Physical Methods in Inorganic Chemistry or How do we know what we made and does it have interesting properties?

What is electronic spectroscopy? Absorption of radiation leading to electronic transitions within a molecule or complex Absorption Absorption [Ru(bpy)3]2+ [Ni(H2O)6]2+ 104 10 ~14 000 25 000 50 000 200 400 700 visible UV UV visible n / cm-1 (frequency) - l / nm (wavelength) UV = higher energy transitions - between ligand orbitals visible = lower energy transitions - between d-orbitals of transition metals - between metal and ligand orbitals

Absorption maxima in a visible spectrum have three important characteristics number (how many there are) This depends on the electron configuration of the metal centre 2. position (what wavelength/energy) This depends on the ligand field splitting parameter, Doct or Dtet and on the degree of inter-electron repulsion intensity This depends on the "allowedness" of the transitions which is described by two selection rules

[Ti(OH2)6]3+ = d1 ion, octahedral complex Absorption of light [Ti(OH2)6]3+ = d1 ion, octahedral complex white light 400-800 nm 3+ Ti blue: 400-490 nm yellow-green: 490-580 nm red: 580-700 nm A This complex is has a light purple colour in solution because it absorbs green light l / nm lmax = 510 nm

[Ti(OH2)6]3+ lmax = 510 nm Do is  243 kJ mol-1 20 300 cm-1 The energy of the absorption by [Ti(OH2)6]3+ is the ligand-field splitting, Do ES ES eg eg hn Do GS GS t2g t2g d-d transition complex in electronic Ground State (GS) complex in electronic excited state (ES) [Ti(OH2)6]3+ lmax = 510 nm Do is  243 kJ mol-1 20 300 cm-1 An electron changes orbital; the ion changes energy state

d2 ion Electron-electron repulsion eg eg z2 x2-y2 z2 x2-y2 t2g t2g xy xz yz xy xz yz xy + z2 xz + z2 z z y y x x lobes overlap, large electron repulsion lobes far apart, small electron repulsion These two electron configurations do not have the same energy

Transition e complexes Selection Rules Transition e complexes Spin forbidden 10-3 – 1 Many d5 Oh complexes Laporte forbidden [Mn(OH2)6]2+ Spin allowed Laporte forbidden 1 – 10 Many Oh complexes [Ni(OH2)6]2+ 10 – 100 Some square planar complexes [PdCl4]2- 100 – 1000 6-coordinate complexes of low symmetry, many square planar complexes particularly with organic ligands Spin allowed 102 – 103 Some MLCT bands in cxs with unsaturated ligands Laporte allowed 102 – 104 Acentric complexes with ligands such as acac, or with P donor atoms 103 – 106 Many CT bands, transitions in organic species

e Tanabe-Sugano diagram for d2 ions 10 000 e 30 000 n / cm-1 - 10 20 000 5 [V(H2O)6]3+: Three spin allowed transitions E/B = 32 n1 = 17 800 cm-1 visible n2 = 25 700 cm-1 visible n3 = obscured by CT transition in UV D/B = 32 n3 = 2.1n1 = 2.1 x 17 800  n3 = 37 000 cm-1 25 700 = 1.44 17 800 D/B

Magnetism

macroscopic world « traditional, classical » magnets N S

macroscopic world N S A pioneering experiment by M. Faraday « Farady lines of forces » about magnetic flux N S

macroscopic world « traditional » magnets N S N S attraction N S

macroscopic world « traditional » magnets N S N S repulsion N S

macroscopic world looking closer to the magnetic domains S N     many sets of domains many sets of     atomic magnetic moments

The magnetic moments order at Curie temperature A set of molecules / atoms : Solid, Magnetically Ordered thermal agitation (kT) weaker than the interaction (J) between molecules … Paramagnetic solid : thermal agitation (kT) larger than the interaction (J) between molecules T C kT ≈ J Magnetic Order Temperature or Curie kT << J kT >> J

ferro-, antiferro- and ferri-magnetism Magnetic Order : ferro-, antiferro- and ferri-magnetism + = Ferromagnetism : Magnetic moments are identical and parallel + = Ferrimagnetism (Néel) : Magnetic moments are different and anti parallel + = 0 Antiferromagnetism : Magnetic moments are identical and anti parallel

Origin of Magnetism … the electron everything, tiny, elementary I am an electron • rest mass me, • charge e-, • magnetic moment µB everything, tiny, elementary

µtotal = µorbital + µspin Origin of Magnetism « Orbital » magnetic moment « Intrinsic » magnetic moment µorbital due to the spin s = ± 1/2 µspin e- µorbital = gl x µB x µspin = gs x µB x s ≈ µB µtotal = µorbital + µspin

Dirac Equation 1905 1928 The Principles of Quantum Mechanics, 1930 Nobel Prize 1933 1905 1928 Equation (10) can be regarded as the Schrödinger equation for an electron interactiong with fields describable by the potentials A and j . http://www-history.mcs.st-and.ac.uk/history/PictDisplay/Dirac.html

Electron : particle and wave Wave function or « orbital » n, l, ml … l = 0 1 2 3 s p d angular representation

Electron : also an energy level Orbitals Energy Empty Singly occupied Doubly occupied

Electron : also a spin ! Up Singly occupied Doubly occupied Down « Paramagnetic » S = ± 1/2 « Diamagnetic » S = 0

Molecules are most often regarded as isolated, non magnetic Dihydrogen diamagnetic Spin S = 0

the dioxygen that we continuously breath is a magnetic molecule orthogonal π molecular orbitals paramagnetic, spin S =1 Two of its electrons have parallel magnetic moments that shapes aerobic life and allows our existence as human beings

Transition Elements

Mononuclear complex ML6 Splitting of the energy levels E

How large is the splitting ? Weak Field Intermediate Field Temperature Dependent Spin Cross-Over Strong Field High spin Low spin L = H2O [C2O4]2- L = CN-

Spin Cross-Over Red 3 The system « remembers » its thermal past ! Room Temperature 3 Red The system « remembers » its thermal past ! O. Kahn, C. Jay and ICMC Bordeaux

Understanding … to get magnetic compounds … why the spins of two neighbouring electrons (S = 1/2) become : antiparallel ? S=O or parallel ? S=1

Interaction Models between Localized Electrons

Energy levels

J = 2 k + 4ßS <0 >0 O2 H2 if S = 0 Orthogonality if S≠0;|ßS|>>k Overlap O2 Hund H2 Aufbau

Exchange interactions can be very weak … Energy ≈ Exchange interactions order of magnitude : cm-1 or Kelvins … « Chemical » bonds Robust ! order of magnitude : >> 150 kJ mol-1 …

How to create the interaction … ? Cu(II) Cu(II) ≈ 5 Å Negligible Interaction ! How to create the interaction … ? Problem :

≈ 5 Å Cu(II) The ligand ! Solution : Ligand Orbital Interaction …

Examples with the ligand B Ligand Examples with the ligand • Cyanide

CN- Cyanide Ligand Friendly ligand : small, dissymetric, forms stable complexes Warning : dangerous, in acid medium gives HCN, lethal

homometallic complexes Dinuclear µ-cyano homometallic complexes

“Models” Compounds Cu(II)-CN-Cu(II) J/cm-1 Compounds exp [Cu2(tren)2CN]3+ [Cu2(tmpa)2CN]3+ -160 -100 Overlap : antiferromatic coupling … Rodríguez-Fortea et al. Inorg. Chem. 2001, 40, 5868