Coordination Chemistry II: Bonding

d x2-y2 b 1g e g d x2-y2 b 1g D 1 t 2 d xy, d yz, d zx D t d d z2, d x2-y2 D o d z2 a 1g d xy D 2 d z2 b 2g a 1g e d z2, d x2-y2 d xy, d yz, d zx d xy b 2g D 3 t 2g e g d yz, d zx e g d yz, d zx 10 Coordination Chemistry II: Bonding

Experimental Facts Thermodynamic Data [Fe(H 2 O) 6 ] 3+ + SCN - (aq) [FeSCN(H 2 O) 5 ] 2+ + H 2 O stability constant (formation constant), K [FeSCN 2+ ] K 1 = = 9 x 10 2 [Fe 3+ ][SCN - ] [Cu(H 2 O) 6 ] 2+ + 4NH 3 (aq) [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ + 4H 2 O [Cu(NH 3 ) 2+ 4 ] K 4 = = 1 x 10 13 [Cu 2+ ][NH 3 ] 4 * HSAB Q) Why is SCN - (or NH 3 ) more favorable to Fe(III) (or Cu(II)) than H 2 O? Q) Why do Ag(I) and Cu(II) have the reverse order of favoring ligands?

Experimental Facts Thermodynamic Data [Ni(CH 3 NH 2 ) 6 ] 2+ + 4 H 2 O Ni(OH) 2 (s) + 6 CH 3 NH 3 + + 4 OH - [Ni(en) 3 ] 2+ Stable in aq soln [Cd(H 2 O) 6 ] 2+ + 4 CH 3 NH 2 [Cd(H 2 O) 6 ] 2+ + 2 en [Cd(CH 3 NH 2 ) 4 (H 2 O) 2 ] 2+ + 4H 2 O [Cd(en) 2 (H 2 O) 2 ] 2+ + 4H 2 O DH o = -57.3 kj/mol K 4 = 3.31 x 10 6 DH o = -56.5 kj/mol K 2 = 3.98 x 10 10 Chelate effect: the enhanced affinity of chelating ligands for a metal ion compared to the affinity of a collection of similar nonchelating (monodentate) ligands for the same metal. [Cu(H 2 O) 6 ] 2+

Experimental Facts Magnetic Susceptibility Gouy method SQUID (Superconducting QUantum Interference Device)

Experimental Facts Magnetic Susceptibility Magnetic Susceptibility (c) = the degree of magnetization of a material in response to a magnetic field = M/H c paramagnetic ferromagnetic Curie Law : c = C/T Curie-Weiss Law : c = C/(T-q) Ferromagnetism : T < T C antiferromagnetic T N T C T C : Curie Temperature T N : Neel Temperature T (K) All magnetic materials should have unpaired electrons. Antiferromagnetism : T < T N Paramagnetism : competition between magnetic and thermal motion

Experimental Facts Magnetic Susceptibility Magnetic Susceptibility (c) Gives information of the magnetic moment (m) of a material m = 2.828 (ct) 1/2 m B (m B : Bohr magneton = magnetic moment of a single electron) Two sources of magnetic moment spin (S) and angular(l) motions of electrons spin quantum number orbital (angular momentum) quantum number Theoretically, m S+L = g [J(J+1)] 1/2 m B total angular momentum quantum number Landé g-factor (gyromagnetic ratio) = 1 + J(J+1) + S(S+1) L(L+1) 2J(J+1) When spin-orbit coupling is negligible, m S+L = g [S(S+1) + 0.25L(L+1)] 1/2 m B true for most cases except heavy metals such as Lanthanides

Experimental Facts Magnetic Susceptibility m S+L = g [S(S+1) + 0.25L(L+1)] 1/2 m B 2 In most cases, L is effectively quenched, 0 0 1 ½ 0 0 1 ½ 1 ½ 1 ½ m S = g [S(S+1)] 1/2 m B Landé g-factor (gyromagnetic ratio) = 1 + J(J+1) + S(S+1) L(L+1) 2J(J+1) J = S, L = 0 g = 2, g free electron = 2.0023 Why is L quenched in crystal field? Q) Why do the transition metal ions have so much diversified magnetic moments (spin states)?

Experimental Facts Electronic Spectra Co(II) Cu(H 2 O) 6 2+ Ni(H 2 O) 6 2+ Co(H 2 O) 6 2+ Fe(H 2 O) 6 2+ Q) Why such colors?

