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Microsoft PowerPoint - Coordination Chemistry II - Bonding.ppt10-1
Experimental evidence for electronic structures
Any successful theory of bonding in coordination complexes must be consistent with experimental data regarding their behavior. This chapter provides a review of some of the types of experimental observations that have been made on coordination complexes, then describes theories of electronic structure & bonding that have been used to account for their properties.
3
10-1-1 Thermodynamic data (enthalpy & free energy)
One of the primary goals of a bonding theory must be to explain the energies of compounds. Experimentally, the energy is frequently not determined directly, but from thermodynamic measurements.
4
Stability constants (K, formation constants) can be as indicators of bonding strengths. The large stability constants indicate that bonding with the incoming ligand is much more favorable than bonding with water.
5
K : stability constants (formation constants) ΔG = -RT lnK = ΔH - TΔS
6
In practice, thermodynamic values alone are rarely sufficient to predict other properties of coordination complexes or their structures or formulas. But, it is more valuable in considering relationship among similar complexes.
7
Hard-Soft Acid Base concept Such qualitative descriptions are useful, but it is difficult to completely rationalize data such as these without extensive theoretical calculations.
Ag+ is softer, while Cu2+ is a borderline cation.
(2,000) (17,000)
(entropy effect dominates))
10-1-2 Magnetic susceptibility ( )
Hund’s rule : maximum multiplicity (maximum number of unpaired electrons) When there are unpaired electrons, the compound is paramagnetic, & is attracted into a magnetic field. The measure of this magnetism is called the magnetic susceptibility (electrons behave as tiny magnets).
no field weak field strong field
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♦ Diamagnetism - spin-paired state (or zero unpaired electron) is very weakly repelled by the magnetic field. ♦ Paramagnetism - with unpaired electron(s) is attracted into the magnetic field. The spins are lining up together under an external magnetic field but are not aligned in the crystal in the absence of the external field (random).
pyrolytic graphite ( ) : A very diamagnetic material.
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♦ Ferromagnetism - The spins are aligned in the crystal even without an external magnetic field.
♦ Antiferromagnetism -The spins are anti-aligned in the crystal even without an external magnetic field.
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The magnetic susceptibility, χ, of noninteracting spins can be modeled by the
Curie Law : χ = C/T, C = Ng2μB
2S(S+1)/3kB
where μB is the Bohr magneton (magnetic moment), N is Avogadro’s number, kB the Boltzmann constant, & g the Landé g Value.
17
Interacting spins either reduce or enhance the susceptibility & can be modeled by the
Curie-Weiss Law :
χ = C/(T− θ)
where θ > 0 signifies an enhanced susceptibility or ferromagnetic (↑↑), & θ < 0 signifies a reduced susceptibility or antiferromagnetic (↑↓).
antiferromagnetic interaction
θ < 0
θ > 0
Diamagnetic : repel each other Paramagnetic : attract each other Gouy balance (Louis Georges Gouy)
⇒ Magnetic susceptibility “χ” (unit: cm3/mole) Effective magnetic moment (μeff) : μeff = 2.828(χT)1/2 [χ = C/T, C = Ng2μB
2S(S+1)/3kB] μeff (spin only) : The unit of magnetic moment is Bohr magneton: μB = 9.27 x 10-24 JT-1 (joules/tesla). Tesla = 104 Gauss (SI magnetic flux density)
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Spin magnetic moment is characterized by S, spin quantum number (maximum total spin) (electron spin, ms = +1/2, -1/2) Orbital angular momentum, characterized by the quantum number, L (the maximum possible sum of the ml values, results in an additional orbital magnetic momentum).
Quantum Mechanics of Magnetism
S = 1 (1/2+1/2+1/2-1/2) L =1 (+1+0-1+1)
L-S coupling [J = total angular momentum = (L-S) ~ (L+S)]
(spin-spin, orbital-orbital, & spin-orbital interactions)
l = +1 0 -1
(1) L-S (Russell-Saunders) coupling scheme For multi-electron atoms where the spin-orbit coupling is weak,
it can be presumed that the orbital angular momenta of the individual electrons add to form a resultant orbital angular momentum L. Likewise, the individual spin angular momenta are presumed to couple to produce a resultant spin angular momentum S. Then L & S combine to form the total angular momentum J = L + S. This gives good agreement with the observed spectral details for many light atoms (Z ≤ 30).
