Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

Quantum Monte Carlo assessment of embedding for for strongly correlated defects: interplay between mean-field starting point and interactions

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read For a strongly correlated iron defect in aluminum nitride, standard quantum embedding methods reproduce QMC excitation energies to within a few tenths of an electron-volt while getting the wave-function character of the lowest excited…

desk verdict Useful benchmark with a genuine new occupation diagnostic, but the QMC reference carries unquantified systematic error and the abstract overclaims a chromium case. read the letter →

arxiv 2505.00845 v2 pith:ZOFFKVXR submitted 2025-05-01 cond-mat.str-el cond-mat.mtrl-sci

Kevin G. Kleiner , Sonali Joshi , Rohan Joshi , Woncheol Lee , Alexander Hampel , Malte Rösner , Cyrus E. Dreyer , Lucas K. Wagner This is my paper · ORCID
classification cond-mat.str-elcond-mat.mtrl-sci
keywords quantumembeddingMonteCarlopointdefectsstronglycorrelatedelectronsdoublecountingcrystalfieldsplittingexcitedstatesFeinAlN
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Quantum embedding methods are cheaper than full many-body treatments of strongly correlated point defects, but they involve uncontrolled approximations. This paper benchmarks several standard embedding variants against quantum Monte Carlo (QMC) for a neutral iron impurity in aluminum nitride, using the same 32-atom cell and the same active space of five iron d orbitals. The central finding is that several embedding methods reproduce the QMC excitation energies to within a few tenths of an electron-volt while predicting the wrong wave-function character: the lowest excited states have the wrong symmetry ordering and a doubly occupied $d_{z^2}$ orbital, whereas QMC finds that orbital less than singly occupied. The paper identifies the dominant error as the one-body crystal-field splitting inherited from the DFT starting point, with double-counting corrections and the cRPA-screened interactions playing secondary roles. The practical message is that matching excitation energies is not enough; embedding methods must also be validated against wave-function properties.

What carries the argument

The load-bearing objects are the five iron d-like orbitals that form the active space, classified under the $C_{3v}$ point group as an $e$ pair, an $e'$ pair, and an $a_1$ orbital, and the occupation of the $a_1$ orbital in each many-body state, which serves as a compact wave-function-character diagnostic. The QMC reference is built from multi-Slater-Jastrow trial wave functions (a Jastrow factor multiplying a sum of Slater determinants) with a Jastrow factor fixed from the ground state, optimized with the ensemble variational principle, a weighted sum of state energies plus an overlap penalty. The embedding models are single-impurity Hamiltonians with one-particle hoppings from DFT or $G_0W_0$ and two-particle interactions from cRPA, with three choices of double-counting correction. The comparison runs on identical Hamiltonians and active spaces, so disagreements must come from the embedding approximations rather than model differences. The mechanism of the argument is the systematic comparison of excitation energies and $a_1$ occupations between QMC and each embedding variant, backed by ligand-field-theory analysis showing which occupations a spherically symmetric interaction would produce.

What would settle it

Run the QMC reference with a complete-basis extrapolation and a Jastrow factor re-optimized for each state instead of fixed from the ground state; if the lowest 4E state then has $\langle n_{a_1}\rangle \approx 1$ (doubly occupied $a_1$) or the 4A2/4E ordering flips, the claimed orbital-character mismatch collapses. Alternatively, if an embedding variant that changes only the double-counting term (leaving DFT orbitals unchanged) corrects both energies and occupations, the attribution to the crystal-field splitting is refuted.

Watch

Extended reading notes

Core claim

The paper's central claim is that for the neutral iron substitutional defect in AlN ($\mathrm{Fe}_{\mathrm{Al}}^0$:AlN), several standard quantum embedding schemes—DFT plus constrained random phase approximation (cRPA) with and without Hartree double counting, and a $G_0W_0$-based embedding—produce low-lying excited states whose excitation energies are within a few tenths of an eV of the QMC reference but whose orbital character is qualitatively different. The QMC ground state is a high-spin $^6A_1$ state and the lowest excited states are $^4A_2$ and $^4E$ with $a_1$ occupation around 0.5–1.0, whereas the embedding models place $^4E$ states with a nearly doubly occupied $a_1$ orbital lowest, or in the Hartree-DC case produce an incorrect $^2A_1$ ground state. The paper argues that the dominant error is the one-body crystal-field splitting in the iron d orbitals inherited from the DFT starting point, not the double-counting correction, and that the cRPA-screened interaction is itself distorted by over-delocalized DFT orbitals. The abstract further states that the best double-counting recipe is opposite for iron and chromium defects, so no universal correction exists.

