Bonding in transition metal complexes

Transcription

1 rystal Field Theory(FT) Bonding in transition metal complexes Assumes electrostatic(ionic) interactions between ligands and metal ions Useful for understanding magnetism and electronic spectra Valence Bond(VB) Theory Assumes covalent M L bonds formed by ligand electron donation to empty metal hybrid orbitals. Useful for rationalizing magnetic properties, but cannot account for electronic spectra. ffers little that cannot be covered better by other theories. Molecular rbital(m) Theory Approach using M L general Ms Excellent quantitative agreement, but less useful in routine qualitative discussions Ligand Field Theory(LFT) Modified FT Makes empirical corrections to account for effects of M L orbital overlap, improving quantitative agreement with observed spectra

2 FT & d-subshell Splitting in an h Field In the octahedral ( h ) environment the fivefold degeneracy among the d orbitals is lifted. If the ligand field is of h symmetry the d subshell will separate into a set of three degenerateorbitals(t 2g =dxy,dyz,dxz)andasetoftwodegenerateorbitals(e g = dx 2 y 2,dz 2 ). Relative to the energy of the hypothetical spherical field, the e g set will rise in energy and the t 2g set will fall in energy, creating an energy separation of o or 10 Dq betweenthetwosetsofdorbitals.

3 The t 2g orbitals point between ligands. The e g orbitals point directly at the ligands. Thus, the t 2g set is stabilized and the e g set is destabilized (relative to the energy of a hypothetical spherical electric field).

4 The energy increase of the e g orbitals and the energy decrease of the t 2g orbitals must be balanced relative to the energy of the hypothetical spherical field (aka the barycenter). Theenergyofeachofthetwoorbitalsofthee g setrisesby+3/5 o (+6Dq)whilethe energyofeachofthethreet 2g orbitalsfallsby-2/5 o (-4Dq). Thisresultsinnonetenergychangeforthesystem: E = E(e g ) + E(t 2g ) = (2)(+3/5 o ) + (3)(-2/5 o ) = (2)(+6Dq) + (3)(-4Dq) = 0 (The magnitude of o depends upon both the metal ion and the attaching ligands)

5 High-Spin and Low-Spin onfigurations In an octahedral complex, electrons fill the t 2g and e g orbitals in an aufbau manner, but for configurations d 4 d 7 there are two possible filling schemes depending on themagnitudeof o relativetothemeanelectronpairingenergy,p. A high-spin configuration avoids pairing by spreading the electrons across both the t 2g ande g levels. A low-spin configuration avoids occupying the higher energy e g level by pairing electronsinthet 2g level. For a given metal ion, the pairing energy is relatively constant, so the spin state dependsuponthemagnitudeofthefieldstrength, o. Low field strength results in a high-spin state. High field strength results in a low-spin state. Forexample,ad 4 configuration,thehigh-spinstate ist 2g3 e g1,andthelow-spinstateist 2g4 e g 0.

6 Low field strength results in a high-spin state. High field strength results in a low-spin state. Forad 4 configuration,thehigh-spinstateist 2g3 e g1,andthelow-spinstateist 2g4 e g 0.

7 M used for most sophisticated and quantitative interpretations LFT used for semi-quantitative interpretations FT used for everyday qualitative interpretations

8 onstruction of M diagrams for Transition Metal omplexes σ bonding only scenario

9 General M Approach for MX n Molecules To construct delocalized Ms we define a linear combination of atomic orbitals (LAs) that combine central-atom As with combinations of pendant ligand orbitals called SALs: Ψ M = a Ψ(Metal A) ± b Ψ (SAL nx) (SAL = Symmetry Adapted Linear ombination) SALs are constructed with the aid of group theory, and those SALs that belong to a particular species of the group are matched with central-atom As with the same symmetry to make bonding and antibonding Ms. Ψ SAL = c 1 Ψ 1 ± c 2 Ψ 2 ± c 3 Ψ 3. ± c n Ψ n

10 1. Use the directional properties of potentially bonding orbitals on the outer atoms (shown as vectors on a model) as a basis for a representation of the SALs in the point group of the molecule.

11 2. Generate a reducible representation for all possible SALs by noting whether vectors are shifted or non-shifted by each class of operations of the group. Each vector shifted through space contributes 0 to the character for the class. Each non-shifted vector contributes 1 to the character for the class.

