{"id":"73dd1173-61d0-44c4-b5c4-f50a14a43c68","arxiv_id":"1908.07081","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Singles-only response methods (CIS/TDHF/TDDFT) produce qualitatively wrong excited-state surfaces beyond the Coulson-Fischer point because the physical triplet becomes a double excitation from the spin-polarized reference.","lead":"This paper shows that excited-state surfaces from CIS, TDHF, and TDDFT develop sharp kinks and wrong dissociation behavior when the ground state becomes spin-polarized past the Coulson-Fischer point. The failure is traced to the absence of double excitations, with analytic and numerical evidence across H2, NH3, C2H6, and LiH.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The TDHF zero-mode and M_S=0 double-excitation claims are sound; the real soft spot is that the abstract/conclusion state the local-TDDFT M_S=±1 result without the 'collinear kernel' qualifier used in Sec III.","rationale":"The reader identifies the analytic zero-mode proof's transfer to polyatomics as the weakest assumption. That transfer is actually supported by the GHF spin-rotation Goldstone-mode argument, which is general for any spin-polarized UHF reference, not merely a numerical observation on NH3, C2H6, and LiH. The more consequential gap is the scoping of the local-TDDFT spin-flip statement. In Sec III the authors are careful to say 'collinear exchange-correlation kernels,' but the abstract and conclusion drop that qualifier, claiming that local functionals cause M_S=±1 T1 TDDFT states to resemble the unphysical M_S=0 shape. For a noncollinear spin-density-functional formulation, the transverse xc kernel is nonzero and should enforce invariance under global spin rotation, restoring the Goldstone zero mode and changing the M_S=±1 T1 surface. The Appendix A proof and the GHF argument are sound, so the main CIS/TDHF findings stand; the conditional is only a precision requirement on the TDDFT statement. A single noncollinear PBE spin-flip TDDFT calculation on stretched H2 would settle whether the abstract needs the 'collinear' qualifier.","tokens_in":20056,"tokens_out":31194,"duration_ms":330972,"concrete_test":"Run a noncollinear spin-flip TDDFT/TDA calculation for stretched H2 (aug-cc-pVTZ) with PBE across the CF point, using an xc kernel that includes the transverse spin-stiffness term. Compare the M_S=±1 T1 surface with the collinear PBE panel of Fig 8. If the noncollinear PBE T1 becomes degenerate with the S0 state (zero excitation energy) beyond the CF point rather than rising like the M_S=0 curve, then the paper's 'local functionals cause M_S=±1 TDDFT to mirror M_S=0' conclusion is false as stated and must be qualified to collinear kernels.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central mechanism is well supported. The Appendix A proof for minimal-basis H2 is internally consistent, and the GHF spin-rotation Goldstone-mode argument gives a general reason why TDHF spin-flip T1 excitation energies vanish beyond the CF point, so transfer to NH3, C2H6, and LiH is not merely numerical. The M_S=0 T1 becoming a double excitation follows directly from the singles-only CI space and is demonstrated cleanly. The load-bearing weakness is the unqualified statement that local exchange-correlation functionals make M_S=±1 TDDFT/TDA T1 surfaces mirror the unphysical M_S=0 shape. Section III explicitly restricts the calculation to collinear xc kernels, where the local f_xc contribution to the spin-flip block vanishes. A noncollinear spin-density-functional kernel is not zero in that block; since a properly constructed local functional is invariant under global spin rotations, its transverse kernel should reinstate the Goldstone mode and change the M_S=±1 T1 surface, likely restoring the S0 degeneracy beyond the CF point. The abstract and conclusion omit this qualifier, so as written they overgeneralize a result that is established only for collinear spin-flip TDDFT/TDA.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript investigates how the spin polarization of the unrestricted ground-state determinant beyond the Coulson-Fischer (CF) point affects excited-state potential energy surfaces computed with configuration interaction singles (CIS), time-dependent Hartree-Fock (TDHF), and linear-response TDDFT/TDA. The authors use minimal-basis H2 as an exactly solvable two-orbital, two-electron model and supplement it with numerical calculations on H2, NH3, C2H6, and LiH in extended basis sets. They show that beyond the CF point the M_S=0 lowest triplet T1 state becomes a double excitation relative to the spin-polarized reference, so that singles-only response methods produce kinked surfaces that connect to incorrect dissociation limits. They further demonstrate that M_S=±1 CIS T1 states provide better