Pith. sign in

REVIEW 3 major objections 4 minor 40 references

Convex Hartree-Fock theory: A simple framework for ground state conical intersections

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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

Pith's one-line read Convex Hartree-Fock keeps ground and excited surfaces continuous at conical intersections by optimizing in a subspace and reintroducing the removed direction at the end.

desk verdict A genuinely new SCF-based route to continuous ground-state conical intersections, held back by an untested continuity assumption and an unsupported geometric-phase claim. read the letter →

arxiv 2508.21453 v1 pith:HIIMKQDD submitted 2025-08-29 physics.chem-ph

Federico Rossi , Henrik Koch This is my paper · ORCID
classification physics.chem-ph
keywords ConvexHartree-Fockconicalintersectionsground-statedegeneracyHessianeigenvectorprojectionTamm-Dancoffapproximationpotentialenergysurfacesgeometricphasenonadiabaticdynamics
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

Conical intersections between ground and excited states are where molecules switch electronic state efficiently, but standard Hartree-Fock and time-dependent Hartree-Fock break down there: the lowest excitation energy collapses toward zero, the Hartree-Fock Hessian develops a zero-curvature direction, and potential energy surfaces become discontinuous or fail to converge. This paper introduces Convex Hartree-Fock (CVX-HF), which optimizes the reference determinant in a subspace with that soft direction projected out, making the ground-state optimization convex, and then reintroduces the removed direction as an explicit configuration in a small final Hamiltonian diagonalization. The claim is that this two-step procedure supplies the missing coupling elements, so the resulting S0 and S1 surfaces are continuous and the intersection has the correct single-point topology, as demonstrated for ammonia, 2,4-cyclohexadien-1-ylamine, and the GFP chromophore HBDI-. If correct, the method offers a mean-field-cost route to ground-state conical intersections for photochemistry and nonadiabatic dynamics, where multiconfigurational methods are often prohibitively expensive.

What carries the argument

The central object is the Hessian eigenvector r1 associated with the smallest curvature direction of the Hartree-Fock energy, together with the full-space Hamiltonian matrix built in the basis {|HF>, |R1>, |~nu>}. r1 is the orbital-rotation direction along which the Hessian eigenvalue vanishes as a conical intersection is approached; removing its projection from the gradient and from the orbital rotation parameter makes the optimization convex (Eqs. 14-15). The reintroduced state |R1> is the single excitation generated by r1 acting on the reference, and |~nu> are the orthogonal single excitations. Diagonalizing this small Hamiltonian reintroduces the coupling between ground and excited state

What would settle it

Compute CVX-HF energies along a closed loop around the ammonia conical intersection and also along a path where the two lowest Hessian eigenvalues cross; if the overlap of r1 with its value at the previous geometry drops sharply and the S0/S1 gap jumps, the smoothness assumption fails. Alternatively, compare the E1-E0 map against FCI on a fine grid near the intersection: any seam or discontinuity beyond the single point would refute the claim.

Watch

Extended reading notes

Core claim

The central claim is that ground-state conical intersections, normally inaccessible to single-reference mean-field methods, can be captured by a modified Hartree-Fock optimization followed by a Hamiltonian diagonalization. Near a degeneracy, the lowest eigenvalue of the TDHF response problem and the corresponding Hessian eigenvalue both approach zero; the first-order gradient along that eigenvector r1 therefore has almost no steering effect, which triggers bifurcations and discontinuous surfaces. CVX-HF solves the projected stationarity condition together with the Hessian eigenvector equation for r1, so the energy is convex in the subspace orthogonal to r1. The removed direction is then used

Load-bearing premise

The method assumes that the selected Hessian eigenvector r1 tracks smoothly with nuclear geometry, so the projected subspace and converged reference are continuous; if r1 changes abruptly between neighboring geometries, the surfaces could regain discontinuities.

Editorial extensions

If this is right

  • CVX-HF gives continuous S0/S1 potential energy surfaces in regions where TDA-TDHF shows negative excitation energies, unconverged Hartree-Fock solutions, or discontinuous surfaces, at essentially Hartree-Fock cost.
  • The converged CVX-HF orbitals can be used as a reference for correlated methods such as coupled cluster or perturbation theory, preventing Hartree-Fock-level discontinuities from propagating into more accurate models.
  • The same orbital-rotation parameterization can be applied within Kohn-Sham DFT, so TDDFT could inherit the same correction to conical-intersection topology.
  • Additional Hessian eigenvectors can be projected and the final space can be enlarged with extra configurations, including double excitations, which covers multichromophore systems and cases where double excitations matter.
  • Excitation energies remain size-intensive when non-interacting molecules or solvent atoms are added, which is important for modeling solvated chromophores.

