Calculating the excitation energy of Mn²⁺ using the QDET method

[ENGRAIS717]

Dear Developers,
I tested the Mn²⁺-doped system using the computational parameters for the QDET method provided in this 2025 paper: https://pubs.acs.org/doi/10.1021/acs.jpclett.5c00287. When calculating the energy of the excited state 4T1 of Mn2+, I employed the PBE functional and SG15 norm-conserving pseudopotentials to compute a supercell containing approximately 50-80 atoms, set the n_pdep_eigen parameter to match the number of electrons, and selected the active space consisting of the five d-electron orbitals.
The results indicate that for some systems (such as ZnAl2O4, MgAl2O4, NaScSi2O6, and KMgF3), the calculated values agree well with experimental data. However, for others (including ZnS, AlN, SrZnOS, ZnSe, MgO, and CaO), the calculated values are significantly underestimated. (details in Sheet1 of Excel)
After examining the KS orbitals for following PBE calculations, I found they are largely identical for tetracoordinated Mn²⁺ (details in Sheet2 of Excel). Therefore, I suspect the issue may lie in subsequent calculations.
I have thoroughly reviewed the computational workflow and parameter settings but remain unable to identify the cause of the underestimation. I have attached my input and output files for your reference. Any additional computational details or insights into possible oversights on my part would be greatly appreciated.
Looking forward to your assistance and response.

calculation results.zip

[ENGRAIS717]

Dear Developer,

I have re-uploaded the comparison data between the calculated excitation energies of Mn²⁺ in different systems using QDET and the corresponding experimental results. I would be truly grateful if you could find some time to provide me with your valuable insights. I sincerely hope to hear back from you.

[vyu16]

Dear @ENGRAIS717, thank you for using QDET and for sharing the results you obtained. It's hard to comment further without additional details of the calculations. Would you be able to share your input files for one or two representative systems? And do you know how the experimental data were measured?

[ENGRAIS717]

Dear Developers @vyu16 , I sincerely appreciate you taking the time to respond. For your convenience, I have attached all the relevant input and output files from my test system in "calculation results.zip“ file.

Regarding the measurement of experimental data, I referenced the spectral measurement results from the following publications:

1. AlN:Mn²⁺ https://doi.org/10.1039/D2DT02171D

2. ZnS:Mn²⁺ https://doi.org/10.1039/D4TC00960F

3. SrZnOS:Mn²⁺ https://doi.org/10.1038/s41467-025-55922-x

4. MgAl2O4:Mn²⁺ https://doi.org/10.1002/adom.201901105

5. MgO:Mn²⁺ https://iopscience.iop.org/article/10.1088/0022-3719/9/6/008

6. NaScSi2O6:Mn²⁺ https://doi.org/10.1039/C6RA24854C

7. KMgF3:Mn²⁺ https://iopscience.iop.org/article/10.1088/0953-8984/18/23/016

Looking forward to your further response. I am ready to provide any additional information if needed.

[vyu16]

Thank you for sharing the files and papers. I haven't gone through the papers yet, but as you know, when comparing computed vertical excitation energies with experimental results, it's important to consider what exactly is being measured and under which conditions. Sometimes things aren't directly comparable. The input files generally look good, though it's always important to check how the results depend on parameters such as the cell size, the plane-wave cutoff energy, and the number of PDEPs. Do you know how well converged your calculations are?

[ENGRAIS717]

Dear Developers,
Thank you once again for your thoughtful previous response. As you rightly pointed out, there are distinctions between experimental observables like excitation/emission energies and the zero-phonon line. Meanwhile, different computational parameters affect the results of the calculation.
In my study, I am focusing on the Mn2+ ion in the same valence state and an identical coordination environment (specifically tetrahedral coordination). The experimental data I collected are primarily excitation energies, with a few emission energies (marked as "emi." in the table). As anticipated, the emission energies are slightly lower than the excitation energies, confirming that they are comparable. Importantly, these energies are also close, meaning the excitation energies of the tetracoordinated Mn2+ ions exhibit consistency.

I employed the same computational methodology and parameters for all systems. Regardless of their absolute agreement with experiment, the computed excitation energies themselves should be similar (expected ~ 2.x eV). However, the results show significant variation across the different systems：

Furthermore, preliminary DFT calculations performed with QE (via the WEST pre-run) indicate that the calculated d orbital energies for these systems are similar (with the lowest orbital as reference):

From nearly identical crystal field energies, the calculation yielded significantly different excitation energies for multiple reference states.
I wonder why these calculations yield significant differences for identical ions in identical coordination environments, rather than systematic deviations relative to experimental results.
I would be very grateful for your insights into this puzzling inconsistency. Thank you again for your time and assistance.

[vyu16]

My understanding is that even though Mn sits in a similar local coordination, the band gap of the host and the positions of the Mn d states relative to the band edges are still very different. So, without a convergence test, one shouldn't assume that the same plane-wave cutoff and supercell size will be adequate for chemically diverse oxides, nitrides, sulfides, etc. Of course it's very likely that there will be other factors to be considered, but ensuring convergence is usually the most straightforward first step.