CCL: accurate computation for active and inactive orbitals

Hi Susi Lehtola,

> From https://pyscf.org/user/ci.html#frozen-orbitals , it still requires the exact list of the orbital indices (which is the question of this thread).

```

# freeze 2 core orbitals
myci = ci.CISD(mf, frozen=[0,1]).run()
# freeze 2 core orbitals and 3 unoccupied orbitals
myci = ci.CISD(mf, frozen=[0,1,16,17,18]).run()

```

Could you tell us more about the use of Improved Virtual orbitals in this particular context ?

Regards,
Phung Cheng Fei
________________________________
> From: owner-chemistry+feiphung==hotmail.com]^[ccl.net <owner-chemistry+feiphung==hotmail.com]^[ccl.net> on behalf of Susi Lehtola susi.lehtola() alumni.helsinki.fi <owner-chemistry]^[ccl.net>
Sent: Friday, March 31, 2023 10:47 PM
To: Phung, Cheng Fei <feiphung]^[hotmail.com>
Subject: CCL: accurate computation for active and inactive orbitals

Sent to CCL by: Susi Lehtola [susi.lehtola-$-alumni.helsinki.fi]
On 3/31/23 07:47, Cheng Fei Phung feiphung-,-hotmail.com wrote:
>
> Sent to CCL by: "Cheng Fei Phung" [feiphung#hotmail.com]
> Could anyone provide accurate computation for active and inactive orbitals to be used in https://qiskit.org/documentation/nature/locale/bn_BN/stubs/qiskit_nature.second_q.transformers.FreezeCoreTransformer.html and
> https://qiskit.org/documentation/nature/stubs/qiskit_nature.second_q.transformers.ActiveSpaceTransformer.html ?
>
> My current inaccurate solution is using HOMO-LUMO approach. See https://github.com/tencent-quantum-lab/tensorcircuit/issues/120#issuecomment-1457932770
>
> I am looking at https://www.scm.com/doc/BAND/index.html which seems to provide [some DFT methods](https://i.imgur.com/mHeWCtl.png) to do so.
>
> However, I do not have access to SCM software.
>
> Any suggestions ?

There is a common misunderstanding here by what is meant by 1) active and
inactive orbitals in many-electron calculations, 2) the selection of the active
space orbitals, and 3) the use of a frozen core in ADF.

1. the active and inactive orbitals in many-electron calculations refer to
whether substitutions from/to the orbital is allowed when building the
many-electron basis, similarly to the complete active space (CAS) method which
is what quantum simulators are approximating. One builds the Hamiltonian and
diagonalizes it in the space of active orbitals, only.

2. the choice of the active space orbitals is a complicated issue, mostly
because of limitations of classical computers. Unoccupied orbitals of
Hartree-Fock theory are often a bad starting point due to the incorrect form of
the potential experienced by the virtual orbitals in Hartree-Fock theory. Many
alternatives have been suggested in the literature, ranging from Improved
Virtual Orbitals to the use of natural orbitals from a lower level of theory,
such as Møller-Plesset perturbation theory truncated at the second order (MP2)
or configuration interaction singles and doubles (CISD). The latter class of
methods is available in PySCF, for example, for which Qiskit has an interface;
see the PySCF documentation for how to build the density matrices and natural
orbitals.

3. the frozen core orbitals in ADF refer to their behavior in self-consistent
field (SCF) calculations, meaning here Hartree-Fock and density functional
theory. Since the core orbitals are much lower in energy, polarization effects
in a chemical environment are smaller for them than for the valence orbitals,
which is the foundation for freezing the core orbitals to the atomic form. This
is also the foundation for the pseudopotential and effective core potential
approaches.

Susi
--
------------------------------------------------------------------------------
Mr. Susi Lehtola, PhD Academy of Finland research fellow
susi.lehtola[*]helsinki.fi Associate professor, computational chemistry
http://susilehtola.github.io/ University of Helsinki, Finland
------------------------------------------------------------------------------
Susi Lehtola, FT akatemiatutkija
susi.lehtola[*]helsinki.fi dosentti, laskennallinen kemia
http://susilehtola.github.io/ Helsingin yliopisto
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
Hi Susi Lehtola,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
 
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof ContentPasted0">
> From <a href="" href="https://pyscf.org/user/ci.html#frozen-orbitals" data-auth="NotApplicable">https://pyscf.org/user/ci.html#frozen-orbitals" id="LPlnk410877">https://pyscf.org/user/ci.html#frozen-orbitals</a> , it still requires the exact list of the orbital indices (which is the question of this thread). 
 
``` 
<pre class="ContentPasted1 elementToProof"># freeze 2 core orbitals
myci = ci.CISD(mf, frozen=[0,1]).run()
# freeze 2 core orbitals and 3 unoccupied orbitals
myci = ci.CISD(mf, frozen=[0,1,16,17,18]).run()</pre>
``` 
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
 
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
Could you tell us more about the use of Improved Virtual orbitals in this particular context ? 
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
 
