{"id":"7eef05fe-b82a-43b8-9b77-3d686671612a","arxiv_id":"2504.14698","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Calculations predict 4f-to-OH electron transfer in DyOH and ErOH, yielding small electric dipoles and a conserved j = 15/2 manifold with about 1000 cm-1 zero-field splittings.","lead":"DyOH and ErOH are predicted to bond in a surprising way: an electron from the inner 4f shell moves to the hydroxyl group while the outer 6s pair stays intact. The ground states form a j = 15/2 spin system with about 1000 cm-1 splittings, relevant to ultracold molecules for precision measurements and quantum control.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Ground-state configuration claim rests on active space omitting 6p/5d; the paper's assertion of unchanged ordering upon inclusion lacks quantitative support.","rationale":"I read the paper in good faith. The computational work is internally consistent but the central novelty is the surprising 4f-to-OH charge transfer. The main methodological risk is that the active space used for the primary scans omits 6p/5d, and when these are added, the paper itself admits assignment difficulty. The assertion that ordering is unchanged lacks a direct quantitative test. The linearity assumption is also a concern, but it is imported from prior DFT and less directly tied to the novel electronic-structure claim; the configuration assignment is the core of the paper's contribution. A concrete check on configuration weights with the larger active space would settle whether the claim is robust. The reader's verdict of CONDITIONAL is appropriate, so I recommend no change, and I partially agree with the reader's weakest-assumption identification.","tokens_in":575,"tokens_out":3579,"duration_ms":85754,"concrete_test":"Perform RAS-SCF calculations for DyOH and ErOH at their equilibrium geometries with an active space that includes the 6p and 5d orbitals (as in Fig. 1(c) or Fig. 3), and compute the weight of the 4f^{n-1}6s^2+2p^6 configuration in the ground-state eigenvector. If this weight is below 50% or another configuration yields a higher occupation, the central bonding claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the ground state has a 4f^{n-1}6s^2+2p^6 configuration is based primarily on RAS-SCF calculations without 6p and 5d orbitals (Figs. 1a-b). When these orbitals are included, the paper states that mixing becomes strong and configuration assignment for excited states is difficult, but it does not demonstrate that the ground-state configuration weight remains dominant. The conclusion that 'differences in basis sets do not change our conclusion regarding the energy ordering of configurations' appears to be a qualitative assertion, not backed by a quantitative analysis of the ground-state wavefunction with 6p/5d. Since the bonding analysis and the subsequent effective spin-j=15/2 model hinge on this configuration being the unambiguous dominant character, the load-bearing assumption is that the restricted active space without 6p/5d captures the correct ground-state configuration ordering. This is not verified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript reports relativistic electronic-structure calculations for the low-lying states of DyOH and ErOH. Using RAS-SCF/RAS-SI and, for the ground-state geometry, CCSD(T), the authors propose that the dominant ground-state configuration is 4f^{n-1}6s^2 + 2p^6, i.e., an electron is transferred from the submerged 4f shell to OH while the 6s^2 pair stays intact, in contrast to the 6s-transfer picture for alkaline-earth monohydroxides and YbOH. They further show that the lowest 16 levels form an effective j = 15/2 manifold with zero-field splittings on the order of hc × 1000 cm−1, and they provide polynomial fits for the Ω dependence of energies, permanent electric dipole moments, and g factors, together with effective spin-spin Hamiltonians.","tokens_in":14974,"tokens_out":5813,"duration_ms":50997,"significance":"If the central bonding picture holds, the paper overturns the prevailing DFT-based model for lanthanide monohydroxides and gives a concrete, experimentally testable prediction: the lowest manifolds of DyOH and ErOH behave as j = 15/2 spin systems with g factors close to those of the excited Dy+ and Er+ ions. The paper has real strengths: it combines two complementary electronic-structure methods, it compares molecular g factors quantitatively with NIST tabulated atomic g factors, and it gives explicit polynomial expressions for energies, dipole moments, and magnetic moments, which makes the predictions falsifiable. The central conclusion is not circular: it is an output of the electronic-structure calculations and is supported by an external comparison to atomic g factors. The fitted coefficients in the effective