Pith. sign in

REVIEW 3 major objections 5 minor 45 references

Unconventional Chemical Bonding of Lanthanide-OH Molecules

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2504.14698 v1 pith:CICL7T2S submitted 2025-04-20 physics.atom-ph quant-ph

Jacek K{l}os , Eite Tiesinga , Lan Cheng , Svetlana Kotochigova This is my paper · ORCID
classification physics.atom-phquant-ph
keywords lanthanidemonohydroxidesDyOHEr4fchemicalbondingspin-orbitcouplingzero-fieldsplittingseffectivespinHamiltonianrelativisticelectronicstructure
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [II.A and Figs. 1(a)-(c)] 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.
  2. [II.A and Methods] 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.
  3. [Abstract and Methods] 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.
minor comments (5)
  1. [I] The introduction cites the CFOUR package as "CFOUR [27?]"; the question mark indicates an unresolved reference and should be corrected.
  2. [II.A] In the ErOH paragraph, "the |Ω| = 1/2 leveld" should read "the |Ω| = 1/2 levels".
  3. [Fig. 2 caption] 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.
  4. [II.C before Eq. (12)] 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.
  5. [Data availability] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ab initio configuration and Omega assignments are derived from electronic-structure calculations, and the tensor Hamiltonians are explicitly fits rather than predictions.

full rationale

The paper's central bonding claim (4f electron transfer to OH leaving 6s2 intact) and the ground-state Omega assignments follow from RAS-SCF/RAS-SI and CCSD(T) electronic-structure calculations; no fitted parameter or self-citation is used to produce these results. The effective tensor operators in Eqs. (3), (7), and (10) are explicitly presented as descriptions of already-computed zero-field splittings, dipole moments, and magnetic moments, with coefficients obtained by comparison with polynomial fits or least-squares fits to the same data; they are not used to derive those quantities, so no fitted input is renamed as a prediction. The j=15/2 assignment is justified by independent level counting (one state for each |Omega| up to 15/2) and by comparison with externally tabulated NIST atomic g factors of Dy+ and Er+, which provides an independent cross-check. The cited DyF analogies (Refs. [28] and [12]) are supporting context, not load-bearing for the DyOH/ErOH conclusions. The linear-geometry premise and the active-space limitation regarding 6p/5d orbitals are substantive correctness risks, but they are assumptions and possible inaccuracies, not circular reductions: the calculation is not defined in terms of the conclusion it draws.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The load-bearing items are the assumed linear geometry, the neglect of 6p/5d orbitals in the main active-space scans, the use of Ω and j = 15/2 as good quantum numbers, and the Born-Oppenheimer framework. Polynomial and g-factor coefficients are fits to the computed data, not first-principles constants.

free parameters (5)
  • ZFS polynomial coefficients for DyOH (Eq. 1) = 3407.59, -25.6016, -1.30506, 0.012168 cm-1
    Fit to RAS-SCF computed zero-field splittings; used to construct the effective Hamiltonian of Eq. (3). Not derived from first principles.
  • ZFS polynomial coefficients for ErOH (Eq. 2) = -3.65105, 14.5863, -0.204103, 0.00388586 cm-1
    Fit to RAS-SCF computed zero-field splittings; used for the ErOH effective spin model.
  • Adjustable g1 for transition magnetic moments (Eq. 12) = 1.32691 for DyOH, 1.19430 for ErOH
    Fit to computed transition magnetic moments assuming j = 15/2. The fitted values are then compared with atomic g factors.
  • Permanent dipole polynomial coefficients (Eqs. 5 and 6) = DyOH: 0.264395, 1.45857e-4, 3.65151e-5, -4.44832e-7; ErOH: 0.205989, -3.53168e-4
    Polynomial fits to computed permanent dipole moments as functions of Ω.
  • gmol polynomial coefficients for DyOH (Eq. 9) = 1.30001, -0.00679486, 2.35401e-4, -1.88066e-6
    Fit to computed molecular g factors as a function of Ω; no satisfactory fit is reported for ErOH.
assumptions (4)
  • domain assumption DyOH and ErOH have linear equilibrium geometries with O-H fixed at 1.80 a0 and only Ln-O scanned.
    All potentials and Ω labels assume collinear Ln-O-H; no bending potential is computed. Linearity is imported from prior DFT.
  • domain assumption Ω and total molecular j = 15/2 are good quantum numbers for the lowest 16 states.
    Used to build Eq. (3) and the magnetic-moment model; supported by level counting and atomic g factors, not by a derivation from the full Hamiltonian.
  • domain assumption RAS-SCF without 6p and 5d orbitals captures the ground-state configuration ordering.
    Main potential curves and configuration assignments use CAS active spaces with 4f and 6s only; adding 6p/5d creates strong mixing and makes excited-state assignment difficult.
  • standard math The Born-Oppenheimer approximation holds for the states computed.
    All adiabatic potentials use the Born-Oppenheimer framework even though the authors note it can break down for heavy triatomic molecules.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Unconventional Chemical Bonding of Lanthanide-OH Molecules." pith.science (2026). https://pith.science/paper/CICL7T2S

