1. ATOMIC/MOLECULAR SPECTROSCOPY  Various spectroscopic techniques are used to elucidate molecular structures (eg. NMR), to study molecular vibrations (IR and Raman spectra – often associated with force field calculations), to study molecular rotational energies (usually microwave spectra but also high resolution gas phase IR, Raman and UV spectra).

2. ELECTRONIC SPECTRA:  Electronic spectra, even of closed shell molecules, can be complex since electronic energies, vibrational energies and rotational energies can all change simultaneously. Rotational energy patterns can be extremely complex for “heavy” molecules or for asymmetric rotors. Additional complications exist when there are unpaired electrons.

3. ELECTRONIC SPECTRA  Electronic spectra of atoms/monatomic ions provide details of atomic structure. Such spectra find practical applications in analytical chemistry (eg. atomic absorption spectroscopy). Atomic emission “spectra” are used in light emitting devices such as sodium vapor lamps and in more complex devices such as the helium neon laser.

4. COMPLEX SPECTRA  Rich spectra are a reflection of complex atomic or molecular atomic energy level patterns (complexity increasing with growing numbers of atoms/electrons and loss of symmetry). Temperature is also a factor. An increase in temperature pushes molecules into higher energy states and allows more spectral lines/transitions to be observed.

5. SPECTRA FOR ONE ELECTRON SPECIES  The simplest electronic spectra, not surprisingly, are due to the one electron (and monatomic) species H, He +, Li 2+, etc. For these species familiar energy degeneracies are seen.  Aside: For the one electron species H 2 + energy level patterns are much more complex. Why?

6. HYDROGEN ATOM ENERGY LEVELS

7. H ATOM DEGENERACIES 

8. H ATOM ANGULAR MOMENTA 

9. QUANTUM NUMBERS – H ATOM  For one electron species we employ lower case letters to designate both quantum numbers and operators. We associate specific l values with subshells. l value 0123 Subshell s p d f

10. MANY ELECTRON ATOMS  For many electron atoms life is more complicated (not surprisingly?). The energy degeneracies seen for H, He +, Li 2+ etc. are removed/lifted due to electron-electron interactions.

11. MULTI-ELECTRON ATOM ENERGY LEVELS

12. MULTI-ELECTRON ATOMS  For multi-electron atoms life is also more complex since angular momenta can “couple” (vector addition). This is most important when there are unpaired electrons. As a final complication, the H atom quantum numbers (n, l …) are not good quantum numbers for multi-electron atoms or multi-electron monatomic ions.

13. MULTI-ELECTRON ATOMS/IONS 

14.  However, the z-components of orbital angular momentum and of spin angular momentum add as scalar quantities and, correspondingly, we have the sums M L and M S which enable us to define the quantum numbers L and S.  M L = ∑ l zi = ∑ m l (i) and M S = ∑ s zi = ∑ m s (i)

15. TOTAL ANGULAR MOMENTUM 

16. RUSSELL-SAUNDERS COUPLING  In earlier courses we wrote electron configurations for both ground and excited state atoms/ions  He atom ground state - 1s 2  He atom first excited state - 1s 1 2s 1  In fact, the electron configuration written above represents two excited states. Why?

17. RUSSELL SAUNDERS COUPLING  We will write so-called term symbols to specify different atomic states. Here only J is strictly a good quantum number. We write the term symbols as (2S+1) L J where J is the total angular momentum, L is the total orbital angular momentum and S is the total spin angular momentum. 2S+1 is the spin multiplicity.

18. RUSSELL SAUNDERS COUPLING  For the H atom the permitted values of orbital angular momentum (due to the lone electron) are specified using either numerical l = 0,1,2,3.. values or lower case letters s, p, d, f….. For multi-electron atoms/ions the possible L values are specified using upper case letters S, P, D F….  1,

19. TERM SYMBOLS  Class examples will illustrate the use/writing of term symbols for atoms and monatomic ions.