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- 1. How do we take interactions with ligands into account? Transition Metals -- Bonding and Spectroscopy Crystal ﬁeld theory Molecular orbital theory Hybrid orbitals and valence bond theory Includes crystal ﬁeld theory for transition metal complexes Density function theory (Ch 11, pp 387 - 413 Huheey; Ch 7 Carter) Look at crystal ﬁeld theory ﬁrst Molecular orbital theory Huheey, Ch. 11; Carter, Chapter 7 Includes MO theory for transition metal complexes (Ch 11, pp 413 - 433 Huheey; Ch 7 Carter)Andrei N. Vedernikov -- University of Marylandhttp://www.chem.umd.edu/groups/vedernikov/VGroup_Teaching-601.htm http://www.tcd.ie/Chemistry/Under/ch3018.html 1 2 Free Atom States --- Term Symbols Free Atoms Molecular Complexes Solids H = E Atkins/Shriver = Hfree atom 3 4 1
- 2. HFree atom contributions Free Atom States -- Term Symbols Lifting of energy degeneracies in a d2 gaseous atom 5 6 Lifting of energy degeneracies in a d2 gaseous atom How do we take interactions with ligands into account? Crystal ﬁeld theory Molecular orbital theory Density function theory Look at crystal ﬁeld theory ﬁrstelectron Huheey, Ch. 11; Carter, Chapter 7configuration Andrei N. Vedernikov -- University of Maryland http://www.chem.umd.edu/groups/vedernikov/VGroup_Teaching-601.htm spin states and terms from sisj multiplets from Experimental http://www.tcd.ie/Chemistry/Under/ch3018.html 7 8 and li lj coupling lisi coupling 2
- 3. The electronic effects of adding ligands to the free atom Electronic structure of Coordination CompoundsH = E Crystal Field Theory • Considers only electrostatic interactions between the ligands and the metal ion. • Ligands are considered as point charges creating an electrostatic field of a particular symmetry Main steps to estimate the relative energies of d-orbitals in a ﬁeld of a particular symmetryThree cases 1) An isolated metal ion. Five d-orbitals are degenerate• Ligands don t a ect outer valence electrons- lanthanides 2) A metal ion in an averaged ligand ﬁeld. The orbital energy increases due to electron (metal) – electron (ligands) repulsions. Oh octahedral• Ligands weakly affect outer valence electrons---many 3d complexesWeak Field case 3) A metal ion in a ligand ﬁeld of certain symmetry. d- energy levels may become split into several sublevels.• Ligands strongly affect outer valence electrons-- Some of d-orbitals become stabilized, some become lessStrong Field case stable. The total orbital energy gain due to the 9 stabilization is equal to the total orbital energy loss. 10 Symmetry and the atom ...reducible representations based Interactions of d-orbitals with octahedral ligand field on angular momentum Characters, [R], for operations in spherical symmetry (group R3) as a function of the angular momentum quantum number, j, of the wave function are given by: These relations can be used with any point group, since all are subgroups of the spherical group, R3 for d orbitals or D term symbol!! 11 12 Carter, page 205 3