Load-bearing premise

The whole comparison rests on the QMC calculation being accurate enough to fix the true state ordering and d-orbital occupations, but the paper's own data show the 4A2 excitation moving from 1.33(7) eV to 1.70(9) eV when the basis set changes and the fixed Jastrow factor altering the state ordering relative to CASCI, so the reference carries an unquantified systematic bias.

Editorial extensions

If this is right

  • Excitation energies are not a sufficient benchmark for embedded defect models; two methods can agree on energies while disagreeing on the many-body wave function, so comparisons must include observables such as orbital occupations.
  • Efforts to improve embedding for strongly correlated defects should focus on correcting the one-body crystal-field splitting inherited from DFT—for example through better starting points—rather than on refining double-counting corrections.
  • cRPA screening computed from DFT orbitals does not automatically fix the orbital-delocalization error; the screened interaction tensor inherits the non-spherical distortion of the DFT orbitals.
  • The optimal double-counting correction is system-dependent (opposite for Fe and Cr in this family), so a universal DC prescription is unlikely to work for transition-metal defects.
  • QMC calculations on small supercells can serve as a practical reference standard for identifying which embedding approximations are reliable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • We infer that if the crystal-field-splitting error is truly dominant, embedding methods that build one-body terms from a more localized or self-consistent starting point should improve both energies and occupations; this is testable beyond the paper's claims.
  • The same diagnostic—comparing a symmetry-resolved orbital occupation such as $\langle n_{a_1}\rangle$—could, we suggest, be applied to other transition-metal and rare-earth defects where DFT orbital delocalization varies across the active space.
  • We further infer that benchmarks ignoring dynamical correlation (e.g., CASCI-only comparisons) may systematically misattribute embedding errors, since the paper shows the fixed Jastrow factor shifts excitation energies by roughly 1 eV and changes state ordering.
  • A concrete extension we propose is repeating the QMC-vs-embedding comparison in the 72-atom cell mentioned in the paper, where cRPA interactions become more spherical; the paper reports the embedding side but not a QMC reference there.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper benchmarks quantum embedding methods (DFT+cRPA with different double-counting schemes and a G0W0-based embedding) against variational quantum Monte Carlo calculations for a substitutional Fe defect in AlN in a 32-atom supercell. The authors compute vertical excitation energies and Fe d-orbital occupations from both approaches, finding that several embedding models obtain excitation energies within a few tenths of an eV of the QMC reference but with different orbital characters and state orderings. They attribute the dominant error to the one-body crystal-field splitting inherited from DFT rather than to double-counting corrections, and further argue that cRPA overestimates the non-spherical part of the screened interaction. The QMC reference is built from multi-Slater-Jastrow trial wave functions optimized with an ensemble variational principle.

Significance. The paper makes a useful methodological contribution by comparing not just excitation energies but also one-particle density-matrix occupations and symmetry labels between embedding models and QMC for the same 32-atom Fe_Al:AlN cell. The use of the ensemble variational principle (Eq. (2)) to construct excited-state trial wave functions and the detailed tabulation of state data (Tables IV–IX) are strengths. If the QMC reference is reliable, the conclusion that energy agreement can be misleading and that the DFT one-body crystal field is a dominant error source is important for the defect-embedding community. However, because the reference itself carries a large unquantified systematic uncertainty, the quantitative and even qualitative conclusions are not yet firmly established.

