Sent to CCL
by: "Rinderspacher, Berend C CIV (US)"
[berend.c.rinderspacher.civ!A!mail.mil]
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Why not define dynamic correlation as the
contribution to the energy from the second order cumulant (D^(2)-1/N D^(1)\wedge
D^(1))?
Since the correlation energy is already defined as the difference
to the HF energy, or more generally, \min_{Slaters \phi}
<\Psi|\phi><\phi|H|\phi><\phi|\Psi>, whatever is left over is
static correlation.
At least that's how I think about
it.
Christopher
-----Original Message-----
From: owner-chemistry+berend.rinderspacher==us.army.mil]_[ccl.net
[mailto:owner-chemistry+berend.rinderspacher==us.army.mil]_[ccl.net] On Behalf
Of Georg Lefkidis lefkidis**physik.uni-kl.de
Sent: Thursday,
March 15, 2012 4:19 AM
To: Rinderspacher, Berend C CIV (US)
Subject: CCL:
AW: CASSCF does not produce spin densities
Sent to CCL by: "Georg
Lefkidis" [lefkidis^^physik.uni-kl.de] Dear Jürgen, dear all
the
problem of defining static vs. dynamical correlations is not an easy one. I have
discussed it many times with my physicists colleagues and the consensus (for
whatever this is worth) is that dynamic correlations are defined by virtual
excitations with well-defined, nonzero energy differences. Following this trail
of thoughts the "measure" of the character of the correlations is the energy
difference of the Slater determinants in the CI expansion. This is also
consistent with the fact that for static correlations one needs multi-reference
expansions. This is also connected to the self-energy, in that the static
correlations stem from its imaginary part while dynamic mainly originate from
its real part. I am not sure I completely understand this, however. My
interpretation is that since the static correlations have no energy difference
in the denominator of the Green's function, they can only be imaginary thus
leading to broadening, while the energy shifting comes from the!
real
part. In view of this I probably agree with the statement that static
correlations mean basically splitting while dynamic basically
shifting.
What do you think?
Best
regards
Georg
On 15/03/2012, at 9:23 AM,
Jürgen Gräfenstein jurgen-$-chem.gu.se
wrote:
Your point about
quasi-deneracy merits some more thought. So,
you're
suggesting that when the broadening of the energies by
the correlation is smaller than their splitting, the >correlation is
"dynamic"? Maybe a self-energy concept can be leveraged here.
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