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arxiv: 2606.02474 · v1 · pith:2G6CYDDFnew · submitted 2026-06-01 · ⚛️ physics.chem-ph

Approximating Hartree-Fock theory via an efficiently local reformulation

Trine Kay Quady , Eric Neuscamman This is my paper

Pith reviewed 2026-06-28 11:55 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords Hartree-Fockorbital localityself-consistent fieldmolecular orbitalsreaction energiesFock buildssparsity patternsMP2
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The pith

Reorganizing the Hartree-Fock equations pairs each local orbital degree of freedom with a matching local solution condition so that any sparsity pattern can be chosen without losing fast self-consistent field optimization.

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

The paper rethinks the structure of the Hartree-Fock equations to make imposed orbital locality more flexible. Instead of first restricting how far orbitals can spread and then minimizing the energy, the new arrangement links every local degree of freedom directly to a solution condition that itself has a local meaning. These paired conditions can be switched on or off independently according to any chosen sparsity pattern. The self-consistent field procedure stays fast and efficient no matter which pattern is selected. Tests with reaction-matched locality schemes produce competitive timings on medium-sized molecules and preserve most of the accuracy in Hartree-Fock and MP2 reaction energies.

Core claim

By reorganizing the Hartree-Fock equations, each local degree of freedom in the molecular orbitals is paired with a specific solution condition that has a naturally local interpretation. These pairs can be independently turned on or off according to any chosen sparsity pattern, and the overall self-consistent field optimization remains fast and efficient. This structure is used to impose reaction-matched locality schemes, leading to Fock builds that exploit locality for competitive timings and minimal impact on reaction energy accuracy in Hartree-Fock and MP2 calculations.

What carries the argument

The reorganized pairing of each local orbital degree of freedom with a corresponding local solution condition, which permits independent activation of locality constraints while preserving SCF efficiency.

If this is right

  • Any sparsity pattern for orbital locality can be selected without changing the speed of the self-consistent field optimization.
  • Reaction-matched locality schemes enable Fock builds that exploit locality to achieve competitive timings in modestly sized molecules.
  • Imposed orbital locality arranged in this way causes minimal damage to Hartree-Fock and MP2 reaction energy predictions.
  • The overall method maintains a highly efficient self-consistent field optimization algorithm regardless of the sparsity pattern used.

Where Pith is reading between the lines

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

  • The pairing structure could be extended to post-Hartree-Fock methods to introduce controlled locality at higher levels of theory.
  • Reaction-specific locality choices might be tuned further to balance speed and accuracy for targeted classes of chemical processes.
  • Verification on properties such as molecular geometries or excitation energies would be required to confirm the absence of hidden systematic errors.
  • The approach could lower the cost of electronic structure calculations on larger systems where full delocalized orbitals become expensive.

Load-bearing premise

The chosen reaction-matched locality schemes can be imposed without introducing systematic bias that appears only in properties or systems outside the tested reaction energies.

What would settle it

A direct comparison in which the locality schemes produce reaction energies or other properties that differ substantially from standard Hartree-Fock results on a molecule or observable not included in the initial tests.

Figures

Figures reproduced from arXiv: 2606.02474 by Eric Neuscamman, Trine Kay Quady.

Figure 1
Figure 1. Figure 1: FIG. 1. An example of assigning reaction-matched atomic reaches. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Preparation of the RLOs and the valence RLVs. a.) Small [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Two sets, A and B, of keto-enol tautomerization reactions [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Reaction energy error of a.) local HF versus standard HF, b.) MP2 calculated atop local HF orbitals versus standard MP2, and c.) the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. . a.) Log-Log plot of wall times of Q- [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. a.) Histogram of the spread of each occupied MO under PM localization and local HF with a 3-2-1 reach, evaluated for the ketone [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We explore a reorganized framework for the Hartree Fock equations that allows varying patterns of locality to be imposed on the molecular orbitals while maintaining a highly efficient self-consistent field optimization algorithm. Rather than limiting orbitals' spread and then variationally minimizing the energy within those limits, our reorganization neatly pairs each local degree of freedom with a specific solution condition that itself has a naturally local interpretation. These pairs can each be turned on or off, and, regardless of the sparsity pattern used to make such choices, the overall method maintains a fast self-consistent field optimization. We use this structure to test reaction-matched schemes for imposing orbital locality and, through Fock builds that exploit this locality, achieve competitive timings even in modestly sized molecules. Our initial tests also suggest that this approach to imposed orbital locality can be arranged so as to do minimal damage to both Hartree Fock and MP2 reaction energy predictions.

