Dear CCl'ers,

A few wanted me to summarize the replies to the CCL list.  Here it comes,
and thanks to the six people who took time to respond.

Monica C. Concha
Research Associate
Dept. Of Chemistry
University of New Orleans
New Orleans LA 70148
E-mail mconcha(-(at)-)


   I have been trying to optimize the vanadium dimer with multiplicity
of 3, using various dft methods. The problem is that depending on the
initial bond length, the dimer optimizes to different bond lengths with
different energies, and differ s**2 values.  The bond lengths only
by about 0.01 Angstroms but the energies differ by 35 kcal.  The odd
thing is that the lowest energy corresponds to an s**2 value of 2.55
rather than the expected value of 2.0. Any suggestions?

Hi Monica,

    If you haven't done much work with metal clusters before, you're quickly going
to find out they are much tougher than simple organics.  The problem is there are
lots of low-lying excited states arising from low overlap of the incomplete d
shells.  In the case of V2, you have two dominantly s1d4 atoms bonded to one
another, with the other atomic states, d5 and s2d3, probably mixing in.  This gives
you a large number of possible spin and orbital combinations to work with.
    As for your DFT calculations, it's a given that you have to specify spin.  But
in these cases, you may also have to play with the orbital occupations in the
initial guess.  It's very easy for most codes to converge to excited states of
these molecules.  The only solid solution is to be very thorough.  You've found two
different triplet states already, but it might not be guaranteed that either is
actually the lowest energy triplet (or the ground state for that matter!).  Be
aware of what states (d orbital occupations) are being converged.  Try switching
around the orbital occupations and converging some other states.  Most codes offer
some way of doing this either with the default initial guess or with a restart
    If you're worried about spin contamination, you might want to try a restricted
open-shell approach.  I'd suggest sticking with unrestricted, though.  In this
case, I'd probably turn off any symmetry restrictions to allow the spins to
localize.  I haven't reviewed the literature on V2, but I'd guess the ground state
is singlet with one V alpha-spin s1d4 and the other beta-spin s1d4.  The strong
exchange interaction between the d orbitals should be enough to localize the spin.
But low-lying spin states could extend up to nonet states.
    Good Luck,

    Jason Perry


Hi Mónica:

You should look at works of Casalot (Marsielle) on V-V bond in V2O4.



Julio César Llópiz Yurell
Zapata y G, Habana 10400, CUBA
Tel (537) 781182  Fax (537) 334247

Hi Monika,

from your non-integer value for <S^2> I conclude that
you used an unrestricted DFT method. Since V2 has
10 valence electrons but 9 bonding and 9 antibonding
combinations of atomic valence orbitals, I assume that
you converged to two different electronic states.

Although the p-functions of transition metals are not
occupied in the free atoms, they DO participate in bond
formation (e.g. 18 valence electron rule for TM complexes).
You can check that by printing out the MO vectors (i.e.
info on what basis functions/atomic orbitals participate in
a given MO) and compare them for your two optimized

If you have two different states, you need a multireference
method like CASSCF or MR-CI (maybe a powerful single
reference correlation method like CCSDT works too, but
that can only be decided after seeing the output from that
calculation). Anyhow, putting enough ligands around your
vanadiums to give them 18 valence electrons,
each, makes the molecule well-behaved again.

Dr. Stefan Fau                    |      fau(-(at)-)
Quantum Theory Project     |     (352) 392-6714
University of Florida
Gainesville, FL 32611-8435

  Before optimizing the V-V bond length, you need to sort out
the electronic structure.  That is, look at the initial guess
for starters, try and get a converged single point SCF and look
at the S**2 and occupation.  Is it reasonable?  Then you can
optimize the V-V bond length for whatever state you have found.
If you have spin contamination problems, you might try an rohf
calulation first to insure a reasonable spin function.
  It sounds like you have one triplet V-V state that is fully
optimized without spin contamination problems.  Compare the
electronic occupation with the 'bad' state.  Perhaps you can
switch around some orbitals in your higher energy but well
behaved case to find a lower energy triplet.  Perhaps a triplet
is a very high energy/unreasonable multiplicity for V2?  Atomic
spectral tables show the lowest doublet V neutral atom to be
10,900 cm-1 above ground state V.  The lowest V doublet without
an s2 population is 18,800 above the ground state.  So you're
paying a 4.7eV promotion simply to form reasonable doublets to
form the V2 triplet.  I don't have much experience with metal
cluster calculations though.  Hope this helps!

    - John
Dear Monica,

I've recently come across a similar problem with VO (4 sigma ground
state). The problem was, that initial guess of occupied MO was totally
wrong (the distribution of electrons between different irreps). As I'm
using G98, the solution was quite easy: Guess=Alter (+ appropriate
labes of MO to exchange), and that was enough to get the proper electronic

Tomek Borowski
Chemistry Department
Jagiellonian Univ.

Dear Monica,

did you check the stability of your wavefunction? You mix in higher spin
states as
can be seen from the S2 value of 2.55

If you need help, please email directly to


Yours sincerely

Thomas Strassner


 n:Concha;Monica C.
 tel;home:504- 456-2325
 org:University of New Orleans;Chemistry
 adr:;;Lakeshore;New Orleans;LA;70148;USA
 title:Research Associate
 fn:Monica C. Concha