Experimental Facts Why? Have to know the characteristics of the bondings and the electronic structures of the complexes.

Valence Bond Theory (VBT) : Hybridization. Description of atomic orbital types used to share electrons or hold lone pairs to form bonds. Crystal Field Theory (CFT) : Electrostatic approach. Describing the split of d-orbtal energies in crystal field. No description of bonds. Ligand Field Theory (LFT) : Molecular orbital (MO) theory approach to describe the bonds and electronic structures of the transition metal complexes. Angular Overlap Method : Estimation of the relative magnitude of MOs.

Valence Bond Theory (Hybridization) First attempt of quantum mechanical explanation of chemical bonding Y = f A (1)f B (2)+f A (2)f B (1) Y = f A (1)f B (2) Each electron is free to migrate to the other atom. Probability to find 2e - s between two nuclei is high. bonding Think forming of a bond as Overlap of atomic orbitals

Valence Bond Theory (Hybridization) Hybridization : the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. sp 3 CH 4 109.5 o four sp 3 orbitals

Valence Bond Theory (Hybridization) HCl CH 4 tetrahedral, 4 equivalent bonds H 4H + C H C H H Cl 2 s bond 90 o H H C 90 o 90 o H??? s bond and one H at not defined position A s bond centers along the internuclear axis.

Valence Bond Theory (Hybridization) sp 3 109.5 o s p 3 h y b r i d a. o. s : CH 4 4 H C ( s p 3 ) H t e t r a h e d r a l s ( s p 3 + 1 s ) C H H H C H H NH 3 N H N H 2 p 2 s s p 3 l o n e p a i r i n s p 3 a. o. s p 3 h y b r i d i z e d s ( s p 3 + 1 s ) N N H H H H H 2 O O H-O-H 2 s 2 p s p 3 s p 3 h y b r i d i z e d O H H l o n e p a i r s i n s p 3 a. o. s s ( s p 3 O + 1 s H )

Valence Bond Theory (Hybridization) sp 2 BF 3 H H B H trigonal planar, 3 equivalent bonds

Valence Bond Theory (Hybridization) sp 2 C 2 H 4 s-bond p-bond all six atoms lie in the same plane A p bond occupies the space above and below the internuclear axis.

Valence Bond Theory (Hybridization) sp linear

Valence Bond Theory (Hybridization) sp linear H-C C-H linear

Valence Bond Theory (Hybridization) dsp 3 PCl 5 B B B B A B B B A B B B trigonal bipyramid PCl 5

Valence Bond Theory (Hybridization) d 2 sp 3 SF 6 B B B A B B B B B A B B octahedral B B

Valence Bond Theory (Hybridization) Metal or Metal Ion (Lewis Acid) + Ligand (Lewis base) => Formation of Complex Hybridization of metal s, p, d orbitals Pt 2+ ([Xe]4f 14 5d 8 ) PtCl 2-4 : diamagnetic Square planar (dsp 2 ) Ni 2+ ([Ar]3d 8 ) NiCl 4 2- : paramagnetic Tetrahedral (sp 3 ) 5d 6s 6p 3d 4s 4p 6p sp 3 hybrids 5d dsp 2 hybrids from ligands 3d from ligands 4 dsp 2 hybrids (abstract figure) 4 sp 3 hybrids (abstract figure)

Valence Bond Theory (Hybridization) [Co(NH 3 ) 6 ] 3+ : diamagnetic Octahedral Co 3+ ([Ar]3d 6 ) [CoF 6 ] 3- : paramagnetic Octahedral 4d 3d 4s 4p 4d 3d d 2 sp 3 hybrids from ligands 3d sp 3 d 2 hybrids from ligands

Valence Bond Theory (Hybridization) VBT has great importance of developing bonding theory for coodination compounds. But It is highly unlikely to use 4d orbital which is high in energy. Many electronic spectra (such as charged complexes) are not well explained. Today, we rarely use it. Forget VBT But, don't foget that VBT is still a good subject for exams.