spin-spin Hamiltonians are a modeling convenience rather than a source of circularity. The main risk is that the configuration assignment and the linear-geometry assumption both need additional quantitative support before the central claim can be considered established.","major_comments":[{"comment":"The ground-state configuration claim is load-bearing and is not quantitatively supported when the basis set is enlarged. Figures 1(a) and 1(b) are obtained from RAS-SCF calculations that explicitly exclude excitations into 6p and 5d molecular orbitals. The text states that including these orbitals \"significantly increases the level density and leads to strong mixing of the 6s, 6p, and 5d molecular orbitals and makes assignment by dominant molecular configurations for excited states difficult\" and then asserts that \"these differences in basis sets do not change our conclusion regarding the energy ordering of configurations.\" No wavefunction composition from the enlarged-basis calculation is reported. Since the paper's central bonding conclusion and the j = 15/2 model both rest on the 4f^{n-1}6s^2 + 2p^6 component remaining dominant in the ground state, please report the dominant-configuration weight of the lowest 16 states from the calculations with 6p and 5d included, and show quantitatively that the ordering conclusion is unchanged.","section":"II.A and Figs. 1(a)-(c)"},{"comment":"All potential-energy slices in Figs. 1(a) and 1(b) keep the molecule linear and fix the O-H distance at 1.80 a0; the linear equilibrium geometry is imported from the DFT study of Ref. [25] rather than tested here. The conserved quantum number Ω and the entire j = 15/2 effective-Hamiltonian analysis in Eqs. (3)-(12) are only defined for linear geometries. A bending potential scan at the RAS-SCF or CCSD(T) level, or at minimum a calculation of the bending harmonic frequency, is needed to confirm that the ground state is not bent. Without this check, a bent equilibrium geometry would invalidate the angular-momentum model.","section":"II.A and Methods"},{"comment":"The abstract states that \"analysis of the results from both methods\" supports the 4f-to-OH electron transfer, but the coupled-cluster calculation is used only to verify the Dy-O equilibrium distance (Sec. II.A) and no coupled-cluster state composition or excitation character is given. Please either provide CCSD(T)-level diagnostics that bear on the configuration assignment (for example T1 amplitudes or EOM-CCSD natural-orbital occupations) or rephrase the claim so that the configuration assignment is attributed to the RAS-SCF/RAS-SI calculations alone.","section":"Abstract and Methods"}],"minor_comments":[{"comment":"The introduction cites the CFOUR package as \"CFOUR [27?]\"; the question mark indicates an unresolved reference and should be corrected.","section":"I"},{"comment":"In the ErOH paragraph, \"the |Ω| = 1/2 leveld\" should read \"the |Ω| = 1/2 levels\".","section":"II.A"},{"comment":"The sentence beginning \"Similarly, panels (c) and (d) show...\" appears to duplicate panels (c) and (d), which were already used in the preceding sentence; presumably panels (b) and (d) are intended.","section":"Fig. 2 caption"},{"comment":"Just before Eq. (12), \"Withj = 15/2\" is missing a space; several other places also have nonstandard spacing such as \"Ω = 15 /2\" and should be cleaned up.","section":"II.C before Eq. (12)"},{"comment":"The data availability statement says datasets are available on reasonable request; for reproducibility, consider depositing the OpenMolcas and CFOUR input files in a permanent repository.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the manuscript fits the journal's scope and the central claim is plausible, but the active-space gap needs a targeted quantitative check before the bonding conclusion can be accepted. The linear-geometry assumption should also be explicitly tested or at least clearly labeled as an imported assumption. I would not reject on the current evidence, but the required additions go beyond simple copyediting."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a credible computational paper with a genuinely new bonding assignment for DyOH and ErOH. The claim that the 4f shell, not the 6s pair, donates the electron to OH contradicts the prior DFT picture and matches analogous behavior in DyF. The authors back the ground-state geometry with two independent methods (RAS-SCF/SI and CCSD(T)), and the computed molecular g factors line up with NIST atomic values for the j=15/2 Ln+ ions. That last comparison is a solid external check, not just an internal fit.