@misc{pith2026250414698,
  author       = {Pith},
  title        = {Pith review of: Unconventional Chemical Bonding of Lanthanide-OH Molecules},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CICL7T2S}},
  note         = {Machine review of arXiv:2504.14698}
}
abstract

We present a theoretical study of the low lying adiabatic relativistic electronic states of lanthanide monohydroxide (Ln-OH) molecules near their linear equilibrium geometries. We focus on heavy, magnetic DyOH and ErOH relevant to fundamental symmetry tests. We use a restricted-active-space self-consistent field method combined with spin-orbit coupling as well as a relativistic coupled-cluster method. In addition, electric dipole and magnetic moments are computed with the self-consistent field method. Analysis of the results from both methods shows that the dominant molecular configuration of the ground state is one where an electron from the partially filled and submerged 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most 6s$^2$ lone electron pair of the lanthanide atom intact in sharp contrast to the bonding in alkaline-earth monohydroxides and YbOH, where an electron from the outer-most s shell moves to the hydroxyl group. For linear molecules the projection of the total electron angular momentum on the symmetry axis is a conserved quantity with quantum number $\Omega$ and we study the polynomial $\Omega$ dependence of the energies of the ground states as well as their electric and magnetic moments. We find that the lowest energy states have $|\Omega|=15/2$ and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these $\Omega$ states is approximately $hc\times 1\,000$~cm$^{-1}$. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units. The magnetic moments are closely related to that of the corresponding atomic Ln$^+$ ion in an excited electronic state. We also realize that the total electron angular momentum is to good approximation conserved and has a quantum number of 15/2 for both triatomic molecules.

Figures

Figures reproduced from arXiv: 2504.14698 by the authors.

Figure 1
Figure 1. FIG. 1. Potential energies of the 4f [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Isosurfaces of electronic Kohn-Sham molecular orbitals (MOs) for DyOH (panels (a) and (b)) and ErOH (panels (c) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Electronic eigenenergies (colored circles) of DyOH [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Permanent dipole moment in atomic units [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: (b) shows the transition magnetic moments between states with projection quantum numbers Ω and Ω − 1 of the c = 4f96s2+2p6 configuration of DyOH and the 4f116s2+2p6 configuration of ErOH. That is, we show matrix elements ⟨c, Ω|µ+1|c, Ω − 1⟩/µB (11) as function of Ω ≥ 1…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 43 canonical work pages

  1. [25]

    On the linear geometry of lanthanide hydroxide (Ln-OH, Ln = La-Lu),

    H. Harb, L. M. Thompson, and H. P. Hratchian, “On the linear geometry of lanthanide hydroxide (Ln-OH, Ln = La-Lu),” Phys. Chem. Chem. Phys. 21, 21890–21897 (2019)

    work page 2019

  2. [1]

    Strongly dipolar Bose-Einstein condensate of Dyspro- sium,

    M. Lu, N. Q. Burdick, S. H. Youn, and B. L. Lev, “Strongly dipolar Bose-Einstein condensate of Dyspro- sium,” Phys. Rev. Lett. 107, 190401 (2011)

    work page 2011

  3. [2]

    Quantum degen- erate dipolar Fermi gas,

    M. Lu, N. Q. Burdick, and B. L. Lev, “Quantum degen- erate dipolar Fermi gas,” Phys. Rev. Lett. 108, 215301 (2012)

    work page 2012

  4. [3]

    Narrow-line magneto-optical trap for erbium,

    A. Frisch, K. Aikawa, M. Mark, A. Rietzler, J. Schindler, E. Zupaniˇ c, R. Grimm, and F. Ferlaino, “Narrow-line magneto-optical trap for erbium,” Phys. Rev. A 85, 051401 (2012)

    work page 2012

  5. [4]

    Bose-einstein condensation of erbium,

    K. Aikawa, A. Frisch, M. Mark, S. Baier, A. Rietzler, R. Grimm, and F. Ferlaino, “Bose-einstein condensation of erbium,” Phys. Rev. Lett. 108, 210401 (2012)

