A starting structure is defined for MM as a list of atomic Cartesian coordinates and a connectivity table that defines the bonds between the atoms.

Typically the positions of only the heavy atoms are specified by the user and the program adds hydrogens and unshared pairs in standardized locations, to make each atom tetrahedral, trigonal, or linear, as appropriate.

• The force fields defined earlier are applied to the input geometry and a total steric energy (TSE) is calculated.

• The molecular geometry then is altered and the TSE is recomputed; the process is repeated until a minimum TSE is found.

• The method of defining a minimum is crucially important; the second major defect of MM, which it shares with most methods for computing molecular geometry, is a tendency to locate the minimum nearest in potential energy space to the input geometry.

A typical molecular mechanics program determines analytically, by the Newton-Raphson method, ¶E / ¶r and ¶²E / ¶²r for each force field.

• Fully applied, this would lead to a derivative matrix 3n x 3n for a molecule of n atoms.

• In fact, the trivial translation and rotation modes for the whole molecule may be eliminated, leading to a matrix 3n - 6 square.

• The work can be further reduced by what is known as the block diagonalization method, in which only the 3 x 3 matrices attributable to the individual atoms are calculated.
  • This technique requires only 9n elements to be calculated, but does result in a loss of information about the nature of the potential surface.

• The PC version of PCModel also offers steepest descent minimization, which is less efficient, but requires calculation of less information.

Once the energy and structure remain constant from iteration to iteration, with the first derivative matrix near zero [how near ?], computation ceases.

• Further evidence that a minimum has been found can be obtained by using the second derivative matrix to compute the normal-mode vibrational frequencies of the molecule.
  • Since any distortion of a molecule from the geometry at a stationary point on the potential energy surface will lead to an increase in energy, the computed frequencies will all be positive (real) for a molecule in such a state.

  • If the molecule lies at a first-order saddle point (transition state), one and only one frequency, corresponding to motion along the reaction coordinate, will be negative (imaginary).

  • Two or more imaginary frequencies imply location at a maximum.

• Most molecular modeling software of all kinds now provides for the computation of vibrational spectra.

How may one ensure that the potential energy surface has been fully explored, that the minimum that has been found corresponds to the deepest valley, the "true" geometry of the molecule?

• This question is known as the "problem of the global minimum."

• Most approaches to its solution begin as is described above.
  • Then some method is used to generate another starting structure, different from the initial one.

  • This structure is minimized, and the result is compared to the first minimum.

  • This process continues until some criterion establishes the thoroughness of the search of conformation space.

The methods used to generate multiple starting geometries, discussed in an excellent paper comparing them [Saunders, M.; Houk, K. N.; Wu, Y.-D.; Still, W. C.; Lipton, M.; Chang, G.; Guida, W. C., J. Am. Chem. Soc., 1990, 112, 1419], can be divided into two broad categories:

• Deterministic searches that cover conformation space systematically

• Stochastic searches, which use some random element in exploring space.

Representative of the latter method is the Cartesian stochastic search originally described by Saunders [Saunders, M., J. Am. Chem. Soc., 1987, 109, 3150; J. Comput. Chem., 1989, 10, 203; see also, Ferguson, D. M.; Raber, D. J. J. Am. Chem. Soc., 1989, 111, 4371].

• This method operates by applying limited, random increments, or "kicks" to the Cartesian coordinates of the atoms in the initial structure, thus generating a new input;

• Simple checks that atoms remain within bonding distance, etc., are applied, and the structure is reminimized.

Representative of the former is a method described by Still and Lipton [Lipton, M.; Still, W. C. J. Comput. Chem., 1988, 9, 343] that uses a tree-search algorithm to search the torsional angle space of molecules.

• Conformations are generated by selection of a set of possible values for each torsion angle,

• Then all possible combinations of angles are formed, subject to simple conditions regarding ring closure, etc.

PCModel implements a combination of the two methods, called the Metropolis-Monte Carlo technique. It searches randomly over rotatable bonds; this technique also is implemented in Spartan. PCModel also allows the choice of the Cartesian stochastic search. [A short tutorial on using these methods is here].

In the end, we must rely on our knolwdge of molecular structure.

• Is the structure reasonable?

• Are the conformations around all of the rotatable bonds realistic?

• Have large groups been placed unreasonably close to each other?

In short, always try to form an idea of what the answer should look like before carrying out the search. Computation will find no mysterious new forces that you didn't learn about in sophomore organic chemistry.