Clarification on Calculation Restrictions

Dear Hamza,

The restrictions set limits to the minimal and maximal occupation of a subset of all spin-orbitals in the calculation. The function “DeterminantString(NFermi,Index[“Ni_3d”])” selects the spin-orbitals that relate to the Ni 3d shell, and “DeterminantString(NFermi,Index[“Ligand”])” to the ligand and “DeterminantString(NFermi,Index[“Ni_2p”])” to the Ni 2p shell. After that you see two numbers, these are the minimal and maximal occupations for the indices included before.

As an example the line

CalcRestrictions = {NFermi, 0, {DeterminantString(NFermi,Index[“Ni_3d”]), nd, nd+2}, {DeterminantString(NFermi,Index[“Ligand”]), 10-2, 10}, {DeterminantString(NFermi,Index[“Ni_2p”]), 6-1, 6}

has 3 restrictions defined.

For the d-shell we have

{DeterminantString(NFermi,Index[“Ni_3d”]), nd, nd+2}

allowing $d^8$, $d^9$ and $d^10$, assuming $nd=8$.

For the Ligand shell we have

{DeterminantString(NFermi,Index[“Ligand”]), 10-2, 10}

allowing $L^8$, $L^9$ and $L^10$

For the Ni 2p shell we have

{DeterminantString(NFermi,Index[“Ni_2p”]), 6-1, 6}

allowing $p^5$ and $p^6$

Combined you allow the following configuration

• $d^{8} L^{10} p^6$
• $d^{9} L^{10} p^6$
• $d^{10} L^{10} p^6$
• $d^{8} L^{9} p^6$
• $d^{9} L^{9} p^6$
• $d^{10} L^{9} p^6$
• $d^{8} L^{8} p^6$
• $d^{9} L^{8} p^6$
• $d^{10} L^{8} p^6$
• $d^{8} L^{10} p^5$
• $d^{9} L^{10} p^5$
• $d^{10} L^{10} p^5$
• $d^{8} L^{9} p^5$
• $d^{9} L^{9} p^5$
• $d^{10} L^{9} p^5$
• $d^{8} L^{8} p^5$
• $d^{9} L^{8} p^5$
• $d^{10} L^{8} p^5$

Some of these configurations look weird, as they do not conserve the electron count. This is not a problem as the Hamiltonian conservers the particle number and you start from a $d^8$ configuration (I suspect).

Note that you probably get the same result if you only include the following

CalcRestrictions = {NFermi, 0, {DeterminantString(NFermi,Index[“Ligand”]), 10-2, 10} }

As the number of $d$ electrons is given by conservation of particle number and the same is true for the core occupation.

Hopes this helped, best wishes, Maurits

Dear Maurits,

Thank you for your reply.

I tried these configurations for calculating the XAS of NiO using MLFT, I found that there is no difference in the spectra—all the restrictions produce the same shape.

However, when I used the Ligand Field approach, as shown in the tutorial, I obtained a different spectral shape for a specific restriction. I have included a link to an image that shows the restrictions and the results.

https://docs.google.com/document/d/e/2PACX-1vRPqx3R5Nx6OXTMgh35h0dXnBJ2yxIfh9CSUgWNVG1NTRAxiunD3bP4bWb-qRA_sctGGodAwK_m1Pdz/pub

I also noticed that the speed of the spectral calculations in MLFT significantly decreases when applying different CalculationRestrictions, especially when dealing with a large number of fermions. However, my main concern is which restriction I should use, as they produce different spectral shapes.

I look forward to your feedback. Thank you very much.

Best regards, Hamza