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arxiv: 2604.27451 · v1 · submitted 2026-04-30 · ⚛️ physics.chem-ph

Recognition: unknown

Relativistic Exact-Two-Component Core-Valence-Separated Algebraic Diagrammatic Construction Theory For Near L-edge X-ray Absorption Spectra

Achintya Kumar Dutta, Somesh Chamoli, Sudipta Chakraborty, Xubo Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-07 08:28 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords relativistic effectsX-ray absorption spectroscopyL-edge spectraalgebraic diagrammatic constructioncore-valence separationfrozen natural spinorsCholesky decompositiontwo-component methods
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The pith

A two-component relativistic CVS-ADC(2) method with state-averaged frozen natural spinors and Cholesky decomposition reproduces four-component accuracy for L-edge X-ray spectra at reduced cost.

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

The paper develops an efficient second-order algebraic diagrammatic construction approach for core excitations that includes exact two-component relativistic effects. It reduces computational expense through state-averaged frozen natural spinors to truncate the orbital space and Cholesky decomposition to compress two-electron integrals. Systematic benchmarks against four-component calculations show close agreement for L-edge spectra in 3d transition-metal compounds, while also matching experimental data and providing a lower-cost alternative to equation-of-motion coupled-cluster methods. The work further demonstrates applicability to medium-sized molecules such as a ruthenium complex.

Core claim

The central claim is that the core-valence-separated algebraic diagrammatic construction at second order, implemented in the exact two-component (X2CMP/X2CAMF) relativistic framework and accelerated by state-averaged frozen natural spinors together with Cholesky decomposition, delivers results for near L-edge X-ray absorption spectra that closely match four-component reference calculations while requiring only a fraction of the computational cost. Benchmark studies on 3d transition-metal compounds confirm that this CVS-ADC(2) variant reproduces experimental L2,3-edge spectra with accuracy comparable to non-Hermitian EOM-CC, and the approach scales to medium-sized relativistic molecular cases

What carries the argument

State-averaged frozen natural spinors (SA-FNS) combined with Cholesky decomposition (CD) applied inside the two-component relativistic core-valence-separated ADC(2) equations to reduce floating-point operations and integral storage for core excitations.

If this is right

  • The method serves as a reliable and computationally efficient alternative to four-component calculations for near L-edge spectra in systems containing heavy elements.
  • CVS-ADC(2) reproduces experimental L2,3-edge spectra for 3d transition-metal compounds with accuracy comparable to non-Hermitian EOM-CC at lower cost.
  • The framework extends to relativistic studies of medium-sized molecular systems such as ruthenium complexes.
  • Systematic benchmarking confirms that the two-component (X2CMP/X2CAMF) framework maintains close agreement with canonical four-component results.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The efficiency gains could enable X-ray absorption calculations on larger molecules or materials with heavy atoms that exceed the reach of four-component methods.
  • The approach could be paired with local correlation techniques or basis-set extrapolation to reach even bigger systems while retaining core-excitation accuracy.
  • Additional comparisons on diverse heavy-element compounds would quantify any residual errors from the two-component approximation beyond the current benchmarks.

Load-bearing premise

The two-component relativistic approximation combined with SA-FNS truncation and Cholesky decomposition preserves sufficient accuracy for L-edge core excitations in the tested heavy-element systems without introducing systematic errors.

What would settle it

Substantial deviations between the two-component SA-FNS CVS-ADC(2) L-edge results and both four-component reference values and experimental spectra on an additional heavy-element molecule outside the current test set would falsify the reliability claim.

Figures

Figures reproduced from arXiv: 2604.27451 by Achintya Kumar Dutta, Somesh Chamoli, Sudipta Chakraborty, Xubo Wang.

