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 （一） 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. 1. Introduction Atoms: Energy states are determined by different arrangements of the electron states; Each line corresponds to an electronic transition • Easy calculation • Hyperfine structure should consider the spin of nuclear. • Quantum states: • orbital angular moment, J • Spin angular moment, S • Electron and nuclear • jj coupling, ls coupling • JI interaction F

3. Molecules: possessing more electronics states; Nuclei can vibrate around their equilibrium positions; The whole molecule rotates around axes through its center of mass; It has lower energy than the individual atom; More complicated than atom because of larger size and more degree of freedom. Electronic states: Vibration states: Rotation states:

4. Molecular spectra can be categorized as : • pure rotational spectra with wavelengths in the microwave region(1mm-1m) • Vibration rotation spectra with wavelengths in the mid infrared region(2-20µm) • Transitions between two different electronic states have wavelength from UV to near Infrared (0.1-2µm)

5. 2. Molecular Electronic States 2.1 Adiabatic Approximation and the Concept of Molecular Potentials 2.1.1 Quantum Mechanical Description of Free Molecules Assuming a molecule consisting of k nuclei(with masses Mk and charges Zke) and N electros(mass m, charge -e) in a state with total energy E S - center of mass A molecule with three atoms and three electrons

6. Schrodinger Equation: • Ignoring the interactions relating to the electronic and nuclear spins; • 2. Relaticistiv treatment • Dirac’s equation Perturbation; • Potential energy ---Relative • distance; • Kinetic energy --- reference • frame: Laboratory frame

7. The simplest molecule, consisting of two protons and one electron. Can’t be solved exactly. Two solutions : • Solve the equation numerically. Depend on software and the speed of computer. The results can not be transfer to other molecules • Physically motivated approximations to simplified molecular model. Understanding physical implications Fundamental approximation: Adiabatic approximation

8. 2.1.2 Separation of Electronic and Nuclear Wavefunctions • Electrons move much faster than the vibrating nuclei; • For each changing of the nuclei structure there exists a well defined electron • distribution; • The electron cloud follows the periodically changing nuclear framework • adiabatically during the vibration; Adiabatic approximation: Perturbation theory to explain this idea. Nuclei Kinetic energy < electronic energy R is a parameter of nuclear coordinate

9. Ansatz Multiplication with using Normalization condition:

10. 2.1.3 Born Oppenheimer Approximation : Coupling between nuclear motion and electron distribution : nulear wavefunction in the electronic state Nuclear kinetic energy and a potential energy Considered as a potential in which the nuclei move Molecular state B-O Approximation

11. 2.1.4 Adiabatic Approximation Keeping the diagonal terms Quadratically on changes in upon variations of nuclear coordinates Different isotopes, shifts smaller comparing to the isotopic effects on

12. 2.2 Deviations from the adiabatic approximation <1 depends on the ratio m/M Adiabatic approximation

13. This situation is encountered for exited molecular states, rarely for the ground states

14. 2.3 Potential curve of diatomic molecules Equilibrium distance Bond energy