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Splitting between terms with different values of J is typically small & occurs only in a magnetic field.
in magnetic field
mJ l +1 0 -1
Ground state term: L = 1, S = 1, J = 0, 1, 2
Zeeman splitting
electron configuration
Spin-orbit coupling
(2) Spin-Orbital coupling scheme
In heavier atoms, the orbital & spin angular momentum of individual electrons first couple, giving a resultant j for each electron; we say that spin-orbital coupling is energetically important. The individual j’s then couple (J-J coupling), produce an overall J.
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Experimentally, μeff can be measured.
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1010--2 Theories of electronic structure2 Theories of electronic structure 10-2-1 Terminology (I) Valence bond theory : This method describes bonding using hybrid orbitals & electron pairs, as an extension of the electron-dot & hybrid orbital methods used for simple molecules.
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(II) Crystal field theory : This is an electrostatic approach, used to describe the split in metal d- orbital energies. It provides an approximate description of the electronic energy levels that determine the ultraviolet & visible (UV-VIS) spectra, but does not describe the bonding.
(III) Ligand field theory : This is a more complete description of bonding in terms of the electronic energy levels of the frontier orbitals. It used some of the terminology of crystal field theory but includes the bonding orbitals.
ex. Cl- ex. CO π*
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(IV) Angular overlap theory : This is a method of estimating the relative magnitudes of the orbital energies in a molecular orbital calculation.
It explicitly takes into account the bonding energy as well as the relative orientation of the frontier orbitals.
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10-2-2 Historical background valence bond theory The valence bond theory, originally proposed by Pauling in the 1930s, used the hybridization ideas. For octahedral complexes, d2sp3 hybrids of the metal orbitals are required. However, the d orbitals used by the first-row transition metals could be either 3d or 4d.
3d 4s 4p 4d
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The valence bond theory was of great importance in the development of bonding theory for coordin- ation compounds. Although it provides a set of orbitals for bonding, the use of the high energy 4d orbitals seems unlikely, & the results do not lend themselves to a good explanation of the electronic spectra of complexes.
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Crystal field theory : the split in metal d-orbital energies by the electrostatic field.
Spherical field Oh field
eg
t2g
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When the d orbitals of a metal ion are placed in an octahedral field of ligand electron pairs, any elec- trons in them are repelled by the field. As a result, the dx2-y2 & dz2 orbitals, which are directed at the surrounding ligands, are raised in energy. The dxy, dxz, & dyz orbitals, which are directed between the surrounding ions, are relatively unaffected by the field.
This approach provides a simple means of identify- ing the d-orbital splitting found in coordination complexes. The chief drawbacks are in its concept of the repulsion of orbitals by the ligands & its lack of any explanation for bonding in coordination complexes. The purely electrostatic approach does not allow for the lower (bonding) molecular orbitals & thus fails to provide a complete picture of the electronic structure.
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10-3 Ligand field theory
Crystal field theory does not consider the effect of molecular bonding & fails to explain many cases. For example, why CO is a strong-field ligand & Cl- a weak one ?
The electrostatic crystal field theory & the molecular orbital theory were combined into a more complete theory called ligand field theory, described qualitatively by Griffith & Orgel.
39
Simple MO treatment
dx2-y2, dz2 : bonding orbitals dxy, dxz, dyz : nonbonding orbitals
The six ligand σ-donor orbitals collectively form a reducible representation Γ in the point group Oh. Γ = A1g + T1u + Eg
4s, 4px, 4py, 4pz, 3dz2 & 3dx2-y2Metal orbitals used for σ-bonding: 40
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The six ligand σdonor orbitals (p orbitals or hybrid orbitals with the same symmetry) match the symmetries of the 4s, 4px, 4py, 4pz, 3dz2 & 3dx2-y2
metal orbitals.
