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Electronic excitations of the charged nitrogenvacancy center in diamond obtained using timeindependent variational density functional calculations
by Aleksei V. Ivanov, Leonard A. Schmerwitz, Gianluca Levi, Hannes Jonsson
This Submission thread is now published as
Submission summary
Authors (as registered SciPost users):  Hannes Jonsson 
Submission information  

Preprint Link:  scipost_202303_00008v2 (pdf) 
Date accepted:  20230522 
Date submitted:  20230504 00:58 
Submitted by:  Jonsson, Hannes 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Computational 
Abstract
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 timeindependent, variational density functional calculations of a prototypical defect, the negatively charged nitrogenvacancy 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 lowlying 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 highlevel, manybody 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 zerophonon 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.
Author comments upon resubmission
Referee 2 does not question the suitability of our manuscript for publication in SciPost Physics, but referee 1 recommends publication in SciPost Physics Core. While we agree with referee 1 that our manuscript does not meet the first listed acceptance criterion for Scipost Physics (see https://scipost.org/SciPostPhys/about), i.e:
"Detail a groundbreaking theoretical/experimental/computational discovery",
we believe that the manuscript fulfills the third criterion:
"Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work".
Note that *only one* of the four listed acceptance criteria needs to be fulfilled for publication in SciPost Physics. The manuscript fulfills the latter criterion as it presents an approach that is much more efficient in terms of implementation and computational effort than previous methods, and yet has the predictive power of higher level approaches that are currently believed to be necessary to calculate excited electronic states in solids. In this way, our approach opens a new pathway for theoretical research on excited defect states in solids and will likely promote numerous studies, especially on large systems of interest for applications such as quantum computing. Such studies are currently limited because commonly used manybody approaches are too tedious and computationally intensive. The referees do not question the approach we present or our claims for its promise. We have already received requests from workers in the field who are interested in using our approach and it will soon be available in commonly used software.
List of changes
In response to question 1 of referee 1:
The following has been added at the end of section 2: "In order to ensure the 511atom supercell (with the vacancy) is large enough, calculations were also carried out with a smaller cell containing 215 atoms, and the results were found to differ by at most 5 meV (see Tables 2, and 3 in the Appendix). Given this small difference, it is appropriate to compare the results obtained here with a 511atom supercell with the previous periodic calculations where a 215atom supercell was used."
In response to question 2 of referee 1:
We have added the following sentence at the end of the second paragraph of section 4: "We note that the commonly used selfconsistent field optimization of orbitals typically converges on a symmetric solution if it is started from a symmetric initial wave function."
In response to question 4 of referee 1:
We have rephrased a bit the discussion in the second paragraph of the Results section to: "The correct ordering of the energy levels is obtained for all of the functionals. The largest absolute changes in excitation energy with respect to the density functional are obtained for the excited singlet state, 1A1, but the relative changes of the two singlet states are similar. The excited triplet state, which is the only state apart from the ground state that can be described using a single determinant, is affected less by the choice of functional.”
In response to question 6 of referee 1:
To clarify this, we have modified slightly a sentence in the last paragraph of section 2 to read "The energy of vertical excitations for both singlet and triplet states is obtained at the geometry optimized in the triplet ground state".
Published as SciPost Phys. 15, 009 (2023)