Skip to main content

Warning : Abstraction!

This is a throwaway mathematical point, that I am not qualified to make, but it looks like three of the previous examples (diamantane, twistane, and cuneane) have a very abstract connection when colored by signature:


what I mean by this diagram is that diamantane has atoms colored by (a) connected to both other (a) atoms, and to (b) atoms. Its (c) atoms are only connected to (b)s; the arrows could well be double-headed, by the way.

The most complex situation is cuneane, where each 'type' of atom is connected to another in its type and to two in another type. Adamantane would just look like : (a)-(b).

Interesting, but it doesn't get the signature canonization methods debugged any faster...

Comments

Rich Apodaca said…
Gilleain, don't know what to make of it, but it looks interesting.

I'm curious - what are you planning on using your signature implementation for?
gilleain said…
Structure generation, mostly. They seem generally quite useful things, but for the moment, making structures is the goal.

This post :

http://gilleain.blogspot.com/2009/06/signature-bond-compatibility.html

has links to the relevant papers, and most of my recent posts have been examples in the form of recreating single structures from their exact signature.

The algorithm seems flexible enough that it can make an entire isomer space (like C4H10), or start from overlapping fragments.
Rich Apodaca said…
@Gilleain, what do you think of the possibility of using your code for molecular canonicalization (canonization?), i.e., converting equivalent molecular representations into a single form.
gilleain said…
Definitely. The molecular canonization is an essential part of the generation process.

Faulon's method relies on checking at each step that a generated structure is canonical. This allows the algorithm to avoid isomorphism checks.

In the paper that describes the algorithm, there are speed tests that are favourable with nauty.

The paper is here.

Popular posts from this blog

Adamantane, Diamantane, Twistane

After cubane, the thought occurred to look at other regular hydrocarbons. If only there was some sort of classification of chemicals that I could use look up similar structures. Oh wate, there is . Anyway, adamantane is not as regular as cubane, but it is highly symmetrical, looking like three cyclohexanes fused together. The vertices fall into two different types when colored by signature: The carbons with three carbon neighbours (degree-3, in the simple graph) have signature (a) and the degree-2 carbons have signature (b). Atoms of one type are only connected to atoms of another - the graph is bipartite . Adamantane connects together to form diamondoids (or, rather, this class have adamantane as a repeating subunit). One such is diamantane , which is no longer bipartite when colored by signature: It has three classes of vertex in the simple graph (a and b), as the set with degree-3 has been split in two. The tree for signature (c) is not shown. The graph is still bipartite accordin

Király's Method for Generating All Graphs from a Degree Sequence

After posting about the Hakimi-Havel  theorem, I received a nice email suggesting various relevant papers. One of these was by Zoltán Király  called " Recognizing Graphic Degree Sequences and Generating All Realizations ". I have now implemented a sketch of the main idea of the paper, which seems to work reasonably well, so I thought I would describe it. See the paper for details, of course. One focus of Király's method is to generate graphs efficiently , by which I mean that it has polynomial delay. In turn, an algorithm with 'polynomial delay' takes a polynomial amount of time between outputs (and to produce the first output). So - roughly - it doesn't take 1s to produce the first graph, 10s for the second, 2s for the third, 300s for the fourth, and so on. Central to the method is the tree that is traversed during the search for graphs that satisfy the input degree sequence. It's a little tricky to draw, but looks something like this: At the top

1,2-dichlorocyclopropane and a spiran

As I am reading a book called "Symmetry in Chemistry" (H. H. Jaffé and M. Orchin) I thought I would try out a couple of examples that they use. One is 1,2-dichlorocylopropane : which is, apparently, dissymmetric because it has a symmetry element (a C2 axis) but is optically active. Incidentally, wedges can look horrible in small structures - this is why: The box around the hydrogen is shaded in grey, to show the effect of overlap. A possible fix might be to shorten the wedge, but sadly this would require working out the bounds of the text when calculating the wedge, which has to be done at render time. Oh well. Another interesting example is this 'spiran', which I can't find on ChEBI or ChemSpider: Image again courtesy of JChempaint . I guess the problem marker (the red line) on the N suggests that it is not a real compound? In any case, some simple code to determine potential chiral centres (using signatures) finds 2 in the cyclopropane structure, and 4 in the