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arxiv: 2605.29924 · v1 · pith:FRKABLYAnew · submitted 2026-05-28 · ⚛️ physics.chem-ph

Diagrammatic Multiplet-Sum Method (MSM) Density-Functional Theory(DFT): III. Inclusion of Relaxation and Application to LiH

Mark E Casida , Abraham Ponra , Gadzikano Munyuki , Bharathi Natarajan This is my paper

Pith reviewed 2026-06-29 00:18 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords density functional theorymultiplet sum methodlithium hydrideavoided crossingnondynamic correlationNOCI relaxationpotential energy curvecharge transfer
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The pith

Incorporating NOCI relaxation into diagrammatic MSM DFT yields an accurate ground-state potential energy curve for LiH across its avoided crossing with charge transfer.

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

The paper extends multiplet sum method density-functional theory to include nondynamic correlation by using a diagrammatic formulation of the two-orbital two-electron model without symmetry arguments. Building on earlier versions that omitted relaxation, it adds nonorthogonal configuration interaction to account for orbital relaxation effects. The resulting method produces an accurate ground-state potential energy curve for lithium hydride, including the region of the ionic-to-open-shell-singlet avoided crossing where charge transfer is large. A sympathetic reader would care because standard density functionals have difficulty with static and nondynamic correlation, while this approach offers a pragmatic route to include them in a single framework. The encouraging result for LiH indicates that the model may extend to other diatomic molecules.

Core claim

The modified diag MSM DFT using the two-orbital two-electron model together with diagrammatic multiplet sums and NOCI relaxation produces an accurate ground-state potential energy curve for LiH even at the ionic-to-open-shell-singlet avoided crossing characterized by significant charge transfer.

What carries the argument

The two-orbital two-electron model (TOTEM) combined with diagrammatic multiplet sum method and nonorthogonal configuration interaction (NOCI) relaxation.

If this is right

  • The approach accounts for dynamic, static, and nondynamic correlation within one density-functional framework.
  • The method can be extended to at least other singly and multiply-bonded diatomic molecules.
  • Nondynamic correlation is included without relying on symmetry arguments.
  • Relaxation effects improve the description of charge-transfer regions in potential energy curves.

Where Pith is reading between the lines

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

  • The same construction may apply to transition states or larger systems that exhibit avoided crossings driven by charge transfer.
  • Direct numerical comparisons with multireference wavefunction methods could quantify the computational trade-offs.
  • The framework might reduce reliance on empirical corrections for strong correlation in certain molecular classes.

Load-bearing premise

The two-orbital two-electron model together with diagrammatic MSM and NOCI relaxation is sufficient to capture the physics of the avoided crossing and charge transfer in LiH without additional fitted parameters or symmetry constraints.

What would settle it

High-level ab initio calculations or experimental data showing that the computed potential energy curve deviates markedly from reference values near the avoided crossing, either in energy or internuclear distance at the crossing point, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.29924 by Abraham Ponra, Bharathi Natarajan, Gadzikano Munyuki, Mark E Casida.

Figure 1
Figure 1. Figure 1: EXACT singlet PECs for LiH. The grey adiabatic curves were [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: EXACT PECs for LiH from Ref. [19], including the lowest triplet [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Two-level two-electron model (TOTEM) of LiH. Here Φ = [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Relaxed GS SDET PEC, relaxed DEX SDET PEC, and a PEC obta [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Matrix elements of the M (b) and the overlap elements (a) used to construct M. (See text.) 14 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Matrix elements of (a) S and (b) S’ (see text). 15 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) The eigenvalues of S and S’ as a function of bond length. (b) Molden [21] images of the HOMO and LUMO calculated for the different references with a contour value of 0.03 a.u. Note how the HOMO and LUMO of the GS and DEX SDETs are bonding and antibonding combinations of similarly sized s-type orbitals while the HOMO of the ENS state is an s-type orbital localized on H and the LUMO of the ENS state is a… view at source ↗
Figure 8
Figure 8. Figure 8: The coupling matrix elements used in our study as a function [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: (a) Comparison of EXACT and MSM-LDA (v0) PECs with the energy shifted so that the a 3Σ curve goes to zero at R = 10.0 bohr. (b) Wave-function decomposition of the v0 MSM-LDA ground state. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (a) Comparison of EXACT and v1 MSM-LDA PECs with the energy shifted so that the a 3Σ curve goes to zero at R = 10.0 bohr. (b) Wave-function decomposition of the v1 MSM-LDA ground state. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a) Comparison of EXACT and v3 MSM-LDA PECs with the energy shifted so that the a 3Σ curve goes to zero at R = 10.0 bohr. (b) Wave-function decomposition of the v3 MSM-LDA ground state. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a) Comparison of EXACT and v4 MSM-LDA PECs with the energy shifted so that the a 3Σ curve goes to zero at R = 10.0 bohr. (b) Wave-function decomposition of the v4 MSM-LDA ground state. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: (a) Comparison of EXACT and v5 MSM-LDA PECs with the energy shifted so that the a 3Σ curve goes to zero at R = 10.0 bohr. (b) Wave-function decomposition of the v5 MSM-LDA ground state. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: (a) Comparison of EXACT and v6 MSM-LDA PECs with the energy shifted so that the a 3Σ curve goes to zero at R = 10.0 bohr. Wave-function decomposition of the v6 MSM-LDA ground state: (b) |C ′′ GS| 2× 100%, (c) Chirgwin-Coulson analysis. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of BS and v5 MSM-LDA GS shifted PECs with the EXACT GS PEC. The BS and v5 MSM-LDA GS PECs have been shifted to have the same value as the EXACT GS PEC at 3.8 bohr: (a) EXACT, BS, and v5 MSM-LDA GS PECs and (b) BS-EXACT and v5-EXACT energy difference. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗
read the original abstract

