双原子分子光谱 Diatomic Molecular Spectroscopy

1. The Spectra and Dynamics of Diatomic Molecules 双原子分子光谱 Diatomic Molecular Spectroscopy （三） 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. Energy Ei(R) from R0 and R to arbitrary intermolecular distance; R0: a united state of united atom; R: a combination of known states of the two separated atoms; Correlation diagram Atomic states: LA and LB; Projections to z axis: (ML)Ah and (ML)Bh A given combination of LA and LB can result in a large number of values for .

3. LA=2 (D state) and LB=1 (P state)

6. A single electron moves in the electrostatic potential of the two nuclei and of the averaged charge distribution of other electrons. • The electronic wavefunction of this electron is called a molecular orbital, which can be occupied by a maximum of two electrons with antiparallel spins. • Under the one electron approximation, the molecular electron configuration can be built as follow: • Molecular orbitals from atomic orbitals (separated atom or united atom) • Ordering the orbital according to the energy: • Pauli principle, the products of all occupied molecular orbitals is called electron configuration

9. For a given quantum numbers l and  the state with maximum multiplicity is lowest .

10. From united atom transition to separated atoms. • Molecular electron configurations at small internulear separations R : • When R increasing, the molecular orbitals become linear combination of the atomic orbitals. • Applying the conservation laws as follow: • a.  is independent of R, • b. Wavefunction parity does not depend on the R • c. If two states have the same symmetry,  and multiplicity 2S+1, they can not degenerate for any R. (potential curves can never cross)

11. Correlation diagram of a homonuclear molecule

12. 变分法，原子轨道的线性组合 Can’t be solved exactly, employing approximative methods : Approximate wavefunction with adjustable parameters. Ritz principle: the calculated energy with approximative wavefunction are always larger than the exact wavefunction Assuming a wavefunction 

13. Quadratically depending on the 

14. Linear combination of atomic oribitals Normalized wavefunction According the variational principle

18. It is not possible to distinguish an individual electron.

19. Considering electron spin, Pauli principle, the total wavefunction  should be antisymmetric with respect to a permutation of two electrons.