Chem3D Users Manual - CambridgeSoft

or dipole/dipole interactions are reached. These
cutoff values are located in the MM2 Constants
parameter table.
Since the charge-charge interaction energy between
two point charges separated by a distance r is
proportional to 1/r, the charge-charge cutoff must
be rather large, typically 30 to 40Å, depending on
the size of the molecule. The charge-dipole, dipoledipole
interactions fall off as 1/r 2 , 1/r 3 and can be
cutoff at much shorter distances, for example 25
and 18Å respectively. To precisely reproduce the
energies obtained with Allinger’s force field: set the
cutoff constants to large values (99) in the MM2
Constants table.
OOP Bending
Atoms that are arranged in a trigonal planar fashion,
as in sp 2 hybridization, require an additional term to
account for out-of-plane (OOP) bending. MM2
uses the following equation to describe OOP
bending:
Ε=K ∑[θ−θ b
() 2 o
+SF
Out ofPlane
The form of the equation is the same as for angle
bending, however, the θ value used is angle of
deviation from coplanarity for an atom pair and θ ο
is set to zero. The illustration below shows the θ
determined for atom pairs DB.
A
D
x
θ y
(θ−θ o
) 6 ]
B
The special force constants for each atom pair are
located in the Out of Plane bending parameters
table. The sextic correction is used as previously
described for Angle Bending. The sextic constant,
SF, is located in the MM2 Constants table.
C
Pi Bonds and Atoms with Pi Bonds
For models containing pi systems, MM2 performs
a Pariser-Parr-Pople pi orbital SCF computation for
each system. A pi system is defined as a sequence of
three or more atoms of types which appear in the
Conjugate Pi system Atoms table. Because of this
computation, MM2 may calculate bond orders
other than 1, 1.5, 2, and so on.
NOTE: The method used is that of D.H. Lo and M.A.
Whitehead, Can. J. Chem., 46, 2027(1968), with
heterocycle parameter according to G.D. Zeiss and M.A.
Whitehead, J. Chem. Soc. (A), 1727 (1971). The SCF
computation yields bond orders which are used to scale the
bond stretching force constants, standard bond lengths and
twofold torsional barriers.
The following is a step-wise overview of the
process:
1. A Fock matrix is generated based on the
favorability of electron sharing between pairs
of atoms in a pi system.
2. The pi molecular orbitals are computed from
the Fock matrix.
3. The pi molecular orbitals are used to compute
a new Fock matrix, then this new Fock matrix
is used to compute better pi molecular orbitals.
Step 2 and 3 are repeated until the computation
of the Fock matrix and the pi molecular
orbitals converge. This method is called the
self-consistent field technique or a pi-SCF
calculation.
4. A pi bond order is computed from the pi
molecular orbitals.
5. The pi bond order is used to modify the bond
length(BL res ) and force constant (K sres ) for
each bond in the pi system.
ChemOffice 2005/Chem3D Computation Concepts • 141
Molecular Mechanics Theory in Brief