dissociation limits but suffer from a broken degeneracy and a fragment-dependent spin-flip error (Delta_alpha_beta), while M_S=±1 TDHF T1 states merge with the ground state, giving zero excitation energy beyond the CF point. For TDDFT/TDA, the authors argue that with collinear exchange-correlation kernels the local f_xc contribution to the spin-flip block vanishes, causing the M_S=±1 T1 surfaces to resemble the unphysical M_S=0 surface. The paper traces these failures to the absence of double excitations and to the structure of the spin-flip response blocks.","tokens_in":20299,"tokens_out":8825,"duration_ms":98894,"significance":"This is a valuable and timely systematic characterization of failures in the most widely used excited-state methods, and the findings, if correct, should guide practitioners in choosing between spin-restricted and spin-unrestricted references for photochemical studies. The analytical Appendix A is a genuine strength: it provides a clean, parameter-free derivation using the standard UHF orbital-stability condition and is benchmarked against FCI for H2. The spin-rotation Goldstone-mode argument gives a general physical reason for the zero TDHF spin-flip excitation energies, so the transfer of the conclusion to polyatomic molecules is not purely numerical. The paper also introduces a quantifiable CIS degeneracy error (Delta_alpha_beta) that is likely to be useful beyond the specific examples studied. The main caveat is that the TDDFT/TDA result for local functionals is established only in the collinear-kernel approximation, a qualification that is present in Section III but missing from the abstract and conclusion.","major_comments":[{"comment":"The abstract and the concluding section state that 'local exchange-correlation functionals' cause the M_S=±1 T1 TDDFT/TDA surfaces to resemble the unphysical M_S=0 surface. Section III, however, explicitly restricts the argument to collinear exchange-correlation kernels, where the local f_xc contribution to the spin-flip block vanishes by spin symmetry. For a noncollinear spin-density-functional kernel the transverse f_xc is generally nonzero, so a properly constructed local functional invariant under global spin rotations should restore the Goldstone mode and hence the S0/T1 degeneracy beyond the CF point. The abstract and conclusion should therefore be qualified to say 'local functionals within the collinear-kernel approximation' (or 'collinear local kernels'), with a sentence noting the expected difference for noncollinear spin-flip TDDFT implementations.","section":"Abstract and Conclusion (cf. Sec. III)"}],"minor_comments":[{"comment":"The sentence 'TDHF further worsens the CIS reuslts' contains a typo; it should read 'results'.","section":"Sec. IV, text around Fig. 3"},{"comment":"The phrase 'via a a rapidly increasing concave segment' contains a duplicated article; it should read 'via a rapidly increasing concave segment'.","section":"Sec. VII, Conclusion"},{"comment":"The captions note that 'small state crossing induced discontinuities might be present on the top surface'; the manuscript would be clearer if the ⟨S²⟩ labeling of TDHF states (taken from the corresponding CIS states) were described as a diagnostic rather than a rigorous assignment, especially where crossings are possible.","section":"Figs. 4 and 5 captions"},{"comment":"The table reports asymptotic T1 energies relative to ROHF and UHF fragments, but the Computational Details state that all internal coordinates other than the stretched bond are frozen; the table caption should state explicitly that the fragment energies are for the unrelaxed geometries used in the scans.","section":"Table II"},{"comment":"The statement that local exchange-correlation contributions render TDA identical to full TDDFT within the spin-flip block is correct for collinear kernels, but it would benefit from the same qualifier used elsewhere in the paper, to avoid confusion with noncollinear spin-flip implementations.","section":"Sec. III, paragraph after Eq. (16)"}],"recommendation":"minor_revision","confidential_remarks":"The paper is sound in its derivations and clearly within the scope of the journal. The only substantive concern is the overgeneralization of the local-functional TDDFT spin-flip result in the abstract and conclusion; this is a local but important fix. I would recommend accepting after the authors add the collinear-kernel qualifier and a brief clarifying sentence about noncollinear kernels. There are no concerns about citation practices or novelty disclosure."