major comments (4)
  1. [Sec. IV A, Table I] The QMC reference 4A2 excitation energy shifts from 1.33(7) eV (HSE06 vtz) to 1.70(9) eV (HSE06 vqz), a variation of 0.37 eV that is comparable to the 'few tenths of an eV' agreement claimed between embedding and QMC in Sec. IV B. The selection of HSE06 vqz is based on minimizing the ensemble cost functional in Eq. (2), but this variational criterion does not control the systematic error of excitation energies, and the error bars shown in Fig. 3 include only single-sigma statistical noise. Consequently, the comparison in Fig. 3 cannot currently distinguish whether the no-DC DFT+cRPA 4E state at 1.35 eV agrees with the QMC 4E at 1.78(4) eV at the claimed accuracy, and the statement that embedding excitation energies agree 'within uncertainties' is not supported.
  2. [Sec. III B and Sec. VII A] The same two-body Jastrow, optimized only for the ground state, is appended to every eigenstate in Eq. (1). Sec. VII A reports that this fixed Jastrow lowers the lowest vertical excitations by roughly 1 eV and changes the ordering of the lowest 4A1 and 4A2 states relative to CASCI. Because the Jastrow is not state-specific, its bias need not cancel in excitation energies, and it directly affects the a1 occupations in Table IV that are used in Sec. IV C to conclude that cRPA's interaction tensor is too non-spherical. The paper does not report how the a1 occupations of the 4E states change between CASCI and QMC, so the conclusion that embedding models have 'different orbital character' (Sec. IV B) is not shown to be robust to the Jastrow choice.
  3. [Sec. IV C and Sec. VII D] The inference that QMC indicates a significantly more spherically symmetric Coulomb interaction than cRPA rests on the a1 occupation of 0.61 in the QMC 4E state (Table IV) and on the ligand-field model of Sec. VII D. That ligand-field model is fitted to the QMC splittings and occupations (B fixed at 0.068 eV and CFS parameters chosen to reproduce the QMC ordering), so it is not an independent confirmation. If the Jastrow bias changes the 4E a1 occupation from ~0.6 to ~1 (as the large Jastrow effect in Sec. VII A suggests), the inferred isotropy of the interaction would no longer hold. The authors should provide evidence that the orbital occupations in Table IV are stable under variation of the Jastrow form or basis set.
  4. [Abstract and full text] The abstract (both in the header and in the arXiv metadata) states that the paper assesses 'iron and chromium defects in aluminum nitride' and finds that 'the best double counting recipe is opposite in these two cases.' The full text, however, presents results only for Fe_Al:AlN and makes no mention of chromium. This is a missing-result claim that must be corrected; either the abstract must be revised to match the actual content or the chromium results must be added.
minor comments (4)
  1. [Introduction] The sentence 'the self-energy way be straightforwardly decomposed' in Sec. I contains a typo and should read 'may be straightforwardly decomposed'.
  2. [Fig. 3 caption] The caption contains the misspelling 'uncertainities' and, more importantly, the phrase 'within uncertainties' should be qualified to indicate that only statistical uncertainties are meant, in light of the basis-set variation documented in Table I.
  3. [Table IV] Table IV reports single-sigma statistical errors on excitation energies but not on the one-particle expectation values ⟨n_e⟩, ⟨n_e'⟩, ⟨n_a1⟩, and ⟨t_ee'⟩; since these expectation values are used to diagnose orbital character, error bars on them would help assess the significance of differences between methods.
  4. [Sec. IV A] The paper describes the QMC results as 'variational best estimates' using the HSE06 vqz orbitals, but the ensemble cost functional in Eq. (2) is minimized over the choice of orbitals, not over the Jastrow or determinant coefficients; a brief statement of what was actually optimized would improve reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the QMC benchmark is computed from the full Hamiltonian and the embedding models are separately diagonalized; the fitted ligand-field model is post hoc and non-load-bearing.

full rationale

The central comparison is not circular by construction. QMC energies and d-orbital occupations are obtained from multi-Slater-Jastrow wave functions evaluated on the full ab initio Hamiltonian, while the embedding Hamiltonians are built independently from DFT/cRPA/G0W0 inputs and solved by exact diagonalization. No embedding parameter is fitted to the QMC reference; the QMC values are used as a benchmark, not as inputs to the embedding models. The selection of HSE06 vqz orbitals by minimizing the ensemble cost functional of Eq. (2) is a variational optimization of the trial basis, not a fit of the excitation energies that are later compared; the excitation energies are computed, not imposed. The ligand-field model in Sec. VII D is admittedly post hoc: its Racah parameter and crystal-field splittings are chosen to match QMC energy splittings, and the resulting occupations are used only 'to gain insight into the physics.' It is therefore a diagnostic reinterpretation of the QMC data, not a prediction that carries the paper's conclusions. Self-citations to Refs. [25] and [50] provide background and a previously proven optimization principle; they do not define the benchmark energies or the embedding errors. A genuine caveat exists, but it is a matter of reference robustness rather than circularity: Table I shows the 4A2 excitation shifts from 1.33(7) eV (HSE06 vtz) to 1.70(9) eV (HSE06 vqz), and Sec. VII A reports that the fixed, ground-state-optimized Jastrow lowers vertical excitations by roughly 1 eV and changes the ordering relative to CASCI. These systematic uncertainties affect the reliability of the QMC reference, but they do not make the derivation equivalent to its inputs. The paper therefore exhibits no significant circularity; the low score reflects only minor, non-load-bearing self-citations in the methodology chain.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central comparison rests on the QMC reference being converged, on the embedding workflow (spin-unpolarized DFT, static cRPA, Wannier-to-IAO rotation) being faithful, and on the ligand-field model as interpretation only. No new entities, particles, or forces are introduced.