Crystal Field Theory Developed to explain metal ions in crystal called Crystal Field Theory (CFT) Also useful for coordination compounds Repulsion between d-orbital e - ligand e - splitting of energy levels of d-orbitals Ex) d x2-y2 and d xy orbitals in octahedral field L L L L L L L L L L bigger repulsion higher energy level L L

Crystal Field Theory Uniform Field (Spherical Field) d free ion

Crystal Field Theory d z2, d x2-y2 Uniform Field (Spherical Field) d free ion Octahedral Field d xy, d yz, d zx

Crystal Field Theory d z2, d x2-y2 e g Uniform Field (Spherical Field) 0.6D o D o (=10Dq) : ligand splitting parameter 0.4D o d free ion Octahedral Field d xy, d yz, d zx t 2g

Crystal Field Theory d x2-y2 b 1g d z2, d x2-y2 e g d z2 a 1g d xy b 2g d xy, d yz, d zx Uniform Field Octahedral Field (O h ) t 2g d yz, d zx Tetragonal elongation (D 4h ) e g

Crystal Field Theory d x2-y2 b 1g d z2 a 1g d z2, d x2-y2 e g d z2 a 1g d x2-y2 b 1g d xy b 2g d yz, d zx e g d xy, d yz, d zx t 2g Uniform Field Octahedral Field (O h ) d yz, d zx e g Tetragonal elongation (D 4h ) Tetragonal compression (D 4h ) d xy b 2g

Crystal Field Theory d x2-y2 b 1g d x2-y2 b 1g D 1 d z2 a 1g d z2, d x2-y2 e g d z2 a 1g d x2-y2 d xy b 1g b 2g D 2 d z2 a 1g d xy b 2g d yz, d zx e g d xy, d yz, d zx t 2g D 3 Uniform Field Octahedral Field (O h ) d yz, d zx Tetragonal elongation (D 4h ) e g d xy b 2g d yz, d zx e g Square-planar field (D 4h )

Crystal Field Theory d xy, d yz, d zx d z2, d x2-y2 e g d z2, d x2-y2 d xy, d yz, d zx t 2g Cubic Field Uniform Field Octahedral Field (O h )

Crystal Field Theory d xy, d yz, d zx e g t 2 d xy, d yz, d zx d z2, d x2-y2 e d z2, d x2-y2 D t 4/9 D o d xy, d yz, d zx d z2, d x2-y2 t 2g Tetrahedral Field (T d ) Cubic Field Uniform Field Octahedral Field (O h )

Crystal Field Theory d x2-y2 b 1g e g d x2-y2 b 1g D 1 t 2 d xy, d yz, d zx D t d d z2, d x2-y2 D o d z2 a 1g d xy D 2 d z2 b 2g a 1g e d z2, d x2-y2 d xy, d yz, d zx d xy b 2g D 3 Tetrahedral (T d ) Uniform Field t 2g e g d yz, d zx e g Octahedral (O h ) d yz, d zx Tetragonal elongation (D 4h ) Square-planar (D 4h )

Crystal Field Theory : CFSE, LFSE Why are complexes formed in crystal field theory? Crystal Field Stabilization Energy (CFSE) or Ligand Field Stabilization Energy (LFSE) LFSE : the stabilization of the d electrons because of the metal-ligand environments d 3 e g LFSE of d 3 in octahedral structure = (-0.4D o ) x 3 = -1.2 D o 0.6D o 0.4D o t 2g Octahedral Field

Crystal Field Theory : CFSE, LFSE Electron configuration (O h ) t 2g 1 t 2g 2 t 2g 3 t 2g3 e g 1 t 2g3 e g 2 t 2g4 e g 2 t 2g5 e g 2 t 2g6 e g 2 t 2g6 e g 3 t 2g6 e g 4 weak field, strong field? LFSE + pairing energy (P c + P e ) = -0.6 D o + 3P e P c : Coulombic energy P e : Exchange energy (=exchanges between the same spins at the same energy ) t 2g 1 t 2g 2 t 2g 3 t 2g 4 t 2g 5 t 2g 6 t 2g6 e g 1 t 2g6 e g 2 t 2g6 e g 3 t 2g6 e g 4 LFSE + pairing energy (P c + P e ) = -1.6 D o + P c + 3P e DE = strong field - weak field = -D o + P c DE > 0 weak field (high spin) DE < 0 strong field (low spin)

Crystal Field Theory : CFSE, LFSE Ligand Field Stabilization Energies and Spin States (O h ) Weak field (high spin) Strong field (low spin)