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a solid paper that deserves a serious referee. The central result — that spin polarization of the UHF/UKS reference turns the M_S=0 T1 into a double excitation, while spin-flip TDHF T1 goes exactly to zero excitation energy past the CF point — is new and well supported. The minimal-basis H2 analysis is clean; the Appendix's analytic zero-eigenvalue proof follows from the standard Szabo-Ostlund stability condition, and the GHF Goldstone-mode argument gives a general reason to expect the same in polyatomics. The numerical examples (H2, NH3, C2H6, LiH) are consistent, and the Table I degeneracy error Δαβ for spin-flip CIS fragments is a useful quantitative contribution. I give real credit for the systematization: the paper explains a failure mode that practitioners will hit, and it does so with the mechanism made explicit rather than just 'TDDFT is bad at dissociation'.\n\nSoft spots, in proportion. The biggest is a precision problem in the abstract and conclusion. Section III correctly restricts the spin-flip TDDFT analysis to collinear xc kernels, where the local f_xc contribution vanishes. But the abstract says 'Use of local exchange-correlation functionals causes M_S=±1 T1 TDDFT states to resemble their unphysical M_S=0 counterpart.' That is only established for collinear kernels; a noncollinear local functional, being spin-rotation invariant, would contribute to the spin-flip block and should reinstate the Goldstone mode. As written, the abstract overgeneralizes. The conclusion does the same ('typical TDDFT/TDA'). That should be fixed by adding 'collinear' before 'local exchange-correlation functionals'. Everything else is either minor or acknowledged: transfer of the zero-mode result to NH3/C2H6 is by numerical observation plus the general GHF argument, not a formal proof, but the paper says as much; possible small state-crossing discontinuities are flagged in the captions; frozen-geometry polyatomic PESs are a reasonable simplification.\n\nWho this is for: anyone doing photochemistry or excited-state PESs with TDDFT/CIS on open-shell or stretched-bond systems. It won't change what code you run, but it will make you check M_S components explicitly and worry less about a 'kink' you might have thought was noise. I'd cite it.\n\nRecommendation: accept, with the abstract/conclusion qualification as a required minor revision. The central argument holds up.","headline":"A careful, mostly convincing mechanistic account of why single-excitation response methods break down past the Coulson-Fischer point; just don't let the abstract's local-functional claim outrun the collinear-kernel caveat.","tokens_in":20819,"tokens_out":1761,"would_cite":true,"duration_ms":18527,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper establishes that singles-only excited-state methods (CIS, TDHF, TDDFT) produce qualitatively wrong lowest-triplet surfaces for single-bond dissociation once the ground state spin-polarizes beyond the Coulson–Fischer point…","keywords":["Coulson-Fischer point","spin polarization","TDDFT","configuration interaction singles","TDHF","excited states","single bond dissociation","double excitations"],"falsifier":"Compute the full singles-plus-doubles (CISD or CC2) T$_1$ surface for a stretched single bond using the same unrestricted reference: if the kink and the rise to the charge-transfer limit persist despite inclusion of double excitations, the paper's diagnosis would be refuted; if the surface becomes smooth and reaches the neutral-fragment limit, the diagnosis is confirmed. A second check is to compare spin-flip TDHF excitation energies for a stretched bond whose unrestricted solution is artificially forced to violate the UHF stability condition, where the claimed zero mode should become nonzero.","tokens_in":19868,"feed_emoji":"🧪","tokens_out":7466,"duration_ms":69054,"temperature":0.7,"pith_summary":"This paper shows that the most widely used excited-state methods—configuration interaction singles (CIS), time-dependent Hartree–Fock (TDHF), and linear-response TDDFT—produce qualitatively wrong lowest-triplet surfaces for single-bond dissociation once the ground-state determinant becomes spin-polarized at the Coulson–Fischer point. Because the spin-polarized ground state is a singlet–triplet mixture, the true $M_S=0$ triplet lies one double excitation away from it, outside the reach of any singles-only response theory; the computed T$_1$ surface therefore kinks, acquires unphysical concave curvature, and runs to a charge-transfer limit rather than to neutral fragments. The paper also proves that the $M_S=\\pm1$ spin-flip TDHF triplet becomes exactly degenerate with the ground state beyond the Coulson–Fischer point, giving zero excitation energy, while the analogous TDDFT states mirror the $M_S=0$ artifact for local functionals. A sympathetic reader should care because photodissociation and photochemistry simulations routinely rely on these methods, and the failure mechanism—missing double excitations in a