Electronic Structure of the Ground and Low-Lying States of MoLi
Molybdenum lithium compounds and materials are being researched and applied in cutting-edge industries; however, their bonding has not been explored in a systematic way. The present study investigates the MoLi molecule, to shed light on its bonding. Specifically, the electronic structure and bonding...
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2025-07-01
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| author | Constantinos Demetriou Demeter Tzeli |
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| description | Molybdenum lithium compounds and materials are being researched and applied in cutting-edge industries; however, their bonding has not been explored in a systematic way. The present study investigates the MoLi molecule, to shed light on its bonding. Specifically, the electronic structure and bonding of the ground and 40 low-lying states of the MoLi molecule are explored, employing multireference methodologies, i.e., CASSCF and MRCISD(+Q) in conjunction with the aug-cc-pV5z(-PP) basis set. Bond distances, dissociation energies, dipole moments as well as common spectroscopic constants are given, while the potential energy curves are plotted. For the ground state, X<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mrow><mo>Σ</mo></mrow><mrow><mo>+</mo></mrow><none></none><mprescripts></mprescripts><none></none><mn>6</mn></mmultiscripts></mrow></semantics></math></inline-formula>, it is found that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 2.708 Å, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 24.1 kcal/mol, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 316.8 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 2.11 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, and <i>μ</i> = 3.63 D. Overall, the calculated states present a variety of bonds, from weak van der Waals up to the formation of 2.5 bonds. The dissociation energies of the calculated states range from 2.3 kcal/mol (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">a</mi><mmultiscripts><mrow><msup><mrow><mo>Σ</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow><none></none><none></none><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></semantics></math></inline-formula>) to 34.7 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">c</mi><mmultiscripts><mrow><mo>Π</mo></mrow><none></none><none></none><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></semantics></math></inline-formula>), while the bond distances range from 2.513 Å to 3.354 Å. Finally, dipole moment values up to 3.72 D are calculated. In most states, a 2s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>2</mn><mi mathvariant="normal">p</mi></mrow></mrow><mrow><mi mathvariant="normal">z</mi></mrow></msub></mrow></semantics></math></inline-formula> hybridization on Li and a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>4</mn><mi mathvariant="normal">d</mi></mrow></mrow><mrow><msup><mrow><mi mathvariant="normal">z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></mrow></semantics></math></inline-formula>5s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>5</mn><mi mathvariant="normal">p</mi></mrow></mrow><mrow><mi mathvariant="normal">z</mi></mrow></msub></mrow></semantics></math></inline-formula> or 5s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>5</mn><mi mathvariant="normal">p</mi></mrow></mrow><mrow><mi mathvariant="normal">z</mi></mrow></msub></mrow></semantics></math></inline-formula> hybridization on Mo are found. Moreover, it is observed that the excited Li(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mrow><mi mathvariant="normal">P</mi></mrow><none></none><none></none><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow></semantics></math></inline-formula>) atom forms the shortest bonds because its empty <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mn>2</mn><mi mathvariant="normal">s</mi></mrow></mrow><mrow><mn>0</mn></mrow></msup></mrow></semantics></math></inline-formula> orbital can easily accept electrons, resulting in a strong σ dative bond. Finally, the present work highlights the exceptional ability of lithium atoms to participate in a variety of bonding schemes, and it could provide the opening gate for further investigation of this species or associated material and complexes. |
| format | Article |
| id | doaj-art-c0c6cb1645e74c0fb95936bccb3fd365 |
| institution | Matheson Library |
| issn | 1420-3049 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Molecules |