12 2. Generate a reducible representation for all possible SALs by noting whether vectors are shifted or non-shifted by each class of operations of the group. Each vector shifted through space contributes 0 to the character for the class. Each non-shifted vector contributes 1 to the character for the class.

13 3. Decompose the reducible representation into its component irreducible representations to determine the symmetry species of the SALs. For complex molecules with a large dimension reducible representation, identification of the component irreducible representations and their quantitative contributions can be carried out systematically using the following equation n i : numberoftimestheirreduciblerepresentationioccursinthereduciblerepresentation h : orderofthegroup c : class of operations g c : numberofoperationsintheclass χ i : characteroftheirreduciblerepresentationfortheoperationsoftheclass χ r : characterofthereduciblerepresentationfortheoperationsoftheclass The work of carrying out a systematic reduction is better organized by using the tabular method, rather than writing out the individual equations for each irreducible representation.

14 haracter Table for h

15 Transformation Properties of entral As Transformation properties for the standard As in any point group can be deduced from listings of vector transformations in the character table for the group. s transforms as the totally symmetric representation in any group. p transform as x, y, and z, as listed in the second-to-last column of the character table. d transformasxy,xz,yz,x 2 -y 2,andz 2 (or2z 2 -x 2 -y 2 ) e.g.,int d and h,aslistedinthelastcolumnofthecharactertable.

16 In non-linear groups: Mulliken Symbols - Irreducible Representation Symbols A : non-degenerate; symmetricto n where χ( n )=1. B : non-degenerate; anti-symmetricto n where χ( n )=-1. E : doubly-degenerate; χ(e) = 2. T : triply-degenerate; χ(t) = 3. G : four-folddegeneracy; χ(g)=4,observed iniandi h H : five-folddegeneracy; χ(h)=5,observediniandi h Inlineargroups v andd h : Σ A non-degenerate; symmetricto ; χ( )=1. Π,, Φ E doubly-degenerate; χ(e)=2.

17 Mulliken Symbols - Modifying Symbols With any degeneracy in any centrosymmetric groups: subscript g : gerade; symmetricwithrespecttoinversion;χ i >0. subscript u : ungerade;anti-symmetricwithrespecttoinversion;χ i <0. With any degeneracy in non-centrosymmetric non-linear groups: prime( ) : symmetricwithrespectto σ h ; χ(σ h )>0. doubleprime( ) : anti-symmetricwithrespectto σ h ; χ(σ h )<0. With non-degenerate representations in non-linear groups: subscript 1 : symmetricwithrespectto m (m<n)or σ v ; χ( m )>0or χ(σ v )>0. subscript 2 : anti-symmetricwithrespectto m (m<n)or σ v ; χ( m )<0or χ(σ v )<0. Withnon-degeneraterepresentationsinlineargroups( v andd h ): subscript + : symmetricwithrespectto 2 or σ v ; χ( 2 )=1or χ( σ h )=1. subscript : anti-symmetricwithrespectto 2 or σ v ; χ( 2 )=-1or χ( σ h )=-1.

18 Systematic Reduction for h h E i 6S 4 8S 6 3 h 6 d n i = /h (h=48) A 1g A 2g E g T 1g T 2g A 1u A 2u E u T 1u T 2u

19 Systematic Reduction for h

20 4. The number of SALs, including members of degenerate sets, must equal the number of ligand orbitals taken as the basis for the representation.

21 5. Determine the symmetries of potentially bonding central-atom As by inspecting unit vector and direct product transformations listed in the character table of the group. r bonding As r non-bonding As A 1g : 4s T 1u : (4p x, 4p y, 4p z ) E g : (3dx 2 -y 2, 3dz 2 ) T 2g : (3dxy, 3dxz, 3dyz)

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23 6. entral-atom As and pendant-atom SALs with the same symmetry species will form both bonding and antibonding LA-Ms. Symmetry bonding Ms anti-bonding Ms E g T 1u A 1g

24 7. entral-atom As or pendant-atom SALs with unique symmetry (no species match between As and SALs) form nonbonding Ms.

