Lecture 4; January 2017

Electrons in Atoms: Magnetism;

Term Symbols, Zeff, and Other Properties Three prototypical kinds of Magnetic Behavior Paramagnetism: atoms, molecules, and solids with unpaired electrons are attracted in a magnetic field Diamagnetic: substances with no unpaired electrons which are weakly repelled in a magnetic field Ferro-magnetism: the unpaired electrons are aligned with their neighbors even in the absence of a magnetic field Magnetic domains: the groups of mutually aligned spins in a ferromagnetic substance

Ferro-magnet Ferro-magnet In the In the absence presence of a of a magnetic magnetic field field Gouy Balance for Magnetic Susceptibility Magnetic Susceptibility ( ) measurement; Faraday Balance to microbalance F =mHdH c z dz g z

sample is moved into }constant range N S H dH dz

Zero Field: Fz = mg g - gravitational constant dE é æ dH ö ù With Field: F = = mêg + H c ú z dz èç dz ø÷ g ë û • Pole pieces shaped to yield field gradient requirements (or “shaping coils” mounted to faces of the magnet). • Advantages: good sensitivity; no ‘packing error’; Small sample allows good thermostatting of sample • Disadvantage: magnetic anisotropies difficult to measure. How do we approach magnetism? Electron Assignments: Identifying each and every quantum number for each and every electron:

n l ml ms Electrons are characterized by ... a) Principal energy level, n b) Orbital or angular momentum, l (= # of angular nodes) c) Azimuthal quantum number, ml , the z 1/2 component of L. (|L| = [l(l+1)] ), (L)z = ml. In the presence of a magnetic field along the z direction, L precesses about the axis with it’s projection on the z-axis equal to one of the 2l +1

possible values of ml. d) Spin-spin and spin-orbital coupling

Summary of Electronic Energy Scales - The Hierarchical Approach

• The largest energy level splittings in atoms and molecules are due to principal quantum number changes (and concomitant differences in screening). This underlies our familiar focus on valence vs. core-levels. • Energy level splittings between different l levels (e.g., between s, p, d… electrons) are often comparable to bonding effects – evident in both the concept of “hybrid orbitals” and in mixed orbital parentage of molecular orbitals. • In T.M. complexes, e–-e– repulsion differences are often comparable to M-L bonding energies. A big part of ligand-field theory deals with the complications that arise from the competition between these energetic effects. Carbon: Atomic Energy Levels Experimental atomic energy levels (cm–1).

? Where do these Hybridization energy cost! levels come from ? http://physics.nist.gov/PhysRefData/ASD/index.html Ti2+ ion energy levels Again, where are all the energy levels coming from?

2 Hint: They are all [Ar]3d , the lowest 1 1 [Ar]3d 4s energy levels are at ~38,000 cm–1

http://physics.nist.gov/PhysRefData/ASD/index.html Box Diagrams

Figure 1.4 The possible sets of quantum numbers for n = 1 and n = 2.

ml values Box Diagrams Figure 1.5 The possible sets of quantum numbers for n = 3.

ml values Ground State vs. Excited State Configurations

2S + 1 Term Symbols: LJ

Spin: S = S ms = total spin angular momentum 2S + 1 (called spin “multiplicity”) L = total orbital angular momentum J = L + S

= S ml

Electrons can have spin and orbital angular momentum

Spin (all electrons): Visualizing orbital angular momentum ± ψ2p±1= ψ2px i ψ2py 2p–1 2p+1 → 휇→ 휇 e– circulation

± i =

ψ Ψ2px 2py |ψ | 2p±1

ml = ±1

Electrons have a net circulation in the ml = ±1 orbitals Visualizing orbital angular momentum ± ψ3d±2= ψ3dx2 –y2 i ψ3dxy 3d–2 3d+2 → 휇→ 휇 e– circulation

± i =

ψ ψ3dx2 –y2 3dxy |ψ | 3d±2

ml = ±2

Electrons have a net circulation in the ml = ±2 orbitals Visualizing orbital angular momentum