Reading between the lines

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

  • The continuity argument implicitly relies on r1 varying smoothly with nuclear coordinates. A natural stress test is to follow a path where the two lowest Hessian eigenvalues cross: if r1 and r2 exchange character, the projected subspace can jump and the CVX-HF surfaces may develop a small seam that the current examples do not probe.
  • Because the final diagonalization is essentially a two-state-plus-bath model built from a mean-field reference, CVX-HF could be viewed as a systematic way to generate diabatic-like states from a single determinant, connecting to diabatization procedures beyond conical intersections.
  • The method's cost profile, one convex Hartree-Fock optimization plus a small eigenvalue problem, suggests it could enable on-the-fly nonadiabatic dynamics for medium-sized chromophores where multireference methods are currently too expensive, though this computational extrapolation is not tested in the paper.
  • For intersections involving more than two states, or seams of higher dimension, the single-vector projection may be insufficient; the paper notes multiple projections are possible, but their robustness along extended seams is not benchmarked.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a modified Hartree–Fock method, 'Convex Hartree–Fock' (CVX-HF), designed to describe ground-state conical intersections at mean-field cost. The HF optimization is constrained to a subspace in which the Hessian is made positive definite by removing the component of the gradient along the lowest Hessian eigenvector r1 (Eqs. (14)–(15)). The ground and excited states are then obtained by diagonalizing the Hamiltonian in the basis {|HF>, |R1>, |~nu>} (Eq. (16)). The method is tested on three systems: ammonia, 2,4-cyclohexadien-1-ylamine, and the HBDI- GFP chromophore. In each case, TDA-TDHF shows discontinuities, negative excitation energies, or non-converged regions, while CVX-HF yields visually smooth S0/S1 surfaces with the intersection appearing as a single point. The paper claims that the framework introduces the coupling elements needed to capture conical intersections and the geometric phase effect.

Significance. If the claims are correct, CVX-HF would provide a practically useful, mean-field-cost route to correct S0/S1 conical intersection topology, with potential applications in nonadiabatic dynamics. The central construction is not circular: the coupling <HF|H|R1> is the residual gradient along the projected mode, determined by the self-consistent equations, and the method is not fitted to known intersections. The paper includes useful numerical experiments on three distinct systems, and the SI provides geometries, g/h vectors, and size-intensivity tests. However, the two strongest claims—continuity of the surfaces and capture of the geometric phase—are not quantitatively established. The continuity of the selected Hessian eigenvector r1 is assumed but never tested, and the geometric phase is asserted without being computed. These are load-bearing gaps that should be addressed before the central claims can be accepted.