- 4. d-Orbital splitting in the ﬁelds of various symmetries Octahedral ﬁeld. ML6 complexes MX4 • The d-orbital splittings presented on diagram E dx2-y2 correspond to the cases of cubic shape MX8 b1g • In the ﬁeld of Oh symmetry ﬁve degenerate d-orbitals will be split into two sets, t2g and (Oh ), tetrahedral shape MX4 (Td), icosahedral eg orbitals (check the Oh point group character table) shape MX12 (Ih), octahedral shape MX6 (Oh) and square planar shape MX4 (D4h). Oh Td Ih Oh D4h • Three t2g orbitals be stabilized by 0.4 o and two e g orbitals will be destabilized by 0.6 o MX6 Td L eg 1 z dz2=0.5(dz2-y2+dz2-x2) z dx2-y2 z L L 1 L L E (2z2-x2-y2 , x2-y2) MX8 dz2 4 4 dx2-y2 L T2 (xy, xz, yz) eg 2x = 3y 4 3 2 eg 1 x+y= o y y y MX4 x dyz 3 3 Ih dxz t2g x = 0.6 o 2 dz2-y2 2 dz2-x2 dxy dxy y x x x MX12 t2g y = 0.4 Hg (2z2-x2-y2 , x2-y2, xy, xz, yz) free ion dyz b2g the ion in an o dxz t2 averaged the ion in an dxy ligand field octahedral dyz D4h ligand field 1 z averaged hg t2gA1g x2+y2, z2 ligand Oh field eB1g x2-y2 a1g … 4 3 dz2 yB2g xy dz2 dz2 Eg (2z2-x2 -y2, x2-y2) dx2-y2 dx2-y2 dyz …Eg (xz, yz) eg dyz eg dxz x 2 dxz t2g 13 T2g (xz, yz, xy) 14… dxy … How does an octahedral array of ligands affect the d orbitals? eg conﬁgurations eg t2g2 t2g d orbitals t2g t2g3 spectrochemical series t2g4 low spin 3rd row > 2nd row > 1st row transition metal atoms higher charge TM > smaller charge strong ﬁeld d4 if weak ﬁeld t2g3 eg1 high spin 15 16 4
- 5. Factors affecting the magnitude of Ligand-ﬁeld splitting parameters O of ML6 complexes • Higher oxidation states of the metal atom correspond to larger : =10,200 cm-1 for [CoII(NH3 )6]2+ and 22,870 cm-1 for [CoIII(NH3)6]3+ =32,200 cm-1 for [FeII(CN)6]4- and 35,000 cm-1 for [FeIII(CN)6 ]3- • values are in multiples of 1000 cm-1 • entries in parentheses are for low-spin complexes • In groups heavier analogues have larger . For hexaammine complexes [MIII(NH3)6 ]3+: = 22,870 cm-1 (Co) 34,100 cm-1 (Rh) 41,200 cm-1 (Ir) • Geometry of the metal coordination unit affects greatly. For example, tetrahedral complexes ML4 have smaller than octahedral ones ML6: = 10,200 cm-1 for [CoII(NH3 )6] 2+ 5,900 cm-1 for [CoII(NH3)4]2+ • Ligands can be arranged in a spectrochemical series according to their ability to increase at a given metal center: I- < Br- < Cl- < F- , OH- < H2O < NH3 < NO2- < Me- < CN- < CO For [CoIIIL 6 ] we have , cm-1: 13,100 (F), 20,760 (H 2 O), 22,870 (NH3) Shriver, Table 7.3 For [CrIIIL 6] we have , cm-1: 15,060 (F), 17,400 (H 2O), 17 26,600 (CN) 18 Some consequences of d-orbital splitting Calculating CFSE for Octahedral species• Magnetism. In the case of large we observe low-spin, while for small high-spin complexes (d4-d7 conﬁgurations). E low spin d6 high spin d6 CFSE = [0.4 x #t2g electrons – 0.6 x # eg electrons)• Energy. If the occupancy (x) of the orbitals eg stabilized by a ligand ﬁeld is more than that of L t 3 e1 the destabilized orbitals (y), the complex Oh dx2-y2 becomes more stable by the Crystal Field L L For Stabilization Energy (CFSE )which is (0.4y- 0.6x) for octahedral species. MX6 dz2 L L 2g g eg L• For d0, d5 (high-spin) and d10 complexes CFSE is always zero. 2xt = 3y (0.4 x 3 - 0.6 