\n\nThe paper is also honest about its limits. It states plainly that adding 6p/5d orbitals causes strong mixing and makes excited-state assignment difficult. Yet the lowest 16 states still form a clean |Omega| ladder in the larger basis (Fig. 1c), and Fig. 3 shows assignments are possible below roughly 10,000 cm^-1. The effective spin-spin Hamiltonians are fits to the ab initio data, so they are compact summaries rather than a circular argument; the reader's circularity burden of 4 feels too high.\n\nSoft spots, in proportion: the linear-geometry assumption is inherited from prior DFT and is never tested here. All scans keep Ln-O-H collinear. If the equilibrium is bent, Omega and the j=15/2 model would need reworking. For heavy lanthanides, linear is plausible, but it is an assumption. Second, the ground-state configuration weight in the full 6p/5d basis is asserted but not quantified. The paper says the energy ordering does not change when 6p/5d are added, but it does not show wavefunction overlaps or composition weights. That is a real gap, though not a fatal one: the energy ladder and g factors give indirect support. The stress-test concern is therefore partly answered, but a referee should ask for the quantitative analysis.\n\nData are not archived; \"available on request\" is weak for a computational paper and should be fixed.\n\nWho this is for: people working on ultracold polar and paramagnetic molecules, and on precision symmetry searches. It deserves a serious referee. My own verdict would be conditional acceptance, with requests for a quantitative ground-state composition analysis in the larger basis and a bending scan, or at least an explicit discussion of the linear assumption.","headline":"Credible computational claim that DyOH/ErOH bond via 4f-to-OH transfer with a j=15/2 manifold, though linear geometry is assumed and configuration weights in the full active space are asserted rather than quantified.","tokens_in":15564,"tokens_out":3005,"would_cite":true,"duration_ms":28729,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In DyOH and ErOH, the bond forms by transferring an electron from the submerged $4f$ shell to OH, leaving the $6s^2$ pair intact, and the lowest sixteen states behave as a $j=15/2$ spin system.","keywords":["lanthanide monohydroxides","DyOH","ErOH","4f chemical bonding","spin-orbit coupling","zero-field splittings","effective spin Hamiltonian","relativistic electronic structure"],"falsifier":"High-resolution spectroscopy of cold DyOH or ErOH would settle this: resolving a bending mode or a non-linear equilibrium geometry would destroy the $\\Omega$ label and the $j=15/2$ model, while observation of the predicted even-$\\Omega$ zero-field ladder, with $|\\Omega|=15/2$ lowest for DyOH and $|\\Omega|=1/2$ lowest for ErOH, would confirm it. A measurement of the permanent dipole moment near $0.2$-$0.3$ atomic units, rather than the near-fully-ionic value expected from $6s$ transfer, would also discriminate between the two bonding pictures.","tokens_in":14575,"feed_emoji":"⚛️","tokens_out":17246,"duration_ms":133158,"temperature":0.7,"pith_summary":"This paper asks which electrons actually form the bond in the heavy magnetic lanthanide monohydroxides DyOH and ErOH, and what the lowest electronic states look like near their linear equilibrium geometries. Using two independent relativistic electronic-structure methods, it establishes that the ground configuration is not the expected $6s$-electron transfer: instead, one electron from the submerged $4f$ shell moves to the OH group, while the closed $6s^2$ lone pair stays intact. The lowest sixteen states of both molecules form an effective spin ladder with total angular momentum $j=15/2$, split by zero-field energies of roughly $hc\\times 1000~\\mathrm{cm}^{-1}$, with $|\\Omega|=15/2$ lowest for DyOH and $|\\Omega|=1/2$ lowest for ErOH. The molecules are simultaneously paramagnetic and weakly polar, with a permanent dipole moment near $0.23$ atomic units, and their magnetic moments match those of the corresponding excited Ln$^+$ ions. This matters because lanthanide monohydroxides are candidate systems for precision tests of fundamental symmetries, and the $j=15/2$ effective Hamiltonian gives a compact, predictive description of the states such experiments would manipulate.","feed_headline":"Buried 4f electron, not 6s, forms the bond in DyOH and ErOH","feed_subtitle":"These magnetic molecules keep their 6s² pair intact and form a 16-state spin ladder split by ~1000 cm⁻¹.","key_machinery":"The object carrying the argument is the spin-tensor expansion of the effective electronic potential for a linear molecule, $\\hat{V} = a_0 + a_2 \\mathbf{T}^2(j,j)\\cdot \\mathbf{C}^2(\\hat{R}) + a_4 \\mathbf{T}^4(\\mathbf{T}^2(j,j),\\mathbf{T}^2(j,j))\\cdot \\mathbf{C}^4(\\hat{R}) + a_6 \\mathbf{T}^6(\\ldots)\\cdot \\mathbf{C}^6(\\hat{R})$, written for total electronic angular momentum $j=15/2$. Evaluated in the body-fixed frame with the symmetry axis