Figure 1
Figure 1. Figure 1: CVS-ADC(2) XAS spectra near Si L2,3 -edge of SiCl4 molecule. An analogous analysis was performed for the Ar atom to further assess the performance of the two-component Hamiltonians for L2,3-edge spectra (see view at source ↗
Figure 2
Figure 2. Figure 2: CVS-ADC(2) XAS spectra near Ar L2,3 -edge for Ar atom. The relative peak positions and their intensities are well reproduced by both two-component approaches, closely matching the 4c reference. The maximum deviation in peak positions with respect to the 4c results is 0.02 eV for X2CAMF and is further reduced to 0.01 eV for X2CMP. Furthermore, the spectral features obtained from CVS-ADC(2) are largely consi… view at source ↗
Figure 3
Figure 3. Figure 3: Effect of higher-order relativistic effects on calculated CVS-ADC(2) XAS spectra view at source ↗
Figure 4
Figure 4. Figure 4: CVS-ADC(2) XAS spectra near Si L2,3 -edge of SiCl4 molecule in different trun￾cation thresholds view at source ↗
Figure 5
Figure 5. Figure 5: CVS-ADC(2) XAS spectra near Si L2,3 -edge of SiCl4 molecule in different trun￾cation thresholds with correction included. Taken together, these results suggest that a truncation threshold of 10−4.5 offers an optimal balance between computational efficiency and spectral accuracy, retaining key spectral fea￾tures and achieving near-converged intensities while substantially reducing the size of the virtual sp… view at source ↗
Figure 6
Figure 6. Figure 6: XAS spectra near M L2,3 -edge of MOn− 4 transition metal oxyanions obtained using (a) experimental method and (b) CVS-ADC(2) method. increase in average M-O bond lengths and the corresponding decrease in the formal charge on the transition metal center. The computed spectra reproduce this trend qualitatively, showing a slight increase in the A-B splitting for CrO2− 4 , consistent with the experimental obse… view at source ↗
Figure 7
Figure 7. Figure 7: CVS-ADC(2) XAS spectra near Ti L2,3 -edge of TiCl4 and its comparison with experimental spectra. overall pattern and relative intensities are well reproduced; however, the spacing between the L3-edge peaks is overestimated, consistent with the trend observed in CVS-EOM-CC47 calculations. The method also captures a weak pre-edge feature appearing just before the L3 edge. This agreement, however, deteriorate… view at source ↗
Figure 8
Figure 8. Figure 8: CVS-ADC(2) XAS spectra near V L2,3 -edge of VOCl3 and its comparison with experimental spectra. substantially reduced computational cost. It therefore serves as an efficient and practical alternative for evaluating L-edge spectra, particularly in systems containing heavy elements. 4.5 Application to Medium-Sized Complex To illustrate the application of the CVS-ADC(2) implementation to medium-sized molecula… view at source ↗
Figure 9
Figure 9. Figure 9: Molecular structure for the RuCl2(DMSO)2(Im)2 Complex 28 view at source ↗
read the original abstract

We present an efficient implementation of the second-order two-component relativistic core-valence-separated algebraic diagrammatic construction method (CVS-ADC(2)) for core-excitation calculations. The approach employs state-averaged frozen natural spinors (SA-FNS) to reduce the number of floating-point operations, together with the Cholesky decomposition (CD) technique, which lowers the storage requirements associated with two-electron integrals. These reductions make the method particularly well-suited for systems containing heavy elements. Systematic benchmarking against four-component reference calculations confirms the reliability and robustness of the two-component (X2CMP/X2CAMF)-based framework. The close agreement with canonical results further demonstrates that the SA-FNS-based CVS-ADC(2) approach achieves comparable accuracy at only a fraction of the computational cost. Moreover, benchmark studies of L$_{2,3}$-edge spectra for 3$d$ transition-metal compounds demonstrate that CVS-ADC(2) serves as a computationally efficient and reliable alternative to the non-Hermitian EOM-CC method for reproducing experimental spectra. Finally, calculations on a ruthenium complex illustrate the method's applicability to relativistic studies of medium-sized molecular systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript presents an efficient implementation of the second-order core-valence-separated algebraic diagrammatic construction method (CVS-ADC(2)) within a two-component relativistic exact-two-component (X2C) framework (X2CMP/X2CAMF) for near L-edge X-ray absorption spectra. It employs state-averaged frozen natural spinors (SA-FNS) to truncate the virtual space and Cholesky decomposition (CD) to reduce integral storage, enabling calculations on heavy-element systems. Systematic benchmarks against four-component reference calculations and experimental L_{2,3}-edge spectra for 3d transition-metal compounds and a ruthenium complex are reported, with claims of close agreement, comparable accuracy to non-Hermitian EOM-CC, and substantial computational savings.

Significance. If the accuracy claims hold, the work provides a practical, scalable route to relativistic core-excitation spectra for medium-sized molecules containing heavy atoms, where four-component methods remain prohibitive. The SA-FNS + CD combination directly tackles the dominant computational costs in ADC(2) while retaining the core-valence separation, potentially enabling routine studies of L-edge XAS in 3d and 4d metal complexes that are currently limited to smaller systems or lower-level methods.

major comments (3)
  1. [Abstract / Benchmarking results] Abstract and benchmarking sections: The claims of 'systematic benchmarking against four-component reference calculations' and 'close agreement with canonical results' are not supported by quantitative error metrics (e.g., mean absolute deviations or maximum errors in excitation energies/intensities), the number or sizes of tested systems, or explicit values of the SA-FNS occupation threshold and CD tolerance. Without these, the assertion that the two-component framework 'preserves sufficient accuracy' for L-edge spectra cannot be evaluated.
  2. [Methodology (SA-FNS)] Methodology section describing SA-FNS: State averaging over frozen natural spinors is used to select a reduced virtual space, but for 2p→3d L_{2,3}-edge transitions the dominant 3d virtuals may receive diluted natural occupations when lower-lying valence states are included in the averaging. The manuscript must specify the occupation threshold, the states included in the average, and provide sensitivity tests (e.g., comparison to untruncated virtual space or varying thresholds) to demonstrate that no systematic shifts are introduced relative to the four-component references.
  3. [Results (L-edge benchmarks)] Results section on L_{2,3}-edge spectra for 3d compounds: The statement that CVS-ADC(2) 'serves as a computationally efficient and reliable alternative to the non-Hermitian EOM-CC method' requires explicit per-system comparisons, including which molecules were tested, the magnitude of deviations from experiment or EOM-CC, and any post-hoc adjustments. The current description supplies no such statistics, weakening the cross-method reliability claim.
minor comments (2)
  1. [Introduction] Define all acronyms (CVS-ADC(2), SA-FNS, X2CMP, X2CAMF, CD) at first use in the introduction and ensure consistent usage thereafter.
  2. [Results / Computational details] In any tables or figures comparing spectra or timings, include explicit error statistics or scaling data to quantify the claimed 'fraction of the computational cost.'