major comments (3)
  1. [Algorithm 1, step 4 and Eq. (15)] The central continuity claim is not verified. The final Hamiltonian in Eq. (16) is built from r1, the lowest Hessian eigenvector, and the projector P = I - r1 r1^T used in Eq. (14). Algorithm 1 obtains r1 by Davidson diagonalization at each SCF iteration (step 4), and step 8 uses a 'diabatization' of SAD guesses that is never defined. Nothing in the manuscript shows that r1 varies smoothly with nuclear coordinates or that the Davidson solver tracks the same eigenvector across adjacent geometries. If the two lowest Hessian eigenvalues cross, or if the solver converges to a different eigenvector, P, the CVX-HF reference, the matrix elements in Eq. (16), and hence S0/S1 become discontinuous—reintroducing the very problem the method is designed to solve. The reported scans are coarse, so kinks smaller than the grid spacing are invisible; the SI extensivity tables do not address this. Please
  2. [Discussion, first paragraph] The assertion that the CVX-HF eigenstates 'correctly capture conical intersections and the geometric phase effect' is not supported by any computation in the manuscript. The paper reports only energy surfaces. The geometric phase is a phase change of the electronic wave function along a closed loop around a conical intersection; no Berry phase, line integral, or sign change of the adiabatic wave function is computed. At minimum, compute the loop integral of the derivative coupling or the sign change of the wave function (for example, using the overlap of |R1> or the full-space eigenstate along a closed path encircling the intersection). If such a calculation is not possible, the claim should be tempered to 'correct conical intersection topology at the mean-field level.'
  3. [Fig. 1 and Applications, ammonia] The claim that the CVX-HF intersection is 'limited to a single point' is based on visual inspection of the colormap in Fig. 1(b). No quantitative analysis of the energy gap is given: no fit of E1-E0 to a linear function of the branching coordinates, no g/h vectors for the CVX-HF intersection, and no loop test to distinguish a true conical intersection from a very narrowly avoided crossing. The SI provides the CVX-HF CI geometry for 2,4-cyclohexadien-1-ylamine (Table S8) but not a characterization of the branching space. Please quantify the degeneracy (e.g., show that E1-E0 scales linearly with displacement in two directions away from the CI) or weaken the claim.
minor comments (4)
  1. [Algorithm 1, step 4] The expression 'n excited' is undefined; it should be 'n_proj' or 'n_projected'. Also, step 8 refers to a 'diabatization step of the new C0 coefficients' that is not described anywhere; please define it or provide a reference.
  2. [SI S2, Eq. (20)] The third component of SFS x - x is written as '-r1,mu r1,nu x_nu', but this should be a sum over nu (or the index nu should be contracted). The notation currently mixes mu and nu inconsistently.
  3. [Fig. 2 caption] The caption uses 'CVX-HF = TDA-TDHF' and 'CVX-HF = TDA-TDHF 2'. This could be misread as equality of methods; clarify that it refers to the orbitals being visually indistinguishable.
  4. [Fig. 4 caption and text] The caption of Fig. 4 says 'The TDHF (a) and CVX-HF (b)', while the text refers to 'TDA-TDHF' throughout. Please make the method labeling consistent.

Circularity Check

0 steps flagged · score 2.0 of 10

No circularity: the residual-gradient coupling is solved self-consistently, not fitted; self-citations are not load-bearing.

full rationale

The central derivation of CVX-HF is self-contained. The modified gradient in Eq. (11) is defined as the full HF gradient minus its projection along the lowest Hessian eigenvector r1, and is solved self-consistently together with the Hessian eigenvalue equation (Eqs. 14–15). The final Hamiltonian in Eq. (16) includes the residual gradient component ⟨HF|H|R1⟩ = r1^T G(0) as the coupling between the HF reference and the single-excitation state |R1⟩. This coupling is not a fitted parameter; it is determined by the SCF solution of the projected equations and is the residual of the full gradient along the mode that was excluded from the optimization. The resulting S0/S1 gap is therefore a nontrivial output of the calculation, not an input. The method does not use known conical intersection geometries, energies, or g/h vectors in constructing the Hamiltonian; those are only used to define coordinates for the scans or for comparison. Benchmarks (FCI, CCSD, GCCSD) are external. The self-citations (Refs. 9, 28, and SI Refs. 3–4) are used for motivation, comparison of surface shapes, and obtaining initial guess g/h vectors; they do not enter the derivation of the CVX-HF equations themselves, and the central claim stands independently. The one assumption highlighted by the skeptic—smooth variation of the Hessian eigenvector r1—is an unproven numerical-stability property, not a circularity: it does not reduce the result to its inputs by definition. No circular step of any of the enumerated kinds could be identified; the score of 2 merely acknowledges the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on three unproved assumptions: the zero-mode correspondence between TDHF and the HF Hessian (cited), the continuous variation of the projected subspace, and the sufficiency of single excitations for the crossing topology. The only adjustable setting is the number of projected states, which the paper shows is not critical for the tested systems. No free parameters are fitted to a target result, and no new physical entities are introduced.