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

2 major / 1 minor

Summary. The manuscript proposes a reorganized framework for the Hartree-Fock equations that pairs each local degree of freedom with a specific solution condition having a naturally local interpretation. This structure permits turning individual locality constraints on or off while preserving a fast self-consistent field optimization, independent of the chosen sparsity pattern. The authors apply the approach to reaction-matched locality schemes, claiming competitive Fock-build timings for modestly sized molecules and suggesting via initial tests that the imposed locality causes only minimal damage to both HF and MP2 reaction energies.

Significance. If the numerical performance and error claims are substantiated, the reorganization could provide a modular alternative to conventional orbital-localization or density-fitting approximations by decoupling locality choices from the variational procedure. The ability to activate or deactivate individual local pairs without disrupting SCF convergence would be a useful feature for balancing cost and accuracy. The current description, however, supplies no quantitative benchmarks, so the practical significance cannot yet be evaluated.

major comments (2)
  1. [Abstract] Abstract: the central claim that the method 'can be arranged so as to do minimal damage to both Hartree Fock and MP2 reaction energy predictions' is unsupported by any numerical error tables, mean absolute deviations, error bars, or comparisons to standard local approximations (e.g., local HF, density fitting, or orbital localization). This quantitative evidence is load-bearing for the assertion of practical utility.
  2. [Abstract] Abstract: the statement that the reorganization 'maintains a fast self-consistent field optimization' 'regardless of the sparsity pattern' is presented without derivation details, pseudocode, convergence analysis, or timing data, leaving the efficiency guarantee unverified and central to the method's advertised advantage.
minor comments (1)
  1. The abstract would be strengthened by indicating the range of molecular sizes or the specific reaction classes used in the 'initial tests'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We respond point-by-point to the major comments below, indicating where we agree that additional support or clarification will strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the method 'can be arranged so as to do minimal damage to both Hartree Fock and MP2 reaction energy predictions' is unsupported by any numerical error tables, mean absolute deviations, error bars, or comparisons to standard local approximations (e.g., local HF, density fitting, or orbital localization). This quantitative evidence is load-bearing for the assertion of practical utility.

    Authors: We agree that the abstract's reference to 'initial tests' would be more persuasive with explicit quantitative support. The body of the manuscript presents reaction-energy results for the chosen locality schemes, but does not include tabulated mean absolute deviations or direct comparisons to other local approximations. In the revised manuscript we will add a dedicated results subsection with error tables, MAD values, and comparisons to standard local HF and orbital-localization approaches to substantiate the claim. revision: yes

  2. Referee: [Abstract] Abstract: the statement that the reorganization 'maintains a fast self-consistent field optimization' 'regardless of the sparsity pattern' is presented without derivation details, pseudocode, convergence analysis, or timing data, leaving the efficiency guarantee unverified and central to the method's advertised advantage.