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have identified opportunities to strengthen the quantitative support for our claims. We address each major point below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract / Benchmarking results] Abstract and benchmarking sections: The claims of 'systematic benchmarking against four-component reference calculations' and 'close agreement with canonical results' are not supported by quantitative error metrics (e.g., mean absolute deviations or maximum errors in excitation energies/intensities), the number or sizes of tested systems, or explicit values of the SA-FNS occupation threshold and CD tolerance. Without these, the assertion that the two-component framework 'preserves sufficient accuracy' for L-edge spectra cannot be evaluated.

    Authors: We agree that explicit quantitative metrics would better substantiate the benchmarking claims. In the revised manuscript we will add a summary table reporting mean absolute deviations and maximum errors in both excitation energies and intensities relative to the four-component references. The table will also list the specific molecules tested (including their sizes) along with the SA-FNS occupation threshold and Cholesky decomposition tolerance employed. These additions will allow direct evaluation of the accuracy of the two-component framework. revision: yes

  2. Referee: [Methodology (SA-FNS)] Methodology section describing SA-FNS: State averaging over frozen natural spinors is used to select a reduced virtual space, but for 2p→3d L_{2,3}-edge transitions the dominant 3d virtuals may receive diluted natural occupations when lower-lying valence states are included in the averaging. The manuscript must specify the occupation threshold, the states included in the average, and provide sensitivity tests (e.g., comparison to untruncated virtual space or varying thresholds) to demonstrate that no systematic shifts are introduced relative to the four-component references.

    Authors: We acknowledge the potential concern about dilution of natural occupations for the relevant virtual orbitals. The revised manuscript will explicitly state the occupation threshold used for virtual-space truncation, describe the states included in the state averaging (the L-edge core-excited states of interest), and include sensitivity tests comparing results at the chosen threshold against both the untruncated virtual space and alternative thresholds. These tests will demonstrate that any shifts remain well below the intrinsic accuracy of the CVS-ADC(2) method and show no systematic bias relative to four-component references. revision: yes

  3. Referee: [Results (L-edge benchmarks)] Results section on L_{2,3}-edge spectra for 3d compounds: The statement that CVS-ADC(2) 'serves as a computationally efficient and reliable alternative to the non-Hermitian EOM-CC method' requires explicit per-system comparisons, including which molecules were tested, the magnitude of deviations from experiment or EOM-CC, and any post-hoc adjustments. The current description supplies no such statistics, weakening the cross-method reliability claim.

    Authors: We agree that per-system statistics are required to support the cross-method comparison. The revised manuscript will include a table listing all tested 3d transition-metal compounds and the ruthenium complex, together with CVS-ADC(2) excitation energies and intensities, the corresponding EOM-CC values, experimental references where available, and the resulting deviations. We will also confirm that no post-hoc adjustments were applied to the computed spectra. This will provide the quantitative basis for the reliability claim. revision: yes

Circularity Check

0 steps flagged

No circularity; claims rest on external four-component benchmarks and experiments

full rationale

The paper presents an implementation of CVS-ADC(2) in a two-component relativistic framework using SA-FNS truncation and Cholesky decomposition for efficiency. Its reliability claims are supported by direct comparisons to independent four-component reference calculations and experimental L-edge spectra for 3d transition-metal compounds, which serve as external validation rather than self-referential fits or derivations. No load-bearing steps in the provided text reduce by construction to the method's own inputs, fitted parameters renamed as predictions, or self-citation chains. The derivation chain follows standard ADC equations adapted to the relativistic and core-valence-separated context without tautological reductions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The method relies on standard quantum-chemistry approximations for relativistic effects and integral compression; no new physical entities are introduced.

free parameters (2)
  • SA-FNS occupation threshold
    Cutoff value for selecting frozen natural spinors is a tunable parameter controlling accuracy-cost trade-off.
  • Cholesky decomposition tolerance
    Threshold for integral compression is a numerical parameter affecting storage and accuracy.
axioms (2)
  • domain assumption The exact two-component (X2C) relativistic Hamiltonian accurately reproduces four-component core-excitation energies for L-edges in the systems studied.
    Invoked when claiming reliability of the two-component framework versus four-component references.
  • domain assumption State-averaged frozen natural spinors preserve the essential correlation effects for core-valence excitations.
    Basis for the efficiency claim without loss of accuracy.

