From owner-chemistry@ccl.net Mon Sep 24 16:12:01 2018 From: "Thomas Manz thomasamanz~~gmail.com" To: CCL Subject: CCL:G: is CAS-SCF first-order density matrix idempotent Message-Id: <-53473-180924160833-2386-UtlwY9E0v0thflnPYwwHgA\a/server.ccl.net> X-Original-From: Thomas Manz Content-Type: multipart/alternative; boundary="000000000000553c110576a38d4b" Date: Mon, 24 Sep 2018 14:08:14 -0600 MIME-Version: 1.0 Sent to CCL by: Thomas Manz [thomasamanz]![gmail.com] --000000000000553c110576a38d4b Content-Type: text/plain; charset="UTF-8" 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 --000000000000553c110576a38d4b Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Dear colleagues,

We recently ran some C= AS-SCF calculations in Gaussian 16. When visualizing the orbitals in GaussV= iew 5 or outputting the natural orbitals to a WFX file (e.g., pop=3DNO=C2= =A0 =C2=A0output=3Dwfx), 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=C2=A0 calculation= s, which print fractional orbital occupancies, and generally speaking have = non-idempotent first-order density matrices. The systems we are studying ar= e some small diatomic molecules (e.g., Be2, B2, etc.)

<= div>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 Ga= ussian software? According to literature references, an N-representable fir= st-order density matrix can in general have fractional natural orbital occu= pancies (i.e., it can be non-idempotent). But also, there is not a one-to-o= ne map between the first-order density matrix and physical observables: two= calculations with identical electron density distributions can have differ= ent 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 de= nsity 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-orde= r density matrix should or should not in general be idempotent? (Please omi= t discussions of trivial one or two-electron systems, since they are too si= mple.) Is there theory or literature references to back this up?
=
(3) If the CAS-SCF first-order density matrix is not suppose= d to be idempotent, is there a reasonably easy and fast way to extract the = CAS-SCF natural orbital fractional occupancies from Gaussian 16 calculation= s? (Caution: This needs to be based on actual experience, rather than conje= ctures.)=C2=A0

By the way, this issue is not new t= o 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?

Since= rely,

Tom Manz
associate professor
=
Chemical & Materials Engineering
New Mexico State Univer= sity
--000000000000553c110576a38d4b-- From owner-chemistry@ccl.net Mon Sep 24 17:51:00 2018 From: "Robert Molt r.molt.chemical.physics:-:gmail.com" To: CCL Subject: CCL:G: is CAS-SCF first-order density matrix idempotent Message-Id: <-53474-180924174957-14297-2vasMp3RUHLwpnQKvALTKA,+,server.ccl.net> X-Original-From: Robert Molt Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8; format=flowed Date: Mon, 24 Sep 2018 17:49:47 -0400 MIME-Version: 1.0 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 From owner-chemistry@ccl.net Mon Sep 24 18:26:00 2018 From: "Thomas Manz thomasamanz]_[gmail.com" To: CCL Subject: CCL:G: is CAS-SCF first-order density matrix idempotent Message-Id: <-53475-180924181806-25224-kL9rNYBxAPqsiWoHq2Pxww{=}server.ccl.net> X-Original-From: Thomas Manz Content-Type: multipart/alternative; boundary="000000000000ac5d810576a55c98" Date: Mon, 24 Sep 2018 16:17:47 -0600 MIME-Version: 1.0 Sent to CCL by: Thomas Manz [thomasamanz|*|gmail.com] --000000000000ac5d810576a55c98 Content-Type: text/plain; charset="UTF-8" Dear Colleagues, I think I may have figured out some answers to questions raised in my previous post. Issue seems to be due to slight difference in output keyword behavior between different Gaussian versions. In Gaussian 09 Rev D.01, the following route line (for Be2 molecule) # opt SAC-CI(SACOnly,TargetState=(SpinState=Singlet,Symmetry=1,Root=0),MacroIter=2)/gen # density = current output = wfx gives the following fractional natural orbital occupancies in the .wfx file 2.000029060591e+00 2.000016615086e+00 1.875796115907e+00 1.746761164896e+00 1.473038579626e-01 6.027116162732e-02 6.027116162253e-02 3.752232512735e-02 3.752232511941e-02 1.827524927720e-02 etc. In Gaussian 16 Rev A.03, exactly the same input file gives the following natural orbital occupancies in the .wfx file 2.000000000000e+00 2.000000000000e+00 2.000000000000e+00 2.000000000000e+00 If Pop=NO is added # opt SAC-CI(SACOnly,TargetState=(SpinState=Singlet,Symmetry=1,Root=0),MacroIter=2)/gen # density = current output = wfx pop=no then once again the following natural orbital occupancies in the .wfx file 2.000000000000e+00 2.000000000000e+00 2.000000000000e+00 2.000000000000e+00 Therefore, it appears the issue is related to the Gaussian software version. It appears the correct orbital occupancies for SAC-CI and CAS-SCF calculations should normally be fractional, but for reasons that are unclear, Gaussian 16 is printing the incorrect orbital occupancies into wfx files for SAC-CI and CAS-SCF calculations. It is also unclear whether in these cases the correct orbitals are being written to the files. For example, if Gaussian 16 Rev A.03 is printing the HF-like orbitals together with whole number occupancies rather than the natural orbitals and their fractional occupancies. Sincerely, Tom On Mon, Sep 24, 2018 at 3:19 PM Thomas Manz thomasamanz~~gmail.com < owner-chemistry.:.ccl.net> 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 > --000000000000ac5d810576a55c98 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Dear Colleagues,

I think I ma= y have figured out some answers to questions raised in my previous post.

