MOLECULAR MODELING AND MOLECULAR MECHANICS 163
even large molecular assemblies with hundreds of atoms are tractable by MM,
and energy surfaces with many minima may be screened successfully. MM has
been used routinely for many years in organic chemistry applications. Studies
on inorganic systems have begun more recently because the effects of variable
coordination numbers, geometries (square planar, tetrahedral, octahedral),
oxidation and spin states, and electronic infl uences based on partly fi lled d
subshells (such as Jahn – Teller effects) have been diffi cult to model with con-
ventional MM approaches.
In reference 3, Comba and Hambley introduce their topic in three parts:
(1) basic concepts of molecular mechanics, (2) applications of the techniques
and diffi culties encountered, and (3) a guide to molecular modeling of a new
system. Only the introductory section of reference 3a is summarized here.
In molecular mechanics calculations, the arrangement of the electrons is
assumed to be fi xed and the positions of the nuclei are calculated. Bonded
atoms are treated as if they are held together by mechanical springs (vibra-
tional frequencies), and nonbonded interactions are assembled from van
der Waals attractive and repulsive forces (gas compressibility data). Finding
suitable values for van der Waals parameters presents one of the greatest
problems in force fi eld development. Fortunately, van der Waals forces have
less infl uence on the fi nal molecular geometry than do bond - stretch and angle -
bend parameters. The typical equations and parameters simulating the various
interactions that describe the potential energy surface of a molecule are
assembled from (1) a function that quantifi es the strain present in all bonds,
(2) a bond angle function, (3) a function that calculates all the dihedral strain,
and (4) a number of nonbonded terms. To use the equations to calculate the
total strain in the molecule, one needs to know (1) the force constants ( k ) for
all the bonds and bond angles in the molecule, (2) all the ideal bond lengths
(r ) and bond angles ( q ), (3) the periodicity of the dihedral angles ( n ) and the
barriers to their rotation ( V ), (4) the van der Waals parameters Aij and Bij
between thei th and j th atoms to simulate the nonbonded van der Waals inter-
actions, and (5) the point changes qi and qj and the effective dielectric constant
(ε ) to model the electrostatic potential.^4 In inorganic molecular mechanics,
these parameters are empirically derived usually by fi tting a number of crystal
structures and are derived for the specifi c force fi eld used. Parameters are
transferable from one molecule to another (within limits described below) but
are not transferable between force fi elds. A “ force fi eld ” is defi ned as a collec-
tion of numbers that parameterize the potential energy functions. These
functions include the force constants, ideal bond distances and angles, and
parameters for van der Waals, electrostatic, and other terms.
To optimize the geometry of a molecule, the total energy from all forces is
minimized by computational methods. This so - called “ strain energy ” is related
to the molecule ’ s potential energy and stability. Because parameters such as
bond length, bond angles, and torsional angles used to derive the strain ener-
gies are fi tted quantities based on experimental data such as X - ray crystallo-
graphic structures, molecular mechanics is often referred to as empirical force