pith-pipeline@v0.9.0 · 5529 in / 1357 out tokens · 70018 ms · 2026-05-07T08:28:40.395007+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

121 extracted references · 1 canonical work pages

  1. [1]

    High-Resolution X-ray Emission and X-ray Absorption Spectroscopy

    de Groot, F. High-Resolution X-ray Emission and X-ray Absorption Spectroscopy. Chemical Reviews 2001, 101, 1779--1808, PMID: 11709999

    2001

  2. [2]

    NEXAFS Spectroscopy; Springer Series in Surface Sciences; Springer Berlin Heidelberg: Berlin, Heidelberg, 1992; Vol

    St \"o hr, J. NEXAFS Spectroscopy; Springer Series in Surface Sciences; Springer Berlin Heidelberg: Berlin, Heidelberg, 1992; Vol. 25

    1992

  3. [3]

    Recent experimental and theoretical developments in time-resolved X-ray spectroscopies

    Milne, C.; Penfold, T.; Chergui, M. Recent experimental and theoretical developments in time-resolved X-ray spectroscopies. Coordination Chemistry Reviews 2014, 277-278, 44--68, Following Chemical Structures using Synchrotron Radiation

    2014

  4. [4]

    T.; Hirsch, K.; Klar, P.; Langenberg, A.; Lofink, F.; Richter, R.; Rittmann, J.; Vogel, M.; Zamudio-Bayer, V.; M\"oller, T.; Issendorff, B

    Lau, J. T.; Hirsch, K.; Klar, P.; Langenberg, A.; Lofink, F.; Richter, R.; Rittmann, J.; Vogel, M.; Zamudio-Bayer, V.; M\"oller, T.; Issendorff, B. v. X-ray spectroscopy reveals high symmetry and electronic shell structure of transition-metal-doped silicon clusters. Phys. Rev. A 2009, 79, 053201

    2009

  5. [5]

    A.; Martini, A.; Bugaev, A

    Soldatov, M. A.; Martini, A.; Bugaev, A. L.; Pankin, I.; Medvedev, P. V.; Guda, A. A.; Aboraia, A. M.; Podkovyrina, Y. S.; Budnyk, A. P.; Soldatov, A. A.; Lamberti, C. The insights from X-ray absorption spectroscopy into the local atomic structure and chemical bonding of Metal–organic frameworks. Polyhedron 2018, 155, 232--253

    2018

  6. [6]

    I.; Suljoti, E.; Garcia-Diez, R.; Lange, K

    Engel, N.; Bokarev, S. I.; Suljoti, E.; Garcia-Diez, R.; Lange, K. M.; Atak, K.; Golnak, R.; Kothe, A.; Dantz, M.; K \"u hn, O.; Aziz, E. F. Chemical Bonding in Aqueous Ferrocyanide: Experimental and Theoretical X-ray Spectroscopic Study. The Journal of Physical Chemistry B 2014, 118, 1555--1563, PMID: 24450820

    2014

  7. [7]

    State of the Art

    Baker, M. L.; Mara, M. W.; Yan, J. J.; Hodgson, K. O.; Hedman, B.; Solomon, E. I. K- and L-edge X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS) determination of differential orbital covalency (DOC) of transition metal sites. Coordination Chemistry Reviews 2017, 345, 182--208, Chemical Bonding: "State of the Art"

    2017

  8. [8]

    Bounding [AnO2]2+ (An = U , Np) covalency by simulated O K-edge and An M-edge X-ray absorption near-edge spectroscopy

    Stanistreet-Welsh, K.; Kerridge, A. Bounding [AnO2]2+ (An = U , Np) covalency by simulated O K-edge and An M-edge X-ray absorption near-edge spectroscopy. Phys. Chem. Chem. Phys. 2023, 25, 23753--23760

    2023

  9. [9]

    Cressey, G.; Henderson, C. M. B.; van der Laan, G. Use of L-edge X-ray absorption spectroscopy to characterize multiple valence states of 3d transition metals; a new probe for mineralogical and geochemical research. Physics and Chemistry of Minerals 1993, 20, 111--119

    1993

  10. [10]

    Study of oxidation states of the transition metals in a series of Prussian blue analogs using x-ray absorption near edge structure (XANES) spectroscopy

    Adak, S.; Hartl, M.; Daemen, L.; Fohtung, E.; Nakotte, H. Study of oxidation states of the transition metals in a series of Prussian blue analogs using x-ray absorption near edge structure (XANES) spectroscopy. Journal of Electron Spectroscopy and Related Phenomena 2017, 214, 8--19

    2017

  11. [11]