    Authors: The reorganized Hartree-Fock framework and the argument that locality constraints can be activated independently without altering the underlying SCF structure are derived in Sections II and III of the manuscript. Nevertheless, we accept that the abstract would benefit from more concrete verification. In the revision we will insert pseudocode for the modified SCF iteration, additional convergence data, and expanded Fock-build timing tables that explicitly vary the sparsity pattern. revision: yes

Circularity Check

0 steps flagged

Reorganization of HF equations shows no circular derivation

full rationale

The paper presents a reorganized framework for the Hartree-Fock equations that pairs local degrees of freedom with naturally local solution conditions, allowing sparsity patterns to be imposed while preserving fast SCF optimization. This is described as a structural change rather than a fit to data or a self-referential definition. No load-bearing steps reduce by construction to inputs, no fitted parameters are renamed as predictions, and no self-citation chains or ansatzes are invoked to justify the core reorganization. The claims about competitive timings and minimal damage to reaction energies are presented as empirical consequences of the framework, not as tautological outputs of the same inputs. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim implicitly assumes that the reorganized equations remain variationally equivalent to standard Hartree-Fock when all pairs are active and that the chosen locality patterns do not violate self-consistency.

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Works this paper leans on

298 extracted references · 288 canonical work pages · 4 internal anchors

  1. [1]

    , year = 1961, month = jan, journal =

    Adams, William H. , year = 1961, month = jan, journal =. On the. doi:10.1063/1.1731622 , urldate =

    work page doi:10.1063/1.1731622 1961

  2. [2]

    Optimization of

    Ammar, Abdallah and Giner, Emmanuel and Scemama, Anthony , year = 2022, month = sep, journal =. Optimization of. doi:10.1021/acs.jctc.2c00556 , urldate =

    work page doi:10.1021/acs.jctc.2c00556 2022

  3. [3]

    Cholesky

    Aquilante, Francesco and Boman, Linus and Bostr. Cholesky. Linear-. doi:10.1007/978-90-481-2853-2_13 , urldate =

    work page doi:10.1007/978-90-481-2853-2_13

  4. [4]

    The Journal of Chemical Physics , volume =

    Fast Noniterative Orbital Localization for Large Molecules , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.2360264 , urldate =

    work page doi:10.1063/1.2360264

  5. [5]

    Aroeira, Gustavo J. R. and Davis, Matthew M. and Turney, Justin M. and Schaefer, Henry F. III , year = 2022, month = feb, journal =. Fermi.Jl:. doi:10.1021/acs.jctc.1c00719 , urldate =

    work page doi:10.1021/acs.jctc.1c00719 2022

  6. [6]

    The Journal of Chemical Physics , volume =

    Quantum. The Journal of Chemical Physics , volume =. doi:10.1063/1.1646356 , urldate =

    work page doi:10.1063/1.1646356

  7. [7]

    and Filippi, Claudia , year = 2017, month = nov, journal =

    Assaraf, Roland and Moroni, S. and Filippi, Claudia , year = 2017, month = nov, journal =. Optimizing the. doi:10.1021/acs.jctc.7b00648 , urldate =

    work page doi:10.1021/acs.jctc.7b00648 2017

  8. [8]

    Assaraf, Roland and Caffarel, Michel , year = 1999, month = dec, journal =. Zero-. doi:10.1103/PhysRevLett.83.4682 , urldate =

    work page doi:10.1103/physrevlett.83.4682 1999

  9. [9]

    and Zubarev, Dmitry Yu

    Austin, Brian M. and Zubarev, Dmitry Yu. and Lester, William A. Jr. , year = 2012, month = jan, journal =. Quantum. doi:10.1021/cr2001564 , urldate =

    work page doi:10.1021/cr2001564 2012

  10. [10]

    The Journal of Chemical Physics , volume =

    An Energy Decomposition Analysis for Intermolecular Interactions from an Absolutely Localized Molecular Orbital Reference at the Coupled-Cluster Singles and Doubles Level , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.3674992 , urldate =

    work page doi:10.1063/1.3674992

  11. [11]

    The Journal of Chemical Physics , volume =

    Chebyshev Expansion Methods for Electronic Structure Calculations on Large Molecular Systems , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.474158 , urldate =

    work page doi:10.1063/1.474158

  12. [12]

    Vanadium Oxide Compounds with Quantum

    Bande, Annika and L. Vanadium Oxide Compounds with Quantum. Physical Chemistry Chemical Physics , volume =. doi:10.1039/B803571G , urldate =

    work page doi:10.1039/b803571g

  13. [13]

