Computational Methods using Force Fields

Allinger:

"We have a great deal of experimental information regarding small molecules, such as bond lengths, angles, strain energy and so on. A large molecule consists of the same features we already know about in small molecules, but combined and strung together in various ways. Can we with help of current structural theory, formulate the structure of a large molecule in terms of elementary features of small molecules ?"

E = _ij k_ij x_ix_j + _ijk k_ijk x_ix_jx_k + ...

Allinger:

"It is important to retain sight of the fact that force field calculations are done a 'molecular model'. This model is assigned properties, e.g. barriers of rotations, which reproduce experimental facts, but this does not mean that it is in every respect a faithful reproduction of the molecule under study. It only means that particular information which has been used to develop the model is reproduced by the model."

The aim is to be able to handle a wide range of molecules with a limited set of transferable parameters.

Example: The TRIPOS Force Field

Forces holding atoms together can be described by potential energy functions of structural features: bond lengths, angles, non-bonded interactions, etc. The combination of all these potential energy functions is called the Force Field.

Force Field calculations include:

• Equations to calculate the energy as function of the molecular geometry:

  E = E_str + E_bend + E_oop + E_tors + E_vdw ( + E_ele + E_{dist_c} + E_{ang_c} + E_{tors_c} + E_{range_c} + E_multi + E_{field_fit} )

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  Main terms:

  Estr :	energy of a bond stretched or compressed from its natural bond length.
  Ebend :	energy of bending bond angles from their natural values.
  Eoop :	energy of bending planar atoms out of the plane.
  Etors :	torsional energy due to twisting about bonds.
  Evdw :	energy due to van der Waals non-bonded interactions.

  Optional terms:

  Eele :	energy due to electrostatic interactions.
  Edist_c :	energy associated with distance constraints.
  Eang_c :	energy associated with angle constrains.
  Etors_c :	energy associated with torsion angle constraints.
  Erange_c :	energy associated with range constraints.
  Emulti :	energy associated with multifitting.
  Efield_fit :	energy associated with fitting fields.

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• Parameters that define the reference points and force constants, allowing for the calculation of the different energies due to deviations from 'natural' values and/or attractive/repulsive interactions between atoms.

• Algorithms to calculate new positions, the so called optimizers/minimizers. Different methods (Steepest Descents / Conjugate Gradients / Powell / Newton-Raphson / BFGS / Line searches) are available. Different techniques to overcome the local/global minima problem are provided for.

Last updated on August 26, 1996.