    Kubin, M. et al. Probing the oxidation state of transition metal complexes: a case study on how charge and spin densities determine Mn L-edge X-ray absorption energies. Chem. Sci. 2018, 9, 6813--6829

    2018

  12. [12]

    K.; Maganas, D.; DeBeer, S.; Neese, F

    Chantzis, A.; Kowalska, J. K.; Maganas, D.; DeBeer, S.; Neese, F. Ab Initio Wave Function-Based Determination of Element Specific Shifts for the Efficient Calculation of X-ray Absorption Spectra of Main Group Elements and First Row Transition Metals. Journal of Chemical Theory and Computation 2018, 14, 3686--3702, PMID: 29894196

    2018

  13. [13]

    Simulating X-ray Spectroscopies and Calculating Core-Excited States of Molecules

    Norman, P.; Dreuw, A. Simulating X-ray Spectroscopies and Calculating Core-Excited States of Molecules. Chemical Reviews 2018, 118, 7208--7248, PMID: 29894157

    2018

  14. [14]

    Besley, N. A. Density Functional Theory Based Methods for the Calculation of X-ray Spectroscopy. Accounts of Chemical Research 2020, 53, 1306--1315, PMID: 32613827

    2020

  15. [15]

    D.; Penfold, T

    Rankine, C. D.; Penfold, T. J. Progress in the Theory of X-ray Spectroscopy: From Quantum Chemistry to Machine Learning and Ultrafast Dynamics. The Journal of Physical Chemistry A 2021, 125, 4276--4293, PMID: 33729774

    2021

  16. [16]

    Besley, N. A. Modeling of the spectroscopy of core electrons with density functional theory. WIREs Computational Molecular Science 2021, 11, e1527

    2021

  17. [17]

    E.; Vidal, M

    Fransson, T.; Brumboiu, I. E.; Vidal, M. L.; Norman, P.; Coriani, S.; Dreuw, A. XABOOM: An X-ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s ^* Transitions. Journal of Chemical Theory and Computation 2021, 17, 1618--1637, PMID: 33544612

    2021

  18. [18]

    Relativistic four-component static-exchange approximation for core-excitation processes in molecules

    Ekstr\"om, U.; Norman, P.; Carravetta, V. Relativistic four-component static-exchange approximation for core-excitation processes in molecules. Phys. Rev. A 2006, 73, 022501

    2006

  19. [19]

    Ikeno, H.; de Groot, F. M. F.; Tanaka, I. Ab-initio CI calculations for 3d transition metal L2,3 X-ray absorption spectra of TiCl4 and VOCl3. Journal of Physics: Conference Series 2009, 190, 012005

    2009

  20. [20]

    X-ray absorption resonances near L2 , 3-edges from real-time propagation of the Dirac–Kohn–Sham density matrix

    Kadek, M.; Konecny, L.; Gao, B.; Repisky, M.; Ruud, K. X-ray absorption resonances near L2 , 3-edges from real-time propagation of the Dirac–Kohn–Sham density matrix. Phys. Chem. Chem. Phys. 2015, 17, 22566--22570

    2015

  21. [21]

    Fransson, T.; Burdakova, D.; Norman, P. K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon , silicon , germanium , and sulfur compounds using damped four-component density functional response theory. Phys. Chem. Chem. Phys. 2016, 18, 13591--13603

    2016

  22. [22]

    K.; Saue, T

    South, C.; Shee, A.; Mukherjee, D.; Wilson, A. K.; Saue, T. 4-Component relativistic calculations of L3 ionization and excitations for the isoelectronic species UO22+ , OUN+ and UN2. Phys. Chem. Chem. Phys. 2016, 18, 21010--21023

    2016

  23. [23]

    L.; Shee, A.; Coriani, S.; Severo Pereira Gomes, A

    Halbert, L.; Vidal, M. L.; Shee, A.; Coriani, S.; Severo Pereira Gomes, A. Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac–Coulomb(−Gaunt) Hamiltonian. Journal of Chemical Theory and Computation 2021, 17, 3583--3598, PMID: 33944570

    2021

  24. [24]

    Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

    Konecny, L.; Vicha, J.; Komorovsky, S.; Ruud, K.; Repisky, M. Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory. Inorganic Chemistry 2022, 61, 830--846, PMID: 34958215

    2022

  25. [25]

    Hess, B. A. Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. Phys. Rev. A 1986, 33, 3742--3748

    1986

  26. [26]

    J.; Snijders, J

    van Lenthe, E.; van Leeuwen, R.; Baerends, E. J.; Snijders, J. G. Relativistic regular two-component Hamiltonians. International Journal of Quantum Chemistry 1996, 57, 281--293

    1996

  27. [27]

    Dyall, K. G. Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation. The Journal of Chemical Physics 1997, 106, 9618--9626

    1997

  28. [28]

    A new relativistic theory: a relativistic scheme by eliminating small components (RESC)

