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Ch 10 Lecture 3 Angular Overlap I.Ligand Field Theory and Square Planar Complexes A.Sigma Bonding 1)Group Theory MO Description for D 4h symmetry.

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Presentation on theme: "Ch 10 Lecture 3 Angular Overlap I.Ligand Field Theory and Square Planar Complexes A.Sigma Bonding 1)Group Theory MO Description for D 4h symmetry."— Presentation transcript:

1 Ch 10 Lecture 3 Angular Overlap I.Ligand Field Theory and Square Planar Complexes A.Sigma Bonding 1)Group Theory MO Description for D 4h symmetry

2 2)Choose d z2, d x2-y2, p x, p y as most likely orbitals from metal ion 3)Three d-orbitals are not involved in  -bonding (d xy, d xz, d yz ) 4)The  -bonding diagram is complex because the d- orbitals are split into three different groups. 5)The energy difference between the lowest 2 d-orbital groups is called 

3  -bonding 1)d xy d xz and d yz can have  -bonding 2)p-orbitals of metal too small C.Complete MO Diagram  -bonding set filled by L electrons  -donor set a)Filled by L electrons if present F - p-orbitals or CN-  -orbitals b)Overall destabilizing on d-set 3)Metal d-orbitals split into 4 groups 4)d 8 metals favor square planar due to large gap to high energy orbital (a 2u )

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5 III.Tetrahedral Complexes and Ligand Field Theory A.Sigma and Pi bonding B.Results 1)4  -bonding orbitals are filled by ligand electrons a)A 1 has no match with metal other than small s-orbital b)T 2 matches d xy, d xz, d yz so these orbitals are raised in energy c)The d x2-y2 an d z2 orbitals are not involved so stay at same energy d)Result is an inversion of the orbital sets from octahedral complexes 2)The  -bonding interactions reinforce  t

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7 III.Angular Overlap Theory A.Development of the Theory 1)Ligand Field Theory shortcomings a)Energy of interactions are ambiguous b)Very complicated for multiple ligand types or non-standard geometries 2)Angular Overlap Theory a)Estimate L—M orbital—orbital interactions b)Combine all such interactions for the total picture of bonding c)“Overlap” depends strongly on the angles of the orbitals to each other d)We consider each ligand’s effect on each metal orbital and add them up B.Sigma Donor Interactions 1)The strongest possible interaction for an octahedral complex is with d z2 orbital a)Most of its electron density is on the z-axis b)All other interactions are measured relative to those of d z2 c)Bonding MO’s = mostly ligand; Antibonding MO’s = mostly metal d)Approximate the MO—AO energy difference = e 

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9 2)Example: [M(NH 3 ) 6 ] 3+ a)Only  interactions are available to NH 3 ligands b)Lone pair can be thought of as isolated in N p z orbital c)Metal d-orbitals i.Add up the values for interaction down the table of ligand positions ii.d z2 = (2 x 1) + (4 x ¼ ) = 3e  iii.d x2-y2 = (2 x 0) + (4 x ¾ ) = 3e  iv.d xz, d xy, d zy, = 0 (no interactions with the ligands) d)Ligand Orbitals i.Total interactions with all metal d-orbitals across the row ii.Ligand #1 and #6 = (1 x 1) + 0 = 1 e  iii.Ligands #2--#5 = (1 x ¼ ) + (1 x ¾ ) = 1 e  e)Results i.Same pattern as LF Theory ii.2 d-orbitals are raised in E iii.3 d-orbitals are unchanged iv.All 6 ligand orbitals lowered E = M—L bonds v.Total of 12 e  destabilization (d z2, d x2-y2 ) and 12 e  stabilization (L)

10 C.  -acceptor interactions  -acceptor interactions in octahedral geometry a)  -acceptor has empty p or  MO’s = CO, CN-, PR 3 b)Strongest overlap is between d xy and  * c)  * is higher in energy than the d xy, so d xy becomes stabilized d)d xy, d xz, and d yz are all stabilized by –4e , d z2 and d x2-y2 are unaffected e)e  < e  (not as good overlap) f)  o is still t 2g —e g * = 3e  + 4e 

11  -donor interactions a)  -donors have reversed signs on the interactions because now the  MO is lower in energy than d-orbitals b)The effected d-orbitals are raised in energy by +4e  c)If the ligand is a  -donor and a  - acceptor, the  -acceptor part wins out (  o is increased) d)  o is still t 2g —e g * = 3e  - 4e  e)d z2, d x2-y2 has +3e  only from  - bonding f)d xy, d xz, d yz has +4e  from only  - bonding

12 D.Magnitudes of e , e , and  o 1)Changes in ligand or metal result in changes in e , e , and  o 2)The number of unpaired electrons might then change as well 3)Example: L = 6 H 2 O a)Co 2+ has n = 3, high spin, but Co 3+ has n = 0, low spin b)Fe 3+ has n = 5 high spin, but Fe(CN) 6 3+ has n = 1, low spin

13 4)Tetrahedral Complexes:  t <  o of a corresponding compound (fewer ligands) 5)Larger halide ligands decrease both e  and e  a)Smaller overlap with d-orbitals b)Less electronegative ligands have less interaction E.The Spectrochemical Series 1)A list of Strong-Field through Weak-Field ligands 2)  -donors only a)en > NH 3 because it is more basic (stronger field ligand) b)F- > Cl- > Br- > I- (basicity) 3)  -donors a)Halides field strength is lowered due to  -donor ability b)For similar reasons H 2 O, OH-, RCO 2 - also are weak field ligands 4)  -acceptors increase ligand field strength: CO, CN- > phen > NO 2 - > NCS- 5)Combined Spectrochemical Series CO, CN- > phen > NO 2 - > en > NH 3 > NCS - > H 2 O > F - > RCO 2 - > OH - > Cl - > Br - > I - Strong field, low spin  -acceptor  -donor only Weak field, high spin  -donor

14 II.The Jahn-Teller Effect A.Unequal occupation of degenerate orbitals is forbidden 1)To obey this theorem, metal complexes with offending electronic structures must distort to “break” the degeneracy 2)Example: octahedral Cu(II) = d 9 a)The e g * set is unequally occupied b)The result is a “tetragonal distortion” to remove the degeneracy of the d z2 and d x2-y2 orbital energies

15 B.First-row metal ions and the Jahn-Teller Effect 1)The effect is greater if e g * is the effected set, rather than t 2g 2)Large J-T effects: Cr 2+ (d 4 ), high spin Mn 3+ (d 4 ), Cu 2+ (d 9 ) 3)Thermodynamic parameters can be effected: a)[Cu(NH 3 ) 3 ] 2+ + NH 3 [Cu(NH 3 ) 4 ] 2+ K 4 = 1.5 x 10 2 b)[Cu(NH 3 ) 4 ] 2+ + NH 3 [Cu(NH 3 ) 5 ] 2+ K 5 = 0.3 c)[Cu(NH 3 ) 5 ] 2+ + NH 3 [Cu(NH 3 ) 6 ] 2+ K 6 ~ 0 III.Four and Six Coordinate Preferences A.Angular overlap calculations 1)Square Planar vs. Octahedral: Only d 8, d 9, d 10 low spin complexes find this geometry energetically favorable 2)Square Planar vs. Tetrahedral: a)d 0, d 1, d 2, d 10 complexes with strong field ligands prefer tetrahedral b)d 5, d 6, d 7 energies the same for weak field cases IV.The Trigonal Bipyramidal case of 5-coordinate complexes (D 3h ) Group Theory Approach yields three sets of d-orbitals

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