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Ground State Electron Configurations and Term Symbols

d 1 (Ti 3+ ). d 2 (V 3+ ). t 2g 3. Spin multiplicity. Degeneracy of system. Describes the whole complexed ion system. Symmetry label. Ground State Electron Configurations and Term Symbols.

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Ground State Electron Configurations and Term Symbols

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  1. d1 (Ti3+) d2 (V3+) t2g3 Spin multiplicity Degeneracy of system Describes the whole complexed ion system Symmetry label Ground State ElectronConfigurations and Term Symbols Electrons are added to d-orbitals according to Hund’s Rule and the Pauli principle. So for d1 in octahedral geometry we have: d3 (Cr3+, Mn4+) t2g1 t2g2 e config Term symbol 2Tg 3Tg 4Ag Spin multiplicity = 2S+1, S = total electron spin: ±1/2 for each e- Degeneracy: T = triply degenerate E = doubly degenerate A = non-degenerate Symmetry: g = centrosymmetric

  2. d1 (Ti3+) d2 (V3+) t2g3 Notes: d3 (Cr3+,Mn4+) t2g1 t2g2 e config Term symbol 2Tg 3Tg 4Ag These diagrams and term symbols represent complexed ions – i.e with ligands bound and in octahedral geometry They are all paramagnetic – i.e. they contain unpaired electrons This does not mean they are unstable – many coordination complexes contain unpaired electrons.

  3. d4 (Cr2+,Mn3+) or t2g4 t2g3eg1 e config For d4 there is a choice of where to place the 4th electron: 2 unpaired e- S = 1 “low spin” 4 unpaired e- S = 2 “high spin” Term symbol 3Tg 5Eg The high spin configuration costs energy = D to raise the 4th electron to the eg orbital set The low spin configuration costs energy = P (electron pairing energy) to pair up 2 electrons in a single orbital in the t2g orbital set The lowest energy configuration will be adopted: high spin if P > D low spin if P < D P is ~ constant but D depends on the nature of the ligands etc – so both high-spin and low-spin d4 complexes can be prepared.

  4. + z z y y + + x x E Free ion Spherical field Recap: Crystal Field Theory for an Octahedral Complex z y x eg Do t2g Octahedral complex Note: it is electrons in orbitals that interact with ligands, not the orbitals themselves. the interaxialt2gorbitals are bothstabilised the axial egorbitals are all destabilised - relative to a spherically symmetric case.

  5. d4 (Cr2+,Mn3+) or t2g4 t2g3eg1 e config Spin multiplicity Degeneracy of system Describes the whole complexed ion system Symmetry label RECAP: 2 unpaired e- S = 1 “low spin” 4 unpaired e- S = 2 “high spin” 3Tg 5Eg Term Symbol Note High-spin and low-spin do NOT mean the same as ground and excited states Spin multiplicity = 2S+1, S = total electron spin: ±1/2 for each e- Degeneracy: T = triply degenerate E = doubly degenerate A = non-degenerate Symmetry: g = centrosymmetric

  6. d5 (Mn2+,Fe3+) d6 (Fe2+, Co3+) or t2g5 t2g3eg2 t2g4eg2 continue: low-spin high-spin d5 high-spin has the maximum possible number of unpaired electrons Term symbol 6Ag 2Tg d6 low-spin is diamagnetic – no unpaired e In d6 high-spin one electron must pair up or t2g6 Term symbol 5Tg 1Ag

  7. d7 (Co2+) or t2g6eg1 t2g5eg2 d8 (Ni2+) d9 (Cu2+) d10 (Cu+, Zn2+) t2g6eg4 t2g6eg2 t2g6eg3 In d7 low-spin one e must be in the eg set There is only one possible d8 config. no high- or low-spin forms d10 diamagnetic, no unpaired e. All 5 3d orbitals filled

  8. Electron configurations and term symbols for tetrahedral complexes can be derived in the same way but: In tetrahedral complexes Dt is always less than P – so, in practice, tetrahedral complexes are always high spin. Since tetrahedral complexes are non-centrosymmetric, their term symbols do not include the symmetry label “g”. • Tutorial question 3: • Sketch the ground state d-orbital occupancy diagram and give the spectroscopic term symbols for: • High spin Co(II) in an octahedral ligand field • Mn(IV) in an octahedral ligand field • Mn(IV) in a tetrahedral ligand field • [CoCl4]2- • A metal ion with a 1Ag ground state • Work them out – don’t look them up! Next: evidence for the electron configurations we have just derived.