spin-polarized reference—is generic rather than functional-specific.","feed_headline":"Beyond the Coulson-Fischer point, TDDFT loses the lowest triplet","feed_subtitle":"Spin polarization hides the T1 state inside a double excitation, so singles-only methods produce kinked, wrong surfaces.","key_machinery":"The central machinery is the two-orbital, two-electron minimal-basis H$_2$ model parametrized by the orbital-mixing angle $\\theta$, with the restricted orbitals recovered at $\\theta = 0$ and fully spin-polarized atomic orbitals at $\\theta = \\pi/4$. In this model every relevant Slater determinant can be written explicitly, so the paper can show exactly which singles survive spin polarization and which character the omitted double excitation carries. The carrying identity is the spin-flip block relation $A = -B$ derived in Appendix A, which follows from the UHF stationarity condition (Eq. A12, from the standard orbital-stability equation of Ref 37); it forces the TDHF spin-flip excitation eigenvalue to zero beyond the Coulson–Fischer point. The same toy model supplies the mechanism for every larger molecule studied: spin polarization moves the T$_1$ character into a double excitation, and the kink-and-rise shape of the computed surfaces follows from singles-only response to that reference.","core_discovery":"The central claim is that beyond the Coulson–Fischer point, where the optimized UHF/UKS ground state develops unequal $\\alpha$ and $\\beta$ orbitals, the lowest triplet excitation as computed by singles-only response theories is not a continuation of the physical T$_1$ state. In the minimal-basis H$_2$ model the authors show analytically that the $M_S=0$ single excitations from the spin-polarized determinant are charge-transfer singlets, so the covalent triplet character that was present before the Coulson–Fischer point now resides in the double excitation, which CIS/TDHF/TDDFT omit. The $M_S=\\pm1$ spin-flip block does retain the triplet, and for CIS it reaches the correct neutral-fragment limit in H$_2$, but TDHF spin-flip solutions collapse onto the ground state (zero excitation energy) because the $A$ and $B$ matrices of the spin-flip block satisfy $A = -B$ once the ground state obeys the UHF stability condition; for local functionals the spin-flip TDDFT excitation reduces to an orbital-energy difference and reproduces the $M_S=0$ artifact. The paper concludes that only restricted CIS gives a reasonable T$_1$ surface, at the price of a badly compromised restricted ground state.","pith_inferences":["The same mechanism should affect any response method that truncates excitations at singles, including CIS(D), CC2, and algebraic diagrammatic construction at lowest order, when the reference is spin-polarized; the paper hints at this but does not test it.","The zero excitation energy of spin-flip TDHF beyond the Coulson–Fischer point may be reinterpreted as a Goldstone-like zero mode of the broken spin-rotation symmetry; a testable consequence is that a functional approximant with non-collinear spin response would restore a nonzero spin-flip gap.","The degeneracy error $\\Delta_{\\alpha\\beta}$ suggests a simple diagnostic: for a stretched radical-pair system, compare CIS spin-flip excitation energies from the two subspaces; a large splitting flags unreliable T$_1$ surfaces and could be used as a black-box warning in production calculations.","For practical photochemistry, spin-restricted references combined with methods that include at least doubles (or non-orthogonal CI) may be a more robust route than unrestricted TDDFT for bond-breaking regions; the paper's holomorphic HF remark points in that direction."],"forward_implications":["Beyond the Coulson–Fischer point, the $M_S=0$ lowest triplet computed by CIS/TDHF/TDDFT should not be trusted for photodissociation dynamics; its apparent local minimum is an artifact of missing double excitations.","The $M_S=\\pm1$ spin-flip TDHF triplet surface is degenerate with the ground state beyond the Coulson–Fischer point, so any TDHF-based interpretation of triplet photochemistry in stretched bonds is invalid there.","For local functionals, the spin-flip TDDFT/TDA triplet surfaces replicate the unphysical $M_S=0$ shape, because the local xc kernel contributes nothing to the spin-flip block and only orbital energy differences remain.","Restricted CIS, despite a badly contaminated ground state, gives qualitatively reasonable T$_1$ surfaces for single bond dissociations and may be safer than unrestricted response for these states.","CIS spin-flip T$_1$ states from unrestricted references are non-degenerate beyond the Coulson–Fischer point for most bonds, incurring a fragment degeneracy error $\\Delta_{\\alpha\\beta}$ that vanishes only for hydrogen-like fragments."],"supporting_citations":[{"why":"Supplies