Wrong state ordering in the Fock-Space CCSD calculation of Th3+-He

[Giorgio Visentin]

Dear sirs,

I am trying to compute the (0,1)-FS-CCSD energies of Th3+-He, starting from the closed-shell Th4+-He. For the former, the ground electronic configuration of Th3+ is 6p^6 5f. The preliminary Th4+ SCF calculation has the 6d atomic orbitals as the lowest empty orbitals. I thus asked the program to reorder the empty orbitals and place the 5f before the 6d. The trick worked at the SCF level. However, when performing the (0,1)-FS-CCSD calculation, the 6p^6 6d configuration appears as the most stable, even though this is not true.

Do you know how I can solve this problem? The output file is attached.

I thank you for your time.

Best wishes,

Giorgio Visentin

[a.bors...@rug.nl]

Try a better basis set perhaps, e.g. s-aug-v4z. This might help.

[Peterson, Kirk]

Have you placed both the 6d and 5f in the FS?

 

Regards,  -Kirk

 

From: dirac...@googlegroups.com <dirac...@googlegroups.com> on behalf of a.bors...@rug.nl <a.bors...@rug.nl>
Date: Friday, December 15, 2023 at 12:50 PM
To: dirac-users <dirac...@googlegroups.com>
Subject: [dirac-users] Re: Wrong state ordering in the Fock-Space CCSD calculation of Th3+-He

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[Giorgio Visentin]

Dear Anastasia,

Thanks for your suggestions.

With a larger basis set the SCF computation for Th IV yields the right orbital ordering. In case of a FS-CCSD calculation, I should start from the closed Th V, that has the empty  7d orbitals above the Valence 6p, instead of the 5f. This is correct for Th V, but wrong for Th IV. Is there the risk for the (0,1) FS-CCSD calculation to converge to a wrong state for Th IV, starting from Th V?

I thank you for your patience and help. 

Best,

Giorgio 

--

[Giorgio Visentin]

Dear Kirk,

Yes, the FS encompasses 22 orbitals above the valence 6p orbitals, thus including both 5f and 6d. However, as in the calculation for Th V the 6d orbitals lie below the 5f, the FS-CCSD calculation converge to a wrong result, showing the 2D as the ground state instead of the 2F.

Does this hinder the use of FS-CCSD for this calculation?

I thank you for your help.

Kind regards,

Giorgio 

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[Peterson, Kirk]

Dear Giorgio,

 

How far above the 2D state is the 2F ?  I agree with Anastasia though, it certainly could be the basis set, as well as which electrons you are correlating.

 

Best regards,  -Kirk

 

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[Giorgio Visentin]

Sorry, I've just rechecked my calculation with the s- aug-dyall.v4z basis: the orbital ordering is still wrong.

Sorry for the confusion.

Best,

Giorgio 

On Fri, 15 Dec 2023, 21:49 a.bors...@rug.nl, <a.bors...@rug.nl> wrote:

--

[Peterson, Kirk]

Also, do you get the same result without the He atom present?

 

Best regards,  -Kirk

 

From: dirac...@googlegroups.com <dirac...@googlegroups.com> on behalf of Giorgio Visentin <grgvi...@gmail.com>

Date: Friday, December 15, 2023 at 3:45 PM
To: dirac...@googlegroups.com <dirac...@googlegroups.com>

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[Giorgio Visentin]

Dear Kirk,

The energy difference amounts to ca. 0.05 hartrees. I did not try the computation without He, as for this test calculation I set the interatomic distance very large, so to be sure the interaction is negligible. 

Do you think the interaction with He may lift the 6f electrons above the 7d? 

I thank you for your patience .

Best,

Giorgio 

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[Peterson, Kirk]

Dear Giorgio,

 

If you’ve set the He very far away, then it shouldn’t affect things to any degree.  50 mHartrees it quite a bit. Are you sure the ground state is 2F?  I’m not sure if the results given on NIST are definitive.

 

Best,  -Kirk

 

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[Giorgio Visentin]

Dear Kirk,

The NIST data tables report only the ground state, that should have a 6p^6 5f electron configuration. This is considered the ground state also in some theoretical papers (by, e.g., Safronova et al. or Porsev et al.).

To reproduce this configuration as the ground one, I tried to reorder the orbitals so that the 5fs go below the 6ds and get populated. This gets me the desired configuration as the ground one, but also does not allow the subsequent FS-CCSD calculation. If I try to do the same reordering for Th V, the SCF will converge to a configuration with the orbital ordering I asked for, but then the subsequent FS-CCSD calculation will reorder the orbitals, thus putting the 5fs above the 6d again. So I'm wondering whether it's possible to ask the FS-CCSD routine not to reorder the orbitals or if some multi-reference level of theory may reproduce the 6p^6 5f ground configuration in a better way than FS-CCSD.

I thank you very much for your help.

Best,

Giorgio 

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[Borschevsky, A.]