Crystal Field Theory : CFSE, LFSE What determines? depends on the relative energies of the metal ions and ligand orbials and on the degree of overlap. e g Spectrochemical Series for Ligands CO > CN - > PPh 3 > NO - 2 > phen > bipy > en > NH 3 > py > CH 3 CN > NCS - > H 2 O > C 2 O 2-4 > OH - > RCO - 2 > F - > N - 3 > NO - 3 > Cl - > SCN - > S 2- > Br - > I- d d z2, d x2-y2 D o π acceptor π donor (strong field ligand) (weak field ligand) Spectrochemical Series for Metal Ions d xy, d yz, d zx t 2g Octahedral (O h ) (ox #,ᇫ ) smaller size and higher charge (down a group in periodic table, ᇫ ) greater overlap between 4d and 5d orbitals and ligand orbitals, decreasing pairing energy Pt 4+ > Ir 3+ > Pd 4+ > Ru 3+ > Rh 3+ > Mo 3+ > Mn 4+ > Co 3+ > Fe 3+ > V 2+ > Fe 2+ > Co 2+ > Ni 2+ > Mn 2+

Crystal Field Theory : CFSE, LFSE Spectrochemical Series for Metal Ions (ox #,ᇫ ) smaller size and higher charge (down a group in periodic table, ᇫ ) greater overlap between 4d and 5d orbitals and ligand orbitals, decreasing pairing energy [Co(H 2 O)] 3+ is the only low-spin agua complex. Pt 4+ > Ir 3+ > Pd 4+ > Ru 3+ > Rh 3+ > Mo 3+ > Mn 4+ > Co 3+ > Fe 3+ > V 2+ > Fe 2+ > Co 2+ > Ni 2+ > Mn 2+

Crystal Field Theory : CFSE, LFSE s ½ 1 3/2 2 5/2 2 3/2 1 ½ 0 Spin States (O h ) ½ 1 3/2 1 1/2 0 1/2 1 ½ 0

Crystal Field Theory : CFSE, LFSE Magnetochemical Series Measure pyrrole 1 H chemical shift in Fe(III)X(TPP) : useful for distinguishing weak ligads weaker I - > ReO - 4 (66.7 ppm) > CF 3 SO - 3 (47.9) > ClO - 4 (27.7) AsF - 6 (-31.5) > CB 11 H - 12 (-58.5) For weak ligand, admixed (in between S = 5/2 and S = 3/2) states are observed. H Full series (2015)

Crystal Field Theory : CFSE, LFSE Qualitative observation of LFSE in thermodynamic data (Hydration Enthalpy) M 2+ (g) + 6H 2 O(l) [M(H 2 O) 6 ] 2+ : DH hyd [ x (= z 2 /r) in first order] Measured by M 2+ (g) + 6H 2 O(l) + 2H + + 2e - [M(H 2 O) 6 ] 2+ + H 2 (g) Corrected with spin-orbit splittings, relaxation effect from the contraction of the metal-ligand distances, and interelectronic repulsion energy, and LFSE. But mostly the differences between the experimental and corrected values are from LFSE. : mostly comes from LFSE

Crystal Field Theory : CFSE, LFSE t 2 d xy, d yz, d zx Ligand Field Stabilzation Energies (T d ) D t d 0.4D t D t ( 4/9 D o ) : all high-spin configuration e d z2, d x2-y2 0.6D t tetrahedral field d electrons ex electron configurations LFSEs (D t ) Spin States (S) 1 Ti 3+ e 1-0.6 ½ 2 V 3+ e 2-1.2 1 3 Cr 3+ e 2 t 1 2-0.8 3/2 4 Cr 2+ e 2 t 2 2-0.4 2 5 Mn 2+ e 2 t 3 2 0 5/2 6 Fe 2+ e 3 t 3 2-0.6 2 7 Co 2+ e 4 t 3 2-1.2 3/2 8 Ni 2+ e 4 t 4 2-0.8 1 9 Cu 2+ e 4 t 5 2-0.4 ½ 10 Zn 2+ e 4 t 6 2 0 0

Ligand Field Theory CFT explains well the magnetic properties and in some degree the electronic spectra of the complexes. However, there is no explaination of the bondings. In other words, the purely electrostatic approach does not allow for the lower (bonding) molecular orbitals, and thus fail to provide a complete picture of the electron structures of complexes. CFT and MO theory combined complete theory Ligand Field Theory (Bonding Theory of Transition-Metal Complexes) Constructring MOs to explain the electronic structure, magnetic properties, and bondings.