x 1) large small eg x+y= o o o• Redox potentials. Some oxidation states may become more stable when stabilized orbitals are x = 0.6 fully occupied. So, d6 conﬁguration becomes more stable than d 7 as o increases. CoL62+ = CoL63+ + e - x = 0.6 o t2g y E0= -1.8 (L=H2O) … +0.8 V (L=CN- ) y = 0.4 Note: t2g o the ion in an• M-L bond lengths and Ionic radii of M n+ are averaged smaller for low-spin complexes and have a the ion in an = 10Dq minimum for d6 conﬁguration (low spin). ligand field octahedral t2gR, Å, of M3+: 0.87 (Sc), 0.81 (Ti), 0.78 (V), 0.74 ligand field (Cr), 0.72 (Mn), 0.69 (Fe), 0.67 (Co), 0.71 (Ni), … 0.78 (Ga) dxy dxz dyz 19 20 5
- 6. Lattice energies of the divalent metal halides of the ﬁrst Radii of some trivalent ions transition series as a function of the number of d electrons low spin -- solid circles Huheey, Fig 11.15 Huheey, Fig 11.14 21 22 Crystal-ﬁeld stabilization energies High and low spin complexes of various geometries • d-d Electron-electron repulsions in d4-d7 metal complexes (3d) correspond to• N is the number of unpaired electrons the energy of 14000-25000 cm-1. If > 14000-25000 cm-1, the complex is low dx2-y2 b1g• CFSE is in units of O for octahedra or for tetrahedra spin. T• the calculated relation is T (4/9) O • For octahedral complexes o ranges from 9000 to 45000 cm -1. It is therefore common to observe both high and low spin octahedral species. tetrahedral MX4 MX4 • For tetrahedral complexes t = (4/9) o ranges from 4000 to 16000 cm-1. Low C C Td D4h spin tetrahedral complexes are very rare. square-planar Nr Nr = d5 IV Nr Co Nr µ=1.8 M Nr • For square planar complexes is very large. Even with weak ﬁeld ligands high-spin d8 complexes are unknown (but known for d6). dxy b2g dyz dxz t2 • Sometimes complexes of different conﬁguration and magnetic properties dxy coexist in equilibrium in solution. For the Ni(II) complexes shown below µ=0 t i M (R = Me; square planar); 3.3 (R = Bu; tetrahedral) and 0-3.3 (R = Pr; both) e R a1g R O N dz2 N dz2 Ni O Ni dx2-y2 N O N dyz 23 R R O 24 eg dxz Shriver, Table 7.3 µ=0 M µ = 3.3 M 6
- 7. How do we determine the magnitude of the crystal ﬁeld? How do we determine the Crystal Field Splitting? Magnetism of octahedral transition metal complexes (from an electron conﬁguration perspective)• The number of unpaired electrons n in a metal complex can be derived from the measure optical absorption... d1 conﬁguration experimentally determined magnetic susceptibility M .• M is related to magnetic moment µ 2.84( M T) 1/2 (Bohr magnetons)• µ is related to n: µ [n(n+2)]1/2.• Calculated magnetic moments for octahedral 3d metal complexes, ML6: M High spin complexes Low spin complexes # of unp. e’s µ, M # of unp. e’s µ, M Ti3+, V4+ 1 (d1) (tg ) 1 1.73 V3+ 2 (d2) (tg ) 1 (tg)1 2.83 500nm V2+, Cr3+ 3 (d3) (tg ) 1 (tg)1(tg ) 1 3.87 Cr2+, Mn3+ 4 (d4) (tg ) 1 (tg)1 (tg)1 (eg) 1 4.90 2 (d4) (tg ) 2 (tg)1 (tg)1 2.83 Mn2+, Fe3+ 5 (d5) (tg ) 1 (tg)1 (tg)1 (eg) 1 (eg)1 5.92 1 (d5) (tg ) 2 (tg)2 (tg)1 1.73 Fe2+, Co3+ 4 (d6) (tg ) 2 (tg)1 (tg)1 (eg) 1 (eg)1 4.90 0 (d6) (tg ) 2 (tg)2 (tg)2 0 Co2+, Ni3+ 3 (d7) (tg ) 2 (tg)2 (tg)1 (eg) 1 (eg)1 3.87 1 (d7) (tg ) 2 (tg)2 (tg)2 (eg) 1 1.73 Ni2+ 2 (d8) (tg ) 2 (tg)2 (tg)2 (eg) 1 (eg)1 2.83 Ti(H2O)63+ 25 26 Cu2+ 1 (d9) (tg ) 2 (tg)2 (tg)2 (eg) 2 (eg)1 1.73 A good guide--- A more complicated problem Tanabe Sugano Diagram d3 What is it? How do you use it? Why multiple peaks? Why the increasing absorption at 200 nm? What is the electronic structure of the chromium atom? What are the magnetic properties? 27 28 7
