Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule
Intensity of transitions from the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="7...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
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| Series: | Physchem |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-7167/3/1/9 |
| _version_ | 1797609391615115264 |
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| author | Lidan Xiao Bing Yan Boris F. Minaev |
| author_facet | Lidan Xiao Bing Yan Boris F. Minaev |
| author_sort | Lidan Xiao |
| collection | DOAJ |
| description | Intensity of transitions from the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup><mo> </mo></mrow></semantics></math></inline-formula> and <i>a</i><sup>1</sup>Δ<sub>g</sub> states to the ground state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>−</mo></msubsup><mo> </mo></mrow></semantics></math></inline-formula> in the near IR emission spectrum of the S<sub>2</sub> molecule has been calculated by the multireference configuration interaction method taking into account spin-orbit coupling (SOC). The intensity of the<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> − <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mo> </mo><mi mathvariant="normal">X</mi></mrow></mrow><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> transition is largely determined by the spin interaction with the electromagnetic wave, which comes from the zero-field splitting of the ground X multiplet and the SOC-induced mixing between <i>b</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mn>0</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> states. The Einstein coefficients for the experimentally detected 0−0, 0−1, 1−1 bands of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup><mo>−</mo><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> emission system are calculated in good agreement with observations. The Einstein coefficient of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>a</mi><mn>1</mn></msup><msub><mo>∆</mo><mi mathvariant="normal">g</mi></msub><mo>−</mo><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> magnetic dipole transition is very low, being equal to 0.0014 s<sup>−1</sup>. Nonetheless, the weakest of all experimentally observed bands (the 0−0 band of the <i>a-X<sub>Ms=</sub></i><sub>±1</sub> transition) qualitatively corresponds to this calculation. Most importantly, we provide many other IR bands for magnetic dipole <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> − <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mo> </mo><mi mathvariant="normal">X</mi></mrow></mrow><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>a</mi><mn>1</mn></msup><msub><mo>∆</mo><mi mathvariant="normal">g</mi></msub><mo>−</mo><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> transitions, which could be experimentally observable in the S<sub>2</sub> transparency windows from a theoretical point of view. We hope that these results will contribute to the further experimental exploration of the magnetic infrared bands in the S<sub>2</sub> dimer. |
| first_indexed | 2024-03-11T06:00:47Z |
| format | Article |
| id | doaj.art-015ff4fc60924ef186bade2f57b1f4df |
| institution | Directory Open Access Journal |
| issn | 2673-7167 |
| language | English |
| last_indexed | 2024-03-11T06:00:47Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Physchem |
| spelling | doaj.art-015ff4fc60924ef186bade2f57b1f4df2023-11-17T13:20:01ZengMDPI AGPhyschem2673-71672023-02-013111012410.3390/physchem3010009Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> MoleculeLidan Xiao0Bing Yan1Boris F. Minaev2Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, ChinaInstitute of Atomic and Molecular Physics, Jilin University, Changchun 130012, ChinaDepartment of Chemistry and Nanomaterials Science, Bohdan Khmelnytsky National University, 18031 Cherkasy, UkraineIntensity of transitions from the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup><mo> </mo></mrow></semantics></math></inline-formula> and <i>a</i><sup>1</sup>Δ<sub>g</sub> states to the ground state <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>−</mo></msubsup><mo> </mo></mrow></semantics></math></inline-formula> in the near IR emission spectrum of the S<sub>2</sub> molecule has been calculated by the multireference configuration interaction method taking into account spin-orbit coupling (SOC). The intensity of the<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo> </mo><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> − <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mo> </mo><mi mathvariant="normal">X</mi></mrow></mrow><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> transition is largely determined by the spin interaction with the electromagnetic wave, which comes from the zero-field splitting of the ground X multiplet and the SOC-induced mixing between <i>b</i> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mn>0</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> states. The Einstein coefficients for the experimentally detected 0−0, 0−1, 1−1 bands of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup><mo>−</mo><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> emission system are calculated in good agreement with observations. The Einstein coefficient of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>a</mi><mn>1</mn></msup><msub><mo>∆</mo><mi mathvariant="normal">g</mi></msub><mo>−</mo><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> magnetic dipole transition is very low, being equal to 0.0014 s<sup>−1</sup>. Nonetheless, the weakest of all experimentally observed bands (the 0−0 band of the <i>a-X<sub>Ms=</sub></i><sub>±1</sub> transition) qualitatively corresponds to this calculation. Most importantly, we provide many other IR bands for magnetic dipole <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>b</mi><mn>1</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mi mathvariant="normal">g</mi><mo>+</mo></msubsup></mrow></semantics></math></inline-formula> − <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mrow><mo> </mo><mi mathvariant="normal">X</mi></mrow></mrow><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>a</mi><mn>1</mn></msup><msub><mo>∆</mo><mi mathvariant="normal">g</mi></msub><mo>−</mo><msup><mi mathvariant="normal">X</mi><mn>3</mn></msup><msubsup><mrow><mstyle mathsize="70%" displaystyle="true"><mo>∑</mo></mstyle></mrow><mrow><mi mathvariant="normal">g</mi><mo>,</mo><mi>M</mi><mi>s</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow><mo>−</mo></msubsup></mrow></semantics></math></inline-formula> transitions, which could be experimentally observable in the S<sub>2</sub> transparency windows from a theoretical point of view. We hope that these results will contribute to the further experimental exploration of the magnetic infrared bands in the S<sub>2</sub> dimer.https://www.mdpi.com/2673-7167/3/1/9magnetic dipole transitionelectro-quadrupole transitionS<sub>2</sub> moleculenear IR bandsEinstein coefficient |
| spellingShingle | Lidan Xiao Bing Yan Boris F. Minaev Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule Physchem magnetic dipole transition electro-quadrupole transition S<sub>2</sub> molecule near IR bands Einstein coefficient |
| title | Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule |
| title_full | Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule |
| title_fullStr | Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule |
| title_full_unstemmed | Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule |
| title_short | Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S<sub>2</sub> Molecule |
| title_sort | near infrared transitions from the singlet excited states to the ground triplet state of the s sub 2 sub molecule |
| topic | magnetic dipole transition electro-quadrupole transition S<sub>2</sub> molecule near IR bands Einstein coefficient |
| url | https://www.mdpi.com/2673-7167/3/1/9 |
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