For newcomers
Nets, tilings and why topology matters
Why a database of abstract graphs is the useful thing to have when you are designing a real material.
The move that makes reticular chemistry work
Take a metal-organic framework and throw away the chemistry. Replace each metal cluster with a point. Replace each linker with a line joining two points. What remains is a periodic graph — an infinite scaffold of vertices and edges.
That graph is the net, and the surprise is how few of them matter. Tens of
thousands of frameworks have been synthesised; the great majority adopt one of
a few dozen nets. MOF-5 and hundreds of unrelated materials are all pcu, the
primitive cubic net.
This is why a database of abstract graphs earns its place next to a database of
structures. If you know that a six-connected node and a linear linker tend to
give pcu, you can predict what you will get before you synthesise it — and
you can ask the opposite question, which is the useful one: given the net I
want, what would I have to build?
What makes one net different from another
Two nets can have the same coordination numbers everywhere and still be different graphs. Distinguishing them takes finer invariants.
Coordination sequence. Stand on a vertex. Count the vertices one step away,
then two steps, then three. For pcu: 6, 18, 38, 66, 102. Nets that agree for
three shells usually diverge by the fourth or fifth — which is why the search
matches on however many shells you give it, and why giving more shells than you
trust will lose you the right answer rather than confirm it.
Vertex symbol. Describes the shortest rings passing through each pair of edges at a vertex. It catches differences in local ring structure that the sequence smooths over.
Transitivity pqrs. How many kinds of vertex, edge, face and tile the net
has. pcu is 1,1,1,1 — one kind of everything. This is not a curiosity: nets
with low transitivity are the ones frameworks actually adopt, because a highly
symmetric net asks less of the chemistry. When you are choosing a target, low
transitivity is a reason to prefer it.
Tilings, and why faces and tiles appear at all
A net can be filled with tiles — the natural cages it encloses — and that
tiling says things the graph alone does not: pore shape, how cages connect,
what would fit inside. The r and s of pqrs count distinct faces and
tiles. Not every record has them, which is why the search treats them as
wildcards by default.
Catenation
Two identical nets can interpenetrate without bonding to each other. The result
is a real, distinct material with half the pore volume, and it is a distinct
record here, named with a -c suffix.
Whether you want catenated nets in your results depends on what you are asking. Designing for porosity: exclude them. Explaining why your synthesis produced half the surface area you expected: they are the answer.
How the nets are ordered
Nets are browsed in RCSR symbol order, which is a column on the record rather than something worked out when the page is drawn. There is a second, unrelated number on every record — the order the nets were ingested in, simplest first — and the two get confused often enough to be worth naming: the two orderings a net carries says which is which, where each comes from, and which fields no source supplies.
Where this leads
The database is organised so that the design question runs forwards. Pick a net by its topology, find building blocks whose connectivity matches its vertices, and assemble — the reverse topological approach.