- 8. Answer to these questions-- Instead of electron conﬁgurations Absorption maxima in a visible spectrum have three -- look at how the free atom states important characteristics Oh are affected d2 correlation1. number of maxima (observed absorption peaks) diagram (note labels)What are the electronic states of the complex?2. position (what wavelength/energy)What is the ligand field splitting parameter, e.g., oct or tet, and the degree of inter-electron repulsion? 3. intensity What is the "allowedness" of the transitions as described by selection rules ground state 29 30 weak field Symmetry and the atom... reducible representations based weak field Example 3F state from d2 conﬁguration with on angular momentum weak ligand ﬁeld Can do the same for other orbitals and/or terms as well d2 correlation Note non-crossing rule: For F ground state term (j = 3) States with the same symmetry and multiplicity do not cross F = A2g + T1g + T2g 31 32 Carter, page 205 8
- 9. Summary of splitting of states for dn conﬁgurations in an d2 correlation What happens if the ligand ﬁeld is strong? octahedral (Oh) ﬁeld Work out strong field side by starting with hypothetical configurations For t2g2 get reducible strong field representation by taking direct product t2g x t2g (t2g)2 = A1g + Eg + T1g + T2g see Carter, page 239 33 34 Now ready to begin interpreting optical spectra and Summary - d2 Correlation Diagram magnetic properties of transition metal complexes d3 Energy states! Why multiple peaks? Why the increasing absorption at 200 nm? What is the electronic structure of the chromium atom? 35 What are the magnetic properties? 36 9
- 10. A good guide--- The color spectrum -- a review Sir Isaac Newton R O Y G B I VTanabe Sugano Diagram IR UV 600 nm 500 nm 400 nm Wavelength E = h = hc/ If a substance absorbs here... 650 nm 600nmWhat is it?How do you use it? 800nm 400 nm 560 nm It appears 430 nm 490 nm as this color If an object is black it absorbs all colors of light An object is white if it reﬂects all colors of light An object is orange if it reﬂects only this color and absorbs all others Ground State An object is also orange if it reﬂects all the colors except blue, 37 the complementary color of orange 38 Energy of transitions Excited State Chromaticity molecular rotations lower energy 3 “virtual” (0.01 - 1 kJ mol-1) colors, which microwave radiation when added electron transitions together give higher energy all other (100 - 104 kJ mol-1) Ground State colors visible and UV radiation molecular vibrations medium energy (1 - 120 kJ mol-1) IR radiation During an electronic transition the complex absorbs energy complex changes energy states http://www.tcd.ie/Chemistry/Under 39 /ch3018.html 40 redistributes the electronic charge //www.cs.rit.edu/~ncs/color/a_chroma.html 10
