Anisotropic chemical bonding of lanthanide-OH molecules
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. In particular, we focus on heavy, magnetic DyOH and ErOH relevant to fundamental symmetry tests. We use a restrict...
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-06281-6 |
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| author | Jacek Kłos Eite Tiesinga Lan Cheng Svetlana Kotochigova |
| author_facet | Jacek Kłos Eite Tiesinga Lan Cheng Svetlana Kotochigova |
| author_sort | Jacek Kłos |
| collection | DOAJ |
| description | 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. In particular, 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 to determine ground and excited electronic states. In addition, electric and magnetic dipole 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 anisotropic 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most $$\hbox {6s}^2$$ 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 for both molecules $$\Omega$$ lies between $$-15/2$$ and $$+15/2$$ , where the degenerate states with the lowest energy have $$|\Omega |=15/2$$ and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these $$\Omega$$ states is approximately $$hc\times 1000$$ $$\hbox {cm}^{-1}$$ , where h is the Planck constant and c is the speed of light in vacuum. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units and are mostly independent of $$\Omega$$ . The magnetic moments are closely related to that of the corresponding atomic $$\hbox {Ln}^+$$ ion in an excited electronic state. From the polynomial $$\Omega$$ dependences, 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. We describe how this observation can be used to construct effective Hamiltonians containing spin–spin operators. |
| format | Article |
| id | doaj-art-d824fb6f70554390b05f5d1af71ae0d2 |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-d824fb6f70554390b05f5d1af71ae0d22025-08-20T03:03:32ZengNature PortfolioScientific Reports2045-23222025-07-0115111010.1038/s41598-025-06281-6Anisotropic chemical bonding of lanthanide-OH moleculesJacek Kłos0Eite Tiesinga1Lan Cheng2Svetlana Kotochigova3Department of Physics, Temple UniversityJoint Quantum Institute, National Institute of Standards and Technology and University of MarylandDepartment of Chemistry, The Johns Hopkins UniversityDepartment of Physics, Temple UniversityAbstract We present a theoretical study of the low lying adiabatic relativistic electronic states of lanthanide monohydroxide (Ln-OH) molecules near their linear equilibrium geometries. In particular, 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 to determine ground and excited electronic states. In addition, electric and magnetic dipole 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 anisotropic 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most $$\hbox {6s}^2$$ 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 for both molecules $$\Omega$$ lies between $$-15/2$$ and $$+15/2$$ , where the degenerate states with the lowest energy have $$|\Omega |=15/2$$ and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these $$\Omega$$ states is approximately $$hc\times 1000$$ $$\hbox {cm}^{-1}$$ , where h is the Planck constant and c is the speed of light in vacuum. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units and are mostly independent of $$\Omega$$ . The magnetic moments are closely related to that of the corresponding atomic $$\hbox {Ln}^+$$ ion in an excited electronic state. From the polynomial $$\Omega$$ dependences, 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. We describe how this observation can be used to construct effective Hamiltonians containing spin–spin operators.https://doi.org/10.1038/s41598-025-06281-6 |
| spellingShingle | Jacek Kłos Eite Tiesinga Lan Cheng Svetlana Kotochigova Anisotropic chemical bonding of lanthanide-OH molecules Scientific Reports |
| title | Anisotropic chemical bonding of lanthanide-OH molecules |
| title_full | Anisotropic chemical bonding of lanthanide-OH molecules |
| title_fullStr | Anisotropic chemical bonding of lanthanide-OH molecules |
| title_full_unstemmed | Anisotropic chemical bonding of lanthanide-OH molecules |
| title_short | Anisotropic chemical bonding of lanthanide-OH molecules |
| title_sort | anisotropic chemical bonding of lanthanide oh molecules |
| url | https://doi.org/10.1038/s41598-025-06281-6 |
| work_keys_str_mv | AT jacekkłos anisotropicchemicalbondingoflanthanideohmolecules AT eitetiesinga anisotropicchemicalbondingoflanthanideohmolecules AT lancheng anisotropicchemicalbondingoflanthanideohmolecules AT svetlanakotochigova anisotropicchemicalbondingoflanthanideohmolecules |