Ligand Field Theory 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals Orbital interactions in O h complexes

Ligand Field Theory 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals Y = c + c a a b b c A = c B c A > c B c A >> c B c A = c B c A < c B c A << c B

Ligand Field Theory Two Primary Influences to Ligand Field 1) Geometries O h, T d, D 4h... 2) Types of Ligands s-donor, p-donor, p-acceptor s-donor ligands : H -, NH 3.. p-acceptor ligands : CO, CN -, NO +, RCN... M :H M :NH 3 p-donor ligands : halides, O 2-, RO -, RS -, RCO 2 -... p-acceptor orbital M X - M C=O p x s-donor orbital

Ligand Field Theory Constructing MOs of Transition-Metal Complexes ML n : Assume central metal ion, M, has available s,p, and d orbitals : 9 orbitals Assume ligands, L, have s and p orbitals : 4n orbitals combination of the 4n orbitals makes s-donor, p-donor, and p-acceptor orbitals O h (ML 6 ) with s-donor ligands M s : A 1g p x, p y, p z : T 1u d z2, d x2-y2 :, E g d xy, d yz, d zx : T 2g x 2 +y 2 +z 2

Ligand Field Theory O h (ML 6 ) with s-donor ligands M s : A 1g p x, p y, p z : T 1u d z2, d x2-y2 :, E g d xy, d yz, d zx : T 2g L : representations of s-donor orbitals G s 6 0 0 2 2 0 0 0 4 2 x 2 +y 2 +z 2 G s = T 1u + E g + A 1g

Ligand Field Theory O h (ML 6 ) with s-donor ligands M s : A 1g p x, p y, p z : T 1u d z2, d x2-y2 :, E g d xy, d yz, d zx : T 2g G s = T 1u + E g + A 1g frontier orbitals electrons from d-orbitals same splitting pattern and d- orbital configuration as in CFT Why are complexes formed in ligand field theory? Because of forming bonding orbitals electrons from ligands

Ligand Field Theory O h (ML 6 ) with s-donor ligands Symmetry Adapted Orbitals Think about what these orbitals look like.

Ligand Field Theory

Ligand Field Theory O h (ML 6 ) with p-acceptor, p-donor ligands M s : A 1g p x, p y, p z : T 1u d z2, d x2-y2 :, E g d xy, d yz, d zx : T 2g L : representations of p orbitals G p 12 0 0 0-4 0 0 0 0 0 G p = T 1g + T 2g + T 1u + T 2u

Ligand Field Theory O h (ML 6 ) with p-acceptor, p-donor ligands G p = T 1g + T 2g + T 1u + T 2u CO (LUMO) p-acceptor + s-donor ligands CO (HOMO) G s = T 1u + E g + A 1g

Ligand Field Theory O h (ML 6 ) with p-acceptor, p-donor ligands G p = T 1g + T 2g + T 1u + T 2u CO (LUMO) p-acceptor + s-donor ligands metal-to-ligand (M L) p bonding = p backbonding CO (HOMO) G s = T 1u + E g + A 1g

Ligand Field Theory O h (ML 6 ) with p-acceptor, p-donor ligands G p = T 1g + T 2g + T 1u + T 2u Spectrochemical Series for Ligands CO > CN - > PPh 3 > NO 2 - > phen > bipy > en > NH 3 > py > CH 3 CN > NCS - > H 2 O > C 2 O 4 2- > OH - > RCO 2 - > F - > N 3 - > NO 3 - > Cl - > SCN - > S 2- > Br - > I- M X - π acceptor (strong field ligand) π donor (weak field ligand) Metal-to-ligand (M L) p bonding (p back-bonding) increases metal-ligand bond strength (transfer of negative charge away from the metal ion) Ligand-to-metal (L M) p bonding decreases metal-ligand bond strength (more negative charge on the metal ion decrease of attraction between the metal ion and the ligands) M C=O

Ligand Field Theory D 4h (ML 4 ) with s-donor ligands (square planar) M s : A 1g p x, p y : E u p z : A 2u d z2 : A 1g d x2-y2 :, B 1g d xy : B 2g d yz, d zx : E g L : representations of s-donor orbitals : representations of p -orbitals : representations of p -orbitals G s 4 0 0 2 0 0 0 4 2 0 G s = A 1g + B 1g + E u G 4 0 0-2 0 0 0 4-2 0 G = A 2g + B 2g + E u G 4 0 0-2 0 0 0-4 2 0 G = A 2u + B 2u + E g