free parameters (3)
  • Racah B (ligand-field model) = 0.068 eV
    Set from a Hund's J of 0.6 eV in Sec. VII D to model spherically symmetric screened interactions; used only to interpret QMC a1 occupancies, not to derive the central benchmark conclusion.
  • Td crystal-field splitting Δe,t2g/B = ≈10
    Estimated in Sec. VII D from the QMC splitting between 4E and 4A1 states; this is fitting to the QMC reference, but the ligand-field model is presented as an interpretive check, not as a prediction.
  • C3v splitting Δa1,e' = <0 (sign chosen)
    Chosen in Sec. VII D to make the 4A2 state lower than 4E as QMC shows; qualitative fitting to the reference spectrum.
assumptions (5)
  • standard math The ensemble variational principle of Eq. (2) is minimized at the true eigenstates (Ref. [50]).
    Invoked in Sec. III B to justify optimizing trial wave functions for the lowest fifteen states; proof is cited from Wheeler, Kleiner, and Wagner 2024, including two present authors.
  • domain assumption The multi-Slater-Jastrow ansatz with HSE06 vqz orbitals and a fixed Jastrow is sufficiently accurate to fix state ordering and d-orbital occupancies.
    This is the QMC reference assumption on which all comparisons rest; basis set moves the 4A2 excitation by 0.3 eV and the fixed Jastrow changes ordering relative to CASCI (Sec. VII A).
  • domain assumption Static cRPA screening with 22 bands per atom gives the relevant effective two-particle interactions in the active space.
    Used in Sec. III C for all DFT+cRPA and G0W0 model Hamiltonians; screening approximations are acknowledged as an open question in the introduction.
  • domain assumption The Wannier-to-IAO basis transformation can be approximated by a unitary round-off of the overlap matrix.
    Sec. VII C reports a raw overlap determinant of 0.85, then rounds entries to nearest +1, -1, or 0; this non-unitary step changes the Hamiltonian before diagonalization.
  • ad hoc to paper Ligand-field theory with a spherically symmetric interaction and F4/F2 = 15/23 describes the relevant low-energy manifold.
    Introduced in Sec. VII D to interpret a1 occupations; parameters are fixed or fitted to QMC and the model is not externally validated.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum Monte Carlo assessment of embedding for for strongly correlated defects: interplay between mean-field starting point and interactions." pith.science (2026). https://pith.science/paper/ZOFFKVXR

@misc{pith2026250500845,
  author       = {Pith},
  title        = {Pith review of: Quantum Monte Carlo assessment of embedding for for strongly correlated defects: interplay between mean-field starting point and interactions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZOFFKVXR}},
  note         = {Machine review of arXiv:2505.00845}
}
read the original abstract

Point defects are of interest for many applications, from quantum sensing to modifying bulk properties of materials. Because of their localized orbitals, the electronic states are often strongly correlated, which has led to a proliferation of quantum embedding techniques to treat this correlation. In these techniques, most of the one-body states are treated with a weakly correlated theory such as density functional theory, and certain one-body states are singled out as an active space to be treated using an effective interaction. We assess these techniques for iron and chromium defects in aluminum nitride using quantum Monte Carlo (QMC) calculations on identical Hamiltonians. For these systems, we find the dominant errors in the embedding arise from the one-body crystal-field splitting in the d orbitals inherited from density functional theory (DFT), rather than double counting corrections, with the screened interactions also affected by the DFT orbitals. Strikingly, the best double counting recipe is opposite in these two cases. Because excitation energies can agree while the underlying wave functions do not, diagnosing these errors requires detailed information about the many-body wave functions, which QMC provides.

Figures

Figures reproduced from arXiv: 2505.00845 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: , CASCI obtains lowest excitation energies 1 eV higher than with the Jastrow. The Jastrow also changes the ordering of excited states relative to CASCI, in par￾ticular switching the ordering of the lowest 4A1 and 4A2 states and lowering the 4E states with 0.6 occupatio…
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Excited state optimization for strongly correlated quantum defects using ensemble variational Monte Carlo

    cond-mat.str-el 2026-07 conditional novelty 5.0 of 10

    Ensemble variational Monte Carlo with optimized multi-Slater-Jastrow wave functions shows that PBE0 orbitals and state-specific parameter optimization change defect excitation energies by up to 0.5 eV, but finite-size...