- 11. Now ready to begin interpreting optical spectra and Estimating from electronic absorption spectra of d1 species magnetic properties of transition metal complexes• Values of are easily obtained from absorption spectra of d1 transition metal complexes d3• In the d1 metal complex [Ti(H2O)6]3+ max = 500 nm, so that = = 1/ max = 1/(5.00 10-5cm)= 20000 cm-1 1 d 2 max Eg 2 Eg = Why multiple peaks? Why the increasing absorption at 200 nm? 2 T2g 2 T2g What is the electronic structure of the chromium atom? 41 What are the magnetic properties? 42 Close relationships between dn electronic properties Free Atom States -- Term Symbols - electrons and holes-- move hole d1 d9 S = 1/2 2S + 1 = 2 behaves like behaves like S=4 2S + 1 = 5 43 44 11
- 12. Putting this in the context of term symbols states… move hole Oh Relationships for octahedral and tetrahedral Oh 10-1 1 d d 2 2 T2g Oh Td Td d1 Eg 2 d1 2 T2 d10-1 2E 2 D Eg 2 D 2 2 2 T2g Eg 2 D D 2 D t t M ML6 M ML6 behaves like behaves like 2 2E 2 T2g T2 Oh 5-1 Oh M ML4 M ML4 5+1 d M ML6 d 5 T2g 5 Eg The term sequence is the opposite for octahedral and tetrahedral complexes of the same configuration 5 D 5 D (not a single term) (not a single term) 5 5 Eg The term sequence is in the same order for dn octahedral and d 10-n T2g tetrahedral complexes. M ML6 M ML6 45 46 Summarize with Orgel Diagram d1 d6 d4 d9 d1 octahdral A [Ti(OH2)6]3+ 2E g 2E 2T g 2g 2D 2T 2g 10 000 20 000 30 000 - / cm-1 Orgel diagram for d1, d 4, d6, d 9 E Eg or E T2g or T2 D T 2g or T2 Eg or E d1, d6 tetrahedral 0 d1, d6 octahedral d4, d9 octahedral d4, d9 tetrahedral 47 LF strength 48 12
- 13. Orgel diagram for d2, d3, d7, d8 ions Quantum MixingEnergy A2 or A2g Couple of things missing: spin multiplicties and electron- T1 or T1g electron repulsion (Racah Parameters B and C) P T1 or T1g T1 or T1g T2 or T2g F Use Tanabe Sugano Diagrams T2 or T2g T1 or T1g A2 or A2g d2, d 7 tetrahedral 0 d2, d 7 octahedral d3, d 8 octahedral d3, d 8 tetrahedral 49 50 Ligand field strength (Dq) A good guide--- Selection Rules Spin Selection Rule Tanabe Sugano Diagram S=0 There must be no change in spin multiplicity during an electronic transition What is it? How do you use it? Laporte Selection Rule l=±1 There must be a change in parity during an electronic transition g u Ground State Selection rules determine the intensity of electronic transitions 51 52 13
- 14. Selection Rules for optical transitions -- Spin Selection Rule Selection Rules for optical transitions ---LaPorte’s Rule A transition matrix element of the form , M = f O i where O is the operator of 2 interaction, can be used to calculate the intensity of a transition according to I f O i Transitions may occur only between energy states with the same spin multiplicity. Such integrals of the type M = f O i are only non-zero if the function fO i is symmetric with respect to all symmetry operations of the group, i.e. if it forms the basis for the totally symmetric irreducible representation of