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
Regards,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof">
Phung Cheng Fei 
</div>
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<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr">From: owner-chemistry+feiphung==hotmail.com]^[ccl.net <owner-chemistry+feiphung==hotmail.com]^[ccl.net> on behalf of Susi Lehtola susi.lehtola() alumni.helsinki.fi
<owner-chemistry]^[ccl.net> 
Sent: Friday, March 31, 2023 10:47 PM 
To: Phung, Cheng Fei <feiphung]^[hotmail.com> 
Subject: CCL: accurate computation for active and inactive orbitals
<div> </div>
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<div class="BodyFragment">
<div class="PlainText"> 
Sent to CCL by: Susi Lehtola [susi.lehtola-$-alumni.helsinki.fi] 
On 3/31/23 07:47, Cheng Fei Phung feiphung-,-hotmail.com wrote: 
> 
> Sent to CCL by: "Cheng Fei  Phung" [feiphung#hotmail.com] 
> Could anyone provide accurate computation for active and inactive orbitals to be used in
<a href="" href="https://qiskit.org/documentation/nature/locale/bn_BN/stubs/qiskit_nature.second_q.transformers.FreezeCoreTransformer.html" data-auth="NotApplicable">https://qiskit.org/documentation/nature/locale/bn_BN/stubs/qiskit_nature.second_q.transformers.FreezeCoreTransformer.html">
https://qiskit.org/documentation/nature/locale/bn_BN/stubs/qiskit_nature.second_q.transformers.FreezeCoreTransformer.html</a> and
 
> <a href="" href="https://qiskit.org/documentation/nature/stubs/qiskit_nature.second_q.transformers.ActiveSpaceTransformer.html" data-auth="NotApplicable">https://qiskit.org/documentation/nature/stubs/qiskit_nature.second_q.transformers.ActiveSpaceTransformer.html">
https://qiskit.org/documentation/nature/stubs/qiskit_nature.second_q.transformers.ActiveSpaceTransformer.html</a> ? 
> 
> My current inaccurate solution is using HOMO-LUMO approach.  See <a href="" href="https://github.com/tencent-quantum-lab/tensorcircuit/issues/120#issuecomment-1457932770" data-auth="NotApplicable">https://github.com/tencent-quantum-lab/tensorcircuit/issues/120#issuecomment-1457932770">
https://github.com/tencent-quantum-lab/tensorcircuit/issues/120#issuecomment-1457932770</a> 
> 
> I am looking at <a href="" href="https://www.scm.com/doc/BAND/index.html">https://www.scm.com/doc/BAND/index.html</a" data-auth="NotApplicable">https://www.scm.com/doc/BAND/index.html">https://www.scm.com/doc/BAND/index.html</a> which seems to provide [some DFT methods](<a href="" href="https://i.imgur.com/mHeWCtl.png">https://i.imgur.com/mHeWCtl.png</a" data-auth="NotApplicable">https://i.imgur.com/mHeWCtl.png">https://i.imgur.com/mHeWCtl.png</a>) to do so. 
> 
> However, I do not have access to SCM software. 
> 
> Any suggestions ? 
 
There is a common misunderstanding here by what is meant by 1) active and 
inactive orbitals in many-electron calculations, 2) the selection of the active 
space orbitals, and 3) the use of a frozen core in ADF. 
 
1. the active and inactive orbitals in many-electron calculations refer to 
whether substitutions from/to the orbital is allowed when building the 
many-electron basis, similarly to the complete active space (CAS) method which 
is what quantum simulators are approximating. One builds the Hamiltonian and 
diagonalizes it in the space of active orbitals, only. 
 
2. the choice of the active space orbitals is a complicated issue, mostly 
because of limitations of classical computers. Unoccupied orbitals of 
Hartree-Fock theory are often a bad starting point due to the incorrect form of 
the potential experienced by the virtual orbitals in Hartree-Fock theory. Many 
alternatives have been suggested in the literature, ranging from Improved 
Virtual Orbitals to the use of natural orbitals from a lower level of theory, 
such as Møller-Plesset perturbation theory truncated at the second order (MP2) 
or configuration interaction singles and doubles (CISD). The latter class of 
methods is available in PySCF, for example, for which Qiskit has an interface; 
see the PySCF documentation for how to build the density matrices and natural 
orbitals. 
 
3. the frozen core orbitals in ADF refer to their behavior in self-consistent 
field (SCF) calculations, meaning here Hartree-Fock and density functional 
theory. Since the core orbitals are much lower in energy, polarization effects 
in a chemical environment are smaller for them than for the valence orbitals, 
which is the foundation for freezing the core orbitals to the atomic form. This 
is also the foundation for the pseudopotential and effective core potential 
approaches. 
 
Susi 
-- 
------------------------------------------------------------------------------ 
Mr. Susi Lehtola, PhD             Academy of Finland research fellow 
susi.lehtola[*]helsinki.fi          Associate professor, computational chemistry 
<a href="" href="http://susilehtola.github.io/">http://susilehtola.github.io/</a" data-auth="NotApplicable">http://susilehtola.github.io/">http://susilehtola.github.io/</a>     University of Helsinki, Finland 
------------------------------------------------------------------------------ 
Susi Lehtola, FT                  akatemiatutkija 
susi.lehtola[*]helsinki.fi          dosentti, laskennallinen kemia 
<a href="" href="http://susilehtola.github.io/">http://susilehtola.github.io/</a" data-auth="NotApplicable">http://susilehtola.github.io/">http://susilehtola.github.io/</a>     Helsingin yliopisto 
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