    Reviews of Modern Physics , volume =

    Coupled-Cluster Theory in Quantum Chemistry , author =. Reviews of Modern Physics , volume =. doi:10.1103/RevModPhys.79.291 , urldate =

    work page doi:10.1103/revmodphys.79.291

  14. [14]

    Correlated Natural Transition Orbital Framework for Low-Scaling Excitation Energy Calculations (

    Baudin, Pablo and Kristensen, Kasper , year = 2017, month = jun, journal =. Correlated Natural Transition Orbital Framework for Low-Scaling Excitation Energy Calculations (. doi:10.1063/1.4984820 , urldate =

    work page doi:10.1063/1.4984820 2017

  15. [15]

    , year = 1980, month = jan, journal =

    Bauschlicher, Jr., Charles W. , year = 1980, month = jan, journal =. The Construction of Modified Virtual Orbitals (. doi:10.1063/1.439243 , urldate =

    work page doi:10.1063/1.439243 1980

  16. [16]

    Physical Chemistry Chemical Physics , volume =

    Spurious Proton Transfer in Hydrogen Bonded Dimers , author =. Physical Chemistry Chemical Physics , volume =. doi:10.1039/D4CP00907J , urldate =

    work page doi:10.1039/d4cp00907j

  17. [17]

    Becca, Federico and Sorella, Sandro , year = 2017, publisher =. Quantum. doi:10.1017/9781316417041 , urldate =

    work page doi:10.1017/9781316417041 2017

  18. [18]

    Benedek, N. A. and Snook, I. K. and Towler, M. D. and Needs, R. J. , year = 2006, month = sep, journal =. Quantum. doi:10.1063/1.2338032 , urldate =

    work page doi:10.1063/1.2338032 2006

  19. [19]

    The Journal of Chemical Physics , volume =

    Orbital Pair Selection for Relative Energies in the Domain-Based Local Pair Natural Orbital Coupled-Cluster Method , author =. The Journal of Chemical Physics , volume =. doi:10.1063/5.0100010 , urldate =

    work page doi:10.1063/5.0100010

  20. [20]

    Physical Chemistry Chemical Physics , volume =

    Approaching Closed-Shell Accuracy for Radicals Using Coupled Cluster Theory with Perturbative Triple Substitutions , author =. Physical Chemistry Chemical Physics , volume =. doi:10.1039/B304542K , urldate =

    work page doi:10.1039/b304542k

  21. [21]

    Systematic Lowering of the Scaling of

    Bienvenu, Antoine and Feldt, Jonas and Toulouse, Julien and Assaraf, Roland , year = 2022, month = aug, journal =. Systematic Lowering of the Scaling of. doi:10.1103/PhysRevE.106.025301 , urldate =

    work page doi:10.1103/physreve.106.025301 2022

  22. [22]

    and Gu, Feng Long and Kirtman, Bernard , year = 2001, month = may, journal =

    Bishop, David M. and Gu, Feng Long and Kirtman, Bernard , year = 2001, month = may, journal =. Coupled-Perturbed. doi:10.1063/1.1356019 , urldate =

    work page doi:10.1063/1.1356019 2001

  23. [23]

    Stein, Christopher , year = 2024, journal =

    Bogo, Nicola and J. Stein, Christopher , year = 2024, journal =. Benchmarking. doi:10.1039/D4CP01866D , urldate =

    work page doi:10.1039/d4cp01866d 2024

  24. [24]

    Nature , volume =

    Towards an Exact Description of Electronic Wavefunctions in Real Solids , author =. Nature , volume =. doi:10.1038/nature11770 , urldate =

    work page doi:10.1038/nature11770

  25. [25]

    and Thom, Alex J

    Booth, George H. and Thom, Alex J. W. and Alavi, Ali , year = 2009, month = aug, journal =. Fermion. doi:10.1063/1.3193710 , urldate =

    work page doi:10.1063/1.3193710 2009

  26. [26]