along $z$, the angular-momentum reduction theorem reduces this operator to a polynomial in $\\Omega^2$ whose coefficients are fixed by the computed energies and the vector-coupling coefficients $\\langle j k \\Omega 0 | j \\Omega\\rangle$. This is what converts sixteen computed electronic levels into a few fitted parameters and makes possible effective Hamiltonians for rotation, electric-field, and magnetic-field control. The energies and moments themselves come from multi-configuration self-consistent-field calculations with spin-orbit coupling included by state interaction, checked against a relativistic coupled-cluster calculation; the good agreement of the molecular $g$-factors with atomic Dy$^+$ and Er$^+$ values is what justifies the $j=15/2$ ansatz.","core_discovery":"The central discovery is the bonding and spin structure of the ground states. In DyOH and ErOH the dominant configuration is $4f^{n-1}6s^2 + 2p^6$, with $n=10$ and $12$ respectively, meaning one electron is removed from the chemically 'buried' $4f$ shell and accepted by the OH $2p$ shell, leaving the outer $6s^2$ pair closed. This is the opposite of the earlier density-functional picture for lanthanide hydroxides, in which a $6s$ electron transfers and the $4f$ shell is nearly untouched. Both the multi-configurational self-consistent-field calculation and the relativistic coupled-cluster calculation place the $4f^{n-1}6s^2+2p^6$ states below the $4f^n6s+2p^6$ states, by up to about $hc\\times 10^4~\\mathrm{cm}^{-1}$. The lowest bundle of states consists of one degenerate doublet for each $|\\Omega|$ from $1/2$ to $15/2$, with energies that are even polynomials in $\\Omega$; treating the electrons as a conserved total angular momentum $j=15/2$ reproduces these energies through a tensor-operator expansion. Molecular $g$-factors are nearly $\\Omega$-independent and close to the $g$-factors of the excited Dy$^+$ and Er$^+$ ions, confirming that the open-shell physics is carried by the $4f$ shell. The permanent dipole moments are small, about $0.28\\,ea_0$ and $0.20\\,ea_0$ for DyOH and ErOH, so the bond is far from a textbook fully ionic transfer despite the electron transfer.","pith_inferences":["If the $j=15/2$ picture is generic, the same two-configuration competition should control other lanthanide monohydroxides, with the ground $|\\Omega|$ set by the $4f^{n-1}$ hole/particle structure; this is a testable prediction for the rest of the series.","The result suggests that 'submerged' $f$ electrons are not inert when a strong electron acceptor is present, so analogous $4f$-to-ligand transfer may appear in other lanthanide-containing molecules used for precision measurements, such as lanthanide fluorides or alkoxides.","A direct experimental test would be high-resolution spectroscopy of the lowest vibrational levels of DyOH and ErOH: the roughly $1000~\\mathrm{cm}^{-1}$ zero-field ladder should be resolvable, and any deviation from the even-$\\Omega$ polynomial, or a detected bending mode, would discriminate between this model and a bent or $6s$-bonded alternative."],"forward_implications":["The lowest 16 states of DyOH and ErOH can be compressed into a $j=15/2$ spin Hamiltonian with a handful of tensor coefficients, so Stark, Zeeman, and rotational maps of the low manifold follow without repeating electronic-structure calculations.","Because the molecules are both polar and paramagnetic, they are amenable to simultaneous electric- and magnetic-field control; the small dipole (about $0.23\\,ea_0$) means electric-field deceleration will be weak, while magnetic trapping and manipulation is the more natural route.","The bonding picture overturns the previous assumption that the $4f$ shell is chemically inert in lanthanide hydroxides, so any derived quantities built on the $6s$-transfer ionic model, such as dipole moments, vibrational constants, and sensitivity factors for CP-violation searches, need to be revisited.","The potential curves of the $\\Omega$ manifold are nearly parallel, implying that all 16 low states share almost the same Ln-O equilibrium distance and force constant, a property relevant to vibrational branching if optical cycling is attempted.","An electric-dipole-allowed excitation to the $4f^n6s6p(^{1}P)+2p^6$ configuration is identified with a transition dipole of $1.79\\,ea_0$, giving a concrete optical transition for future spectroscopy."],"supporting_citations":[{"why":"Supplies the earlier density-functional prediction of a linear Ln-OH geometry and 6s-electron transfer that the present study argues against.","marker":"[25]"},{"why":"Four-component relativistic configuration-interaction study of isoelectronic DyF showing analogous 4f participation in the bond.","marker":"[28]"},{"why":"Relativistic coupled-cluster study confirming the DyF