25 E g T 1u A 1g dz 2 dx 2 -y 2

26 r r 6 4p(t 1u ) E g 4s(a 1g ) T 1u 3d(t 2g,e g ) A 1g dz 2 dx 2 -y 2 e g t 1u a 1g

27 r r 6 4p(t 1u ) E g 4s(a 1g ) T 1u 3d(t 2g,e g ) A 1g dz 2 dx 2 -y 2 e g t 1u a 1g

28 r r 6 4p(t 1u ) a 1g * E g 4s(a 1g ) T 1u 3d(t 2g,e g ) A 1g dz 2 dx 2 -y 2 e g t 1u a 1g a 1g

29 r r 6 t 1u * 4p(t 1u ) a 1g * E g 4s(a 1g ) T 1u 3d(t 2g,e g ) A 1g dz 2 dx 2 -y 2 e g t 1u t 1u a 1g a 1g

30 r r 6 t 1u * 4p(t 1u ) a 1g * E g 4s(a 1g ) e g * T 1u 3d(t 2g,e g ) A 1g dz 2 dx 2 -y 2 e g e g t 1u t 1u a 1g a 1g

31 r r 6 t 1u * 4p(t 1u ) a 1g * E g 4s(a 1g ) e g * T 1u 3d(t 2g,e g ) t 2g A 1g dz 2 dx 2 -y 2 e g e g t 1u t 1u a 1g a 1g

32 r r 6 t 1u * 4p(t 1u ) a 1g * E g 4s(a 1g ) e g * T 1u 3d(t 2g,e g ) t 2g A 1g dz 2 dx 2 -y 2 e g e g t 1u t 1u a 1g a 1g

33 r r 6 t 1u * 4p(t 1u ) 4s(a 1g ) a 1g * LUM E g e g * T 1u 3d(t 2g,e g ) t 2g A 1g HM dz 2 dx 2 -y 2 e g e g t 1u t 1u a 1g a 1g

34 SALS for ommon Geometries (σ bonding) N = 2 D h u + g +

35 SALS for ommon Geometries (σ bonding) N = 3 3v E A 1

36 N = 3 SALS for ommon Geometries (σ bonding)

37 N = 4 SALS for ommon Geometries (σ bonding)

38 SALS for ommon Geometries (σ bonding) N = 4 D 4h B 1g E u A 1g

39 N = 5 SALS for ommon Geometries (σ bonding)

40 N = 6 SALS for ommon Geometries (σ bonding)

41 onstruction of M diagrams for Transition Metal omplexes π bonding complexes

42 Example: onstructing a M for hromium Hexacarbonyl, r() 6 Each vector shifted through space contributes 0 to the character for the class. Each non-shifted vector contributes 1 to the character for the class. Each vector shifted to the negative of itself(180 ) contributes-1 to the character for the class.

43 Example: onstructing a M for hromium Hexacarbonyl, r() 6

44 Example: onstructing a M for hromium Hexacarbonyl, r() 6 h E i 6S 4 8S 6 3 h 6 d /h h=48 A 1g A 2g E g T 1g T 2g A 1u A 2u E u T 1u T 2u

45 Example: onstructing a M for hromium Hexacarbonyl, r() 6

46 Example: onstructing a M for hromium Hexacarbonyl, r() 6 r σ-bonding As r π-bonding As r non-bonding As

47 Example: onstructing a M diagram for hromium Hexacarbonyl, r() 6 r σ-bonding As A 1g : 4s T 1u : (4p x, 4p y, 4p z ) E g : (3dx 2 -y 2, 3dz 2 ) r non-bonding As T 2g :(3dxy, 3dxz, 3dyz) r π-bonding As T 2g :(3dxy,3dxz,3dyz) T 1u :(4p x,4p y,4p z ) T 2g previously considered nonbonding in σ-bonding scheme T 1u combines with T 1u SAL in in σ-bonding scheme T 1g, T 2u π-sals are nonbonding

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49 T 1u As overlap more effectively with T 1u σ-sal thus the π-bonding interaction is considered negligible or at most only weakly-bonding.

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51 dz 2 dx 2 -y 2

52 3x T 2g dz 2 dx 2 -y 2

53 3x T 2g dz 2 dx 2 -y 2

54 3x T 2g dz 2 dx 2 -y 2

55 3x T 2g LUM HM dz 2 dx 2 -y 2

56 Dewar-hatt-Duncanson model v() cm -1 [Ti() 6 ] [V() 6 ] r() [Mn() 6 ] [Fe() 6 ]

57 Summary of π-bonding in h complexes π donor ligands result in L M π bonding, a smaller o favoring high spin configurations and a decreased stability. πacceptorligandsresultinm L πbonding,alarger o favoring low spin configurations with an increased stability.