    Nakajima, T.; Hirao, K. A new relativistic theory: a relativistic scheme by eliminating small components (RESC). Chemical Physics Letters 1999, 302, 383--391

    1999

  29. [29]

    Barysz, M.; Sadlej, A. J. Two-component methods of relativistic quantum chemistry: from the Douglas–Kroll approximation to the exact two-component formalism. Journal of Molecular Structure: THEOCHEM 2001, 573, 181--200

    2001

  30. [30]

    Exact two-component Hamiltonians revisited

    Liu, W.; Peng, D. Exact two-component Hamiltonians revisited. The Journal of Chemical Physics 2009, 131, 031104

    2009

  31. [31]

    Relativistic Hamiltonians for Chemistry: A Primer

    Saue, T. Relativistic Hamiltonians for Chemistry: A Primer. ChemPhysChem 2011, 12, 3077--3094

    2011

  32. [32]

    Quasirelativistic theory equivalent to fully relativistic theory

    Kutzelnigg, W.; Liu, W. Quasirelativistic theory equivalent to fully relativistic theory. The Journal of Chemical Physics 2005, 123, 241102

    2005

  33. [33]

    An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation

    Iliaš, M.; Saue, T. An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation. The Journal of Chemical Physics 2007, 126, 064102

    2007

  34. [34]

    G.; Faegri, K

    Dyall, K. G.; Faegri, K. Introduction to Relativistic Quantum Chemistry; Oxford University Press, 2007

    2007

  35. [35]

    An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling

    Liu, J.; Cheng, L. An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling. The Journal of Chemical Physics 2018, 148, 144108

    2018

  36. [36]

    Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac-Coulomb-Breit Hamiltonian

    Zhang, C.; Cheng, L. Atomic Mean-Field Approach within Exact Two-Component Theory Based on the Dirac-Coulomb-Breit Hamiltonian. The Journal of Physical Chemistry A 2022, 126, 4537--4553, PMID: 35763592

    2022

  37. [37]

    Knecht, S.; Repisky, M.; Jensen, H. J. A.; Saue, T. Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple. The Journal of Chemical Physics 2022, 157, 114106

    2022

  38. [38]

    Infinite-order quasirelativistic density functional method based on the exact matrix quasirelativistic theory

    Liu, W.; Peng, D. Infinite-order quasirelativistic density functional method based on the exact matrix quasirelativistic theory. The Journal of Chemical Physics 2006, 125, 044102

    2006

  39. [39]

    from atoms to molecule

    Peng, D.; Liu, W.; Xiao, Y.; Cheng, L. Making four- and two-component relativistic density functional methods fully equivalent based on the idea of “from atoms to molecule”. The Journal of Chemical Physics 2007, 127, 104106

    2007

  40. [40]

    Relativistic two-electron contributions within exact two-component theory

    Wang, X.; Zhang, C.; Liu, J.; Cheng, L. Relativistic two-electron contributions within exact two-component theory. Chemical Physics Reviews 2025, 6, 031404

    2025

  41. [41]

    M.; Lestrange, P

    Kasper, J. M.; Lestrange, P. J.; Stetina, T. F.; Li, X. Modeling L2,3-Edge X-ray Absorption Spectroscopy with Real-Time Exact Two-Component Relativistic Time-Dependent Density Functional Theory. Journal of Chemical Theory and Computation 2018, 14, 1998--2006, PMID: 29561613

    2018

  42. [42]

    F.; Kasper, J

    Stetina, T. F.; Kasper, J. M.; Li, X. Modeling L2,3-edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory. The Journal of Chemical Physics 2019, 150, 234103

    2019

  43. [43]

    H.; Dunford, R

    Southworth, S. H.; Dunford, R. W.; Ray, D.; Kanter, E. P.; Doumy, G.; March, A. M.; Ho, P. J.; Kr\"assig, B.; Gao, Y.; Lehmann, C. S.; Pic\'on, A.; Young, L.; Walko, D. A.; Cheng, L. Observing pre-edge K -shell resonances in Kr, Xe, and XeF _ 2 . Phys. Rev. A 2019, 100, 022507

    2019

  44. [44]

    H.; Cheng, L

    Zheng, X.; Zhang, C.; Jin, Z.; Southworth, S. H.; Cheng, L. Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements. Phys. Chem. Chem. Phys. 2022, 24, 13587--13596

    2022

  45. [45]

    H.; Doumy, G.; Young, L.; Cheng, L

    Wu, Y.; Lin, Z.; Wang, X.; Wang, S.; Southworth, S. H.; Doumy, G.; Young, L.; Cheng, L. Relativistic core–valence-separated equation-of-motion coupled-cluster singles and doubles method: Efficient implementation and benchmark calculations. The Journal of Chemical Physics 2025, 163, 244114

    2025

  46. [46]