Did you try using  both the d and f orbitals as open shells in the initial SCF calculation?

----------------------------------------------------------------------
Prof. Dr. Anastasia Borschevsky
Van Swinderen Institute for Particle Physics and Gravity
Faculty of Science and Engineering 
University of Groningen
Nijenborgh 4, 9747AG Groningen
The Netherlands.
Tel: +31 50 3634850
mail: A.Bors...@rug.nl
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[Giorgio Visentin]

Yes I can and I did. If I follow this strategy, the program will still see the d orbitals as more stable than the f ones. For this reason, I tried to reorder the orbitals to place f above d and then place the open shell electron there. I then run a MRCI calculation, that crashed after the final iterations on the first CI roots due to memory issues. Moreover, I think in this case the CCSD method cannot be used. 

Thanks a lot for your patience and support.

Best,

Giorgio 

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Sent: Saturday, December 16, 2023 10:47:02 AM

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[Peterson, Kirk]

Dear Giorgio,

 

I’m running some tests here now but with the bare Th atom. If I run Th+3 with both the d3/2 and f5/2 spinors in the open shell definition (1/4,6), the 2F is lower than the 2D state at the DHF level by about 2700 cm-1 with a vtz basis set. I’m running the FSCCSD using the closed-shell Th+4 orbitals now.  How far away are you placing the He atom in your calculations?

 

Best,  -Kirk

 

From: dirac...@googlegroups.com <dirac...@googlegroups.com> on behalf of Giorgio Visentin <grgvi...@gmail.com>
Date: Saturday, December 16, 2023 at 2:16 AM
To: dirac...@googlegroups.com <dirac...@googlegroups.com>
Subject: Re: [dirac-users] Re: Wrong state ordering in the Fock-Space CCSD calculation of Th3+-He

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[Giorgio Visentin]

Dear Kirk,

Thanks a lot for your help! In my test calculation I placed He 30 angstroms far from Th3+.

Best,

Giorgio 

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[Peterson, Kirk]

Dear Giorgio,

 

My FSCCSD easily converged to give a 2F ground state.  Can you post your FSCCSD output?

 

Best,  -Kirk

 

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[Giorgio Visentin]

Dear Kirk,

my output (Th3+-He, 30 Ang distance), is attached. How did you manage to converge it correctly?

Thanks again for your support.

Best,

Giorgio 

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[Peterson, Kirk]

Dear Giorgio,

 

Well, I did full 4c-FSCCSD and not X2C-AMFI as in your case.  I also didn’t bother with the intermediate Hamiltonian method. Just regular FS was very well behaved.  I would suggest trying X2C-mmf.

 

Best,  -Kirk

 

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[Peterson, Kirk]

Dear Giorgio,

 

I also just noted that you’re correlating 52 electrons, which is way more than the basis set you’ve chosen is designed to treat (cvtz is presumably only down through the 5s). Probably not causing this particular problem, but it could/will cause problems….

 

Best,  -Kirk

 

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[Giorgio Visentin]

Dear Kirk,

I've just started a new calculation embodying your suggestions (4c, no IH, correlation starting from 5s). 

I will also try the X2cmmf and keep you updated on the progress.

Is there a reason why X2C perform so worse compared to 4C for Th? Usually X2C behaves quite accurately.

Thanks a lot again for your help!

Best,

Giorgio 

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[Peterson, Kirk]

Dear Giorgio,

 

It could be the AMFI approximation. I might also test this here since I’m curious as well.

 

Best,  -Kirk

 

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[Borschevsky, A.]

If you are looking at Th--He3+, please also use the same basis set for both (i.e. dyall).

I think the problem is not in X2C, but let's see what happens.

----------------------------------------------------------------------
Prof. Dr. Anastasia Borschevsky
Van Swinderen Institute for Particle Physics and Gravity
Faculty of Science and Engineering 
University of Groningen
Nijenborgh 4, 9747AG Groningen
The Netherlands.
Tel: +31 50 3634850
mail: A.Bors...@rug.nl
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[Giorgio Visentin]

Dear Anastasia and Kirk,

Thanks for your suggestions again. I will then use the same relativistic basis set for He as well as for Th. Just my own curiosity: why is the use of a different basis set for He detrimental to the calculation accuracy? 

Best,

Giorgio 

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Sent: Saturday, December 16, 2023 9:47:22 PM

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[Borschevsky, A.]

It doesn't have to be. However, there is no reason why this calculation should misbehave, so I would remove any unusual factors first :).