    Bostr. Coupled. Journal of Chemical Theory and Computation , volume =. doi:10.1021/ct3003018 , urldate =

    work page doi:10.1021/ct3003018

  27. [27]

    and Pulay, Peter , year = 1993, journal =

    Boughton, James W. and Pulay, Peter , year = 1993, journal =. Comparison of the Boys and. doi:10.1002/jcc.540140615 , urldate =

    work page doi:10.1002/jcc.540140615 1993

  28. [28]

    Configuration Interaction with

    Bou. Configuration Interaction with. Chemical Physics Letters , volume =. doi:10.1016/S0009-2614(01)00896-X , urldate =

    work page doi:10.1016/s0009-2614(01)00896-x

  29. [29]

    The Journal of Chemical Physics , volume =

    Elucidating the Molecular Orbital Dependence of the Total Electronic Energy in Multireference Problems , author =. The Journal of Chemical Physics , volume =. doi:10.1063/5.0090342 , urldate =

    work page doi:10.1063/5.0090342

  30. [30]

    Buckingham, A. D. , year = 1967, pages =. Permanent and. Advances in. doi:10.1002/9780470143582.ch2 , urldate =

    work page doi:10.1002/9780470143582.ch2 1967

  31. [31]

    Numerische Mathematik , volume =

    Rank-One Modification of the Symmetric Eigenproblem , author =. Numerische Mathematik , volume =. doi:10.1007/BF01396012 , urldate =

    work page doi:10.1007/bf01396012

  32. [32]

    Bunge, C. F. and Barrientos, J. A. and Bunge, A. V. , year = 1993, month = jan, journal =. Roothaan-. doi:10.1006/adnd.1993.1003 , urldate =

    work page doi:10.1006/adnd.1993.1003 1993

  33. [33]

    and Faver, John C

    Burns, Lori A. and Faver, John C. and Zheng, Zheng and Marshall, Michael S. and Smith, Daniel G. A. and Vanommeslaeghe, Kenno and MacKerell, Jr., Alexander D. and Merz, Jr., Kenneth M. and Sherrill, C. David , year = 2017, month = sep, journal =. The. doi:10.1063/1.5001028 , urldate =

    work page doi:10.1063/1.5001028 2017

  34. [34]

    , year = 2016, month = jul, journal =

    Busemeyer, Brian and Dagrada, Mario and Sorella, Sandro and Casula, Michele and Wagner, Lucas K. , year = 2016, month = jul, journal =. Competing Collinear Magnetic Structures in Superconducting. doi:10.1103/PhysRevB.94.035108 , urldate =

    work page doi:10.1103/physrevb.94.035108 2016

  35. [35]

    Science , volume =

    Solving the Quantum Many-Body Problem with Artificial Neural Networks , author =. Science , volume =. doi:10.1126/science.aag2302 , urldate =

    work page doi:10.1126/science.aag2302

  36. [36]

    Reviews of Modern Physics , volume =

    The Electronic Properties of Graphene , author =. Reviews of Modern Physics , volume =. doi:10.1103/RevModPhys.81.109 , urldate =

    work page doi:10.1103/revmodphys.81.109

  37. [37]

    Correlated Geminal Wave Function for Molecules:

    Casula, Michele and Attaccalite, Claudio and Sorella, Sandro , year = 2004, month = oct, journal =. Correlated Geminal Wave Function for Molecules:. doi:10.1063/1.1794632 , urldate =

    work page doi:10.1063/1.1794632 2004

  38. [38]

    Ceperley, D. M. and Alder, B. J. , year = 1980, month = aug, journal =. Ground. doi:10.1103/PhysRevLett.45.566 , urldate =

    work page doi:10.1103/physrevlett.45.566 1980

  39. [39]

    Nature Reviews Physics , volume =

    Variational Quantum Algorithms , author =. Nature Reviews Physics , volume =. doi:10.1038/s42254-021-00348-9 , urldate =

    work page doi:10.1038/s42254-021-00348-9

  40. [40]

