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双原子分子光谱 Diatomic Molecular Spectroscopy

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The Spectra and Dynamics of Diatomic Molecules. 双原子分子光谱 Diatomic Molecular Spectroscopy. （二）. 马维光 量子光学与光量子器件国家重点实验室 山西大学物理电子工程学院 激光光谱研究室. 2.4 Electronic states of diatomic molecules. From diatomic to polyatomic molecules: Vector model of angular momentum coupling;

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双原子分子光谱 Diatomic Molecular Spectroscopy

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  1. The Spectra and Dynamics of Diatomic Molecules 双原子分子光谱 Diatomic Molecular Spectroscopy （二） 马维光 量子光学与光量子器件国家重点实验室 山西大学物理电子工程学院 激光光谱研究室

  2. 2.4 Electronic states of diatomic molecules • From diatomic to polyatomic molecules: • Vector model of angular momentum coupling; • Symmetry properties of molecular states; • Molecular orbital concept—many electron molecules to a combination of one electron states • Solving H2+molecule ion exactly within BO approximation: • Introducing properties and quantum numbers; • With only one unpaired electron in the highest energy level. Starting from quantum numbers, angular momenta, and symmetries  molecules with many electrons; Introducing the classification of electronic states of diatomic molecule; Two limiting cases of electronic molecular states for R  (separated atoms) and R 0 (united atom) Assuming the nuclear framework is rigid and nonrotating.  each electronic state corresponds a potential energy curve En(R)

  3. 2.4.1 Exact treatment of the rigid H2+ Molecule A and B with nuclear charges Z1e and Z2e and one electron, here Z1=Z2=1

  4. =const. describes all planes which contain the internuclear axis; =const. are confocal rotational ellipsoids with the nuclei as focal point; =const. are two shell rotational hyperboloides;

  5. Wavefunction of electronic state: Schrodinger Equation: Which can be converted to  and  are separation constants.

  6.  must be normalizable continuous and single valued for all values of • Physical meaning of : • The system is not a center force field, l is not constant; • |l| and lz are constant;

  7. Notes: • Depend on 2 ; • (n,l,) principle QN, angular momentum QN, projection QN. • Nodal surface: • 4. , number of ; • l total number of  and ; • n total number of , and .

  8. l=0,1,2,3,4….s, p, d, f =0,1,2…., , 

  9. 1g corresponds to a stable molecule

  10. 2.4.2 Classification of electronic molecular states 2.4.2.1 Energetic ordering of electronic states Ground state with the letter X; The optically-allowed-transition next states: A, B, C… The inaccessible states: a,b,c

  11. 2.4.2.2 symmetries of electronic wavefunctions The electron distribution does not change during a symmetry operation, |el|2 is incariant; Mirror operation Inversion operation

  12. 2.4.2.3 Electronic angular momenta l orbital angular momenta; s spin angular momenta; For small nuclear charges l and s coupling is weaker than the coupling of l to the molecular axis. l and s precess independently around axis. Their projections are h and h. The interaction between spin and orbital >0, splits into a doublet.

  13. United molecules: for light atoms, L-S coupling Increasing the internuclear distance: =0,1,2…., , 

  14. Molecular state: principal quantum number n, QN , spin S, =|+|  has 2S+1 values, call fine structure terms. Fine structure splitting (light many electron/ one electron)

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