Reference graph

Works this paper leans on

73 extracted references · 60 canonical work pages · cited by 1 Pith paper

  1. [1]

    Shockley and W

    W. Shockley and W. T. Read, Statistics of the Recombi- nations of Holes and Electrons, Physical Review 87, 835 (1952)

    work page 1952

  2. [2]

    R. N. Hall, Electron-Hole Recombination in Germanium, Physical Review 87, 387 (1952)

    work page 1952

  3. [3]

    J. R. Weber, W. F. Koehl, J. B. Varley, A. Janotti, B. B. Buckley, C. G. Van De Walle, and D. D. Awschalom, Quantum computing with defects, Proceedings of the Na- tional Academy of Sciences 107, 8513 (2010)

    work page 2010

  4. [4]

    B. E. Kane, A silicon-based nuclear spin quantum com- puter, Nature 393, 133 (1998)

    work page 1998

  5. [5]

    Aharonovich, S

    I. Aharonovich, S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, Diamond-based single- photon emitters, Reports on Progress in Physics 74, 076501 (2011)

    work page 2011

  6. [6]

    Aharonovich, D

    I. Aharonovich, D. Englund, and M. Toth, Solid-state single-photon emitters, Nature Photonics 10, 631 (2016)

    2016

  7. [7]

    Schirhagl, K

    R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, Nitrogen-Vacancy Centers in Diamond: Nanoscale Sen- sors for Physics and Biology, Annual Review of Physical Chemistry 65, 83 (2014)

    2014

  8. [8]

    Shang, Q

    L. Shang, Q. Chen, W. Jing, C.-G. Ma, C.-K. Duan, and J. Du, First-principles study of transition metal dopants as spin qubits, Physical Review Materials 6, 086201 (2022)

    work page 2022

Show all 73 references
  1. [9]

    C.-W. Lee, M. Singh, A. C. Tamboli, and V. Stevanovi´ c, Transition metal impurities in silicon: Computational search for a semiconductor qubit, npj Computational Ma- terials 8, 172 (2022)

    2022

  2. [10]

    L. Otis, Y. Jin, V. W.-z. Yu, S. Chen, L. Gagliardi, and G. Galli, Strongly correlated states of transition metal spin defects: The case of an iron impurity in aluminum nitride (2025), arXiv:2501.16280 [cond-mat]

    2025 arXiv

  3. [11]

    A. I. Lvovsky, B. C. Sanders, and W. Tittel, Optical quantum memory, Nature Photonics 3, 706 (2009)

    2009

  4. [12]

    Kolesov, K

    R. Kolesov, K. Xia, R. Reuter, R. St¨ ohr, A. Zappe, J. Meijer, P. Hemmer, and J. Wrachtrup, Optical detec- tion of a single rare-earth ion in a crystal, Nature Com- munications 3, 1029 (2012)

    2012

  5. [13]

    D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Quantum technologies with optically interfaced solid-state spins, Nature Photonics 12, 516 (2018)

    2018

  6. [14]

    Zhang, G

    J. Zhang, G. D. Grant, I. Masiulionis, M. T. Solomon, J. C. Marcks, J. K. Bindra, J. Niklas, A. M. Dibos, O. G. Poluektov, F. J. Heremans, S. Guha, and D. D. Awschalom, Optical and spin coherence of Er spin qubits in epitaxial cerium dioxide on silicon, npj Quantum In- formati...

    2024

  7. [15]

    Freysoldt, B

    C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van De Walle, First- principles calculations for point defects in solids, Reviews of Modern Physics 86, 253 (2014)

    2014

  8. [16]

    Mori-S´ anchez, A

    P. Mori-S´ anchez, A. J. Cohen, and W. Yang, Many- electron self-interaction error in approximate density functionals, The Journal of Chemical Physics 125, 201102 (2006)

    2006

  9. [17]

    Y. Ma, M. Rohlfing, and A. Gali, Excited states of the negatively charged nitrogen-vacancy color center in dia- mond, Physical Review B 81, 041204 (2010)

    2010

  10. [18]

    M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen- vacancy colour centre in diamond, Physics Reports 528, 1 (2013). 9

    2013

  11. [19]

    M. L. Goldman, M. W. Doherty, A. Sipahigil, N. Y. Yao, S. D. Bennett, N. B. Manson, A. Kubanek, and M. D. Lukin, State-selective intersystem crossing in nitrogen- vacancy centers, Physical Review B 91, 165201 (2015)

    2015

  12. [20]

    Alkauskas, C

    A. Alkauskas, C. E. Dreyer, J. L. Lyons, and C. G. Van De Walle, Role of excited states in Shockley-Read-Hall recombination in wide-band-gap semiconductors, Physi- cal Review B 93, 201304 (2016)

