Systematic Molecular Fragmentation Fragmentation Method

SMF Fragmentation 05

Deev and Collins11 introduced a means of fragmenting large covalently bonded molecules. As originally presented, the SMF fragmentation method was used to define the fragments, intersections, and energy expansion coefficients. The procedure is parameterized by a non-zero integer \(\ell\) and is refered to as a level \(\ell\) procedure. Using our terminology the level \(\ell\) procedure is:

  1. Assign pseudoatoms

  2. Establish connectivity, the result is the graph \(G_0\)

  3. Find the pseudoatom in \(G_0\) which has the highest degree and that is at least \(\ell\) edges away from two different pseudoatoms. Define this pseudoatom as \(A_0\). If no such pseudoatom exists, then \(G_0\) is a fragment and not considered further.

  4. Let \(B_i\) be the set of pseduoatoms which are \(i\) edges away from \(A_0\). Starting from \(B_1\) select the two pseudoatoms of highest degree. Let these pseudoatoms be \(A_1\) and \(A_1'\).

  5. From \(B_2\) select the pseudoatom which has the hightest degree and is bonded to \(A_1\). This is atom \(A_2\). Similarly, from \(B_2\) select the pseudoatom which has the highest degree and is bonded to \(A_1'\). This is atom \(A_2'\).

  6. Repeat the above for pseudoatoms in \(B_3\) through \(B_{\ell -1}\).

  7. Finally from \(B_{\ell}\) select the pseudoatom with the lowest degree that is bonded to pseudo atom \(A_{\ell -1}\); this is atom \(A_\ell\). Similarly, \(A_\ell'\) is the pseudoatom in \(B_{\ell}\) that is bonded to pseudoatom \(A_{\ell - 1}'\). The result is a path of 2|l| edges that is centered on \(A_0\).

  8. Break the \(A_{\ell -1}\)-\(A_\ell\) bond. The resulting graphs are \(G_1\) and \(G_2\).

  9. Break the \(A_{\ell - 1}'\) - \(A_\ell'\) bond. The resulting graphs are \(G_3\) and \(G_4\).

  10. Break both the \(A_{\ell -1}\)-\(A_\ell\) and \(A_{\ell - 1}'\)-\(A_\ell'\) bonds. The resulting graphs are \(G_5\), \(G_6\), and \(G_7\).

  11. Let \(G\) be the set of graphs which is in either the set “\(G_1\), \(G_2\), \(G_3\), \(G_4\)” or the set “\(G_5\), \(G_6\), \(G_7\)” (i.e. ignore graphs which appear in both sets), repeat steps 3-11 for each graph in \(G\)

  12. The previous step terminates when none of the graphs generated in step 11 survive step 3 of the next cycle. The resulting set of fragments is \(F\).

The original presentation contains a few other details we have omitted, namely:

  • How to calculate the coefficients of the fragments; we instead opt to use the IEP.

  • Restrictions on what size rings can be broken for a given \(\ell\). The motivation for these rules stems from their capping method choice. To be more general we instead adopt the view that if a ring shouldn’t be broken, it should be protected as a pseudoatom.

Ring Repair Variation

In a subsequent paper Collins and Deev6 ammended the original SMF fragmentation method to include what they term the “ring repair rule”. This amounts to performing the following steps after the orginal SMF fragmentation method:

  1. For each fragment :math`F_i` in \(F\), consider pairs of pseudoatoms \(A_0\) and \(A_1\)

  2. If \(A_0\) and \(A_1\) are both bonded to another pseudoatom \(A_2\), and \(A_2\) is not in :math`F_i`, add \(A_2\) to :math`F_i`

  3. If \(A_0\) is bonded to a pseudoatom \(A_2\), which is not in :math`F_i`, and \(A_3\) is bonded to a different pseudoatom \(A_3\), which is also not in :math`F_i`, then add \(A_2\) and \(A_3\) to :math`F_i` if \(A_2\) and \(A_3\) are bonded.

  4. If either of the previous two steps modifies a fragment repeat the original SMF fragmentation method with the new set.