From owner-chemistry@ccl.net Sun Mar 18 19:52:00 2012 From: "Seth Olsen seth.olsen===uq.edu.au" To: CCL Subject: CCL: AW: CASSCF does not produce spin densities (UNCLASSIFIED) Message-Id: <-46521-120318194506-6997-Vj2MaYDSxCq7XZsOMHmBxg[*]server.ccl.net> X-Original-From: Seth Olsen Content-Type: multipart/alternative; boundary=Apple-Mail-11--527772197 Date: Mon, 19 Mar 2012 09:43:49 +1000 Mime-Version: 1.0 (Apple Message framework v1084) Sent to CCL by: Seth Olsen [seth.olsen(a)uq.edu.au] --Apple-Mail-11--527772197 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=iso-8859-1 This sounds like a reasonable operational definition, since the = expectation value of the interelectronic repulsion should be determined = by the two-body RDM. It doesn't clarify the physics too much, though. = I'll think about it some more. -Seth On 15/03/2012, at 9:58 PM, Rinderspacher, Berend C CIV (US) = berend.c.rinderspacher.civ[*]mail.mil wrote: >=20 > Sent to CCL by: "Rinderspacher, Berend C CIV (US)" = [berend.c.rinderspacher.civ!A!mail.mil] > Classification: UNCLASSIFIED > Caveats: NONE >=20 > 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))? >=20 > 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. >=20 >=20 > At least that's how I think about it. >=20 >=20 > Christopher >=20 > -----Original Message----- >> From: owner-chemistry+berend.rinderspacher=3D=3Dus.army.mil]_[ccl.net = [mailto:owner-chemistry+berend.rinderspacher=3D=3Dus.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 >=20 >=20 > Sent to CCL by: "Georg Lefkidis" [lefkidis^^physik.uni-kl.de] Dear = J=FCrgen, dear all >=20 > 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. >=20 > What do you think? >=20 > Best regards > Georg >=20 >> On 15/03/2012, at 9:23 AM, J=FCrgen Gr=E4fenstein jurgen-$-chem.gu.se = wrote: >=20 >> 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.http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/che= mistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txtClassification: = UNCLASSIFIED > Caveats: NONE >=20 >=20 >=20 > -=3D This is automatically added to each message by the mailing script = =3D- > To recover the email address of the author of the message, please = change>=20>=20>=20 > Subscribe/Unsubscribe:=20>=20>=20 > Job: http://www.ccl.net/jobs=20 > Conferences: = http://server.ccl.net/chemistry/announcements/conferences/ >=20>=20>=20>=20 >=20 --------------------------------------------------- Seth Olsen ARC Australian Research Fellow 6-431 Physics Annexe School of Mathematics and Physics The University of Queensland Brisbane QLD 4072 Australia seth.olsen(a)uq.edu.au +61 7 3365 2816 --------------------------------------------------- Unless stated otherwise, this e-mail represents only the views of the = Sender and not the views of The University of Queensland --Apple-Mail-11--527772197 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=iso-8859-1 This = sounds like a reasonable operational definition, since the expectation = value of the interelectronic repulsion should be determined by the = two-body RDM.  It doesn't clarify the physics too much, though. =  I'll think about it some more. = -Seth


On 15/03/2012, at 9:58 PM, = Rinderspacher, Berend C CIV (US) berend.c.rinderspacher.civ[*]mail.mil = wrote:


Sent to CCL by: "Rinderspacher, Berend C CIV = (US)" [berend.c.rinderspacher.civ!A!mail.mil]
Classification: = UNCLASSIFIED
Caveats: NONE

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=3D=3Dus.army.mil]_[ccl.net = [mailto:owner-chemistry+berend.rinderspacher=3D=3Dus.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 J=FCrgen, 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, J=FCrgen Gr=E4fenstein = 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.http://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/che= mistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txtClassification: = UNCLASSIFIED
Caveats: NONE



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<= /div>
seth.olsen(a)uq.edu.au
+61 7 3365 = 2816
---------------------------------------------------
Unless = stated otherwise, this e-mail represents only the views of the = Sender and not the views of The University of = Queensland