Ligand Field Theory D 4h (ML 4 ) with s-donor ligands (square planar) M s : A 1g p x, p y : E u p z : A 2u d z2 : A 1g d x2-y2 :, B 1g d xy : B 2g d yz, d zx : E g G s = A 1g + B 1g + E u CFT d x2-y2 b 1g D 1 D 2 d xy d z2 b 2g a 1g D 3 d yz, d zx e g

Ligand Field Theory D 4h (ML 4 ) with s-donor ligands (square planar) Symmetry Adapted Orbitals G s = A 1g + B 1g + E u Think about what these orbitals look like.

Ligand Field Theory D 4h (ML 4 ) with s-donor ligands (square planar) M s : A 1g p x, p y : E u p z : A 2u d z2 : A 1g d x2-y2 :, B 1g d xy : B 2g d yz, d zx : E g G s = A 1g + B 1g + E u G = A 2g + B 2g + E u G = A 2u + B 2u + E g metal d orbitals p-bonding orbitals : ligand p-donor 16 electrons s-bonding orbitals : ligand s-donor 8 electrons [Pt(CN) 4 ] 2-

Ligand Field Theory D 4h (ML 4 ) with s-donor ligands (square planar) [Pt(CN) 4 ] 2- CFT d x2-y2 b 1g D 1 up and down depending on metals and ligands D 2 d xy d z2 b 2g a 1g D 3 e g d yz, d zx [Ni(CN) 4 ] 2- : a 2u > b 1 g > a 1g > e g > b 2g always b 1g > a 1g, e g, b 2g D 1 >> D 2, D 3 d 8 (sq. pl) low-spin

Ligand Field Theory T d (ML 4 ) M s : A 1 p x, p y, p z : T 2 d z2, d x2-y2 :, E d xy, d yz, d zx : T 2 L G s 4 1 0 0 2 G p 8-1 0 0 0 G s = A 1 + T 2 G p = E + T 1 + T 2 : representations of s-donor orbitals : representations of p ligand orbitals

Ligand Field Theory T d (ML 4 ) M s : A 1 p x, p y, p z : T 2 d z2, d x2-y2 :, E d xy, d yz, d zx : T 2 with s-donors only t 2 3t 2 2a 1 G s = A 1 + T 2 Symmetry Adapted Orbitals a 1 2t 2 CFT e + t 2 e Think about the shapes of the MOs a 1 + t 2 t 2 d xy, d yz, d zx e D t d z2, d x2-y2 1t 2 1a 1 M ML 4 L 4

Ligand Field Theory T d (ML 4 ) with s-donors and p-interactions M s : A 1 p x, p y, p z : T 2 d z2, d x2-y2 :, E d xy, d yz, d zx : T 2 G s = A 1 + T 2 G p = E + T 1 + T 2

Angular Overlap Model Ligand Field Model No explicit use of energy Difficult to use when considering an assortment of ligands or structures with symmetry other than O h, D 4h, T d. Angular Overlap Model A variation with the flexibility to deal with a variety of possible geometries and with a mixture of ligands Estimates the strength of interaction between individual ligand orbitals and metal d orbitals based on overlap between them Determine the energy level of a metal d orbital and a ligand orbital in a coordination complex

Angular Overlap Model s-donor interactions Basic criteria: the strongest s interaction overlap between d z2 and ligand p z (or hybrid) : e s bonding orbitals: stabilized by e s antibonding orbitals: destabilized by e s The magnitudes of other interactions between d-orbitals and ligand s-orbitals: determined relative to e s

Angular Overlap Model s-donor interactions Ex) s-donor interactions of [M(NH 3 ) 6 ] n+ d z2 : strength of s-interaction = 1 + ¼ + ¼ + ¼ + ¼ + 1 = 3 d x2-y2 : strength of s-interaction = 0 + ¾ + ¾ + ¾ + ¾ + 0 = 3 d xy, d yz, d zx : strength of s-interaction = 0 + 0 + 0 + 0 + 0 + 0 = 0 ligand 1,6 orbitals : strength of s-interaction = 1 + 0 + 0 + 0 + 0 + 0 = 1 ligand 2, 3, 4, 5 orbitals : strength of s-interaction = ¼ + ¾ + 0 + 0 + 0 + 0 = 1