    Chaitanya, K. V. S. Shiv and Bambah, B. A. , year = 2018, month = jan, number =. A. doi:10.48550/arXiv.1801.00544 , urldate =. arXiv , keywords =:1801.00544 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1801.00544 2018

  41. [41]

    Calculations of

    Champagne, Beno. Calculations of. Advances in. doi:10.1002/0471428019.ch2 , urldate =

    work page doi:10.1002/0471428019.ch2

  42. [42]

    Estimating Local Bonding/Antibonding Character of Canonical Molecular Orbitals from Their Energy Derivatives

    Chaquin, Patrick and Canac, Yves and Lepetit, Christine and Zargarian, Davit and Chauvin, Remi , year = 2016, journal =. Estimating Local Bonding/Antibonding Character of Canonical Molecular Orbitals from Their Energy Derivatives. doi:10.1002/qua.25174 , urldate =

    work page doi:10.1002/qua.25174 2016

  43. [43]

    The Journal of Chemical Physics , volume =

    Discrete Energy Representation and Generalized Propagation of Physical Systems , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.476017 , urldate =

    work page doi:10.1063/1.476017

  44. [44]

    The Journal of Chemical Physics , volume =

    A General and Efficient Filter-diagonalization Method without Time Propagation , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.471997 , urldate =

    work page doi:10.1063/1.471997

  45. [45]

    A Theoretical Investigation of the Structure and Vibrational Frequencies of

    Cho, Han-Gook and Cheong, Byeong-Sea , year = 2000, month = jan, journal =. A Theoretical Investigation of the Structure and Vibrational Frequencies of. doi:10.1016/S0166-1280(99)00183-9 , urldate =

    work page doi:10.1016/s0166-1280(99)00183-9 2000

  46. [46]

    Variational

    Chowdhury, Sujaul , editor =. Variational. Monte. doi:10.1007/978-3-031-23294-7_5 , urldate =

    work page doi:10.1007/978-3-031-23294-7_5

  47. [47]

    and Morales, Miguel A

    Clark, Bryan K. and Morales, Miguel A. and McMinis, Jeremy and Kim, Jeongnim and Scuseria, Gustavo E. , year = 2011, month = dec, journal =. Computing the Energy of a Water Molecule Using Multideterminants:. doi:10.1063/1.3665391 , urldate =

    work page doi:10.1063/1.3665391 2011

  48. [48]

    The Journal of Chemical Physics , volume =

    An Excitation Matched Local Correlation Approach to Excited State Specific Perturbation Theory , author =. The Journal of Chemical Physics , volume =. doi:10.1063/5.0280479 , urldate =

    work page doi:10.1063/5.0280479

  49. [49]

    Clune, Rachel and Shea, Jacqueline A. R. and Neuscamman, Eric , year = 2020, month = oct, journal =. N5-. doi:10.1021/acs.jctc.0c00308 , urldate =

    work page doi:10.1021/acs.jctc.0c00308 2020

  50. [50]

    and Hall, Michael B

    Couty, Marc and Bayse, Craig A. and Hall, Michael B. , year = 1997, month = oct, journal =. Extremely Localized Molecular Orbitals (. doi:10.1007/s002140050242 , urldate =

    work page doi:10.1007/s002140050242 1997

  51. [51]

    Daniel and Schaefer III, Henry F

    Crawford, T. Daniel and Schaefer III, Henry F. , year = 2000, pages =. An. Reviews in. doi:10.1002/9780470125915.ch2 , urldate =

    work page doi:10.1002/9780470125915.ch2 2000

  52. [53]

    M ller--

    Cremer, Dieter , year = 2011, journal =. M ller--. doi:10.1002/wcms.58 , urldate =

    work page doi:10.1002/wcms.58 2011

  53. [54]

    Evaluation of

    Csonka, G. Evaluation of. Journal of Chemical Theory and Computation , volume =. doi:10.1021/ct8004479 , urldate =

    work page doi:10.1021/ct8004479

  54. [55]

    and Zerner, Michael C

    Cullen, John M. and Zerner, Michael C. , year = 1982, month = oct, journal =. The Linked Singles and Doubles Model:. doi:10.1063/1.444319 , urldate =

    work page doi:10.1063/1.444319 1982

  55. [56]

