From owner-chemistry ":at:" ccl.net Mon Sep 24 17:51:00 2018
From: "Robert Molt r.molt.chemical.physics:-:gmail.com" <owner-chemistry,+,server.ccl.net>
To: CCL
Subject: CCL:G: is CAS-SCF first-order density matrix idempotent
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X-Original-From: Robert Molt <r.molt.chemical.physics]*[gmail.com>
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Date: Mon, 24 Sep 2018 17:49:47 -0400
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Sent to CCL by: Robert Molt [r.molt.chemical.physics===gmail.com]
a.)  Yes, using Molcas, GAMESS, or Molpro

b.) There is no restriction to integer values for natural orbitals in CAS.

See Rodney Bartlett's book on coupled cluster theory (Many-Body Methods 
in Chemistry and Physics), or Peter Szalay's review article on MR-CI in 
Chemical Reviews, 2012, or Mark Gordon's tutorials on MC-SCF 
http://www.msg.ameslab.gov/tutorials/mcscf2.pdf

c.) I have no idea what Gaussian does. Sorry.


On 9/24/18 4:08 PM, Thomas Manz thomasamanz~~gmail.com wrote:
> Dear colleagues,
>
> We recently ran some CAS-SCF calculations in Gaussian 16. When 
> visualizing the orbitals in GaussView 5 or outputting the natural 
> orbitals to a WFX file (e.g., pop=NO   output=wfx), the natural 
> orbitals are listed as fully occupied or fully empty. (In other words, 
> the CAS-SCF first-order density matrix is claimed to be idempotent.) 
> This is different than the behavior that occurs with Gaussian's MP2, 
> coupled-cluster, SAC-CI, or CISD  calculations, which print fractional 
> orbital occupancies, and generally speaking have non-idempotent 
> first-order density matrices. The systems we are studying are some 
> small diatomic molecules (e.g., Be2, B2, etc.)
>
> I am confused about whether the claimed whole number occupancies of 
> the CAS-SCF natural orbitals is a real effect or whether it is a bug 
> in the Gaussian software? According to literature references, an 
> N-representable first-order density matrix can in general have 
> fractional natural orbital occupancies (i.e., it can be 
> non-idempotent). But also, there is not a one-to-one map between the 
> first-order density matrix and physical observables: two calculations 
> with identical electron density distributions can have different 
> first-order density matrices. Consequently, I have not yet been able 
> to rule out whether this is just a representation issue.
>
> Can anyone offer specific insights into the following questions:
>
> (1) Has anyone observed a non-idempotent first-order density matrix 
> (i.e., fractional natural orbital occupancies) when performing CAS-SCF 
> calculations using any software program?
>
> (2) Can anyone offer a concrete answer as to whether the CAS-SCF 
> first-order density matrix should or should not in general be 
> idempotent? (Please omit discussions of trivial one or two-electron 
> systems, since they are too simple.) Is there theory or literature 
> references to back this up?
>
> (3) If the CAS-SCF first-order density matrix is not supposed to be 
> idempotent, is there a reasonably easy and fast way to extract the 
> CAS-SCF natural orbital fractional occupancies from Gaussian 16 
> calculations? (Caution: This needs to be based on actual experience, 
> rather than conjectures.)
>
> By the way, this issue is not new to Gaussian 16; we observed the same 
> behavior for Gaussian 09. At this point, I do not understand whether 
> this behavior is "real" or a "bug". Can anyone provide clarification?
>
> Sincerely,
>
> Tom Manz
> associate professor
> Chemical & Materials Engineering
> New Mexico State University

-- 
Dr. Robert Molt Jr.
r.molt.chemical.physics-,-gmail.com