Angular Overlap Model s-donor interactions Ex) s-donor interactions of [M(NH 3 ) 6 ] n+ destabilization : 0 or (3xn)e s d z2 : strength of s-interaction = 1 + ¼ + ¼ + ¼ + ¼ + 1 = 3 d x2-y2 : strength of s-interaction = 0 + ¾ + ¾ + ¾ + ¾ + 0 = 3 d xy, d yz, d zx : strength of s-interaction = 0 + 0 + 0 + 0 + 0 + 0 = 0 ligand 1,6 orbitals : strength of s-interaction = 1 + 0 + 0 + 0 + 0 + 0 = 1 e g CFT d z2, d x2-y2 D o stabilization : 12e s Angular overlap model: not a complete picture of MOs, but can estimate the energy levels of the orbitals ligand 2, 3, 4, 5 orbitals : strength of s-interaction = ¼ + ¾ + 0 + 0 + 0 + 0 = 1 t 2g d xy, d yz, d zx

Angular Overlap Model p-acceptor interactions Basic criteria: the strongest p interaction overlap between d xz and ligand p* orbital : e p e p < e s

Angular Overlap Model p-acceptor interactions Ex) p-acceptor interactions of [M(CN) 6 ] n- d z2, d x2-y2 : strength of p-interaction = 0 + 0 + 0 + 0 + 0 +0 = 0 d xy, d yz, d zx : strength of p-interaction = 0 + 1 + 1 + 1 + 1 + 0 = 4 ligand 1, 2, 3, 4, 5, 6 orbitals : strength of p-interaction = 0 + 0 + 0 + 0 + 1 + 1 = 2

Angular Overlap Model p-acceptor interactions Ex) Energy level diagram of d-orbitals, s-donor and p-acceptor ligands in octahedral complexes s-donor interactions p-acceptor interactions d d z2, d x2-y2 : 0 z2, d x2-y2 : 3 d d xy, d yz, d zx : 4 xy, d yz, d zx : 0 ligand 1,2, 3, 4, 5, 6 orbitals : 1 ligand 1, 2, 3, 4, 5, 6 orbitals : 2 2e p s-donor + p-acceptor interactions

Angular Overlap Model p-donor interactions Basic criteria: same as in p-acceptor interaction : e p usually, e p for p-acceptor interation > e p for p-donor interation Ex) p-donor interaction of [MX 6 ] n- d z2, d x2-y2 : strength of p-interaction = 0 + 0 + 0 + 0 + 0 +0 = 0 d xy, d yz, d zx : strength of p-interaction = 0 + 1 + 1 + 1 + 1 + 0 = 4 ligand 1, 2, 3, 4, 5, 6 orbitals : strength of p-interaction = 0 + 0 + 0 + 0 + 1 + 1 = 2

Angular Overlap Model p-donor interactions Ex) Energy level diagram of d-orbitals, s-donor and p-acceptor ligands in octahedral complexes s-donor interactions p-donor interactions d d z2, d x2-y2 : 0 z2, d x2-y2 : 3 d d xy, d yz, d zx : 4 xy, d yz, d zx : 0 ligand 1,2, 3, 4, 5, 6 orbitals : 1 ligand 1, 2, 3, 4, 5, 6 orbitals : 2 s-donor + p-donor interactions

Angular Overlap Model s-donor s-donor + p-donor LFT s-donor + p-acceptor

Angular Overlap Model Magnitudes of e s, e p, and D : depend on both ligands and metals s-donor + p-donor e s, e p D = 3e s - 4e p generally follows the spectrochemical series. e s > e p e s, e p as size of X - and electronegativity of X - (bond length increase metal-ligand interaction decrease)

