*From*: Thomas Manz <thomasamanz]~[gmail.com>*Subject*: CCL:G: is CAS-SCF first-order density matrix idempotent*Date*: Mon, 24 Sep 2018 14:08:14 -0600

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