the group. S=0 Consider the irreducible representation of the direct product M = f µ i where is the operator of an electric dipole violated by spin orbit or jj coupling transition. This operator transforms as the irreducible representation of the cartesian coordinates. In a centrosymmetric point group, must be an odd (u) function f and i must be of opposite parity (u g or g u) LaPorte’s Rule 10,000 This means that d p, s p, . . . are allowed, but d d, s d, . . . are not 5 - 100 53 54 Selection Rules for optical transitions ---LaPorte’s Rule Selection Rules and note size of Intensity for d-d transitions 0.03 Vibronic Mechanism For a centrosymmetric structure (e.g. Oh ) vibrations [Ti(OH2)6]3+ , d1, Oh field 0.02 of odd parity (e.g. T1u) distorts the octahedron, 0.01 which partially relaxes LaPorte’s rule, so get a small Spin allowed absorption, 5 - 100 - / cm-1 Laporte forbidden 10 000 20 000 30 000 Transition between d orbitals Tetrahedral (Td), noncentrosymmetric, complexes 2E have d d transition intensities greater than those for E g octahedral (Oh) 100 - 200 since no g or u symmetry 2D 2T 2g 55 oct 56 14
- 15. Relaxation of the Laporte Selection Rule for Tetrahedral Complexes [V(H2O)6 ]3+, d2 Oh600 [CoCl4 ]2-, d7 Td 10 Octahedral complex Tetrahedral complex400 Centrosymmetric Non-centrosymmetric 5200 Laporte rule applies Laporte rule relaxed v / cm -1 25 000 20 000 15 000 10 000 5 000 / cm-1 30 000 20 000 10 000 Spin allowed; Laporte forbidden 4A A2g 2g inversion 3T 4T 1 T1 1g centre P T1g T1 T2g 4T 3T 2g 1 T2 F 3T 2 Oh complex d eg and t2g p t1u T1g 4T Orbital mixing: 1g 3A A2 Td complex d e and t2 p t2 2 d7 tetrahedral d2 octahedral 0 57 58 Dq In tetrahedral complexes, d-orbitals have some p character Intenstity of transitions in d5 complexes Laporte forbidden Spin forbidden transitions d5 octahedral complexEnergy (cm-1) Spin forbidden Multiple absorption bands 4T [Mn(H2O)6 ]2+50 000 2(g) 4T Very weak intensity 4F 1(g) 4A40 000 2(g) 4T 4D 1(g)30 000 4E 4P 4T (g) Transitions are forbidden 2(g) 4E (G) 4G g 4E , 4A (g) 1(g) 4A20 000 0.03 1g (G) 4T 2(g) 4T (D) 4T 2g10 000 1(g) 4E Ground State 0.02 4T (D) 1g (G) g 6A 1g 6S 4T 500 1000 6A 1(g) 2g (G) 0.01 Dq (cm-1) v / cm-1Weak transitions occur due to: Unsymmetrical Vibrations (vibronic transitions) 20 000 25 000 30 000 Spin-orbit Coupling 59 60 15
- 16. Selection rules and observed intensities A good guide--- Tanabe Sugano DiagramTransition complexesSpin forbidden 10-3 – 1 Many d5 OhLaporte forbidden [Mn(OH2 )6]2+Spin allowedLaporte forbidden 1 – 10 Many Oh What is it? [Ni(OH2 )6]2+ How do you use it? 10 – 100 Some square planar [PdCl4] 2- 100 – 1000 6-coordinate complexes of low symmetry, many square planar particularly with organic ligandsSpin allowed 102 – 103 Some MLCT bands in complexes with unsaturated ligandsLaporte allowed 102 – 104 Acentric complexes with ligands such as acac, or with P donor atoms Ground State 103 – 106 61 Many CT bands, transitions in organic species 62 Understanding Cr3+ Understanding Cr(NH3)63+ --- Tanabe Sugano Diagram g g Expect two main d-d transition bands g g g g g g Measure energies accurately is at 21550 cm-1 Why multiple peaks? g is at 28500 cm-1 Why the increasing absorption at 200 nm? 28500/21550 = 1.32 What is the electronic structure of the Chromium? Note: slope = 1 is ~ 15400 cm-1 = 650nm What are the magnetic properties? 63 64 16