Angular Overlap Model Magnitudes of e s, e p, and D : depend on both ligands and metals Spectrochemical Series for Ligands CO > CN - > PPh 3 > NO - 2 > phen > bipy > en > NH 3 > py > CH 3 CN > NCS - > H 2 O > C 2 O 2-4 > OH - > RCO - 2 > F - > N - 3 > NO - 3 > Cl - > SCN - > S 2- > Br - > I- Spectrochemical Series for Metal Ions (ox #,ᇫ ) smaller size and higher charge (down a group in periodic table, ᇫ ) greater overlap between 4d and 5d orbitals and ligand orbitals, decreasing pairing energy π acceptor (strong field ligand) π donor (weak field ligand) Pt 4+ > Ir 3+ > Pd 4+ > Ru 3+ > Rh 3+ > Mo 3+ > Mn 4+ > Co 3+ > Fe 3+ > V 2+ > Fe 2+ > Co 2+ > Ni 2+ > Mn 2+

angular overlap energy Theories of Bonding and Electronic Angular Overlap Model Four- and six coordinate preference Angular overlap calculation can provide us with some indication of relative stabilities depending on the number of d electrons and geometries. E = 12x(-e s ) + 5x(0e s ) + 2x(3e s ) = -6e s O h is favorable. Both sq. pl and O h are favorable.

angular overlap energy Theories of Bonding and Electronic Angular Overlap Model Four- and six coordinate preference Angular overlap calculation can provide us with some indication of relative stabilities depending on the number of d electrons and geometries. Strong-field sq. pl is favorable. Angular overlap calculation gives just an approximate. There are many other factors to get a complete picture.

angular overlap energy Theories of Bonding and Electronic Angular Overlap Model Application to hydration enthalpy M 2+ (g) + 6H 2 O(l) [M(H 2 O) 6 ] 2+ : DH hyd [ x (= z 2 /r) in first order] Assume -1.8 e s per each d electron added (-0.3 e s in the textbook is something wrong) M 2+ LFSE + -1.8 e s x number of d electrons weak field octahedral [M(H 2 O) 6 ] 2+

Angular Overlap Model Other shapes Consideration of both group theory and angular overlap model can be used to determine which d orbitals interact ligand s orbitals and give estimations of the energy levels of the MOs for geometries other than octahedral and square planar. trigonal bipyramidal ML 5 (D 3h ) L 5 s-donor ligands L M L L L G s 5 2 1 3 0 3 G s = 2A 1 ' + A 2 '' + E' M d z2 : A 1 ' d x2-y2, d xy : E' d yz, d zx : E'' d a 1 e e e a 1 e which one? M ML 5

Angular Overlap Model Other shapes trigonal bipyramidal ML 5 (D 3h ) M d z2 : A 1 ' d x2-y2, d xy : E' d yz, d zx : E'' d z2 : strength of s-interaction = 2¾ d x2-y2, d xy : strength of s-interaction = 9/8 d yz, d zx : strength of s-interaction = 0 ligands : strength of s-interaction = 1 2¾ e s 9/8 e s e s

Jahn-Teller Effect There cannot be unequal occupation of orbitals with identical orbitals. To avoid such unequal occupation, the molecule distorts so that these orbitals no longer degenerate. In other words, if the ground electron configuration of a nonlinear complex is orbitally degenerate, the complex will distort to remove the degeneracy and achieve a lower energy. d 9 (Cu(II)) [Cu(H 2 O) 6 ] 2+ d(cu-o eq ) = 1.95 Å d(cu-o ax ) = 2.38 Å [Cu(H 2 O) 6 ] 2+ + NH 3 [Cu(NH 3 )(H 2 O) 5 ] 2+ + H 2 O K 1 = 20,000 [Cu(NH 3 )(H 2 O) 5 ] 2+ + NH 3 [Cu(NH 3 ) 2 (H 2 O) 4 ] 2+ + H 2 O K 2 = 4,000 [Cu(NH 3 ) 2 (H 2 O) 4 ] 2+ + NH 3 [Cu(NH 3 ) 3 (H 2 O) 3 ] 2+ + H 2 O K 3 = 1,000 [Cu(NH 3 ) 3 (H 2 O) 3 ] 2+ + NH 3 [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ + H 2 O K 4 = 200 [Cu(NH 3 ) 4 (H 2 O) 2 ] 2+ + NH 3 [Cu(NH 3 ) 5 (H 2 O)] 2+ + H 2 O K 5 = 0.3 [Cu(NH 3 ) 5 (H 2 O)] 2+ + NH 3 [Cu(NH 3 ) 6 ] 2+ K 6 = very small [Cu(NH 3 ) 6 ] 2+ : difficult to make in aqueous solution. Can be made in ammonical solution. [Cu(H 2 O) 6 ] 2+ + 2 en [Cu(en) 2 (H 2 O) 5 ] 2+ + 4 H 2 O N H 2 O N N N OH 2

Jahn-Teller Effect d 1 (Ti(III)) favor

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