Torsion driving conformational sampling methods such as described in the
*OMEGA Theory* section often perform poorly
for macrocyclic molecules due to the problem of ring closure after the torsion driving step.
Conformational sampling of macrocycles therefore requires a different approach;
for example distance geometry (DG) [Crippen-1988], molecular dynamic (MD/LLMOD) [Watts-2014],
MD with perturbation along low energy eigenvectors [Labute-2010], or inverse kinematics
[Coutsias-2016] have all been applied to this problem.

**OMEGA**‘s method of conformational sampling of macrocycles is an adaptation of the distance geometry method
of Spellmeyer et al. [Spellmeyer-1997]. In this method a traditional embedding DG algorithm is replaced
with a direct error function minimization of the random atomic coordinates, followed by force field
refinement. Each initial Cartesian atomic coordinate *x* is assigned by choosing a random number *r*
between *-1* and *1*, multiplied by a factor \(f\sqrt{N}\) which determines the box of maximum extent
for molecule with *N* atoms:

(1)\[x = f\sqrt{N}r\]

Alternatively, instead of randomly placing atoms in Cartesian space, the method allows for random placement of rigid fragments such as aromatic rings, nitro groups etc. After randomly placing molecules atoms or rigid fragments, an error function of the form:

(2)\[F = \sum_{i,j} (d_{ij}-c_{i,j})^2 + \sum_k V_k\]

is optimized. In the above equation the first sum runs over all pairs of atoms in the molecule,
where \(d_{ij}\) are the interatomic distances and \(c_{ij}\) are elements of the constraint matrix
respectively; they are obtained from the MMFF94 force field parameters. When atoms *(i,j)* are
bonded or are the first and last atoms in a bond angle, the upper and lower bounds
are the same and are taken as the corresponding equilibrium force field distances. When
atoms *(i,j)* are the first and last atoms of a torsion angle, the lower bound corresponds to the cis configuration and
the upper bound to the trans configuration of those atoms. Finally, when atoms *(i,j)* are separated
with more than 3 bonds, the lower bound is taken as the sum the vdW radii and the upper
bound as the sum of bond lengths which separate the pair. The second summation in
equation (2) is over the tetrahedral constraints which result from:

- planarity
- chirality
- cis-trans isomerism

Optimization of the error function (2) leads to a rough conformation. No hydrogen atoms except those which are bonded to chiral atoms are included in the error function minimization. Each rough conformation is checked for chirality correctness before refinement. If the rough conformation passes the chirality checks it is refined against a forcefield, MMFF94 ([Halgren-1996-1], [Halgren-1996-2], [Halgren-1996-3], [Halgren-1996-4], [Halgren-1996-5]). Solvent forces can included in the refinement step using a simple continuum solvation model (the Sheffield model [Grant-2007]). When the sequence of: random placement followed by error function minimization and force field refinement is repeated for large enough number of times for a given macrocycle, its conformational space is reasonably well covered.

This method of conformation sampling is completely general, and can be used to generate conformations
for any molecule, whether or not it contains a large ring. However the ‘macrocycle’ mode in **OMEGA** has
been specifically developed and parameterized to perform well on macrocycles, therefore its performance
on linear and small ring molecules is worse than ‘classic’ **OMEGA**.