free parameters (1)
  • n_proj (number of projected Hessian eigenvectors)
    User-selected; the paper uses n_proj=1 for most results and tests n_proj=1..5 (Tables S2, S3). The choice affects the energies and excitation energies, though the paper shows the results are rather insensitive. It is a hand-chosen setting, not fitted to a target.
assumptions (4)
  • domain assumption Zero-energy eigenvectors of the TDHF eigenvalue problem coincide with zero-energy eigenvectors of the HF Hessian.
    Used to argue that near a conical intersection the lowest Hessian eigenvalue lambda_1 approaches zero, motivating the projection (paragraph near Eq. 10). Cited from Cui et al. (Ref. 25), not proved in this paper.
  • ad hoc to paper The modified gradient equations (14)-(15) have a solution that varies continuously with nuclear coordinates.
    The method's central promise of continuous PES depends on this unproved property. The algorithm's diabatization of the SAD guess is a practical workaround, not a mathematical guarantee that the converged r1 changes smoothly.
  • domain assumption The reference determinant plus the set of single excitations (including |R1>) is sufficient to describe the topology of the S0/S1 crossing.
    The final diagonalization is restricted to the space spanned by |HF>, |R1>, and the orthogonal single-excitation manifold. The paper acknowledges (Discussion, last paragraph) that double excitations are sometimes needed, so the general validity of this assumption is open for systems beyond the three tested.
  • standard math The SAD guess and the orthogonalization of the excitation manifold yield a well-defined, non-redundant basis for the final diagonalization.
    Standard linear algebra for constructing the CI-singles-like subspace; the SI (Sections S1, S2) verifies the metric can be replaced by the identity under stated conditions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Convex Hartree-Fock theory: A simple framework for ground state conical intersections." pith.science (2026). https://pith.science/paper/HIIMKQDD

@misc{pith2026250821453,
  author       = {Pith},
  title        = {Pith review of: Convex Hartree-Fock theory: A simple framework for ground state conical intersections},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HIIMKQDD}},
  note         = {Machine review of arXiv:2508.21453}
}
read the original abstract

Accurate modeling of conical intersections is crucial in nonadiabatic molecular dynamics, as these features govern processes such as radiationless transitions and photochemical reactions. Conventional electronic structure methods, including Hartree-Fock, density functional theory, and their time-dependent extensions, struggle in this regime. Due to their single reference nature and separate treatment of ground and excited states, they fail to capture ground state intersections. Multiconfigurational approaches overcome these limitations, but at a prohibitive computational cost. In this work, we propose a modified Hartree-Fock framework, referred to as Convex Hartree-Fock, that optimizes the reference within a tailored subspace by removing projections along selected Hessian eigenvectors. The ground and excited states are then obtained through subsequent Hamiltonian diagonalization. We validate the approach across several test cases and benchmark its performance against time-dependent Hartree-Fock within the Tamm-Dancoff approximation.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references · 36 canonical work pages

  1. [1]

    author Gozem, S. et al. title Shape of multireference, equation-of-motion coupled-cluster, and density functional theory potential energy surfaces at a conical intersection . journal J. Chem. Theory Comput. volume 10 , pages 3074--3084 ( year 2014 )

    work page 2014

  2. [2]

    , author Ullrich, C

    author Capelle, K. , author Ullrich, C. A. & author Vignale, G. title Degenerate ground states and nonunique potentials: Breakdown and restoration of density functionals . journal Phys. Rev. A volume 76 , pages 012508 ( year 2007 )

    work page 2007

  3. [3]

    title Assessment of density functional methods for obtaining geometries at conical intersections in organic molecules

    author Filatov, M. title Assessment of density functional methods for obtaining geometries at conical intersections in organic molecules . journal J. Chem. Theory Comput. volume 9 , pages 4526--4541 ( year 2013 )

    work page 2013

  4. [4]

    author Thouless, D. J. title The quantum mechanics of many-body systems ( publisher Courier Corporation , year 2013 )

    work page 2013

  5. [5]

    & author Öhrn, Y

    author Linderberg, J. & author Öhrn, Y. title Propagators in Quantum Chemistry ( publisher Academic Press, London and New York , year 1973 )

    work page 1973

  6. [6]

    & author Paldus, J

    author C C \' z z ek, J. & author Paldus, J. title Stability conditions for the solutions of the hartree-fock equations for atomic and molecular systems. v.the nonanalytic behavior of the broken-symmetry solutions at the branching point . journal Phys. Rev. A volume 3 , pages 525--527 ( year 1971 )

    work page 1971

  7. [7]

    author Coulson, C. A. & author Fischer, I. title Xxxiv. notes on the molecular orbital treatment of the hydrogen molecule . journal Lond. Edinb. Dubl. Phil. Mag. volume 40 , pages 386--393 ( year 1949 )

    work page 1949

  8. [8]