  9. Evidence for d-orbital configurations: 1. Geometry of complexes The geometry of complexes is normally controlled by 3 factors: • Relative size of metal ion and ligands. • The electroneutrality principle. Generally, cations will try to achieve an effective charge close to zero. e.g. [FeF6]4–is octahedralbut [FeCl4]2– is tetrahedral– both are stable: Cl– is a good electron donor so Fe(II) achieves an effective charge close to zero with 4 Cl– ions coordinated. There is no electrostatic driving force to bind more anions and the tetrahedral [FeCl4]2– ion forms. F– is a poor donor, so more ligands are required to reduce the effective charge at the Fe(II), octahedral [FeF6]4– forms. (c) The influence of the d-orbitals - examples follow.

  10. dx2-y2 dxy dz2 } dxz dyz } tetrahedral low spin a) Square Planar Geometry Tetrahedral geometry should be preferred in 4-coordinate complexes for steric reasons. So why do some metals readily form square-planar complexes? Square planar geometry is chiefly observed for d8ions, e.g. Ni2+, Pd2+, Pt2+. The explanation lies in the d-orbital splitting for square planar geometry. In the d8 low-spin configuration: square planar geometry leaves the dx2-y2 orbital empty - minimises the interaction of the d electrons with ligands. Square planar is favoured if its total energy is less than for the tetrahedral equivalent. high spin Square planar complexes are likely for d8 complexes where D is large – as larger splitting of the d-orbitals favours low-spin square planar.

  11. L L L L Cu L L d9 Cu2+ b) Jahn-Teller Effects Consider Cu2+ (d9) in octahedral geometry: One of the axial orbitals has 2 electrons in it, the other has only one Ligands approaching the filled orbital will experience more shielding from the positive charge on the metal than ligands approaching the half-filled orbital. The balance of attraction/repulsion effects will be different – so the equlibrium metal-ligand bond distances will be different. The complex will distort from octahedral geometry. Jahn-Teller Theorem – no non-linear molecule can be stable in a degenerate electronic state. It will distort to remove the degeneracy.

  12. L L L L M L L L L L M L L L The Jahn-Teller theorem does not predict how the complex will distort. In Cu2+ complexes we usually see extended tetragonal geometry – four strongly bound donors in the square plane and two axial donors bound more weakly (e.g.[Cu(NH3)4(H2O)2]2+). Tetragonal contraction is less commonly observed Tetragonal extension dz2 full dx2-y2 half-full Tetragonal contraction dz2 half-full dx2-y2 full e.g. [Cu(NH3)4(H2O)2]2+ Other configurations which show Jahn-Teller distortions in the ground state are high-spin d4, low spin d7 etc…

  13. Evidence for d-orbital configurations: 2. Ionic radii Measurements of ionic radii are taken from X-ray studies: Na Cl

  14. Oct. 2+ ions – first transition series expected trend due to increasing nuclear charge 100 h.s. Mn2+ 80 Ionic radii (pm) 60 low spin l.s. Fe2+ high spin 10 0 1 2 3 4 5 6 7 8 9 Number of 3d electrons Evidence for d-orbital configurations: 2. Ionic radii Measurements of ionic radii (from X-ray studies) show that, for the first transition series the radii depend not only on charge – but also on d-electron configuration. Only d0, d5 and d10 configurations fit the expected curve (empty, half-full and full configs – ie spherically symmetric).

  15. 80 70 Ionic radii (pm) 60 low spin 50 high spin 10 0 1 2 3 4 5 6 7 8 9 Number of 3d electrons Radii decrease when electrons go into interaxial orbitals and increase when electrons go into axial orbitals For high-spin, radii start to increase when the first electron goes into the eg orbitals (d4). The pattern then repeats for d6 to d10. For low spin, radii decrease up to d6(all electrons into t2g set) then increase as 7th electron goes into eg set. These data provide direct evidence for the electron distributions derived previously

  16. 7th electron must go into the axial orbitals – directed towards the ligands. M-L bond lengthens and ionic radius increases Low-spin – radii decrease until t2g6 config is reached (Fe2+ or Co3+). Electrons are going into the interaxial orbitals – ligands experience less shielding than in spherical arrangement – so they approach more closely – radius appears smaller. 80 70 Ionic radii (pm) 60 low spin 50 high spin 10 0 1 2 3 4 5 6 7 8 9 Number of 3d electrons 3+ ions – first transition series – same pattern • Smooth curve passes through d0 d5 & d10 • the spherically symmetrical distributions. • non-spherical arrangements are all below this line