    J.; Wilson, R

    Wang, X.; Doumy, G.; Marie March, A.; Otolski, C. J.; Wilson, R. E.; Walko, D. A.; Cheng, L.; Southworth, S. H. Resonant x-ray emission across the L3 edge of uranium compounds. Journal of Physics B: Atomic, Molecular and Optical Physics 2025, 58, 045602

    2025

  47. [47]

    R.; Cooper, B

    Banerjee, S.; Li, R. R.; Cooper, B. C.; Zhang, T.; Valeev, E. F.; Li, X.; DePrince, I., A. Eugene Relativistic core–valence-separated molecular mean-field exact-two-component equation-of-motion coupled cluster theory: Applications to L-edge x-ray absorption spectroscopy. APL Computational Physics 2026, 2, 016101

    2026

  48. [48]

    A.; Marian, C

    Heß, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. A mean-field spin-orbit method applicable to correlated wavefunctions. Chemical Physics Letters 1996, 251, 365--371

    1996

  49. [49]

    Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost

    Konecny, L.; Komorovsky, S.; Vicha, J.; Ruud, K.; Repisky, M. Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost. The Journal of Physical Chemistry A 2023, 127, 1360--1376, PMID: 36722848

    2023

  50. [50]

    Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

    Moitra, T.; Konecny, L.; Kadek, M.; Rubio, A.; Repisky, M. Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy. The Journal of Physical Chemistry Letters 2023, 14, 1714--1724, PMID: 36757216

    2023

  51. [51]

    Analysis of self-interaction correction for describing core excited states

    Imamura, Y.; Nakai, H. Analysis of self-interaction correction for describing core excited states. International Journal of Quantum Chemistry 2007, 107, 23--29

    2007

  52. [52]

    J.; Nguyen, P

    Lestrange, P. J.; Nguyen, P. D.; Li, X. Calibration of Energy-Specific TDDFT for Modeling K-edge XAS Spectra of Light Elements. Journal of Chemical Theory and Computation 2015, 11, 2994--2999, PMID: 26575736

    2015

  53. [53]

    ROWE, D. J. Equations-of-Motion Method and the Extended Shell Model. Rev. Mod. Phys. 1968, 40, 153--166

    1968

  54. [54]

    F.; Bartlett, R

    Stanton, J. F.; Bartlett, R. J. The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties. The Journal of Chemical Physics 1993, 98, 7029--7039

    1993

  55. [55]

    Nooijen, M.; Bartlett, R. J. Equation of motion coupled cluster method for electron attachment. The Journal of Chemical Physics 1995, 102, 3629--3647

    1995

  56. [56]

    S.; Domcke, W.; Schirmer, J

    Cederbaum, L. S.; Domcke, W.; Schirmer, J. Many-body theory of core holes. Phys. Rev. A 1980, 22, 206--222

    1980

  57. [57]

    Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework

    Coriani, S.; Koch, H. Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework. The Journal of Chemical Physics 2015, 143, 181103

    2015

  58. [58]

    L.; Pokhilko, P.; Krylov, A

    Vidal, M. L.; Pokhilko, P.; Krylov, A. I.; Coriani, S. Equation-of-Motion Coupled-Cluster Theory to Model L-Edge X-ray Absorption and Photoelectron Spectra. The Journal of Physical Chemistry Letters 2020, 11, 8314--8321, PMID: 32897075

    2020

  59. [59]

    Relativistic coupled-cluster and equation-of-motion coupled-cluster methods

    Liu, J.; Cheng, L. Relativistic coupled-cluster and equation-of-motion coupled-cluster methods. WIREs Computational Molecular Science 2021, 11, e1536

    2021

  60. [60]

    Schirmer, J.; Trofimov, A. B. Intermediate state representation approach to physical properties of electronically excited molecules. The Journal of chemical physics 2004, 120, 11449--11464

    2004

  61. [61]

    Algebraic propagator approaches and intermediate-state representations

    Mertins, F.; Schirmer, J. Algebraic propagator approaches and intermediate-state representations. I. The biorthogonal and unitary coupled-cluster methods. Physical Review A 1996, 53, 2140

    1996

  62. [62]

    Closed-form intermediate representations of many-body propagators and resolvent matrices

    Schirmer, J. Closed-form intermediate representations of many-body propagators and resolvent matrices. Physical Review A 1991, 43, 4647

    1991

  63. [63]

    Beyond the random-phase approximation: A new approximation scheme for the polarization propagator

    Schirmer, J. Beyond the random-phase approximation: A new approximation scheme for the polarization propagator. Physical Review A 1982, 26, 2395

    1982

  64. [64]

    von Niessen, W.; Schirmer, J.; Cederbaum, L. S. Computational methods for the one-particle green's function. Computer Physics Reports 1984, 1, 57--125

    1984

  65. [65]

    The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states

    Dreuw, A.; Wormit, M. The algebraic diagrammatic construction scheme for the polarization propagator for the calculation of excited states. Wiley Interdisciplinary Reviews: Computational Molecular Science 2015, 5, 82--95