    , author Jorgensen, P

    author Helgaker, T. , author Jorgensen, P. & author Olsen, J. title Molecular electronic-structure theory ( publisher John Wiley & Sons , year 2013 )

    work page 2013

Show all 40 references
  1. [9]

    author Kj nstad, E. F. & author Koch, H. title Understanding failures in electronic structure methods arising from the geometric phase effect . journal arXiv preprint arXiv:2411.08209 ( year 2024 )

    2024 arXiv

  2. [10]

    , author Head-Gordon, M

    author Shao, Y. , author Head-Gordon, M. & author Krylov, A. I. title The spin--flip approach within time-dependent density functional theory: Theory and applications to diradicals . journal J. Chem. Phys. volume 118 , pages 4807--4818 ( year 2003 )

    2003

  3. [11]

    author Maitra, N. T. , author Zhang, F. , author Cave, R. J. & author Burke, K. title Double excitations within time-dependent density functional theory linear response . journal J. Chem. Phys. volume 120 , pages 5932--5937 ( year 2004 )

    2004

  4. [12]

    & author Subotnik, J

    author Teh, H.-H. & author Subotnik, J. E. title The simplest possible approach for simulating s 0--s 1 conical intersections with dft/tddft: Adding one doubly excited configuration . journal J. Phys. Chem. Lett. volume 10 , pages 3426--3432 ( year 2019 )

    2019

  5. [13]

    author Li, S. L. , author Marenich, A. V. , author Xu, X. & author Truhlar, D. G. title Configuration interaction-corrected tamm--dancoff approximation: A time-dependent density functional method with the correct dimensionality of conical intersections . journal J. Phys. Chem....

    2014

  6. [14]

    author Evangelista, F. A. , author Shushkov, P. & author Tully, J. C. title Orthogonality constrained density functional theory for electronic excited states . journal J. Phys. Chem. A volume 117 , pages 7378--7392 ( year 2013 )

    2013

  7. [15]

    author Hedeg rd, E. D. , author Toulouse, J. & author Jensen, H. J. A. title Multiconfigurational short-range density-functional theory for open-shell systems . journal J. Chem. Phys. volume 148 , pages 214103 ( year 2018 )

    2018

  8. [16]

    title Spin-restricted ensemble-referenced kohn--sham method: basic principles and application to strongly correlated ground and excited states of molecules

    author Filatov, M. title Spin-restricted ensemble-referenced kohn--sham method: basic principles and application to strongly correlated ground and excited states of molecules . journal Wiley Interdiscip. Rev. Comput. Mol. Sci. volume 5 , pages 146--167 ( year 2015 )

    2015

  9. [17]

    author Schmerwitz, Y. L. , author Levi, G. & author J \'o nsson, H. title Calculations of excited electronic states by converging on saddle points using generalized mode following . journal J. Chem. Theory Comput. volume 19 , pages 3634--3651 ( year 2023 )

    2023

  10. [18]

    , author Bradbury, N

    author Duston, T. , author Bradbury, N. , author Tao, Z. & author Subotnik, J. E. title Conical intersections and electronic momentum as viewed from phase space electronic structure theory . journal arXiv preprint arXiv:2506.11963 ( year 2025 )

    2025 arXiv

  11. [19]

    title Electronic structure methods for the description of nonadiabatic effects and conical intersections

    author Matsika, S. title Electronic structure methods for the description of nonadiabatic effects and conical intersections . journal Chemical Reviews volume 121 , pages 9407--9449 ( year 2021 )

    2021

  12. [20]

    , author Yu, J

    author Bannwarth, C. , author Yu, J. K. , author Hohenstein, E. G. & author Martínez, T. J. title Hole–hole tamm–dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation . journal J. Chem. Phys....

    2020

  13. [21]

    , author F gri Jr, K

    author Alml \"o f, J. , author F gri Jr, K. & author Korsell, K. title Principles for a direct scf approach to licao--moab-initio calculations . journal J. Comput. Chem. volume 3 , pages 385--399 ( year 1982 )

    1982

  14. [22]

    , author Zwaans, R

    author Van Lenthe, J. , author Zwaans, R. , author Van Dam, H. J. & author Guest, M. title Starting scf calculations by superposition of atomic densities . journal J. Comput. Chem. volume 27 , pages 926--932 ( year 2006 )

    2006

  15. [23]