| spelling | doaj-art-c0c6cb1645e74c0fb95936bccb3fd3652025-07-11T14:41:17ZengMDPI AGMolecules1420-30492025-07-013013287410.3390/molecules30132874Electronic Structure of the Ground and Low-Lying States of MoLiConstantinos Demetriou0Demeter Tzeli1Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, 15772 Athens, GreeceLaboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, 15772 Athens, GreeceMolybdenum lithium compounds and materials are being researched and applied in cutting-edge industries; however, their bonding has not been explored in a systematic way. The present study investigates the MoLi molecule, to shed light on its bonding. Specifically, the electronic structure and bonding of the ground and 40 low-lying states of the MoLi molecule are explored, employing multireference methodologies, i.e., CASSCF and MRCISD(+Q) in conjunction with the aug-cc-pV5z(-PP) basis set. Bond distances, dissociation energies, dipole moments as well as common spectroscopic constants are given, while the potential energy curves are plotted. For the ground state, X<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mrow><mo>Σ</mo></mrow><mrow><mo>+</mo></mrow><none></none><mprescripts></mprescripts><none></none><mn>6</mn></mmultiscripts></mrow></semantics></math></inline-formula>, it is found that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 2.708 Å, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 24.1 kcal/mol, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 316.8 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></mrow></semantics></math></inline-formula> = 2.11 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi>cm</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, and <i>μ</i> = 3.63 D. Overall, the calculated states present a variety of bonds, from weak van der Waals up to the formation of 2.5 bonds. The dissociation energies of the calculated states range from 2.3 kcal/mol (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">a</mi><mmultiscripts><mrow><msup><mrow><mo>Σ</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow><none></none><none></none><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></semantics></math></inline-formula>) to 34.7 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">c</mi><mmultiscripts><mrow><mo>Π</mo></mrow><none></none><none></none><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></semantics></math></inline-formula>), while the bond distances range from 2.513 Å to 3.354 Å. Finally, dipole moment values up to 3.72 D are calculated. In most states, a 2s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>2</mn><mi mathvariant="normal">p</mi></mrow></mrow><mrow><mi mathvariant="normal">z</mi></mrow></msub></mrow></semantics></math></inline-formula> hybridization on Li and a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>4</mn><mi mathvariant="normal">d</mi></mrow></mrow><mrow><msup><mrow><mi mathvariant="normal">z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></mrow></semantics></math></inline-formula>5s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>5</mn><mi mathvariant="normal">p</mi></mrow></mrow><mrow><mi mathvariant="normal">z</mi></mrow></msub></mrow></semantics></math></inline-formula> or 5s<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mrow><mn>5</mn><mi mathvariant="normal">p</mi></mrow></mrow><mrow><mi mathvariant="normal">z</mi></mrow></msub></mrow></semantics></math></inline-formula> hybridization on Mo are found. Moreover, it is observed that the excited Li(<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mmultiscripts><mrow><mi mathvariant="normal">P</mi></mrow><none></none><none></none><mprescripts></mprescripts><none></none><mrow><mn>2</mn></mrow></mmultiscripts></mrow></semantics></math></inline-formula>) atom forms the shortest bonds because its empty <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mn>2</mn><mi mathvariant="normal">s</mi></mrow></mrow><mrow><mn>0</mn></mrow></msup></mrow></semantics></math></inline-formula> orbital can easily accept electrons, resulting in a strong σ dative bond. Finally, the present work highlights the exceptional ability of lithium atoms to participate in a variety of bonding schemes, and it could provide the opening gate for further investigation of this species or associated material and complexes.https://www.mdpi.com/1420-3049/30/13/2874diatomic moleculemulti-reference configuration interactionMoLichemical bondingelectronic structure |
| spellingShingle | Constantinos Demetriou Demeter Tzeli Electronic Structure of the Ground and Low-Lying States of MoLi Molecules diatomic molecule multi-reference configuration interaction MoLi chemical bonding electronic structure |
| title | Electronic Structure of the Ground and Low-Lying States of MoLi |
| title_full | Electronic Structure of the Ground and Low-Lying States of MoLi |
| title_fullStr | Electronic Structure of the Ground and Low-Lying States of MoLi |
| title_full_unstemmed | Electronic Structure of the Ground and Low-Lying States of MoLi |
| title_short | Electronic Structure of the Ground and Low-Lying States of MoLi |
| title_sort | electronic structure of the ground and low lying states of moli |
| topic | diatomic molecule multi-reference configuration interaction MoLi chemical bonding electronic structure |
| url | https://www.mdpi.com/1420-3049/30/13/2874 |
| work_keys_str_mv | AT constantinosdemetriou electronicstructureofthegroundandlowlyingstatesofmoli AT demetertzeli electronicstructureofthegroundandlowlyingstatesofmoli |