Lecture 4; January Electrons in Atoms: Magnetism; Term Symbols, Z eff, and Other Properties

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1 Lecture 4; January 2017 Electrons in Atoms: Magnetism; Term Symbols, Z eff, and Other Properties

2 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 In the absence of a magnetic field Ferro-magnet In the presence of a magnetic field

3 Gouy Balance for Magnetic Susceptibility

4 Magnetic Susceptibility ( ) measurement; Faraday Balance to microbalance z F dh z =mh c dz g sample is moved into } constant range N S H dh dz Zero Field: F z = mg g - gravitational constant With Field: F z = de dz = m é g + æ ê è ç ë H dh dz ö ø c ù g ú 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.

5 How do we approach magnetism? Electron Assignments: Identifying each and every quantum number for each and every electron: n l m l m s

6 Electrons are characterized by... a) Principal energy level, n b) Orbital or angular momentum, l (= # of angular nodes) c) Azimuthal quantum number, m l, the z component of L. ( L = [l(l+1)] 1/2 ), (L) z = m l. 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 m l. d) Spin-spin and spin-orbital coupling

8 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.

9 Carbon: Atomic Energy Experimental atomic energy levels (cm 1 ). Levels Hybridization cost!? Where do these energy levels come from?

10 Ti 2+ ion energy levels Again, where are all the energy levels coming from? Hint: They are all [Ar]3d 2, the lowest [Ar]3d 1 4s 1 energy levels are at ~38,000 cm 1

11 Box Diagrams Figure 1.4 The possible sets of quantum numbers for n = 1 and n = 2. m l values

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

13 Ground State vs. Excited State Configurations Term Symbols: 2S + 1 L J Spin: S = S m s = total spin angular momentum 2S + 1 (called spin multiplicity ) L = total orbital angular momentum J = L + S = S m l

14 Electrons can have spin and orbital angular momentum Spin (all electrons):

15 Visualizing orbital angular momentum ψ 2p±1 = ψ 2px ± i ψ 2py e circulation 2p 1 μ 2p+1 μ ± i = Ψ 2px ψ 2py ψ 2p±1 m l = ±1 Electrons have a net circulation in the m l = ±1 orbitals

16 Visualizing orbital angular momentum ψ 3d±2 = ψ 3dx 2 y 2 ± i ψ 3dxy e circulation 3d 2 μ 3d+2 μ ± i = ψ 3dx 2 y 2 ψ 3dxy ψ 3d±2 m l = ±2 Electrons have a net circulation in the m l = ±2 orbitals

17 Visualizing orbital angular momentum ψ 3d±1 = ψ 3dxz ± i ψ 3dyz e circulation 3d 1 μ 3d+1 μ ± i = ψ ψ 3dxz 3dyz ψ 3d±1 m l = ±1 Electrons have a net circulation in the m l = ±1 orbitals

996 0.998 L = [l(l+1)] 1/2 E = 2µ B H H z H 1.000 H (along z axis) See section 8.

18 m l = l, l 1,, l Pictorial View of L, m l m l relative populations at 298 K, H = 1.0 T E E = +2µ B H l = 2 Precession of L E = +µ B H L E = 0 E = µ B H L = [l(l+1)] 1/2 E = 2µ B H H z H H (along z axis) See section 8.7 and p. 264 in the text. Also see similar discussion in NMR in McMurray, Chap. 13.

19 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 1 st * Maximum value of S 2 nd * Maximum value of L within that S

20 Russell Saunders Coupling (L-S Coupling) for Ground States Configuration => Term Symbol Sm L = max. M L or L 2 S S + 1 Sm S = M S or S Spin Multiplicity J # unpaired e - S 2 S + 1 L State 1 1/2 2 doublet 0 S triplet 1 P 3 3/2 4 quartet 2 D pentet 3 F 4 G

21 Russell Saunders Coupling: Spin/Orbit Coupling

22 Inorganic Chemistry Chapter 1: Figure W.H. Freeman

23 Trends in Atomic Properties Size (atomic, ionic, covalent, van der Waals radii) Ionization Potential (A 0 (g) + I.E. A + + e - ) Electron Affinity Energies (A 0 (g) + e - A - + E.A.E.) Electronegativity: Ability of an atom, within a molecule to attract electrons to itself.

24 Inorganic Chemistry Chapter 1: Figure W.H. Freeman

25 Inorganic Chemistry Chapter 1: Table W.H. Freeman

26 Inorganic Chemistry Chapter 1: Figure W.H. Freeman

27 Metallic Single-Bond Distances (useful for M-M bonding and intermetallic compounds)

28 Inorganic Chemistry Chapter 1: Table 1.4 Cations are smaller than Neutral atom Anions are Larger than Neutral atom 2009 W.H. Freeman

29 Trends in Atomic Properties Size (atomic, ionic, covalent, van der Waals radii) Ionization Potential energy (A 0 (g) + I.E. A + + e - ) Electron Affinity Energy (A 0 (g) + e - A - + E.A.E.) Electronegativity: Ability of an atom, within a molecule to attract electrons to itself.

31 Inorganic Chemistry Chapter 1: Figure W.H. Freeman

32 Inorganic Chemistry Chapter 1: Table W.H. Freeman

35 nd vs. (n + 1)s in the Transition Metals

36 kj/mol Ionization Energies Transition Metals - some complications d9 d10 d5 d 6 d 7 d 8 d10s1 d4 d3 2nd IP d2 dn-1 dn-2 dn-2s2 dn-1 or d10s2 dn-1s1 dn-1 d6s2 d 7s2 d5s2 d8s2 d10s1 d2s2 d1s2 d3s2 1st IP d5s1 Sc Ti V Cr MnFe Co Ni Cu Zn

37 Inorganic Chemistry Chapter 1: Table W.H. Freeman

38 BDE: kj/mol

39 Electronegativity Pauling c M - c M = E A-B - 1 ( 2 E A- A + E ) B-B c M - c M = E A-B E A- A E B-B Mulliken c M = 1 2 ( IE + EA) Rochow Allred and Rochow Scale This scale considers electronegativity as the force acting on electrons at a distance of the covalent radius. c M = Z eff Z eff 2 r cov = effective nuclear charge r cov = Covalent radius of the atom, in Å.

Linus Pauling BDE H 2 = 436 kj/mol BDE Cl 2 = 239 BDE HCl = 427 Pauling: If strictly covalent: BDE HCl should be average of H 2 and Cl 2 Which would be ½ (436 + 239) = 338 kj/mol.

40 Linus Pauling BDE H 2 = 436 kj/mol BDE Cl 2 = 239 BDE HCl = 427 Pauling: If strictly covalent: BDE HCl should be average of H 2 and Cl 2 Which would be ½ ( ) = 338 kj/mol. The extra stability is Due to electronegativity difference, and electrostatic attraction. But... BDE H 2 = 436 kj/mol BDE I 2 = 153 BDE HI = 299 Average ½ ( ) = 295 kj/mol Note that χ H = 2.2 and χ I = 2.6 and we expect that because HI isn t stable!

42 Inorganic Chemistry Chapter 1: Figure W.H. Freeman

45 Inorganic Chemistry Chapter 1: Figure W.H. Freeman

362 Lecture 6 and 7. Spring 2017 Monday, Jan 30

362 Lecture 6 and 7. Spring 2017 Monday, Jan 30 362 Lecture 6 and 7 Spring 2017 Monday, Jan 30 Quantum Numbers n is the principal quantum number, indicates the size of the orbital, has all positive integer values of 1 to (infinity) l is the angular