The document provides information about electronic spectra and terms for carbon p electrons and transition metal d electron configurations. It discusses: 1) Possible terms that arise from carbon's 2p electrons, including 1D2, 3P2, 3P1, 3P0 and 1S0 terms. Hund's rules are used to determine the ground state term. 2) Microstate tables that list all possible combinations of orbital angular momentum (L) and spin (S) for electron configurations. 3) Tanabe-Sugano diagrams that show the splitting of d electron terms in an octahedral ligand field and allow determination of transition energies. 4) Charge transfer transitions that can occur from the

1. Electronic Spectra
Exercises
Dr. Chris, UP 2019
1

2. Free atom/ion terms
Consider the electron configuration of Carbon:
2s
2p
1 0 -1
Consider only the 2 p electrons, each has l = 1 with possible
sums of mL = 2, 1 and 0 => D, P and S Terms
(L = l1 + l2, l1 + l2 – 1, l1 + l2 -2, …. 0)
The Spins can be parallel or antiparallel, so S = 1 or 0
So the multiplicities can be 2S+1 = 1 (singlet) or 3 (triplet)
2

3. microstates
With L = 2, 1, 0 and S = 1, 0 we may think that J = L + S , L + S – 1, ….
would be 3, 2, 1, 0 -> BUT that is not possible because for L = 2 the
two electrons must be in the same orbital and then they cannot
have S = 1:
2p
1 0 -1 => L = 2
Possible combinations of L (as sum of mL) and S (as sum of
spins) can be listed in a table, called “microstates”
If we want to know all possible electrons states (terms) we
have to go through this process
3

4. 4

5. 5
From that we can find 1D2, 3P2, 3P1, 3P0 and 1S0 terms
– the ground state is 3P0 (highest spin, highest L)
5 x
3P
(9)
1S
(1)
1S0
1D
(5)
3P2
3P1
3P0
1D2

6. 6
Hund's rule (for groundstate term symbol)
1. The term with maximum multiplicity lies lowest in energy
2. For a given multiplicity, the term with the largest value of
L lies lowest in energy.
3. For atoms with less than half-filled shells, the level with
the lowest value of J lies lowest in energy. When the shell
is more than half full, the opposite rule holds (highest J
lies lowest).
15 microstates for p2
Remember:
This is the energy
splitting of the 2 p
electrons because of
L-S coupling, NOT
because of an
external field !!

7. d1 microstates
7

8. d2 microstates
…..
8

9. 9

10. 10

11. 11

12. Energies of Terms
The spin multiplicity rule is fairly reliable for predicting the
ordering of terms, but the ‘greatest L’ rule is reliable only
for predicting the ground term, the term of lowest energy;
there is generally little correlation of L with the order of the
higher terms.
Thus, for d2 the rules predict the order
3F < 3P < 1G < 1D < 1S
but the order observed for Ti2+ from spectroscopy is
3F < 1D < 3P < 1G < 1S
12

13. Term splitting (by el-el repulsion)
Ground state
(we get 3 groups of ground states which give similar splitting in Oh field)
13

14. Ground states
14

15. FREE ION TO COMPLEX ION
15

16. Splitting in octahedral field
16
L = 1
L = 2
L = 3

17. The same but in different symmetries:
17

18. Ground Terms of d configurations
Assign the Term symbols !
18

19. d1 complex
19

20. 20

21. 21
Tanabe-Sugano

22. Splitting of terms with electron-hole analogy
22

23. 23

24. For d1,d9 and d4(HS), d6(HS) o can be directly measured:
24

25. 25

26. d2: from ion to complex
26

27. d2 case:
Correlation between free ion and complex terms:
27

28. excited state t2g
1 eg
1
Including spin possibilities:
28

29. Tanabe-SuganoDiagram
Correlationsbetweenweak
andstrongfield
29

30. 30
https://www.academia.edu/6871688/Term_and_correlati
on_diagram_for_d2_system_in_octahedral_environment_
cubic_field_

31. Ground and excited triplet states d2
3F 3A2g 3T1g
3T2g
Ground
state
3P
3T1g 31

32. Why 2 T1 states ?
It requires more energy to bring an electron from
the xy plane to the z2 orbital
z2 x2-y2
xy xz yz
Than from an xz or yz to the z2 orbital
32

