Everyday Examples of colored transition metal complexes A. Electronic Spectra A characteristic of transition metal complexes is color arising from electronic transitions between d-orbitals of different energies Everyday Examples of colored transition metal complexes The UV-Vis Experiment and the spectral result “Both rubies and sapphires owe their intense colors to impurities, ruby to the presence of chromium, and blue sapphire to both titanium and iron. In rubies, the color can be explained by crystal field theory, but in sapphire, a slightly different process, known as charge transfer, produces the color blue.” http://www.webexhibits.org/causesofcolor/8.html

The Beer-Lambert Law Absorbance = A = log (Io/I) Most modern systems give readings in A directly, so you don’t have to do the math. A has no unit. A = elc describes the absorption of light in a solution l = the length of the cell containing the solution, usual 1 cm c = concentration in mol/L = M e = Molar extinction coefficient = constant for a given molecule at a given wavelength of light = how well the molecule absorbs light Plotting Spectra E = hn c = ln = 3 x 108 m/s h = 6.626 x 10-34 Js = Planck’s constant Wavenumber = higher energy = larger wavenumbers Higher energy = smaller wavelength

Color What we see as the color of a compound is the complementary color to what the compound absorbs Example: Absorbs red, we see green Example: Absorbs yellow/orange, we see blue/purple Many complexes have multiple absorption band, so prediction is hard

Quantum Numbers of Multi-Electron Atoms: Free Ion Terms Review of Quantum Numbers

2. Russell-Saunders Coupling (or LS Coupling) The Orbital angular momenta (ml) and Spin angular momenta (ms) of multi-electron atom electrons interact with each other The result are multiple atomic states called Microstates New Quantum Numbers are used to describe these states ML = Sml = Total orbital angular momentum MS = Sms = Total spin angular momentum Determine the Microstates of a p2 electron configuration Shorthand: ms = +1/2 will be indicated by a superscript (+) ms = -1/2 will be indicated by a superscript (-) Example: ml = 1 and ms = +1/2 will be symbolized by 1+ Example: ml = 0 and ms = -1/2 will be symbolized by 0- Using the following two precautions, generate a table of all possible microstates No two electrons can have identical quantum numbers (Pauli Exclusion) Count only unique microstates (1+0- is the same as 0-1+) Arrange the microstates generated into a table according to ML and MS values Microstate 1+0- -1 0 +1

The p2 Microstate Table Example: Prepare a microstate table for an s1p1 configuration New Quantum numbers from ML and MS Combine (ml) and (ms) to get ML and MS which describe atomic microstates Combine ML and MS to get L, S, and J, which describe collections of microstates 1. Energy 2. Symmetry 3. Possible transitions between states of different energies (Electronic Spectra)

L = total orbital angular momentum quantum number = Largest possible value of ML ML describes component of L in the direction of a magnetic field for atomic state (just like ml describes component of l in direction of a magnetic field for an e-) d. S = total spin angular momentum quantum number = Largest possible value of MS MS describes component of S in a reference direction for atomic state (just like ms describes component of spin of an e- in a reference direction) Spin Multiplicity = 2S + 1 (1,2,3,4 = singlet, doublet, triplet, quartet); Left superscript Atomic states designated by L and S = Free Ion Terms (Term Symbols)

Examples of Determining Microstate Table from Free Ion Terms 1S (singlet S) L = 0, so ML = 0 2S + 1 = 1, so S = 0 Must be at least 2 e- to get S = 0 b. 2P (doublet P) L = 1, so ML = -1, 0, +1 2S + 1 = 2, so S = 1/2 , MS = +1/2, -1/2 (Minimum of 1 e- for S = ½) c. Exercise: Determine L, ML, S, and MS for: 2D, 1P, 2S 2D: L = 2, ML= -2,-1,0,1,2 S = ½, MS = +1/2,-1/2

Examples of Determining Term Symbols from Microstate Tables Can use “x” for each microstate; doesn’t need to be fully written out Determine rectangular arrays of microstates in the table Spin Multiplicity = # columns in the rectangle L value comes from largest value of ML in the rectangle Ground State (lowest energy) has maximum Spin Multiplicity (and largest L value if deciding between two with same Spin Multiplicity) = 3P for p2 case below Ground State 3P (Hund’s Rule) Example: d2 microstate table, Term Symbols, and ground state

Spin-Orbit Coupling L (orbital angular momentum) and S (spin angular momentum) interact with each other in multi-electron atoms J = L+S, L+S-1, L+S-2,….ǀL-Sǀ J value is listed as right subscript on the Term Symbol (3P2) Example: Determine J values for the p2 Term Symbols we just identified (1D,1S,3P) 1D: L = 2, S = 0, so J = 2 only and Term Symbol = 1D2 1S: L = 0, S = 0, so J = 0 only and Term Symbol = 1S0 3P: L = 1, S = 1, so J = 2,1,0 and Term Symbols = 3P2, 3P1, and 3P0 Spin-Orbit Coupling splits Free Ion Terms into different energies Hund’s 3rd Rule: subshells less than half full: Lowest J value = Lowest Energy subshells more than half full: Highest J value = Lowest Energy