bonding picture and connecting lanthanide molecules to nuclear Schiff-moment sensitivity.","marker":"[12]"},{"why":"Atomic spectroscopy dataset giving the experimental g-factors of the excited Dy+ and Er+ j=15/2 levels used to validate the molecular j=15/2 assignment.","marker":"[31]"},{"why":"Gives the pseudospin Hamiltonian formalism used to turn computed energies and moments into effective spin operators.","marker":"[35]"},{"why":"Defines the restricted-active-space self-consistent-field method used for the electronic-structure calculations.","marker":"[36]"},{"why":"Describes the state-interaction treatment of spin-orbit coupling used to obtain the relativistic adiabatic potentials.","marker":"[37]"},{"why":"Provides the relativistic atomic-natural-orbital basis sets for the lanthanide atoms in the self-consistent-field calculations.","marker":"[38]"}],"fun_headline_variants":["4f electron, not 6s, bonds in DyOH and ErOH","Lanthanide-OH bonds break the 6s-transfer rule","Buried 4f electron takes charge in DyOH and ErOH","16-state spin ladder from 4f bonding in DyOH/ErOH","Buried 4f electron takes the bond in DyOH/ErOH"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the molecule stays perfectly linear with the O-H length fixed, taken from an earlier density-functional study and never tested here; only the Ln-O distance is scanned, and if the true equilibrium is bent, the $\\Omega$ quantum number and the $j=15/2$ model no longer apply.","fun_headline_variants_meta":{"raw":{"variants":["4f electron, not 6s, bonds in DyOH and ErOH","Lanthanide-OH bonds break the 6s-transfer rule","Buried 4f electron takes charge in DyOH and ErOH","16-state spin ladder from 4f bonding in DyOH/ErOH","Buried 4f electron takes the bond in DyOH/ErOH"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000972,"raw_usage":{"total_tokens":4301,"prompt_tokens":1285,"completion_tokens":3016,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":901,"completion_tokens_details":{"reasoning_tokens":2917}},"tokens_in":901,"tokens_out":3016,"duration_ms":18167,"temperature":1.0,"reasoning_tokens":2917,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:42:21.620000+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"High-resolution spectroscopy of cold DyOH or ErOH would settle this: resolving a bending mode or a non-linear equilibrium geometry would destroy the $\\Omega$ label and the $j=15/2$ model, while observation of the predicted even-$\\Omega$ zero-field ladder, with $|\\Omega|=15/2$ lowest for DyOH and $|\\Omega|=1/2$ lowest for ErOH, would confirm it. A measurement of the permanent dipole moment near $0.2$-$0.3$ atomic units, rather than the near-fully-ionic value expected from $6s$ transfer, would also discriminate between the two bonding pictures.","supporting_citations":[{"cited_title":"On the linear geometry of lanthanide hydroxide (Ln-OH, Ln = La-Lu),","cited_arxiv_id":null,"evidence_quote":"Supplies the earlier density-functional prediction of a linear Ln-OH geometry and 6s-electron transfer that the present study argues against."},{"cited_title":"Electronic spectra of DyF studied by four-component relativistic configura- tion interaction methods,","cited_arxiv_id":null,"evidence_quote":"Four-component relativistic configuration-interaction study of isoelectronic DyF showing analogous 4f participation in the bond."},{"cited_title":"Relativistic exact two- component coupled-cluster study of molecular sensitivity factors for nuclear Schiff moments,","cited_arxiv_id":null,"evidence_quote":"Relativistic coupled-cluster study confirming the DyF bonding picture and connecting lanthanide molecules to nuclear Schiff-moment sensitivity."},{"cited_title":"Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their deriva- tion,","cited_arxiv_id":null,"evidence_quote":"Gives the pseudospin Hamiltonian formalism used to turn computed energies and moments into effective spin operators."},{"cited_title":"The re- stricted active space self-consistent-field method, imple- mented with a split graph unitary group approach,","cited_arxiv_id":null,"evidence_quote":"Defines the restricted-active-space self-consistent-field method used for the electronic-structure calculations."},{"cited_title":"The restricted active space (RAS) state interaction approach with spin–orbit coupling,","cited_arxiv_id":null,"evidence_quote":"Describes the state-interaction treatment of spin-orbit coupling used to obtain the relativistic adiabatic potentials."},{"cited_title":"New relativistic atomic natural orbital basis sets for lanthanide atoms with ap- plications to the Ce diatom and LuF 3,","cited_arxiv_id":null,"evidence_quote":"Provides the relativistic atomic-natural-orbital basis sets for the lanthanide atoms in the self-consistent-field calculations."}],"review_version":1}