33. Two triplet states with different energy
mL = 2 1 0 -1 -2
Repulsion: LOW HIGH HIGH
Repulsion: HIGH LOW LOW
3F
3P
33

34. Here o has to calculated from Tanabe-Sugano:
(d7) (d3) 34

35. d2 spectrum
35

36. 36

37. 37

38. Compare d1, d2 and d3
38

39. 39

40. Tanabe Sugano Diagrams
What are the term symbols ?
Which excited states are relevant ?
https://chem.libretexts.org/Bookshelves/Physical_and
_Theoretical_Chemistry_Textbook_Maps/Supplement
al_Modules_(Physical_and_Theoretical_Chemistry)/S
pectroscopy/Electronic_Spectroscopy/Electronic_Spe
ctroscopy%3A_Interpretation 40

41. 41

42. Charge Transfer (CT) transitions
-acceptor
ligand
MLCT
From metal to ligand antibonding
42

43. -donor ligand
LMCT
From ligand to metal antibonding
CT transitions are
1. more intense than d-d
2. at higher energy than d-d
43

44. d3 case
The three unpaired electrons are in t3
2g orbitals which give
rise to 4A2g,2Eg,2T1g and 2T2g states.
Which one is the ground state and why ?
How does it look like ?
If one electron is excited, the configuration is t2
2ge1
g which
gives two quartet states 4T1g and 4T2g
How do they look like ?
44

45. Analyse the first excited states for each configuration !
d4 case
45

46. Get  for d2 case
46

47. The energy ratio
of the 2 peaks is
1,49
That gives / B = 29
 That gives me E2/ = 40.0
2 peaks in UV/VIS: at 25.600 cm-1 and 17.200 cm-1
http://wwwchem.uwimona.edu.jm/spectra/swingjs/TSd2.html 47

48. d3 case
4T2g <--- 4A2g
4T1g <--- 4A2g
4T1g(P) <--- 4A2g
Calculate the value of B and Δ for the Cr3+ ion in [Cr(H2O)6)]3+ if
1=17000 cm-1, 2=24000 cm-1 and 3=37000 cm-1.
SOLUTION.
These values have been assigned to the following spin-allowed
transitions.
From the information given, the ratio 2 / 1 = 24000 / 17000 = 1.412
Using a Tanabe-Sugano diagram for a d3 system this ratio is found at
Δ/B=24.0
48

49. The energy ratio 2/1 is 1.4
 /B = 24.0
 E1/B = 24
 17.000/B = 24
 B = 17000/24= 708 cm-1
 /708 = 24.0
  = 708 cm-1* 24 =
17.000 cm-1
49

50. https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Supplemental
_Modules_(Inorganic_Chemistry)/Crystal_Field_Theory/
Tanabe-Sugano_Diagrams
• For a d7 metal ion determine the energy ratios for allowed transitions
at Δoct/B of 20.
• For a d6 metal ion of Δoct/B = 30 and B=530 cm-1 what would the
energies of the 5 allowed transitions be? How many are in the UV-Vis
range? How many are in the IR range?
• Write out the allowed transitions for a d5 metal ion in a E/B> 28 ligand
field.
• A d4 complex exhibits absorptions at 5500 cm-1 (strong) and 31350 cm-1
(weak). What are the transitions that are being exhibited in the
complex? What is the corresponding Δoct for the complex?
• A spectrum of d7 metal complex seemingly exhibits only two intense
transitions. What is the Δoct/B that this situation occurs? Please use
reference to specific transitions and energy splitting. 50

51. d7 high and low spin
51

52. • Δoct/B of 20 yields E/B values of 38, 32, 18. Ratios then are 2.11 and 1.78
• Δoct/B = 30 yields E/B heights of 27, 40, 57, 65, 85. Energies are then
14310, 21200, 30210, 34450 and 45050 cm-1. All are in the UV-Vis range.
*note you need to infer the E/B value for the last transition as the
diagram does not extend that far up.
• 2A2g<-2T2g,
2T1g<-2T2g, 2Eg<-2T2g, and 2A1g<-2T2g.
• 31,350/5,500 gives a ratio of 5.7/1. The only Δoct/B value that matches is
at 10. B value is then 550 cm-1. Δoctequals 5500 cm-1.
• Three transitions are generated at low Δoct/B. However, at about a value
of Δoct/B = 13 the transitions 4A2g<-4T1g, and 4T1g<-4T1g have the same
energies which results in the appearance of only two absorptions.
52

53. Jahn-Teller distortion
53