    2012

  6. [5]

    Toward surface orbitronics: Giant orbital magnetism from the orbital Rashba effect at the surface of sp- metals,

    D. Go, J.-P. Hanke, P. M. Buhl, F. Freimuth, G. Bihlmayer, H.-W. Lee, Y. Mokrousov, and S. Bl¨ ugel, “Toward surface orbitronics: Giant orbital magnetism from the orbital Rashba effect at the surface of sp- metals,” Scientific Reports 7, 46742 (2017)

    work page 2017

  7. [6]

    Orbi- tronics: The intrinsic orbital current in p-doped silicon,

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, “Orbi- tronics: The intrinsic orbital current in p-doped silicon,” Phys. Rev. Lett. 95, 066601 (2005)

    work page 2005

  8. [7]

    Laser- coolable polyatomic molecules with heavy nuclei,

    T. A. Isaev, A. V. Zaitsevskii, and E. Eliav, “Laser- coolable polyatomic molecules with heavy nuclei,” J. Phys. B 50, 225101 (2017)

    work page 2017

Show all 45 references
  1. [8]

    Sisyphus laser cooling of a polyatomic molecule,

    I. Kozyryev, L. Baum, K. Matsuda, B. L. Augenbraun, L. Anderegg, A. P. Sedlack, and J. M. Doyle, “Sisyphus laser cooling of a polyatomic molecule,” Phys. Rev. Lett. 118, 173201 (2017)

    2017

  2. [9]

    Hypermetallic po- lar molecules for precision measurements,

    M. J. O’Rourke and N. R. Hutzler, “Hypermetallic po- lar molecules for precision measurements,” Phys. Rev. A 100, 022502 (2019)

    2019

  3. [10]

    Polyatomic molecules as quantum sen- sors for fundamental physics,

    N. R. Hutzler, “Polyatomic molecules as quantum sen- sors for fundamental physics,” Quantum Sci. Technol. 5, 044011 (2020)

    2020

  4. [11]

    Molecular asymmetry and optical cycling: Laser cooling asymmetric top molecules,

    B. L. Augenbraun, J. M. Doyle, T. Zelevinsky, and I. Kozyryev, “Molecular asymmetry and optical cycling: Laser cooling asymmetric top molecules,” Phys. Rev. X 10, 031022 (2020)

    2020

  5. [12]

    Relativistic exact two- component coupled-cluster study of molecular sensitivity factors for nuclear Schiff moments,

    T. Chen, C. Zhang, L. Cheng, K. B. Ng, S. Malbrunot- Ettenauer, V. V. Flambaum, Z. Lasner, J. M. Doyle, P. Yu, C. J. Conn, C. Zhang, N. R. Hutzler, A. M. Jayich, B. Augenbraun, and D. DeMille, “Relativistic exact two- component coupled-cluster study of molecular sensitivity fa...

    2024

  6. [13]

    Col- lective T- and P-odd electromagnetic moments in nuclei with octupole deformations,

    N. Auerbach, V. V. Flambaum, and V. Spevak, “Col- lective T- and P-odd electromagnetic moments in nuclei with octupole deformations,” Phys. Rev. Lett. 76, 4316– 4319 (1996)

    1996

  7. [14]

    Nuclear time-reversal vio- lation and the Schiff moment of 225Ra,

    J. Dobaczewski and J. Engel, “Nuclear time-reversal vio- lation and the Schiff moment of 225Ra,” Phys. Rev. Lett. 94, 232502 (2005)

    2005

  8. [15]

    Actinide and lanthanide molecules to search for strong CP-violation,

    L. V. Skripnikov, N. S. Mosyagin, A. V. Titov, and V. V. Flambaum, “Actinide and lanthanide molecules to search for strong CP-violation,” Phys. Chem. Chem. Phys. 22, 18374–18380 (2020)

    2020

  9. [16]

    Probing fundamental sym- metries of deformed nuclei in symmetric top molecules,

    P. Yu and N. R. Hutzler, “Probing fundamental sym- metries of deformed nuclei in symmetric top molecules,” Phys. Rev. Lett. 126, 023003 (2021)

    2021

  10. [17]

    Enhanced mag- netic quadrupole moments in nuclei with octupole de- formation and their CP-violating effects in molecules,

    V. V. Flambaum and A. J. Mansour, “Enhanced mag- netic quadrupole moments in nuclei with octupole de- formation and their CP-violating effects in molecules,” 9 Phys. Rev. C 105, 065503 (2022)