  17. You should now be able to do tutorial question 4 Tutorial question 4 Use CFT to deduce the trends in ionic radii of the first transition series 2+ ions in tetrahedral symmetry. Sketch a curve similar to those opposite* for the tetrahedral case * Opposite on the handout • At this point you should be able to: • Draw d orbital energy level diagrams for dn ions • Write electron configurations and term symbols for various octahedral or tetrahedral ions • Understand the terms “high-spin” and “low-spin” • Understand the relationship between D, P (electron pairing energy), and spin state. • Explain the effect of d orbital occupancy on geometry in d8 ions and Jahn-Teller ions. • Define and account for the Jahn-Teller effect • Explain the variation of ionic radii with dn and spin state

  18. Magnetic Properties Unpaired electrons in the d shells lead to the distinctive magnetic properties of transition metal complexes. There are several classes of magnetic behaviour: 1) Diamagnetism - a property of all matter. The planes of orbitals are slightly tipped in an applied magnetic field, generating a small magnetic moment which opposes the applied field causing weak repulsion from magnetic fields. (http://www.youtube.com/watch?v=rotTjRY5lRw) 2) Paramagnetism - due to the presence of unpaired electrons causing quite strong attraction into a magnetic field. We will consider paramagnetism in more detail. 3) Ferromagnetism, antiferromagnetism, and ferrimagnetism all depend on interactions between unpaired electrons of neighbouring metal ions. These are important effects but will not be discussed in this course.

  19. Paramagnetism - due to the presence of unpaired electrons causing quite strong attraction into a magnetic field. If the unpaired electron is considered (crudely) as a spinning charge orbiting the nucleus, then it will have a magnetic field associated with it. This has two components: (i) the electron spins on its axis, generating a spin magnetic moment, ms (ii) the electron orbits the nucleus, generating an orbital magnetic moment, ml Paramagnetic materials also possess diamagnetism (due to all the paired electrons in closed shells) but because the paramagnetic effects are much stronger, paramagnetic behaviour will dominate.

  20. Magnetic behaviour can be described in terms of the molar magnetic susceptibility, M, of the sample, where M = force exerted by the magnetic field per mole of sample. A negative value implies repulsion from the magnetic field: Paramagnetism is a much stronger effect than diamagnetism – but ferromagnetism can be much stronger again.

  21. balance sample electro- N S magnet Gouy balance Measurement of magnetic properties - gives information on unpaired electrons Need a way to measure the attraction or repulsion of the sample by a magnetic field. The simplest method is a Gouy balance. Sample is in a glass tube hanging from a sensitive balance so that the bottom of the sample is between the poles of an electromagnet magnet and in the middle of the magnetic field. The sample is weighed with the magnet off, and again with the magnetic field on. Paramagnetic samples are pulled into the field and show an apparentincrease in weight. Diamagnetic samples are repelled from the field and show an apparent decrease in weight. For paramagnets the apparent increase in weight is related to the number of unpaired electrons in the complex. (The Evans balance used in the teaching lab employs a variation of this method – the sample stays still and the magnet moves.)

  22. Sample tube guide

  23. Sample tube guide Magnet Balancing wire

  24. Keep “ x 10-6” format throughout calc 2 decimal places No d.p. here, 056 = 56, not 0.56 appropriate balance! Measure T Evans Balance Calculations: Calculate M , (molar magnetic susceptibility)using: in cgs units Where C = calibration constant - measured as 1.044 L = length of the sample in cm R and Ro are the balance readings for the full and empty tubes M is the formula weight of the sample m is the mass of the sample in grams Use Pascal's constants to evaluate the diamagnetic correction (DC)* Calculate the corrected molar susceptibility of the sample: 'M = M - (DC) Calculate meff, the effective (experimental)magnetic moment (in Bohr Magneton): BM (where T = temp (K))

  25. Where 1BM = meff = 2.83cMT in units of BM Where T = Temp (K), e = electron charge, = (Planck’s Constant)/2p, cM = molar susceptibility, m = electron mass and c = speed of light eh 4pmc Also because quantum mechanics gives the following simple expression for ms in units of BM: h ms = 2S(S+1) BM Where S = total spin of the ion (±½ per unpaired electron). For paramagnets the apparent increase in weight is related to the number of unpaired electrons in the complex. The molar magnetic susceptibility cM can be obtained from the weighings, RMM and some calibration (for the strength of the magnetic field, the glass of the sample tube, the contribution of diamagnetic atoms etc. - See lab manual) Results are usually quoted in terms of the effective magnetic moment, meff, which has units of Bohr Magnetons (BM or, sometimes mB). This odd unit (Bohr magneton) is used because it incorporates constants which would otherwise have to be included specifically in the calc.

