*From*: Robert Molt <r.molt.chemical.physics]*[gmail.com>*Subject*: CCL:G: is CAS-SCF first-order density matrix idempotent*Date*: Mon, 24 Sep 2018 17:49:47 -0400

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.

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. Whenvisualizing the orbitals in GaussView 5 or outputting the naturalorbitals to a WFX file (e.g., pop=NO output=wfx), the naturalorbitals 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 fractionalorbital occupancies, and generally speaking have non-idempotentfirst-order density matrices. The systems we are studying are somesmall diatomic molecules (e.g., Be2, B2, etc.)I am confused about whether the claimed whole number occupancies ofthe CAS-SCF natural orbitals is a real effect or whether it is a bugin the Gaussian software? According to literature references, anN-representable first-order density matrix can in general havefractional natural orbital occupancies (i.e., it can benon-idempotent). But also, there is not a one-to-one map between thefirst-order density matrix and physical observables: two calculationswith identical electron density distributions can have differentfirst-order density matrices. Consequently, I have not yet been ableto 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-SCFcalculations using any software program?(2) Can anyone offer a concrete answer as to whether the CAS-SCFfirst-order density matrix should or should not in general beidempotent? (Please omit discussions of trivial one or two-electronsystems, since they are too simple.) Is there theory or literaturereferences to back this up?(3) If the CAS-SCF first-order density matrix is not supposed to beidempotent, is there a reasonably easy and fast way to extract theCAS-SCF natural orbital fractional occupancies from Gaussian 16calculations? (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 samebehavior for Gaussian 09. At this point, I do not understand whetherthis 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