    2016

  13. [21]

    Wickramaratne, J.-X

    D. Wickramaratne, J.-X. Shen, C. E. Dreyer, M. En- gel, M. Marsman, G. Kresse, S. Marcinkeviˇ cius, A. Alka- uskas, and C. G. Van De Walle, Iron as a source of effi- cient Shockley-Read-Hall recombination in GaN, Applied Physics Letters 109, 162107 (2016)

    2016

  14. [22]

    Wickramaratne, J.-X

    D. Wickramaratne, J.-X. Shen, C. E. Dreyer, A. Alka- uskas, and C. G. Van De Walle, Electrical and optical properties of iron in GaN, AlN, and InN, Physical Re- view B 99, 205202 (2019)

    2019

  15. [23]

    Von Barth, Local-density theory of multiplet struc- ture, Physical Review A 20, 1693 (1979)

    U. Von Barth, Local-density theory of multiplet struc- ture, Physical Review A 20, 1693 (1979)

    1979

  16. [24]

    Lischner, J

    J. Lischner, J. Deslippe, M. Jain, and S. G. Louie, First- Principles Calculations of Quasiparticle Excitations of Open-Shell Condensed Matter Systems, Physical Review Letters 109, 036406 (2012)

    2012

  17. [25]

    Muechler, D

    L. Muechler, D. I. Badrtdinov, A. Hampel, J. Cano, M. R¨ osner, and C. E. Dreyer, Quantum embedding meth- ods for correlated excited states of point defects: Case studies and challenges, Physical Review B 105, 235104 (2022)

    2022

  18. [26]

    Bockstedte, F

    M. Bockstedte, F. Sch¨ utz, T. Garratt, V. Iv´ ady, and A. Gali, Ab initio description of highly correlated states in defects for realizing quantum bits, npj Quantum Ma- terials 3, 31 (2018)

    2018

  19. [27]

    H. Ma, M. Govoni, and G. Galli, Quantum simulations of materials on near-term quantum computers, npj Com- putational Materials 6, 85 (2020)

    2020

  20. [28]

    H. Ma, N. Sheng, M. Govoni, and G. Galli, First- principles studies of strongly correlated states in defect spin qubits in diamond, Physical Chemistry Chemical Physics 22, 25522 (2020)

    2020

  21. [29]

    H. Ma, N. Sheng, M. Govoni, and G. Galli, Quantum Em- bedding Theory for Strongly Correlated States in Mate- rials, Journal of Chemical Theory and Computation 17, 2116 (2021)

    2021

  22. [30]

    Aryasetiawan, M

    F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency- dependent local interactions and low-energy effective models from electronic structure calculations, Physical Review B 70, 195104 (2004)

    2004

  23. [31]

    Aryasetiawan, K

    F. Aryasetiawan, K. Karlsson, O. Jepsen, and U. Sch¨ onberger, Calculations of Hubbard U from first- principles, Physical Review B 74, 125106 (2006)

    2006

  24. [32]

    Miyake, F

    T. Miyake, F. Aryasetiawan, and M. Imada, Ab Initio procedure for constructing effective models of correlated materials with entangled band structure, Physical Re- view B 80, 155134 (2009)

    2009

  25. [33]

    S ¸a¸ sıo˘ glu, C

    E. S ¸a¸ sıo˘ glu, C. Friedrich, and S. Bl¨ ugel, Effective Coulomb interaction in transition metals from con- strained random-phase approximation, Physical Review B 83, 121101 (2011)

    2011

  26. [34]

    Pavarini, E

    E. Pavarini, E. Koch, D. Vollhardt, A. I. Licht- enstein, Institute for Advanced Simulation, Ger- man Research School for Simulation Sciences, and D. Forschungsgemeinschaft, eds., The LDA+DMFT Ap- proach to Strongly Correlated Materials: Lecture Notes of the Autumn School 2011...

    2011

  27. [35]

    A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Or- bital ordering in Mott-Hubbard insulators, Physical Re- view B 52, R5467 (1995)

    1995

  28. [36]

    Ryee and M

    S. Ryee and M. J. Han, The effect of double count- ing, spin density, and Hund interaction in the different DFT+U functionals, Scientific Reports 8, 9559 (2018)

    2018

  29. [37]

    Sheng, C

    N. Sheng, C. Vorwerk, M. Govoni, and G. Galli, Green’s Function Formulation of Quantum Defect Embedding Theory, Journal of Chemical Theory and Computation 18, 3512 (2022)

    2022

  30. [38]

    E. G. C. P. Van Loon, M. R¨ osner, M. I. Katsnelson, and T. O. Wehling, Random phase approximation for gapped systems: Role of vertex corrections and applicability of the constrained random phase approximation, Physical Review B 104, 045134 (2021)

    2021

  31. [39]

    Chang, E

    Y. Chang, E. G. C. P. Van Loon, B. Eskridge, B. Buse- meyer, M. A. Morales, C. E. Dreyer, A. J. Millis, S. Zhang, T. O. Wehling, L. K. Wagner, and M. R¨ osner, Downfolding from ab initio to interacting model Hamil- tonians: Comprehensive analysis and benchmarking of the DFT+cR...

