1. 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.”

2. 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 = x Js = Planck’s constant
Wavenumber =
higher energy = larger wavenumbers
Higher energy = smaller wavelength

3. 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

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

5. 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-

6. 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)

7. 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)

8. 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

9. 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

10. 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