    Advances in Physics , volume =

    Atomic Polarizabilities and Shielding Factors , author =. Advances in Physics , volume =. doi:10.1080/00018736200101302 , urldate =

    work page doi:10.1080/00018736200101302

  56. [57]

    Damour, Yann and Scemama, Anthony and Jacquemin, Denis and Kossoski, F. State-. Journal of Chemical Theory and Computation , volume =. doi:10.1021/acs.jctc.4c00034 , urldate =

    work page doi:10.1021/acs.jctc.4c00034

  57. [58]

    Dash, Monika and Feldt, Jonas and Moroni, Saverio and Scemama, Anthony and Filippi, Claudia , year = 2019, month = sep, journal =. Excited. doi:10.1021/acs.jctc.9b00476 , urldate =

    work page doi:10.1021/acs.jctc.9b00476 2019

  58. [59]

    The Journal of Chemical Physics , volume =

    Analytic Energy Derivatives for the Calculation of the First-Order Molecular Properties Using the Domain-Based Local Pair-Natural Orbital Coupled-Cluster Theory , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.4962369 , urldate =

    work page doi:10.1063/1.4962369

  59. [60]

    Competing

    David, Rolf and Tu. Competing. Journal of the American Chemical Society , volume =. doi:10.1021/jacs.4c03445 , urldate =

    work page doi:10.1021/jacs.4c03445

  60. [61]

    Dereka, Bogdan and Lewis, Nicholas H. C. and Keim, Jonathan H. and Snyder, Scott A. and Tokmakoff, Andrei , year = 2022, month = jan, journal =. Characterization of. doi:10.1021/acs.jpcb.1c09572 , urldate =

    work page doi:10.1021/acs.jpcb.1c09572 2022

  61. [62]

    Dereka, Bogdan and Lewis, Nicholas H. C. and Zhang, Yong and Hahn, Nathan T. and Keim, Jonathan H. and Snyder, Scott A. and Maginn, Edward J. and Tokmakoff, Andrei , year = 2022, month = may, journal =. Exchange-. doi:10.1021/jacs.2c00154 , urldate =

    work page doi:10.1021/jacs.2c00154 2022

  62. [64]

    Birgitta and Lin, Lin , year = 2021, month = aug, doi =

    Dong, Yulong and Whaley, K. Birgitta and Lin, Lin , year = 2021, month = aug, doi =. A

    2021

  63. [65]

    Failure of

    Dreuw, Andreas and. Failure of. Journal of the American Chemical Society , volume =. doi:10.1021/ja039556n , urldate =

    work page doi:10.1021/ja039556n

  64. [66]

    The Journal of Chemical Physics , volume =

    Long-Range Charge-Transfer Excited States in Time-Dependent Density Functional Theory Require Non-Local Exchange , author =. The Journal of Chemical Physics , volume =. doi:10.1063/1.1590951 , urldate =

    work page doi:10.1063/1.1590951

  65. [67]

    Dreuw, Andreas and. Single-. Chemical Reviews , volume =. doi:10.1021/cr0505627 , urldate =

    work page doi:10.1021/cr0505627

  66. [68]

    , year = 2007, month = aug, journal =

    Drukarev, Evgenii G. , year = 2007, month = aug, journal =. Atomic Physics: Computer Calculations and Theoretical Analysis , shorttitle =. doi:10.1070/PU2007v050n08ABEH006372 , urldate =

    work page doi:10.1070/pu2007v050n08abeh006372 2007

  67. [69]

    , year = 1989, month = jan, journal =

    Dunning, Jr., Thom H. , year = 1989, month = jan, journal =. Gaussian Basis Sets for Use in Correlated Molecular Calculations. doi:10.1063/1.456153 , urldate =

    work page doi:10.1063/1.456153 1989

  68. [70]

    and Jasien, Paul G

    Dykstra, Clifford E. and Jasien, Paul G. , year = 1984, month = aug, journal =. Derivative. doi:10.1016/0009-2614(84)85607-9 , urldate =

    work page doi:10.1016/0009-2614(84)85607-9 1984

  69. [71]