    2024

  32. [40]

    W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Ra- jagopal, Quantum Monte Carlo simulations of solids, Re- views of Modern Physics 73, 33 (2001)

    2001

  33. [41]

    Alf` e and M

    D. Alf` e and M. J. Gillan, Schottky defect formation en- ergy in MgO calculated by diffusion Monte Carlo, Phys- ical Review B 71, 220101 (2005)

    2005

  34. [42]

    W. D. Parker, J. W. Wilkins, and R. G. Hennig, Accuracy of quantum Monte Carlo methods for point defects in solids, physica status solidi (b) 248, 267 (2011)

    2011

  35. [43]

    R. Q. Hood, P. R. C. Kent, and F. A. Reboredo, Diffusion quantum Monte Carlo study of the equation of state and point defects in aluminum, Physical Review B85, 134109 (2012)

    2012

  36. [44]

    Ertekin, L

    E. Ertekin, L. K. Wagner, and J. C. Grossman, Point- defect optical transitions and thermal ionization energies from quantum Monte Carlo methods: Application to the F -center defect in MgO, Physical Review B 87, 155210 (2013)

    2013

  37. [45]

    J. Yu, L. K. Wagner, and E. Ertekin, Fixed-node diffusion Monte Carlo description of nitrogen defects in zinc oxide, Physical Review B 95, 075209 (2017)

    2017

  38. [46]

    R. Q. Hood, P. R. C. Kent, R. J. Needs, and P. R. Brid- don, Quantum Monte Carlo Study of the Optical and Diffusive Properties of the Vacancy Defect in Diamond, Physical Review Letters 91, 076403 (2003)

    2003

  39. [47]

    Saritas, W

    K. Saritas, W. Ming, M.-H. Du, and F. A. Reboredo, Excitation Energies of Localized Correlated Defects via Quantum Monte Carlo: A Case Study of Mn 4+ -Doped Phosphors, The Journal of Physical Chemistry Letters 10, 67 (2019)

    2019

  40. [48]

    Y. Chen, T. Jiang, H. Chen, E. Han, A. Alavi, K. Yu, E. Wang, and J. Chen, Multiconfigurational nature of electron correlation within nitrogen vacancy centers in diamond, Physical Review B 108, 045111 (2023)

    2023

  41. [49]

    K. A. Simula and I. Makkonen, Calculation of the ener- gies of the multideterminant states of the nitrogen va- 10 cancy center in diamond with quantum Monte Carlo, Physical Review B 108, 094108 (2023)

    2023

  42. [50]

    W. A. Wheeler, K. G. Kleiner, and L. K. Wagner, En- semble variational Monte Carlo for optimization of corre- lated excited state wave functions, Electronic Structure 6, 025001 (2024)

    2024

  43. [51]

    Sugano, Y

    S. Sugano, Y. Tanabe, and H. Kamimura, Multiplets of Transition-Metal Ions in Crystals , Pure and Applied Physics, v. 33 (Academic Press, 1970)

    1970

  44. [52]

    Masenda, D

    H. Masenda, D. Naidoo, K. Bharuth-Ram, H. Gunnlaugsson, K. Johnston, R. Mantovan, T. Mølholt, M. Ncube, S. Shayestehaminzadeh, H. G´ ıslason, G. Langouche, S. ´Olafsson, and G. Weyer, Lattice sites, charge states and spin–lattice relaxation of Fe ions in 57 Mn + implanted GaN ...