= --Apple-Mail-11--527772197-- From owner-chemistry@ccl.net Sun Mar 18 20:26:01 2012 From: "Seth Olsen seth.olsen===uq.edu.au" To: CCL Subject: CCL: AW: CASSCF does not produce spin densities Message-Id: <-46522-120318195101-5836-+OoiMN6fSgbzGqkl1RuueA a server.ccl.net> X-Original-From: Seth Olsen Content-Type: multipart/alternative; boundary=Apple-Mail-12--527453025 Date: Mon, 19 Mar 2012 09:49:08 +1000 Mime-Version: 1.0 (Apple Message framework v1084) Sent to CCL by: Seth Olsen [seth.olsen{=}uq.edu.au] --Apple-Mail-12--527453025 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=windows-1252 I think that this is a reasonable way to approach the problem, but it = needs some generalization from the way that most physicists I know think = about it. In my experience, one is almost always referring to an = underlying Fermi liquid model, in which case there are simple poles in = the response function. In the case of e.g. CAS models, it is not clear = that the poles are all simple. If state-averaged methods are also to = be treated, then it would seem that the self-energy must be described = using an operator formalism (i.e. an operator acting on the target = space), which would complicate things. For non-evenly weighted = averages, it is not clear how to think about the weights (because the = state-averaged density matrix is no longer dual to a von Neumann = measurement, but instead to a POVM - a metric needs to be introduced). = -SEth On 15/03/2012, at 6:19 PM, Georg Lefkidis lefkidis**physik.uni-kl.de = wrote: >=20 > Sent to CCL by: "Georg Lefkidis" [lefkidis^^physik.uni-kl.de] > Dear J=FCrgen, dear all >=20 > 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 =93measure=94 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=92s 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. >=20 > What do you think? >=20 > Best regards > Georg >=20 >> On 15/03/2012, at 9:23 AM, J=FCrgen Gr=E4fenstein jurgen-$-chem.gu.se = wrote: >=20 >> 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. >=20 >=20 >=20 > -=3D This is automatically added to each message by the mailing script = =3D- > To recover the email address of the author of the message, please = change>=20>=20>=20 > Subscribe/Unsubscribe:=20>=20>=20 > Job: http://www.ccl.net/jobs=20 > Conferences: = http://server.ccl.net/chemistry/announcements/conferences/ >=20>=20>=20>=20 >=20 --------------------------------------------------- Seth Olsen ARC Australian Research Fellow 6-431 Physics Annexe School of Mathematics and Physics The University of Queensland Brisbane QLD 4072 Australia seth.olsen~~uq.edu.au +61 7 3365 2816 --------------------------------------------------- Unless stated otherwise, this e-mail represents only the views of the = Sender and not the views of The University of Queensland --Apple-Mail-12--527453025 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=windows-1252 I = think that this is a reasonable way to approach the problem, but it = needs some generalization from the way that most physicists I know think = about it.  In my experience, one is almost always referring to an = underlying Fermi liquid model, in which case there are simple poles in = the response function.  In the case of e.g. CAS models, it is not = clear that the poles are all simple.   If state-averaged methods = are also to be treated, then it would seem that the self-energy must be = described using an operator formalism (i.e. an operator acting on the = target space), which would complicate things.  For non-evenly = weighted averages, it is not clear how to think about the weights = (because the state-averaged density matrix is no longer dual to a von = Neumann measurement, but instead to a POVM - a metric needs to be = introduced).  -SEth

On 15/03/2012, at 6:19 PM, = Georg Lefkidis lefkidis**physik.uni-kl.de wrote:


Sent to CCL by: "Georg Lefkidis" = [lefkidis^^physik.uni-kl.de]
Dear J=FCrgen, 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 =93measure=94 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=92s 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, J=FCrgen Gr=E4fenstein 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.



-=3D This is automatically added to = each message by the mailing script =3D-
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Before posting, check wait time at: = http://www.ccl.net

Job: http://www.ccl.net/jobs =
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Search = Messages: http://www.ccl= .net/chemistry/searchccl/index.shtml

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<= /div>
seth.olsen~~uq.edu.au
+61 7 3365 = 2816
---------------------------------------------------
Unless = stated otherwise, this e-mail represents only the views of the = Sender and not the views of The University of = Queensland

= --Apple-Mail-12--527453025--