Mihaly Andras Csirik

• Laestadius, Andre; Csirik, Mihaly Andras; Penz, Markus; Tancogne-Dejean, Nicolas; Ruggenthaler, Michael & Rubio, Angel [Show all 7 contributors for this article] (2024). Exchange-only virial relation from the adiabatic connection. Journal of Chemical Physics. ISSN 0021-9606. 160(8). doi: 10.1063/5.0184934. Full text in Research Archive
• Tancogne-Dejean, Nicolas; Penz, Markus; Laestadius, Andre; Csirik, Mihaly Andras; Ruggenthaler, Michael & Rubio, Angel (2024). Exchange energies with forces in density-functional theory. Journal of Chemical Physics. ISSN 0021-9606. 160(2). doi: 10.1063/5.0177346.
• Faulstich, Fabian M.; Kristiansen, Håkon Emil; Csirik, Mihaly Andras; Kvaal, Simen; Pedersen, Thomas Bondo & Laestadius, Andre (2023). The S-diagnostic - an a posteriori error assessment for single-reference coupled-cluster methods. Journal of Physical Chemistry A. ISSN 1089-5639. 127(43), p. 9106–9120. doi: 10.1021/acs.jpca.3c01575. Full text in Research Archive Show summary

  We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S-diagnostic. We provide a derivation of the S-diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S-diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+. Throughout the numerical investigations, the S-diagnostic is compared to other SRCC diagnostic procedures, that is, the T1, D1, and D2 diagnostics as well as different indices of multi-determinantal and multi-reference character in coupled-cluster theory. Our numerical investigations show that the S-diagnostic outperforms the T1, D1, and D2 diagnostics and is comparable to the indices of multi-determinantal and multi-reference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S-diagnostic for geometry optimizations using SRCC reveal that the S-diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S-diagnostic for electronic correlation simulations show that the S-diagnostic correctly predicts strong multi-reference regimes. The S-diagnostic moreover correctly detects the successful SRCC computations for [CuCl4]2-, [Cu(NH3)4]2+, and [Cu(H2O)4]2+, which have been known to be misdiagnosed by T1 and D1 diagnostics in the past. This shows that the S-diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

• Penz, Markus; Tellgren, Erik Ingemar; Csirik, Mihaly Andras; Ruggenthaler, Michael & Laestadius, Andre (2023). The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields. ACS Physical Chemistry Au. doi: 10.1021/acsphyschemau.3c00006. Full text in Research Archive Show summary

  TheHohenberg−Kohntheoremof density-functionaltheory(DFT)is broadlyconsideredtheconceptualbasisfora fullcharacterizationof an electronicsystemin its groundstateby justone-bodyparticledensity.In thisPartII of a seriesof twoarticles,weaimat clarifyingthestatusof thistheoremwithindifferentextensionsofDFTincludingmagneticfields.Wewillin particulardiscusscurrent-density-functionaltheory(CDFT)andreviewthedifferentformulationsknownintheliterature,includingtheconventionalparamagneticCDFTandsomenonstandardalternatives.Fortheformer,it is knownthattheHohenberg−Kohntheoremis nolongervaliddueto counterexamples.Nonetheless,paramagneticCDFThasthemathematicalframeworkclosestto standardDFTand,justlikein standardDFT,nondifferentiabilityof thedensityfunctionalcanbe mitigatedthroughMoreau−Yosidaregularization.Interestinginsightscanbe drawnfrombothMaxwell−SchrödingerDFTandquantum-electrodynamicDFT,whicharealsodiscussedhere.

• Penz, Markus; Tellgren, Erik Ingemar; Csirik, Mihaly Andras; Ruggenthaler, Michael & Laestadius, Andre (2023). The Structure of Density-Potential Mapping. Part I: Standard Density-Functional Theory. ACS Physical Chemistry Au. 3(4), p. 334–347. doi: 10.1021/acsphyschemau.2c00069. Full text in Research Archive
• Penz, Markus; Csirik, Mihaly Andras & Laestadius, Andre (2023). Density-potential inversion from Moreau-Yosida regularization. Electronic Structure. ISSN 2516-1075. 5(1). doi: 10.1088/2516-1075/acc626. Full text in Research Archive Show summary

  For a quantum-mechanical many-electron system, given a density, the Zhao–Morrison–Parr method allows to compute the effective potential that yields precisely that density. In this work, we demonstrate how this and similar inversion procedures mathematically relate to the Moreau–Yosida regularization of density functionals on Banach spaces. It is shown that these inversion procedures can in fact be understood as a limit process as the regularization parameter approaches zero. This sheds new insight on the role of Moreau–Yosida regularization in density-functional theory and allows to systematically improve density-potential inversion. Our results apply to the Kohn–Sham setting with fractional occupation that determines an effective one-body potential that in turn reproduces an interacting density.

• Csirik, Mihaly Andras & Laestadius, Andre (2023). Coupled-Cluster theory revisited: Part II: Analysis of the single-reference Coupled-Cluster equations. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). ISSN 2822-7840. 57(2), p. 545–583. doi: 10.1051/m2an/2022099. Full text in Research Archive
• Csirik, Mihaly Andras & Laestadius, Andre (2023). Coupled-Cluster theory revisited: Part I: Discretization. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN). ISSN 2822-7840. 57(2), p. 645–670. doi: 10.1051/m2an/2022094. Full text in Research Archive
• Homa, G.; Csordás, A.; Csirik, Mihály András & Bernád, J.Z. (2020). Range of applicability of the Hu-Paz-Zhang master equation. Physical Review A (PRA). ISSN 2469-9926. 102(2). doi: 10.1103/PhysRevA.102.022206.

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• Csirik, Mihaly Andras & Laestadius, Andre (2022). Topological Index and Homotopy in Coupled-Cluster theory. Show summary

  We propose a comprehensive mathematical framework for Coupled-Cluster-type methods based on topological degree theory. This allows us to establish more general existence results than Schneider's and deduce local information about the solutions of the CC equations. The idea of constructing a homotopy for CC theory is not new, and has been extensively studied in the past. We consider the more recent Kowalski--Piecuch (KP) homotopy from a mathematical point of view and use it as a theoretical tool to prove the existence of a truncated CC solution. This follows from a more general result guaranteeing the existence of a whole solution curve of the KP homotopy.

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