The electronic spectra of d-complexes

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Chemistry 481(01) Winter 2009

• Instructor Dr. Upali Siriwardane
• e-mail upali_at_chem.latech.edu
• Office CTH 311 Phone [phone]
• Office Hours
• 800-900 a.m. 1100-1200 a.m. M, W
• 800-1000 a.m. Tu, Th, F.
• April 10, 2009(Test 1) Chapter 1,2,3 4
• April 24, 2009 (Test 2) Chapter 5,6,7
• May 19, 2009 (Test 3) Chapter 18 19
• May 21, Make Up Comprehensive covering all
  Chapters

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Chapter 13. The Electronic Spectra of Complexes

• The electronic spectra of atoms 13.1
  Spectroscopic terms 13.2 Terms of a d2
  configuration
• The electronic spectra of complexes 13.3
  Ligand-field transitions 13.4 Charge-transfer
  bands 13.5 Selection rules and intensities
  13.6 Luminescence  13.7 Spectra of f-block
  complexes  13.8 Circular dichroism  13.9
  Electron paramagnetic resonance
• Bonding and spectra of M-M bonded compounds
  13.10 The ML5 fragment   13.11 Binuclear
  complexes

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Electronic Spectra

• Why are so many coordination compounds colored,
  in contrast to most organic compounds?
• Low energy transitions between different electron
  configurations.
• Co(OH2)62 CoCl42-
• Pink Blue
• Ni(OH2)62 Ni(NH3)62-
• Green Blue

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UV-vis Spectra of Transition Metal Complexes
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What causes the change in color of Solution?

• Electronic Transitions
• One-Electron Model for hydrogen Doesnt work
  for electronic spectra
• Must consider how electrons interact with one
  another.
• Quantum Numbers of Multi-electron Atoms Electron
  configurations are more complicated than weve
  considered so far

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Quantum Numbers for single Electrons
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Electron-Electron Repulsions

• Hunds Rule
• Electron Repulsions result in
• Electrons occupying separate orbitals when
  possible
• Electrons in separate orbitals have parallel
  spins
• Easy to describe individual electrons, more
  complicated to describe sets of electrons.
• p2, p3, d2, d3, d4, f2, f3, f5 etc

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Vector Addition of ml and ms

• These are obtained by the vectorial addition of
  the individual electron Orbital Angular Momentum
  i.e. the ml values and the Spin Angular Momentum
  i.e. the ms values
• Must first ask which order is the vectorial
  addition to be carried out ? If we consider just
  2 electrons in an
• incomplete shell
• Which is the stronger coupling ms1.ms2 and
  ml1.ml2
• Or ms1.ml1 and ms2.ml2 ?
• This choice gives rise to 2 coupling schemes
• a) Russell-Saunders coupling (RS) b) jj-coupling

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Example

• Consider a Carbon Atom
• Electron Configuration 1s2 2s2 2p2
• Do the 2-p electrons have the same energy?
• Three major energy levels for the p2 electron
  configuration
• Lowest energy major level is further split into
  three levels
• The two electrons in p2 configuration are not
  independent
• Orbital angular momenta interact
• Spin angular momenta interact

Russell-Saunders or LS Coupling
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Russell-Saunders orLS Coupling

• LS Coupling
• Interactions produce atomic states called
  microstates described by new quantum numbers
• ML Sml Total orbital angular momentum
• Ms Sms Total spin angular momentum

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Labelling Term Symbols

• Maximum Values of
• L 0, 1, 2, 3, 4 etc
• S P D F G etc cf 1 -electron case
  (orbitals)
• Maximum Values of
• S 0, 1/2, 1, 11/2, 2 etc
• 2S1 1 2 3 4 5 etc as superscript

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How do we determine the Microstates for p2?

• 1. Determine the possible values of ML and MS.
• max. ML? 2
• values of ML? 2, 1, 0, -1, -2
• max. MS? 1
• values of Ms? 1, 0, -1

Total Orbital Momentum L 0 1 2 3
4 5 6 S P D F G H I
Spin multiplicity 2S1 1 2 3 4 5
The Russell Saunders term symbol that results
from these considerations is given by (2S1)L
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l 1 x2 Microstates for p2 15

• Determine the electron configurations allowed by
  the Pauli principle.

