Not a quantum mechanical method

Empirical model: atoms held together by bonds

Analytical expression for potential (or steric) energy:

V = V (bond stretching) + V (angle bending) + V (torsional) +

Describes interactions between all the atoms in the molecule

A molecular mechanics "force field" is defined by:

The particular mathematical form used for each term in V, along with the values of the parameters in each term.

Some force fields have additional terms compared to the above expression.

The parameters are fit to reproduce experimental data or high-level ab initio molecular orbital calculations

A molecular mechanics force field can be used to calculate

Equilibrium geometry of a molecule

Relative energies of conformers of a molecule

Barriers to internal rotation

Vibrational frequencies

Dipole moments

Intermolecularinteractions

Molecular mechanics cannot be used to calculate

Structures (i.e. transition states) and properties (reaction energies)

far from equilibrium

There are many different types of force fields and some computer programs offer the option of choosing different force fields:

Spartan has the following force field options:

MMFF94 (Merck Molecular Modeling Force Field, 1994 version),

T.A. Halgren, J. Comput. Chem., 17, several articles starting on pages 490, 520, 553, 616, 587 (1996)

SYBYL (developed by Tripos, Inc.)

M. Clark, et al., J. Comput. Chem. 10, 982 (1989)

Force fields are always being updated & improved, so it is important to specify the version & year

Bond Stretching: V_{str, i,j} = (k/2) (r _i,j - r_{eq, i,j})²

k = force constant

r _i,j = bond length between atoms i & j

r_{eq, i,j} = equilibrium bond length

Angle Bending: V_{bend, i,j} = (k/2) (q _i,j - q _{eq, i,j})²

k = force constant

q _i,j = angle

q _{eq, i,j} = equilibrium angle

Torsion: V_tors = (1/2) [V₁ (1 + cos f ) + V₂ (1 - cos 2f ) +

Van der Waals: V_{VDW, ij} = e _IJ [ (R_IJ^*/Rij)¹² - 2 (R_IJ^*/Rij)⁶]

Rij = distance between atoms i & j (4 or more atoms apart)

R_IJ^* = value of Rij at the minimum in V_{VDW, ij}

e _IJ = minimum value of V_{VDW, ij}

Electrostatic: V_{es, ij} = Q_i Q_j / (e _r Rij)

e _r = dielectric constant

Choose an initial set of parameters based on high quality ab initio or experimental data

Choose a representative set of molecules (training set)

Vary parameters so as to minimize the deviations of the calculated properties from the ab initio or experimental properties

Iterate (adjusting parameters to reproduce one type of property may throw off the calculation of another type of property)

Drawbacks

Results of a force field calculation are only as good as the data with which the force field was parameterized

Structures and properties can only reasonably be calculated for moleculessimilar in type to those in the training set

Force field calculations are fast because no integrals need be calculated

The energy (as well as its first and second derivatives which are needed for geometry optimization and energy minimization) is calculated from simple analytical expressions with parameters added from a table.

MMFF94 has the following numbers of parameters:

Stretching: 500 force constants, 500 bond lengths

Bending: 2300 force constants, 2300 bond angles

Torsion: 2800

Van der Waals: 400

Electrostatic: 600

Calculated from the steric energy of the equilibrium geometry plus bond energies