    & author Simons, J

    author J rgensen, P. & author Simons, J. title Second quantization-based methods in quantum chemistry ( publisher Elsevier , year 2012 )

    2012

  16. [24]

    & author Head-Gordon, M

    author Hirata, S. & author Head-Gordon, M. title Time-dependent density functional theory within the tamm--dancoff approximation . journal Chem. Phys. Lett. volume 314 , pages 291--299 ( year 1999 )

    1999

  17. [25]

    , author Bulik, I

    author Cui, Y. , author Bulik, I. W. , author Jim \'e nez-Hoyos, C. A. , author Henderson, T. M. & author Scuseria, G. E. title Proper and improper zero energy modes in hartree-fock theory and their relevance for symmetry breaking and restoration . journal J. Chem. Phys. volum...

    2013

  18. [26]

    author Li, Z. H. , author Valero, R. & author Truhlar, D. G. title Improved direct diabatization and coupled potential energy surfaces for the photodissociation of ammonia . journal Theor. Chem. Acc. volume 118 , pages 9--24 ( year 2007 )

    2007

  19. [27]

    author Xu, L. et al. title Conical intersections studied by the configuration-interaction-corrected tamm--dancoff method . journal J. Chem. Theory Comput. volume 21 , pages 3600--3611 ( year 2025 )

    2025

  20. [28]

    , author Kj nstad, E

    author Rossi, F. , author Kj nstad, E. F. , author Angelico, S. & author Koch, H. title Generalized coupled cluster theory for ground and excited state intersections . journal J. Phys. Chem. Lett. volume 16 , pages 568--578 ( year 2025 )

    2025

  21. [29]

    author Kjønstad, E. F. & author Koch, H. title Communication: Non-adiabatic derivative coupling elements for the coupled cluster singles and doubles model . journal J. Chem. Phys. volume 158 , pages 161106 ( year 2023 )

    2023

  22. [30]

    author MacDonell, R. J. title Polyene meci dataset ( year 2019 ). ://github.com/ryjmacdonell/polyene-meci-dataset.git. note Date of access: 2024-12-09

    2019

  23. [31]

    author Jones, C. M. , author List, N. H. & author Mart \' nez, T. J. title Resolving the ultrafast dynamics of the anionic green fluorescent protein chromophore in water . journal Chem. Sci. volume 12 , pages 11347--11363 ( year 2021 )

    2021

  24. [32]

    author Tsien, R. Y. title The green fluorescent protein . journal Annu. Rev. Biochem. volume 67 , pages 509--544 ( year 1998 )

    1998

  25. [33]

    author List, N. H. , author Jones, C. M. & author Mart \' nez, T. J. title Chemical control of excited-state reactivity of the anionic green fluorescent protein chromophore . journal Commun. Chem. volume 7 , pages 25 ( year 2024 )

    2024

  26. [34]

    author Cogdell, R. J. , author Gall, A. & author K \"o hler, J. title The architecture and function of the light-harvesting apparatus of purple bacteria: from single molecules to in vivo membranes . journal Q. Rev. Biophys. volume 39 , pages 227--324 ( year 2006 )

    2006

  27. [35]

    , author Cupellini, L

    author Segatta, F. , author Cupellini, L. , author Garavelli, M. & author Mennucci, B. title Quantum chemical modeling of the photoinduced activity of multichromophoric biosystems: focus review . journal Chem. Rev. volume 119 , pages 9361--9380 ( year 2019 )

    2019

  28. [36]

    author Folkestad, S. D. et al. title eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods . journal J. Chem. Phys. volume 152 , pages 184103 ( year 2020 )

    2020

  29. [37]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter doi edition editor eid eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url volume year archivePrefix primaryClass adsurl adsnote version label extra.labe...

  30. [38]

    write newline

    " write newline "" before.all 'output.state := FUNCTION add.period duplicate empty 'skip "." * add.blank if FUNCTION if.digit duplicate "0" = swap duplicate "1" = swap duplicate "2" = swap duplicate "3" = swap duplicate "4" = swap duplicate "5" = swap duplicate "6" = swap dupl...

  31. [39]

    , " * write output.state after.block = add.period write newline

    ENTRY address archive author booktitle chapter edition editor eprint howpublished institution journal key keywords month note number organization pages publisher school series title type url doi volume year archivePrefix primaryClass eid adsurl adsnote version label INTEGERS o...

  32. [40]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.