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Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations
by Aleksei V. Ivanov, Leonard A. Schmerwitz, Gianluca Levi, Hannes Jonsson
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|Authors (as registered SciPost users):||Hannes Jonsson · Gianluca Levi|
|Preprint Link:||scipost_202303_00008v1 (pdf)|
|Date submitted:||2023-03-07 22:40|
|Submitted by:||Jonsson, Hannes|
|Submitted to:||SciPost Physics|
Elucidation of the mechanism for optical spin initialization of point defects in solids in the context of quantum applications requires an accurate description of the excited electronic states involved. While variational density functional calculations have been successful in describing the ground state of a great variety of systems, doubts have been expressed in the literature regarding the ability of such calculations to describe electronic excitations of point defects. A direct orbital optimization method is used here to perform time-independent, variational density functional calculations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. The calculations include up to 512 atoms subject to periodic boundary conditions and the excited state calculations require similar computational effort as ground state calculations. Contrary to some previous reports, the use of local and semilocal density functionals gives the correct ordering of the low-lying triplet and singlet states, namely 3A2 < 1E < 1A_1 < 3E. Furthermore, the more advanced meta generalized gradient approximation functionals give results that are in remarkably good agreement with high-level, many-body calculations as well as available experimental estimates, even for the excited singlet state which is often referred to as having multireference character. The lowering of the energy in the triplet excited state as the atom coordinates are optimized in accordance with analytical forces is also close to the experimental estimate and the resulting zero-phonon line triplet excitation energy is underestimated by only 0.15 eV. The approach used here is found to be a promising tool for studying electronic excitations of point defects in, for example, systems relevant for quantum technologies.
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- Cite as: Anonymous, Report on arXiv:scipost_202303_00008v1, delivered 2023-04-27, doi: 10.21468/SciPost.Report.7111
The manuscript is a nice application of the authors' recently developed method(https://doi.org/10.1021/acs.jctc.1c00157) for calculating excited states using density functional theory. Using their recent developments, they are able to show that they can obtain the same ordering as many-body calculations (and experimental estimates) for the low-lying triplet and singlet states of the NV- center in diamond, namely 3A2 < 1E < 1A1 < 3E.
The manuscript is well written and shows results for their promising new method for calculating excited states and electron transfer calculations. I found the section on the "Relation between multi-determinant states and single determinants" particularly interesting. Their presentation seems to follow traditional quantum chemistry logic and spin-contamination/symmetry breaking. Obviously, for some solid state systems, e.g., iron-oxides, spin-contamination is excepted, whereas for small molecules such symmetry breaking is thought to be bad, mostly due to our experience of using UHF theory with many organic molecules. However, I'm not as sure I understand the rules of the road for spin contamination anymore, since it has been recently suggested that spin-symmetry breaking in the simple C2 molecule gives the correct energetics of the C2 singlet and low-lying triplet, especially when the SCAN meta-GGA is used (https://pubs.acs.org/doi/10.1021/acs.jpca.2c07590). I guess my question about their excited state results for NV- center, are they seeing a similar result in their calculations? Where SCAN is producing the correct energetics for low-lying excited states.....or do the authors think the results of these studies are unrelated.
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- Cite as: Anonymous, Report on arXiv:scipost_202303_00008v1, delivered 2023-04-25, doi: 10.21468/SciPost.Report.7101
In this manuscript A. V. Ivanov and co-workers applied time-dependent variational density functional theory to describe the electronic excitations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. They used 4 local and semi-local density functionals and compared their results with previous density functional based calculations, high-level many-body calculations and available experimental data.
They report that their method is more robust and predictive than DFT based calculations, since a correct ordering of the low-lying triplet and singlet states is obtained, in qualitative and quantitative agreement with the aforementioned high-level methods.
The resolution of the correct order controversy raised by previous studies is the major advance of the paper.
The paper is well written, interesting and it deserves to be published, but in my opinion it should go to Scipost core, as it’s not a breakthrough. Here are my comments and remarks.
1) The authors used a 512 atoms supercell, how did the authors check if the supercell is “big enough” ?
2) It seems to me that people in the literature claim that the correct order of the low lying triplet and singlet states is not recovered because of the fact that the methods used are not able to describe multi-configurational states. However, as far as I understand, the Delta SCF method is also based on a single determinant state. So then what is the strength of this method? Is it the fact that the orbitals are variationally optimised and then the forces can, in principle, be calculated analytically?
3) Did the authors rely on this point to optimize the triplet excited states and calculate the ZPL?
4) From Fig. 2 and the discussion, it seems that the A1 state is most affected by the type of calculation, do the authors have an opinion on this?
5) The most complex functional r2SCAN gives vertical excitations in very good agreement with quantum embedding calculations beyond the random phase approximation (called Emb. bRPA). What makes this method so similar to the Emb. bRPA?
6) What geometry did the authors impose for the evaluation of the vertical excitation of the singlet states? They say that the energy decrease due to changes in atomic coordinates was not evaluated.
7) Would it be possible to provide a pictorial view of the electronic energy surfaces, with saddle points, position of triplet and singlet state geometries and the ZPL? I think that even a simple sketch would also help to follow the discussion.