- 17. Tanabe-Sugano diagram interpretation Determining and B for [Cr(NH3)6]3+ 1 = 21550 cm-1 [Cr(NH3) 6]3+: Three spin allowed transitions = 21550 cm-1 visible 1 2 = 28500 cm-1 2 = 28500 cm-1 visible E/B 3 = obscured by CT transition When 1 = E =21550 cm-1 2 28500 = = 1.32 E/B = 32.8E/B 1 21550 so B = 657 cm-1 /B = 32.8 E/B = 43 cm-1 3 = 2.2 x 1 = 2.2 x 21500E/B = 3 = 47300 cm-1 ~ 211nm E/B = 32.8 cm-132.8 If /B = 32.8cm-1 = 32.8 x 657 = 21550 cm-1 One spin forbidden transition 4 = 15400 cm-1 visible For spin forbidden transition 4 15400 /B = 20.8 = = 0.72 1 21550 = 15400 cm-1 visible /B = 32.8 65 4 66 /B = 32.8 B = 740 cm-1 Energy diagram for octahedral d3 complex Understanding Cr3+ 4T 1 = 21550 cm-1 visible 1g x 2 = 28500 cm-1 visible 3 = obscured by CT transition 15 B x For Oh d3, o = 1 = 21550 cm-1E 4T 1g 6 Dq 2 Dq o / B = 32.8 4T 2g 10 Dq B = 657 cm-1 Why multiple peaks? 4A 2g Why the increasing absorption at 200 nm? What is the electronic structure of the Chromium? 67 What are the magnetic properties? 68 17
- 18. Tanabe-Sugano diagram for weaker field d3 ions Determining and B 1 = 17 400 cm-1 [Cr(H2O)6]3+: Three spin allowed transitions 1 = 17 400 cm-1 visible 2 = 24 500 cm-1 2 = 24 500 cm-1 visible E/B E/B When = E =17 400 cm-1 3 = obscured by CT transition 1 E/B = 24 24 500 = 1.41 so B = 725 cm-1 17 400 /B = 24 When 2 = E =24 500 cm-1 E/B = 34 3 = 2.1 x 1 = 2.1 x 17400 so B = 725 cm-1 E/B = 34 cm-1 3 = 36 500 cm-1E/B = E/B = 24 cm-124 If /B = 24cm-1 = 24 x 725 = 17 400 cm-1 69 70 /B = 24 /B = 24 Energy diagram for octahedral d3 complex What color is this Cr3+ complex? If a substance absorbs here... 650 nm 600nm 1 = 17 400 cm-1 visible 4T 800nm 1g 560 nm = 24 500 cm-1 visible 400 nm x 2 3 = obscured by CT It appears 430 nm 490 nm as this color transition 15 B x For Oh d3, o = 1= 17 400 cm-1 4T 1g 6 Dq o / B = 24 2 Dq 4T 2g B = 725 cm-1 10 Dq 4A 2g 71 72 18
- 19. Tanabe-Sugano diagram for d2 ions 10 Getting spectrochemical parameters for a d2 conﬁguration E/B [V(H2O)6]3+: Three spin allowed transitions 5E/B 1 = 17 800 cm-1 2 = 25 700 cm-1 30 000 20 000 10 000 / cm-1 2 E/B = 43 cm-1 1 = 17 800 cm-1 visible 2 = 25 700 cm-1 visible E/B = 30 cm-1 1 3 = obscured by CT transition in UV E/B = 43 cm-1 E = 25 700 cm-1 25 700 = 1.44 /B = 32 17 800 B = 600 cm-1 o /B = 32 o = 19 200 cm-1 /B = 32 3 = 2.1 1 = 2.1 x 17 800 3 = 37 000 cm-1 73 74 /B = 32 Energy level diagram for oct d 2, d7, tet d3, d8 Phosphorescence ---radiative decay from an excited state of different 1: x + 8 Dq spin multiplicity than ground state (generally slow!) 2: 2 x + 6 Dq + 15 B A2(g) 3: x + 18 Dq 3 T1(g) 2 x 10 Dq 1: T2(g) T1(g) P 2: T1(g)(P) T1(g) second 3: A2(g) T1(g) lifetime 15 B 15 B T2(g) F 1 2 Dq 6 Dq T1(g) x 627 nm 75 Ruby - Cr3+ in Al2O3 76 1st laser in 1960 19

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