    2016

  45. [53]

    Y. Jin, M. Govoni, G. Wolfowicz, S. E. Sullivan, F. J. Heremans, D. D. Awschalom, and G. Galli, Photolumi- nescence spectra of point defects in semiconductors: Val- idation of first-principles calculations, Physical Review Materials 5, 084603 (2021)

    2021

  46. [54]

    A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials 1, 011002 (2013)

    2013

  47. [55]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Computational Materials Science 6, 15 (1996)

    1996

  48. [56]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters 77, 3865 (1996)

    1996

  49. [57]

    Q. Sun, T. C. Berkelbach, N. S. Blunt, G. H. Booth, S. Guo, Z. Li, J. Liu, J. D. McClain, E. R. Sayfut- yarova, S. Sharma, S. Wouters, and G. K.-L. Chan, P y SCF: The Python-based simulations of chemistry frame- work, WIREs Computational Molecular Science 8, e1340 (2018)

    2018

  50. [58]

    Annaberdiyev, G

    A. Annaberdiyev, G. Wang, C. A. Melton, M. C. Ben- nett, L. Shulenburger, and L. Mitas, A new generation of effective core potentials from correlated calculations: 3d transition metal series, The Journal of Chemical Physics 149, 134108 (2018)

    2018

  51. [59]

    L. K. Wagner and L. Mitas, Energetics and dipole mo- ment of transition metal monoxides by quantum Monte Carlo, The Journal of Chemical Physics 126, 034105 (2007)

    2007

  52. [60]

    W. A. Wheeler, S. Pathak, K. G. Kleiner, S. Yuan, J. N. B. Rodrigues, C. Lorsung, K. Krongchon, Y. Chang, Y. Zhou, B. Busemeyer, K. T. Williams, A. Mu˜ noz, C. Y. Chow, and L. K. Wagner, PyQMC : An all-Python real-space quantum Monte Carlo module in PySCF, The Journal of Chemi...

    2023

  53. [61]

    J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid func- tionals based on a screened Coulomb potential, The Jour- nal of Chemical Physics 118, 8207 (2003)

    2003

  54. [62]

    Hybrid functionals based on a screened Coulomb po- tential

    J. Heyd, G. E. Scuseria, and M. Ernzerhof, Erratum: “Hybrid functionals based on a screened Coulomb po- tential” [J. Chem. Phys. 118, 8207 (2003)], The Journal of Chemical Physics 124, 219906 (2006)

    2003

  55. [63]

    Knizia, Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Con- cepts, Journal of Chemical Theory and Computation 9, 4834 (2013)

    G. Knizia, Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Con- cepts, Journal of Chemical Theory and Computation 9, 4834 (2013)

    2013

  56. [64]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavaz- zoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carn- imeo, A. Dal Corso, S. De Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Ge...

    2017

  57. [65]

    A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions, Computer Physics Communications 185, 2309 (2014)

    2014

  58. [66]

    Nakamura, Y

    K. Nakamura, Y. Yoshimoto, Y. Nomura, T. Tadano, M. Kawamura, T. Kosugi, K. Yoshimi, T. Misawa, and Y. Motoyama, RESPACK: An ab initio tool for deriva- tion of effective low-energy model of material, Computer Physics Communications 261, 107781 (2021)

    2021

  59. [67]

    Kurita, T

    K. Kurita, T. Misawa, K. Yoshimi, K. Ido, and T. Ko- retsune, Interface tool from Wannier90 to RESPACK: Wan2respack, Computer Physics Communications 292, 108854 (2023)

    2023

  60. [68]

    M. S. Hybertsen and S. G. Louie, Electron correlation in semiconductors and insulators: Band gaps and quasipar- ticle energies, Physical Review B 34, 5390 (1986)

    1986

  61. [69]

    Deslippe, G

    J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, BerkeleyGW: A mas- sively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures, Computer Physics Communications183, 1269 (2012)

    2012

  62. [70]

    J. Baur, K. Maier, M. Kunzer, U. Kaufmann, and J. Schneider, Determination of the GaN/AlN band off- set via the (-/0) acceptor level of iron, Applied Physics Letters 65, 2211 (1994)

    1994

  63. [71]

    Plasser, M

    F. Plasser, M. Ruckenbauer, S. Mai, M. Oppel, P. Mar- quetand, and L. Gonz´ alez, Efficient and Flexible Compu- tation of Many-Electron Wave Function Overlaps, Jour- nal of Chemical Theory and Computation 12, 1207 (2016)

    2016

  64. [72]

    M. E. A. Coury, S. L. Dudarev, W. M. C. Foulkes, A. P. Horsfield, P.-W. Ma, and J. S. Spencer, Hubbard-like Hamiltonians for interacting electrons in s , p , and d orbitals, Physical Review B 93, 075101 (2016)

    2016

  65. [73]

    Parcollet, M

    O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, TRIQS: A toolbox for research on interacting quantum systems, Computer Physics Communications 196, 398 (2015). 11 0 1 2 3 4Excitation energy (eV) CASCI Best Estimate QMC Best Estimate 6A1 4E...

    2015

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.