants window.
These force constants are specifically for carbons
with one or two attached hydrogens. The following
force constants are available.
The numbers refer to atom types, which can be
found in the Atom Types Table in Chem3D.
• -CHR- Bending K for 1-1-1 angles
• -CHR- Bending K for 1-1-1 angles in
4-membered rings.
• -CHR- Bending K for 22-22-22 angles in
3-membered rings.
The -CHR- Bending K b for 1-1-1 angles allows
more accurate force constants to be specified for
Type 1 (-CHR-) and Type 2 (-CHR-) interactions.
The -CHR-Bending K b for 1-1-1 angles in
4-membered rings and the -CHR- Bending K b for
22-22-22 angles (22 is the atom type number for C
Cyclopropane) in 3-membered rings differ from the
-CHR- Bending K b for 1-1-1 angles and require
separate constants for accurate specification.
Torsion Energy
Ε Twist
=
∑ V n
1 + cos(nφ − φ)
2
Torsions
[ ]
This term accounts for the tendency for dihedral
angles (torsionals) to have an energy minimum
occurring at specific intervals of 360/n. In
Chem3D, n can equal 1, 2, or 3.
Ε Twist
=
∑
Torsions
V 1
( 1 + cosφ)+ V 2
2
2 ( 1 + cos2φ)+
V 3
2
( 1+ cos3φ )
The V n /2 parameter is the torsional force constant.
It determines the amplitude of the curve. The n
signifies its periodicity. nφ shifts the entire curve
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Molecular Mechanics Theory in Brief