Issue seems to be due to slight difference in output= keyword behavior between different Gaussian versions.

=
In Gaussian 09 Rev D.01, the following route line (for Be2 molecule)= =C2=A0
# opt SAC-CI(SACOnly,TargetState=3D(SpinState=3DSingl= et,Symmetry=3D1,Root=3D0),MacroIter=3D2)/gen
# density =3D curren= t output =3D wfx

gives the following fractio= nal natural orbital occupancies in the .wfx file
=C2=A0 2.00= 0029060591e+00
=C2=A0 2.000016615086e+00
=C2=A0 1.87579= 6115907e+00
=C2=A0 1.746761164896e+00
=C2=A0 1.47303857= 9626e-01
=C2=A0 6.027116162732e-02
=C2=A0 6.02711616225= 3e-02
=C2=A0 3.752232512735e-02
=C2=A0 3.752232511941e-= 02
=C2=A0 1.827524927720e-02
=C2=A0 etc.

In Gaussian 16 Rev A.03,=C2=A0 exactly the same input file= gives the following natural orbital occupancies in the .wfx file
=C2=A0 2.000000000000e+00
=C2=A0 2.000000000000e+00
=C2=A0 2.000000000000e+00
=C2=A0 2.000000000000e+00

If Pop=3DNO is added
# opt SAC-CI(SACOn= ly,TargetState=3D(SpinState=3DSinglet,Symmetry=3D1,Root=3D0),MacroIter=3D2)= /gen
# density =3D current output =3D wfx pop=3Dno

then once again the following natural orbital occupancies = in the .wfx file
=C2=A0 2.000000000000e+00
=C2= =A0 2.000000000000e+00
=C2=A0 2.000000000000e+00
=C2=A0= 2.000000000000e+00

Therefore, it appears the issue is related to the Gaussian software = version. It appears the correct orbital occupancies for SAC-CI and CAS-SCF = calculations should normally be fractional, but for reasons that are unclea= r, Gaussian 16 is printing the incorrect orbital occupancies into wfx files= for SAC-CI and CAS-SCF calculations. It is also unclear whether in these c= ases the correct orbitals are being written to the files. For example, if G= aussian 16 Rev A.03 is printing the HF-like orbitals together with whole nu= mber occupancies rather than the natural orbitals and their fractional occu= pancies.

Sincerely,

Tom

On Mon, Sep 24, 2018 at 3:19 PM Thomas Manz thomasamanz~~gmail.com <owner-chemistry.:.ccl.net> wrote:
Dear colleagues,

We recen= tly ran some CAS-SCF calculations in Gaussian 16. When visualizing the orbi= tals in GaussView 5 or outputting the natural orbitals to a WFX file (e.g.,= pop=3DNO=C2=A0 =C2=A0output=3Dwfx), the natural orbitals are listed as ful= ly occupied or fully empty. (In other words, the CAS-SCF first-order densit= y matrix is claimed to be idempotent.) This is different than the behavior = that occurs with Gaussian's MP2, coupled-cluster, SAC-CI, or CISD=C2=A0= calculations, which print fractional orbital occupancies, and generally sp= eaking 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 occupa= ncies of the CAS-SCF natural orbitals is a real effect or whether it is a b= ug in the Gaussian software? According to literature references, an N-repre= sentable first-order density matrix can in general have fractional natural = orbital occupancies (i.e., it can be non-idempotent). But also, there is no= t a one-to-one map between the first-order density matrix and physical obse= rvables: 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 ques= tions:

(1) Has anyone observed a non-idempotent fi= rst-order density matrix (i.e., fractional natural orbital occupancies) whe= n performing CAS-SCF calculations using any software program?
(2) Can anyone offer a concrete answer as to whether the CAS-SC= F first-order density matrix should or should not in general be idempotent?= (Please omit discussions of trivial one or two-electron systems, since the= y 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, rathe= r than conjectures.)=C2=A0

By the way, this issue = is not new to Gaussian 16; we observed the same behavior for Gaussian 09. A= t this point, I do not understand whether this behavior is "real"= or a "bug". Can anyone provide clarification?

Sincerely,

Tom Manz
associate pro= fessor
Chemical & Materials Engineering
New Mexico = State University
--000000000000ac5d810576a55c98--