the UHF orbital-stability equation (Eq. 3.374) used in Appendix A to prove that the spin-flip TDHF excitation is zero beyond the Coulson–Fischer point.","marker":"[37]"},{"why":"Gives the TDDFT/TDHF response equations and the stability-eigenvalue connection that frames the entire analysis.","marker":"[4]"},{"why":"Defines the Coulson–Fischer point as the onset of spin polarization in stretched bonds, the object of study in this paper.","marker":"[35]"},{"why":"Provides the orbital stability conditions and the GHF stability Hessian whose zero modes underlie the spin-flip zero eigenvalues.","marker":"[32]"},{"why":"Establishes the zero-eigenvalue normal modes of the GHF stability matrix from the arbitrary direction of spin density, the general argument for zero spin-flip TDHF energies.","marker":"[55]"},{"why":"Defines CIS as the singles-only excited-state method whose failure beyond the Coulson–Fischer point is characterized.","marker":"[11]"},{"why":"Supplies the PBE local functional whose spin-flip block lacks exchange-correlation kernel contributions, explaining the corresponding TDDFT artifact.","marker":"[51]"},{"why":"Supplies the LRC-ωPBEh range-separated hybrid functional used to show that the spin-flip TDDFT artifact persists for hybrids with local correlation parts.","marker":"[53]"},{"why":"Documents the spurious zero singlet excitation energy at dissociation for symmetric bonds in restricted TDDFT, a related failure of linear response.","marker":"[39]"}],"fun_headline_variants":["TDDFT's triplet vanishes at the Coulson-Fischer point","No double excitations means no physical triplet","CIS, TDHF, TDDFT fail at Coulson-Fischer point","Spin polarization hides the triplet in double excitations","Single-bond dissociation: TDDFT excited states go wrong"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof that spin-flip TDHF triplets have exactly zero excitation energy rests on the optimized unrestricted ground state satisfying the UHF orbital-stability equation precisely; for molecules beyond H$_2$ this is transferred by numerical observation rather than proven.","fun_headline_variants_meta":{"raw":{"variants":["TDDFT's triplet vanishes at the Coulson-Fischer point","No double excitations means no physical triplet","CIS, TDHF, TDDFT fail at Coulson-Fischer point","Spin polarization hides the triplet in double excitations","Single-bond dissociation: TDDFT excited states go wrong"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.002082,"raw_usage":{"total_tokens":8199,"prompt_tokens":1153,"completion_tokens":7046,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":769,"completion_tokens_details":{"reasoning_tokens":6962}},"tokens_in":769,"tokens_out":7046,"duration_ms":54569,"temperature":1.0,"reasoning_tokens":6962,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:26:36.705766+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full singles-plus-doubles (CISD or CC2) T$_1$ surface for a stretched single bond using the same unrestricted reference: if the kink and the rise to the charge-transfer limit persist despite inclusion of double excitations, the paper's diagnosis would be refuted; if the surface becomes smooth and reaches the neutral-fragment limit, the diagnosis is confirmed. A second check is to compare spin-flip TDHF excitation energies for a stretched bond whose unrestricted solution is artificially forced to violate the UHF stability condition, where the claimed zero mode should become nonzero.","supporting_citations":[{"cited_title":"Szabo \\ and\\ author N","cited_arxiv_id":null,"evidence_quote":"Supplies the UHF orbital-stability equation (Eq. 3.374) used in Appendix A to prove that the spin-flip TDHF excitation is zero beyond the Coulson–Fischer point."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Coulson–Fischer point as the onset of spin polarization in stretched bonds, the object of study in this paper."},{"cited_title":"Seeger \\ and\\ author J","cited_arxiv_id":null,"evidence_quote":"Provides the orbital stability conditions and the GHF stability Hessian whose zero modes underlie the spin-flip zero eigenvalues."},{"cited_title":"Cui , author I","cited_arxiv_id":null,"evidence_quote":"Establishes the zero-eigenvalue normal modes of the GHF stability matrix from the arbitrary direction of spin density, the general argument for zero spin-flip TDHF energies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines CIS as the singles-only excited-state method whose failure beyond the Coulson–Fischer point is characterized."},{"cited_title":"Giesbertz \\ and\\ author E","cited_arxiv_id":null,"evidence_quote":"Documents the spurious zero singlet excitation energy at dissociation for symmetric bonds in restricted TDDFT, a related failure of linear response."}],"review_version":1}