  26. ms = 25/2(5/2 +1) B.M. ms = 2 2.5(3.5) B.M. ms = 2 (8.75) B.M. ms = 2S(S+1) BM Using this expression the spin-only magnetic moment can be calculated for any electron configuration eg for a high spin Mn2+ complex: Mn2+ is ad5 ion ms = 5.92 B.M. S = 5/2 The measured magnetic moment (meff) is made up of two components, the spin magnetic moment and the orbital magnetic moment: meff = ms +ml For the first transition series ms is much larger than ml Also ms is independent of the environment but ml is not. Contributions from ml are significant only for T ground states Key point: ms usually gives a good approximation to the experimental value of meff for first row transition ions.

  27. ms = 2S(S+1) BM Comparison of spin-only and experimental values of magnetic moments: High Spin Octahedral Configurations

  28. Comparison of spin-only and experimental values of magnetic moments: Low Spin Octahedral Configurations Measurement of meff allows the number of unpaired electrons to be found meff is often a little lower (LHS of the transition series) or higher (RHS) than the spin only moment ms- but the difference is not enough to prevent assigning the number of unpaired electrons in the first transition series. Note: ml is significant for the 2ndand 3rdtransition series and for the f-block. msis not a reliable guide to the expected magnetic moment in these cases.

  29. theycan be measured quite easily • meff = 2.83cMT in units of BM (Bohr magneton) balance Measured, experimental magnetic moment Orbital magnetic moment Spin magnetic moment sample electro- N S magnet ms, the spin-only magnetic moment can be calculated for any electron configuration : Gouy balance ms = 2S(S+1) BM Recap: magnetic moments are due to the presence of unpaired electrons - They are made up of 2 components: meff = ms + ml - For the first transition series, ml is small or absent, so: meff ≈ ms Punchline: the number of unpaired electrons in a complex can be experimentally determined from magnetic moment measurements

  30. You should now be able to: Explain the meaning of “diamagnetic”, “paramagnetic” and “magnetic moment” Explain the basis of the Gouy method for measuring magnetic moments Calculate spin-only magnetic moments for any dn configuration Determine the number of unpaired electrons in a sample by experiment Tutorial Question 5: [Co(H2O)6]Cl3 is a low spin complex but [Co(H2O)6]Cl2 is high-spin. Calculate the spin-only magnetic moments expected for each complex and account for the difference in their behaviour. Tutorial Question 6: A compound of empirical formula Fe(H2O)4(CN)2 is found to have a magnetic moment corresponding to 2.67 unpaired electrons per iron. How is this possible? (Hint: all the iron ions have octahedral geometry but there is more than one iron species in the complex.)

  31. high-spin Fe2+ high-spin Fe3+ low-spin Fe2+ low-spin Fe3+ Measurements of magnetic moment often give additional information besides the number of unpaired electrons. Some examples follow: 1) You make an iron complex, believed to be six-coordinate. Four combinations of redox and spin states are possible but the correct one can be found by measuring the magnetic moment: oxidation state spin state number of upe- ms (BM) Fe(II) high-spin 4 4.9 Fe(II) low-spin 0 0 Fe(III) high-spin 5 5.9 Fe(III) low-spin 1 1.7 Magnetics give information on spin-state and oxidation state

  32. dx2-y2 dxy dz2 } dxz dyz ````` 3) A six-coordinate Ni2+ complex is found to be diamagnetic, what does this imply about the geometry? Ni2+ is d8 Octahedral 2 unpaired e− S=1 ms = 2.83 BM Tetragonal high-spin 2 unpaired e− S=1 ms = 2.83 BM Tetragonal low-spin 0 unpaired e− S=0 diamagnetic If the sample is diamagnetic it cannot be regular octahedral – most likely there is significant tetragonal distortion.

  33. phen N N or Spin Transitions (spin crossover). The magnetic moment of the complex [ Fe(phen)2(NCS)2] is 5.2 BM at room temperature but 0.5 BM at 100K. For Fe2+ (d6) in octahedral geometry there are two possible electronic configurations: high-spin P > D 5Tg S = 2 ms= 4.8 BM low-spin P < D 1Ag S = 0 ms= 0 BM What happens if P ≈D ? If the difference between P and D is small (comparable to the thermal energy of the system - kT), the spin state of the complex will be temperature- dependent.

  34. 5.2 meff (BM) • 0.5 T (K) Spin Transitions (spin crossover). if P ≈D ; At low temperatures the complex is low spin, but at higher temperatures the thermal energy can switch the complex to a high spin state. The 5Tg ↔ 1Ag spin transition is often very sharp. There are not many complexes in which the P D condition is met. [Fe(phen)2(NCS)2] is one of the most well-studied examples. Since the spin transition is accompanied by a change in other properties (eg colour), such systems can be used in electronic switching devices or sensors.

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