    Science , volume =

    Direct Observation of Chirality-Induced Spin Selectivity in Electron Donor--Acceptor Molecules , author =. Science , volume =. doi:10.1126/science.adj5328 , urldate =

    work page doi:10.1126/science.adj5328

  70. [72]

    Conformational

    Ehlert, Sebastian and Grimme, Stefan and Hansen, Andreas , year = 2022, month = jun, journal =. Conformational. doi:10.1021/acs.jpca.2c02439 , urldate =

    work page doi:10.1021/acs.jpca.2c02439 2022

  71. [73]

    Entwistle, M. T. and Sch. Electronic Excited States in Deep Variational. Nature Communications , volume =. doi:10.1038/s41467-022-35534-5 , urldate =

    work page doi:10.1038/s41467-022-35534-5

  72. [74]

    Epifanovsky, Evgeny and Gilbert, Andrew T. B. and Feng, Xintian and Lee, Joonho and Mao, Yuezhi and Mardirossian, Narbe and Pokhilko, Pavel and White, Alec F. and Coons, Marc P. and Dempwolff, Adrian L. and Gan, Zhengting and Hait, Diptarka and Horn, Paul R. and Jacobson, Leif D. and Kaliman, Ilya and Kussmann, J. Software for the Frontiers of Quantum Che...

    work page doi:10.1063/5.0055522

  73. [75]

    and Lin, Lin and Nakatsukasa, Yuji , year = 2021, month = oct, number =

    Epperly, Ethan N. and Lin, Lin and Nakatsukasa, Yuji , year = 2021, month = oct, number =. A. arXiv , keywords =:2110.07492 , primaryclass =

    arXiv 2021

  74. [76]

    and Lin, Lin and Nakatsukasa, Yuji , year = 2021, month = oct, number =

    Epperly, Ethan N. and Lin, Lin and Nakatsukasa, Yuji , year = 2021, month = oct, number =. A. doi:10.48550/arXiv.2110.07492 , urldate =. arXiv , keywords =:2110.07492 , primaryclass =

    work page doi:10.48550/arxiv.2110.07492 2021

  75. [77]

    and Lin, Lin and Nakatsukasa, Yuji , year = 2022, month = sep, journal =

    Epperly, Ethan N. and Lin, Lin and Nakatsukasa, Yuji , year = 2022, month = sep, journal =. A. doi:10.1137/21M145954X , urldate =

    work page doi:10.1137/21m145954x 2022

  76. [78]

    Evers et al, Theory of Chirality Induced Spin Selectivity: Progress and Challenges, Adv

    Evers, Ferdinand and Aharony, Amnon and. Theory of. Advanced Materials , volume =. doi:10.1002/adma.202106629 , urldate =

    work page doi:10.1002/adma.202106629

  77. [79]

    Excited States in Variational

  78. [80]

    and Dixon, David A

    Fang, Zongtang and Vasiliu, Monica and Peterson, Kirk A. and Dixon, David A. , year = 2017, month = mar, journal =. Prediction of. doi:10.1021/acs.jctc.6b00971 , urldate =

    work page doi:10.1021/acs.jctc.6b00971 2017

  79. [81]

    and Dixon, David A

    Fang, Zongtang and Lee, Zachary and Peterson, Kirk A. and Dixon, David A. , year = 2016, month = aug, journal =. Use of. doi:10.1021/acs.jctc.6b00327 , urldate =

    work page doi:10.1021/acs.jctc.6b00327 2016

  80. [82]

    , year = 2021, month = feb, journal =

    Fay, Thomas P. , year = 2021, month = feb, journal =. Chirality-. doi:10.1021/acs.jpclett.1c00009 , urldate =

    work page doi:10.1021/acs.jpclett.1c00009 2021

Showing first 80 references.