    2015

  66. [66]

    L.; Schneider, M.; Hodecker, M.; Dreuw, A

    Dempwolff, A. L.; Schneider, M.; Hodecker, M.; Dreuw, A. Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed-and open-shell molecules. The Journal of Chemical Physics 2019, 150

    2019

  67. [67]

    Banerjee, S.; Sokolov, A. Y. Efficient Implementation of the Single-Reference Algebraic Diagrammatic Construction Theory for Charged Excitations: Applications to the TEMPO Radical and DNA Base Pairs. The Journal of Chemical Physics 2021, 154, 074105

    2021

  68. [68]

    Core-level electronic spectra in ADC (2) approximation for polarization propagator: Carbon monoxide and nitrogen molecules

    Trofimov, A.; Moskovskaya, T.; Gromov, E.; Vitkovskaya, N.; Schirmer, J. Core-level electronic spectra in ADC (2) approximation for polarization propagator: Carbon monoxide and nitrogen molecules. Journal of Structural Chemistry 2000, 41, 483--494

    2000

  69. [69]

    Calculating X-ray absorption spectra of open-shell molecules with the unrestricted algebraic-diagrammatic construction scheme for the polarization propagator

    Wenzel, J.; Wormit, M.; Dreuw, A. Calculating X-ray absorption spectra of open-shell molecules with the unrestricted algebraic-diagrammatic construction scheme for the polarization propagator. Journal of chemical theory and computation 2014, 10, 4583--4598

    2014

  70. [70]

    Wenzel, J.; Wormit, M.; Dreuw, A. Calculating core-level excitations and X-ray absorption spectra of medium-sized closed-shell molecules with the algebraic-diagrammatic construction scheme for the polarization propagator. Journal of computational chemistry 2014, 35, 1900--1915

    2014

  71. [71]

    Simulating X-ray emission spectroscopy with algebraic diagrammatic construction schemes for the polarization propagator

    Fransson, T.; Dreuw, A. Simulating X-ray emission spectroscopy with algebraic diagrammatic construction schemes for the polarization propagator. Journal of chemical theory and computation 2018, 15, 546--556

    2018

  72. [72]

    Consistent third-order one-particle transition and excited-state properties within the algebraic-diagrammatic construction scheme for the polarization propagator

    Maier, R.; Bauer, M.; Dreuw, A. Consistent third-order one-particle transition and excited-state properties within the algebraic-diagrammatic construction scheme for the polarization propagator. The Journal of Chemical Physics 2023, 159

    2023

  73. [73]

    Scheurer, M.; Fransson, T.; Norman, P.; Dreuw, A.; Rehn, D. R. Complex excited state polarizabilities in the ADC/ISR framework. The Journal of Chemical Physics 2020, 153

    2020

  74. [74]

    The relativistic polarization propagator for the calculation of electronic excitations in heavy systems

    Pernpointner, M. The relativistic polarization propagator for the calculation of electronic excitations in heavy systems. The Journal of Chemical Physics 2014, 140

    2014

  75. [75]

    Pernpointner, M.; Visscher, L.; Trofimov, A. B. Four-component polarization propagator calculations of electron excitations: Spectroscopic implications of spin--orbit coupling effects. Journal of Chemical Theory and Computation 2018, 14, 1510--1522

    2018

  76. [76]

    The one-particle Green’s function method in the Dirac--Hartree--Fock framework

    Pernpointner, M.; Trofimov, A. The one-particle Green’s function method in the Dirac--Hartree--Fock framework. I. Second-order valence ionization energies of Ne through Xe. The Journal of chemical physics 2004, 120, 4098--4106

    2004

  77. [77]

    The four-component two-particle propagator for the calculation of double-ionization spectra of heavy-element compounds: I

    Pernpointner, M. The four-component two-particle propagator for the calculation of double-ionization spectra of heavy-element compounds: I. Method. Journal of Physics B: Atomic, Molecular and Optical Physics 2010, 43, 205102

    2010

  78. [78]

    The effect of the Gaunt interaction on the molecular ionization spectra of CO, H2S and TlH

    Pernpointner, M. The effect of the Gaunt interaction on the molecular ionization spectra of CO, H2S and TlH. Journal of Physics B: Atomic, Molecular and Optical Physics 2005, 38, 1955

    2005

  79. [79]

    Mandal, S.; Dutta, A. K. A third-order relativistic algebraic diagrammatic construction method for double ionization potentials: Theory, implementation, and benchmark. The Journal of Chemical Physics 2026, 164

    2026

  80. [80]

    K.; Dutta, A

    Chakraborty, S.; Mukhopadhyay, T.; Nayak, M. K.; Dutta, A. K. A relativistic third-order algebraic diagrammatic construction theory for electron detachment, attachment, and excitation problems. The Journal of Chemical Physics 2025, 162, 104106

    2025

Showing first 80 references.