----------------------------------------------------------------------
Prof. Dr. Anastasia Borschevsky
Van Swinderen Institute for Particle Physics and Gravity
Faculty of Science and Engineering 
University of Groningen
Nijenborgh 4, 9747AG Groningen
The Netherlands.
Tel: +31 50 3634850
mail: A.Bors...@rug.nl
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[Andre Gomes]

Hi,

I think the problem in your original FS calculations is that  you've placed all virtuals in the intermediate (Pi) space:

 Spinor class : active virtual            12   12    9    9    6    6    2    2
 Spinor class : active Pi virt            12   12    9    9    6    6    2    2

when you do have virtuals in the main (Pm) space, for each symmetry/mj value you should have more orbitals in the "active virtual" line than in the "active Pi virt" line (the difference then being the number or orbitals/spinors in Pm). The same reasoning would apply if you were doing ionizations or excitations.

this is because by defining

EPMIN                                                                                              
-0.97                                                                                              
.EPMAX                                                                                              
-0.44        

you define the boundaries of Pi, and in this case they comprise all your virtuals (see below). The problem with this is that the configurations dominated by spinors in the Pi space are not treated accurately, unlike those made up of spinors in the Pm space. if you had defined something like

EPMIN                                                                                              
-0.90                                                                                             
.EPMAX                                                                                              
-0.44 

then you'd have the first 13 virtuals (in terms of energy) in the Pm space (i am not saying such a definition would converge, I haven't actually tested it)

I think it doesn't hurt to recall that that for the (1,0)/(0,1) sector you may also use EOM-IP/EA, if you can afford it, since the results will be equivalent to FSCC and are unsure of the active space (since for EOM-IP/EA there's no need to define one).

besides that, in the reordering of orbitals, if you want to control the ordering after the SCF, there's another keyword (.POST SCF REORDER MO) that may or may not be useful.

and i don't understand why you decided to tweak with parameters with the parallel calculation - you can sure do that, personally I don't really do that.

best regards, 

Andre

* Electronic eigenvalue no.  44: -0.9884509326115       (Occupation : f = 1.0000)  m_j=  1/2

============================================================================================
* Electronic eigenvalue no.  52: -0.9653025758604       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  53: -0.9653025773583       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  54: -0.9458675572352       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  55: -0.9458675576197       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  56: -0.9458675584539       (Occupation : f = 0.0000)  m_j=  5/2
* Electronic eigenvalue no.  45: -0.9424628273519       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  46: -0.9424628278295       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  47: -0.9424628282719       (Occupation : f = 0.0000)  m_j=  5/2
* Electronic eigenvalue no.  48: -0.9265925812786       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  49: -0.9265925814990       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  50: -0.9265925813055       (Occupation : f = 0.0000)  m_j=  5/2
* Electronic eigenvalue no.  51: -0.9265925811474       (Occupation : f = 0.0000)  m_j= -7/2
* Electronic eigenvalue no.  57: -0.9121013421251       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  58: -0.7520107998959       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  59: -0.6995997487990       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  60: -0.6995997453674       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  61: -0.4973677733502       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  62: -0.4940745574935       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  63: -0.4940745507857       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  64: -0.4867554308497       (Occupation : f = 0.0000)  m_j=  5/2
* Electronic eigenvalue no.  65: -0.4867554254488       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  66: -0.4867554226501       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  67: -0.4521891298240       (Occupation : f = 0.0000)  m_j=  5/2
* Electronic eigenvalue no.  68: -0.4521891254155       (Occupation : f = 0.0000)  m_j= -3/2
* Electronic eigenvalue no.  69: -0.4521891212369       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  70: -0.4501257621310       (Occupation : f = 0.0000)  m_j= -7/2
* Electronic eigenvalue no.  71: -0.4501257570457       (Occupation : f = 0.0000)  m_j=  5/2
* Electronic eigenvalue no.  72: -0.4501257551392       (Occupation : f = 0.0000)  m_j=  1/2
* Electronic eigenvalue no.  73: -0.4501257531015       (Occupation : f = 0.0000)  m_j= -3/2

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[Peterson, Kirk]

Good catch Andre.  I just did a standard FSCCSD with X2C and it converges fine to a 2F ground state.

 

Best,  -Kirk

 

 

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[Giorgio Visentin]

Dear Anastasia, Andre and Kirk,

Thanks a lot again for your responses and support. Let me recapitulate the reasons of the issue, to check whether I have correctly understood. The main reason of the  strange convergence of the calculation is the choice of the intermediate Hamiltonian. Its wrong choice may make the calculation inaccurate.

Actually, I did some calculations for atomic Th IV with X2C and Th3+-He with 4C and X2C, with the atomic orbitals from 5s up to the virtuals lying at 30 hartrees correlated. The two formers converged, while the latter (molecule with X2C) diverged. I should still check the reason for the divergence.

I thank you a lot for your support.

Best,

Giorgio 

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[Borschevsky, A.]

Dear Giorgio,

For this calculation you indeed do not need the IH at all.

Best,

Anastasia.

----------------------------------------------------------------------
Prof. Dr. Anastasia Borschevsky
Van Swinderen Institute for Particle Physics and Gravity
Faculty of Science and Engineering 
University of Groningen
Nijenborgh 4, 9747AG Groningen
The Netherlands.
Tel: +31 50 3634850
mail: A.Bors...@rug.nl
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