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TERMS SYMBOLS

• are referred to as singlet, doublet, triplet etc.
  according to value of 2S1. Denotes Spin
  multiplicity or spin degeneracy of term.
• Thus the terms for p2 can be derived as 1D, 3P,
  1S
• The total degeneracy of each term (2S1)(2L1)
• Thus the original set of 15 microstates for p2
  has become sub divided into 3 terms
• 3P 3x3 9
• 1D 1x5 5
• 1S 1x1 1
• 15

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d1 configuration

• As an example, for a d1 configuration
• S ½, hence (2S1) 2
• L2
• and the Ground Term is written as 2D
• d9 has the same configuration

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d2 term symbols

• Microstates for d2 45
• max. ML? 4
• values of ML? 4, 3, 2, 1, 0, -1, -2, -3, -4
• max. MS? 1
• values of Ms? 1, 0, -1
• 1S 3S 1P 3P 1D 3D 1F 3F 1G 3G
• 1 3 3 9 5 15 7 21 9 27
• For d2 terms 1S 1D 1G 3P 3F the lowest is 3F
• 1S 1x1 1
• 3P 3x3 9
• 1D 1x5 5
• 3F 3x7 21
• 1G 1x9 9
• 45

Nl2(2l1) l2 10!/2!(8!)
L 0 1 2 3 4 S P D
F G S 1 3
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Spin-Orbit Coupling

• In the Russell-Sunders coupling scheme after
  allowing for the coupling of the individual spins
  to give a resultant spin (S) and the individual
  orbital angular momenta to give a resultant value
  (L) then we can consider spin-orbit coupling (J)
• S.L ? J (the total angular momentum)
• The J values are given by L S, L S - 1,L -
  S
• The levels then arising are labelled 2S1LJ
• For example consider the ground state term 3F
  for d2
• Here S 1, L 3 hence J 4, 3 ,2
• 3F level into three new closely separated levels
  3F4, 3F3, 3F2

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Spin-orbit coupling constant l or z
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Terms for 3dn free ion configurations
Note that dn gives the same terms as d10-n
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Ground Term Symbol

• Have the maximum spin multiplicity
• If there is more than 1 Term with maximum spin
  multipicity, then the Ground Term will have the
  largest value of L.

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The Crystal Field Splitting of Russell-Saunders
terms

• Crystal or Ligand Field affect the different
  orbitals (s, p, d, etc.) will result in splitting
  into subsets of different energies based on
  character table.
• Octahedral (Oh)field environment will cause the
• d orbitals to split to give t2g and eg subsets
  of 5 states
• D term symbol into T2g and Eg(where upper case is
  used to denote term symbols and lower case
  orbitals).
• f orbitals are split to give subsets known as
  t1g, t2g and a2g subsets of 7 states.
• F term symbol will split by a crystal field will
  give states known as T1g,T2g, and A2g.

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Crystal Field Splitting of RS terms in high spin
octahedral crystal fields.
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Orgel diagrams

• Diagram showing the terms arising from crystal
  field splitting The spin multiplicity and the g
  subscripts are dropped for simplicity

right (Oh) d2 , d7
Left (Oh) d3 , d8 (Td) d7
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Racah Parameters

• Racah Parameters
• In practice, however, two alternative parameters
  are used for dn terms
• B F2 - 5F4
• C 35F4
• These are called Racah Parameters Racah
  recognised that these relationships appeared
  frequently and thus it is
• more convenient to use B and C.

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Tanabe-Sugano Diagrams
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Term reversal on going dn to d10-n

• d1 and d9 ? 2D
• d2 and d8 ? 3F and 3P
• d3 and d7 ? 4F and 4P
• d4 and d6 ? 5D

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Tanabe-Sugano Diagrams d2 in Oh field
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