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双原子分子光谱 Diatomic Molecular Spectroscopy

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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