Ideal density-functional approximations (DFAs) should account for dynamic, static, and nondynamic correlation. While common DFAs struggle with the latter two, the Ziegler-Rauk-Baerends-Daul multiplet sum method (MSM) provides a pragmatic way to include static correlation. In this article, we use diagrammatic MSM density-functional theory (diag MSM DFT) using the two-orbital two-electron model (TOTEM) to extend MSM DFT to include nondynamic correlation without relying on symmetry arguments. Building on previous formulations [A. Ponra, C. Bakasa, A.J. Etindele,and M.E. Casida, J. Chem. Phys. 159, 244306 (2023); M.E. Casida, A. Ponra, C. Bakasa, and A.J.Etindele, J. Chem. Phys. 162, 144317 (2025)] that lacked relaxation effects, this article incorporates relaxation via nonorthogonal configuration interaction (NOCI). We demonstrate that this modified diag MSM DFT produces an accurate ground-state potential energy curve (PEC) for lithium hydride (LiH), even at the ionic-to-open-shell-singlet avoided crossing characterized by significant charge transfer. This encouraging result suggests that the model can be extended to (at least) other singly and multiply-bonded diatomic molecules, while providing insight into a novel way to include strong correlation in DFT.

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 extends diagrammatic multiplet-sum method density-functional theory (diag MSM DFT) using the two-orbital two-electron model (TOTEM) to incorporate nondynamic correlation without symmetry arguments and adds relaxation via nonorthogonal configuration interaction (NOCI). It applies the resulting method to lithium hydride and claims that the modified approach produces an accurate ground-state potential energy curve even at the ionic-to-open-shell-singlet avoided crossing with significant charge transfer.

Significance. If the quantitative results support the claim, the work would supply a parameter-free route to static and nondynamic correlation in DFT for systems exhibiting avoided crossings and charge transfer, with possible extension to other singly and multiply bonded diatomics.

major comments (2)
  1. Abstract: the central claim that the modified diag MSM DFT 'produces an accurate ground-state potential energy curve (PEC) for lithium hydride (LiH)' is unsupported by any numerical values, error metrics, dissociation energies, equilibrium distances, or direct comparisons to experiment or reference methods, rendering the accuracy assertion at the avoided crossing unverifiable.
  2. Abstract: the reported accuracy for the LiH PEC rests on the two-orbital two-electron model (TOTEM) together with MSM and NOCI components defined in the authors' prior self-citations (J. Chem. Phys. 159, 244306 (2023) and 162, 144317 (2025)); the claim therefore reduces in part to quantities introduced in those earlier works without independent validation or sensitivity tests in the present manuscript.
minor comments (1)
  1. Title: 'Theory(DFT)' is missing a space before the parenthesis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their comments on our manuscript. We address each major comment below and indicate where revisions will be made to improve clarity and verifiability.

read point-by-point responses

  1. Referee: Abstract: the central claim that the modified diag MSM DFT 'produces an accurate ground-state potential energy curve (PEC) for lithium hydride (LiH)' is unsupported by any numerical values, error metrics, dissociation energies, equilibrium distances, or direct comparisons to experiment or reference methods, rendering the accuracy assertion at the avoided crossing unverifiable.

    Authors: We agree that the abstract would be strengthened by including quantitative support. The manuscript body contains figures and discussion comparing the computed PEC to reference data, but the abstract itself does not quote specific metrics. We will revise the abstract to report key values such as the dissociation energy, equilibrium distance, and the energy error at the avoided crossing relative to experiment and high-level reference calculations. revision: yes

  2. Referee: Abstract: the reported accuracy for the LiH PEC rests on the two-orbital two-electron model (TOTEM) together with MSM and NOCI components defined in the authors' prior self-citations (J. Chem. Phys. 159, 244306 (2023) and 162, 144317 (2025)); the claim therefore reduces in part to quantities introduced in those earlier works without independent validation or sensitivity tests in the present manuscript.

    Authors: The present manuscript introduces the combination of diag MSM DFT with NOCI relaxation and demonstrates its performance on LiH, including at the ionic-to-open-shell avoided crossing. While the underlying TOTEM, MSM, and NOCI formalisms are developed in the cited prior works, the current paper provides the first application and validation of the relaxed version to a charge-transfer avoided-crossing problem. We will add a brief paragraph in the introduction summarizing the key prior elements and their assumptions to make the manuscript more self-contained. Additional sensitivity tests could be included if specific parameters are identified as critical. revision: partial

Circularity Check

0 steps flagged

Self-citations define base method but central result is independent validation on LiH

full rationale

The paper extends prior diag MSM DFT (defined in two self-cited works) by adding NOCI relaxation and applies the result to compute the LiH ground-state PEC, claiming accuracy through the ionic-to-open-shell avoided crossing. This constitutes an empirical test against the known physical behavior of LiH rather than a derivation that reduces to its own inputs by construction. No equations or steps are shown where a prediction equals a fitted parameter, where an ansatz is smuggled via self-citation, or where a uniqueness theorem is invoked to force the outcome. The self-citations supply the starting formalism but do not bear the load of the new accuracy claim, which rests on the explicit inclusion of relaxation and the numerical comparison for this molecule. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete and based on statements in the abstract; the method appears to inherit parameters and models from the two cited prior papers by the same group.

axioms (1)
  • domain assumption The two-orbital two-electron model (TOTEM) is adequate to describe the electronic structure changes at the ionic-to-open-shell-singlet avoided crossing in LiH.
    Invoked as the foundation for extending MSM DFT without symmetry arguments.

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discussion (0)

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Reference graph

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