± ψ3d±1= ψ3dxz i ψ3dyz 3d–1 3d+1 → 휇→ 휇 e– circulation

± i =

ψ ψ3dxz 3dyz |ψ | 3d±1

ml = ±1

Electrons have a net circulation in the ml = ±1 orbitals m = l, l –1, … , – l l Pictorial View of L, ml

relative populations at 298 K, m l H = 1.0 T E E = +2µBH 0.991

Precession E = +µ H 0.994 l = 2 B of L E = 0 0.996 L

E = –µBH 0.998

E = –2µ H 1.000 |L| = [l(l+1)]1/2 B H Hz H (along z axis)

See section 8.7 and p. 264 in the text. Also see similar discussion in NMR in McMurray, Chap. 13. Term Symbols for Ground State Electronic Configurations

• Pauli Exclusion Principle => Assignments to n and to l quantum numbers. But there are other possibilities within assignment

• Hund’s Rule: Describes ground state only.

• Ground states will have

1st * Maximum value of S

2nd * Maximum value of L within that S Russell Saunders Coupling (L-S Coupling) for Ground States Configuration => Term Symbol Sm = max. M or L L L 2 S + 1 2 S + 1 ≈ Sm = M or S Spin J S S Multiplicity

# unpaired e- S 2 S + 1 L State

1 1/2 2  doublet 0  S 2 1 3  triplet 1  P 3 3/2 4  quartet 2  D

4 2 5  pentet 3  F 4  G etc. Russell Saunders Coupling: Spin/Orbit Coupling Inorganic Chemistry Chapter 1: Figure 1.22

• Size (atomic, ionic, covalent, van der Waals radii)

0 + - • Ionization Potential (A (g) + I.E. A + e )

0 - - • Electron Affinity Energies (A (g) + e A + E.A.E.)

• Electronegativity: Ability of an atom, within a molecule to attract electrons to itself. Inorganic Chemistry Chapter 1: Figure 1.23

Inorganic Chemistry Chapter 1: Table 1.4

Neutralatom AnionsarethanLarger

Neutral atom Neutral Cations are smaller smaller than are Cations

• Size (atomic, ionic, covalent, van der Waals radii)

• Ionization Potential energy

0 + - (A (g) + I.E. A + e )

0 - - • Electron Affinity Energy (A (g) + e A + E.A.E.)

• Electronegativity: Ability of an atom, within a molecule to attract electrons to itself. https://www.nist.gov/pml/ground-levels-and- ionization-energies-neutral-atoms Inorganic Chemistry Chapter 1: Figure 1.25

nd vs. (n + 1)s in the Transition Metals • d10 1900 dn-1®dn-2 Ionization 1800 d9 • 1700 d8 • Energies d5 d7 • d10s1 1600 • d6 • 1500 d4 • 1400 • d3 2nd IP 1300 d2 • • • 900 d10s2 dn-2s2®dn-1 kJ/mol 850 or n-1 1 n-1 800 d s ®d Transition d6s2d7s2 • • 750 d5s2 • • • 8 2 d10s1 Metals - some 700 d2s2 d s 1 2 d3s2 complications 650 d s • • • 1st IP • d5s1 600 Sc Ti V Cr MnFe Co Ni Cu Zn Inorganic Chemistry Chapter 1: Table 1.6

1 • Pauling c M - c M = 0.208 EA-B - 2 ( EA- A + EB-B ) 1 c M - c M = 0.208 EA-B - 2 EA- A ´ EB-B

• 1 Mulliken c = ( IE + EA) M 2

Allred and Rochow Scale This scale considers electronegativity as the force • Rochow acting on electrons at a distance of the covalent radius. 0.359 Z c = 0.744 + eff M r 2 cov Z = effective nuclear charge eff r = Covalent radius of the atom, in Å. cov Linus Pauling

BDE H2 = 436 kJ/mol BDE Cl2 = 239 BDE HCl = 427

Pauling: If strictly covalent: BDE HCl should be average of H2 and Cl2

Which would be ½ (436 + 239) = 338 kJ/mol. The extra stability is Due to electronegativity difference, and electrostatic attraction.

But ...

BDE H2 = 436 kJ/mol BDE I2 = 153 BDE HI = 299 Average ½ (436 + 153) = 295 kJ/mol

Note that χH = 2.2 and χI = 2.6 – and we expect that because HI isn’t stable!

Inorganic Chemistry Chapter 1: Figure 1.27

Inorganic Chemistry Chapter 1: Figure 1.28