    2022

  11. [18]

    Possibility of investigation P- and T-odd nuclear forces in atomic and molecular experiments,

    O. P. Sishkov, V. V. Flambaum, and I. B. Khriplovich, “Possibility of investigation P- and T-odd nuclear forces in atomic and molecular experiments,” Sov. Phys. JETP 60, 873–883 (1984)

    1984

  12. [19]

    Spin hedgehog and collective mag- netic quadrupole moments induced by parity and time invariance violating interaction,

    V. V. Flambaum, “Spin hedgehog and collective mag- netic quadrupole moments induced by parity and time invariance violating interaction,” Phys. Lett. B320, 211– 215 (1994)

    1994

  13. [20]

    Time- reversal symmetry violation in molecules induced by nu- clear magnetic quadrupole moments,

    V. V. Flambaum, D. DeMille, and M. G. Kozlov, “Time- reversal symmetry violation in molecules induced by nu- clear magnetic quadrupole moments,” Phys. Rev. Lett. 113, 103003 (2014)

    2014

  14. [21]

    Laser cooling without repumping: A magneto-optical trap for erbium atoms,

    J. J. McClelland and J. L. Hanssen, “Laser cooling without repumping: A magneto-optical trap for erbium atoms,” Phys. Rev. Lett. 96, 143005 (2006)

    2006

  15. [22]

    Trapping ultracold dysprosium: A highly magnetic gas for dipolar physics,

    M. Lu, S. H. Youn, and B. L. Lev, “Trapping ultracold dysprosium: A highly magnetic gas for dipolar physics,” Phys. Rev. Lett. 104, 063001 (2010)

    2010

  16. [23]

    An optical tweezer array of ultracold polyatomic molecules,

    N. B. Vilas, P. Robichaud, C. Hallas, G. K. Li, L. An- deregg, and J. M. Doyle, “An optical tweezer array of ultracold polyatomic molecules,” Nature 628, 282–286 (2024)

    2024

  17. [24]

    Laser- cooled polyatomic molecules for improved electron elec- tric dipole moment searches,

    B. L. Augenbraun, Z. D. Lasner, A. Frenett, H. Sawaoka, C. Miller, T. C. Steimle, and J. M. Doyle, “Laser- cooled polyatomic molecules for improved electron elec- tric dipole moment searches,” New J. Phys. 22, 022003 (2020)

    2020

  18. [26]

    Modern quantum chem- istry with [Open]Molcas,

    F. Aquilante, J. Autschbach, A. Baiardi, S. Battaglia, V. A. Borin, L. F. Chibotaru, I. Conti, L. De Vico, M. Delcey, I. Fdez. Galv´ an, N. Ferr´ e, L. Freitag, M. Garavelli, X. Gong, S. Knecht, E. D. Larsson, R. Lindh, M. Lundberg, P.- ˚A. Malmqvist, A. Nenov, J. Norell, M. O...

    2020

  19. [27]

    J. F. Stanton, J. Gauss, L. Cheng, M. E. Harding, D. A. Matthews, and P. G. Szalay, With contributions from A. Asthana, A.A. Auer, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, S. Blaschke, Y. J. Bomble, S. Burger, O. Christiansen, D. Datta, F. Engel, R. Faber, J. Gre...

  20. [28]

    Electronic spectra of DyF studied by four-component relativistic configura- tion interaction methods,

    S. Yamamoto and H. Tatewaki, “Electronic spectra of DyF studied by four-component relativistic configura- tion interaction methods,” J. Chem. Phys. 142, 094312 (2015)

    2015

  21. [29]

    Th´ eorie g´ en´ erale de la rotation para- magn´ etique dans les cristaux,

    H. A. Kramers, “Th´ eorie g´ en´ erale de la rotation para- magn´ etique dans les cristaux,” Proc. Amst. Acad. 33, 959–972 (1930)

    1930

  22. [30]

    CODATA recommended values of the fundamental physical constants: 2018,

    E. Tiesinga, P. J. Mohr, D. B. Newell, and B. N. Tay- lor, “CODATA recommended values of the fundamental physical constants: 2018,” Rev. Mod. Phys. 93, 025010 (2021)

    2021

  23. [31]

    NIST Atomic Spectra Database (version 5.11), [Online],

    A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (version 5.11), [Online],” (2023), https://doi.org/10.18434/T4W30F, available: https://physics.nist.gov/asd. National Insti- tute of Standards and Technology, Gaithersburg, MD

