Solid State Chemistry Chapter 3 Atomic Structure and Spectra

AGENDA The structure and spectra of Hydrogenic atoms The structure of many-Electron atoms 1.Pauli’s principle 2.Penetration and shielding 3. Building up principle The spectra of complex atoms 1. Quantum defects 2. Singlet and triplets 3. Spin-orbit coupling 4. The total angular momentum 5. Term symbols and selection rules

The Structure of Many-electron Atoms The Orbital Approximation Justification 10.5

The Pauli Principle Pauli principle: When the labels of any two identical fermions are exchanged, the total wavefunction changes sign. When the labels of any two identical bosons are exchanged, the total wavefunction retains the same sign  (2,1) = -  (1,2) for two electrons

Penetration and Shielding

The Building-up (Aufbou) Principle

Ionization Energies and Electron Affinities

Self-consistent Field Orbitals The first term on the left is the contribution of the kinetic energy and the attraction of the electron to the nucleus, just as in a hydrogenic atom The second takes into account the potential energy of the electron of interest due to the electrons in the other occupied orbitals The third term takes into account the spin correlation effects.

The Spectra of Complex Atoms Quantum defects and ionization limits

Singlet and Triplet States

The Spectrum of Atomic Helium

Spin-Orbit Coupling

The Total Angular Momentum

Fine Structure

Term Symbols and Selection Rules

Total Orbital Angular Momentum Total angular momentum quantum number L Angular momentum = {L(L + 1)} 1/2 h L = l 1 +l 2, l 1 +l 2 -1….,|l 1 -l 2 | Clebsch-Gordan series L: 0,1,2,3,4,… (S,P,D,F,G…) Example: d 2 electron

Multiplicity Total spin angular momentum quantum number S Spin angular momentum = {S(S + 1)} 1/2 h S = s 1 +s 2, s 1 +s 2 -1….,|s 1 -s 2 | Multiplicity: 2S + 1 Example: Two unpaired electrons

Total Angular Momentum Total angular momentum quantum number J J = j where j = l + ½, |l – ½| Example: [Ne]3s 1 [Ne]3p 1 Russell-Saunders coupling: If spin-orbit coupling is weak, then it is effective only when all the orbital momenta are operating cooperatively J = L + S, L + S – 1,….., |L – S| Example: [Ne]2p 1 3p 1 Selection rules  S = 0  L = 0,±1  l = ±1  J = 0,±1

Short Summary The Structures and spectra of many electron atoms 1. The Pauli principle 2. Penetration and shielding 3. Singlet and triplet states 4. Spin-orbit coupling 5. Term symbols and selection rules HW#2: 10.3d, 10.7d, Exe: 10.4b, 10.6a, 10.8a, 10.12b, 10.18b, 10.19a