[seqfan] Re: Chemistry sequence

Richard Mathar mathar at strw.leidenuniv.nl
Sat Aug 29 16:08:36 CEST 2009

http://list.seqfan.eu/pipermail/seqfan/2009-August/002255.html asks
in addition

dw> I doubt we'll run into these problems for molecules of, say, 10 protons or 
dw> fewer.
dw> I guess I'm curious as to what the problems are at the small-molecule end.

The remaining problem is to decide for each partition
of the total number of protons (say for the 42 possibilities at n=10
if A000041 is correct), whether a stable molecule with that composition exists:

n=1: H stable
n=2: H_2 stable, He stable
n=3: H_3 (unstable I guess), HeH (?), Li stable
n=4: H_4 (?), HeH_2 (?), He_2 probably unstable, LiH (likely stable, but don't touch) Be stable
n=5: H_5 (unstable I guess), HeH_3 (unstable I guess), He_2H probably unstable,
     LiH_2 (probably unstable) HeBe (probably unstable), BeH (?), B stable

As long as the number of protons stays low such that the various bending
structures of carbon rings are not to be decided, this is as close at
it gets to mathematics as I can imagine. So the sequence that is defined
above starts as a(1)=1 (the math-oriented people would add a(0)=1, which is
the vacuum or what they call the empty set), a(2)=2, a(3)>=1, likely a(3)=2.

I am not sure whether the question of stability is an easy one. Marginally
stable molecules may exist isolated in the ultra-high vacuum in
the insterstellar medium, but would not be detectable in any laboratory
because they would immediately collide (=interact and decompose) with the
surrounding vessel. But if you ask in the associated chemistry related
news groups (seqfan is not a suitable forum for that), you may find answers to
those questions.

For the H_3 case see for example the article
"H_3^{2+} molecular ions can exist in strong magnetic field",
JETP Lett, vol 69 (11) (1999), p 800-805
which claims that with magnetic fields larger than 10^11 Gauss
this can be stabilized. Does this qualify to count H_3 ?
The article on the Ag-clusters in JCP 118 (2003) 9241 clearly indicates
that H_3 is unstable with respect to the standard dissociation into the dimer and 

For HeH see for example Phys Rev Lett 43 (1979) 1719 which 
discusses the infrared spectrum of the singly charged molecule, or the earlier
article in JCP 23 (1955) 1169. Since the dissociation energy is around 1 eV, this
ionized form is stable under standard conditions.


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