    2023 doi

  24. [32]

    D. M. Brink and G. R. Satchler, Angular momentum, 3rd ed. (Oxford University Press, Oxford, 1993)

    1993

  25. [33]

    Gaussian 16 Revision B.01,

    M. J. Frisch et al , “Gaussian 16 Revision B.01,” (2016), Gaussian Inc. Wallingford CT

    2016

  26. [34]

    Advances in molecular quantum chemistry contained in the Q-Chem 4 program package,

    Y. Shao et al, “Advances in molecular quantum chemistry contained in the Q-Chem 4 program package,” Mol. Phys. 113, 184–215 (2015)

    2015

  27. [35]

    Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their deriva- tion,

    L. F. Chibotaru and L. Ungur, “Ab initio calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their deriva- tion,” J. Chem. Phys. 137, 064112 (2012)

    2012

  28. [36]

    The re- stricted active space self-consistent-field method, imple- mented with a split graph unitary group approach,

    P.-˚A. Malmqvist, A. Rendell, and B. O. Roos, “The re- stricted active space self-consistent-field method, imple- mented with a split graph unitary group approach,” J. Phys. Chem. 94, 5477–5482 (1990)

    1990

  29. [37]

    The restricted active space (RAS) state interaction approach with spin–orbit coupling,

    P.-˚A. Malmqvist, B. O. Roos, and B. Schimmelpfen- nig, “The restricted active space (RAS) state interaction approach with spin–orbit coupling,” Chem. Phys. Lett. 357, 230–240 (2002)

    2002

  30. [38]

    New relativistic atomic natural orbital basis sets for lanthanide atoms with ap- plications to the Ce diatom and LuF 3,

    B. O. Roos, R. Lindh, P.- ˚A. Malmqvist, V. Veryazov, P.- O. Widmark, and A. C. Borin, “New relativistic atomic natural orbital basis sets for lanthanide atoms with ap- plications to the Ce diatom and LuF 3,” J. Phys. Chem. A 112, 11431–11435 (2008)

    2008

  31. [39]

    Coupled-cluster techniques for compu- tational chemistry: The CFOUR program package,

    D. A. Matthews, L. Cheng, M. E. Harding, F. Lipparini, S. Stopkowicz, T.-C. Jagau, P. G. Szalay, J. Gauss, and J. F. Stanton, “Coupled-cluster techniques for compu- tational chemistry: The CFOUR program package,” J. Chem. Phys. 152, 214108 (2020)

    2020

  32. [40]

    A full coupled- cluster singles and doubles model: The inclusion of dis- connected triples,

    G. D. III Purvis and R. J. Bartlett, “A full coupled- cluster singles and doubles model: The inclusion of dis- connected triples,” J. Chem. Phys.76, 1910–1918 (1982)

    1982

  33. [41]

    A fifth-order perturbation compari- son of electron correlation theories,

    K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, “A fifth-order perturbation compari- son of electron correlation theories,” Chem. Phys. Lett. 157, 479–483 (1989)

    1989

  34. [42]

    The equation of motion coupled-cluster method. a systematic biorthogonal ap- proach to molecular excitation energies, transition prob- abilities, and excited state properties,

    J. F. Stanton and R. J. Bartlett, “The equation of motion coupled-cluster method. a systematic biorthogonal ap- proach to molecular excitation energies, transition prob- abilities, and excited state properties,” J. Chem. Phys. 98, 7029–7039 (1993)

    1993

  35. [43]

    An atomic mean-field spin-orbit approach within exact two-component theory for a non- perturbative treatment of spin-orbit coupling,

    J. Liu and L. Cheng, “An atomic mean-field spin-orbit approach within exact two-component theory for a non- perturbative treatment of spin-orbit coupling,” J. Chem. Phys. 148, 144108 (2018)

    2018

  36. [44]

    Atomic mean-field ap- proach within exact two-component theory based on the Dirac–Coulomb–Breit hamiltonian,

    C. Zhang and L. Cheng, “Atomic mean-field ap- proach within exact two-component theory based on the Dirac–Coulomb–Breit hamiltonian,” J. Phys. Chem. A 10 126, 4537–4553 (2022)

    2022

  37. [45]

    Gaussian basis sets for use in corre- lated molecular calculations. I. the atoms boron through neon and hydrogen,

    T. H. Jr. Dunning, “Gaussian basis sets for use in corre- lated molecular calculations. I. the atoms boron through neon and hydrogen,” J. Chem. Phys. 90, 1007–1023 (1989)

    1989

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.