The combination of the ligand & metal orbitals form six bonding & six antibonding orbitals with a1g, eg & t1u symmetries. The six bonding orbitals are filled by electrons donated by the ligands.
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The metal t2g orbitals (dxy, dxz & dyz) do not have appropriate symmetry to interact with the ligands & are nonbonding.
Electrons of the metal occupy these nonbonding orbitals (t2g) & the higher energy antibonding orbitals (eg).
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Δο (10Dq)
From σ donor ligands (all π interactions are ignored here)
Metal Ligand
Figure 10-6
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Most of the discussion of octahedral ligand fields is concentrated on the t2g & higher orbitals (eg). Electrons in bonding orbitals provide the potential energy that holds molecules together, & electrons in the higher levels affected by ligand field effects help determine the details of the structure, magnetic properties, & electronic spectrum.
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10-3-2 Orbital splitting & electron spin
In octahedral complexes, electrons from the ligands fill all six bonding MOs, & any electrons from the metal ion occupy the nonbonding (t2g) & antibonding (eg) orbitals.
The splitting between these two sets of orbitals (t2g & eg) is called Δo (10 Dq, o for octahedral).
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Strong-field ligands : ligands whose orbitals interact strongly with the metal orbitals (large Δo). Weak-field ligands : ligands with weak inter- actions (small Δo).
* d0, d3, d8, d10 : only one electron configuration * d4-7 : high-spin & low-spin states
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Strong ligand field large Δo low spin Weak ligand field small Δo high spin
Electron configurations depend on Πc, Πe, & Δο. Δo : Π (Πc + Πe)
Πc: Coulombic energy Πe: Exchange energy
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Example (p349): Determine the exchange energies for high-spin & low-spin d6 ions in an octahedral complex.
4 Πe
6 Πe
4-5, 1-2, 1-3, 2-3
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[Co(H2O)6]3+ is the only low-spin aqueous complex. Π ~ Δo
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From Table 10-6 1. Δo for 3+ ions is larger than Δo for 2+ ions with
the same number of electrons. Π ? 2. Most of the first-row transition metals require a
stronger field ligand than H2O to give low-spin complexes.
3. Second- & third-row transition metals forms low-spin complexes.
*** Δo > Π : low-spin; Δo < Π : high-spin ***
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Why 2nd, 3rd transition series favor low-spin ? (1) The greater overlap between the larger 4d &
5d orbitals & the ligand orbitals, giving larger Δo (major) - smaller L-L repulsion
(2) A decreased pairing energy Π due to the larger volume available for electrons in the 4d & 5d orbitals compared with 3d orbitals. (minor)
Δo > Π : low-spin
10-3-3 Ligand field stabilization energy (LFSE)
The LFSE represents the stabilization of the d electrons because of the metal-ligand environment.
Δo = 10 Dq
(aq)
Ions with spherical symmetry should have ΔH becoming increasingly exothermic (more negative) continuously across the transition series due to the decreasing radius of the ions with increasing nuclear charge & corresponding increase in electrostatic attraction for the ligands.
Enthalpy of hydration of transition metal ions Effects of LFSE
ΔH increases (< 0)
The almost linear curve of the “corrected” enthalpies is expected for ions with decreasing radius.
Experimental curve
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The differences between the “corrected” & double- humped () experimental values are approxi mately equal to :
(1) LFSE values (for high-spin complexes : weak- field ligands, H2O)
(2) Spin-orbit splittings (0 to 16 kJ/mol) * H-bonding interactions : 1 ~ 40 kJ/mol
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(3) A relaxation effect caused by contraction of the metal-ligand distance (0 to 24 kJ/mol)
(4) An interelectronic repulsion energy that depends on the exchange interactions with the same spin (0 to -19 kJ/mol for M2+, 0 to -156 kJ/mol for M3+)
(2) ~ (4) are less important than LFSE, but they improve the shape of the curve for the corrected values significantly.
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In the case of the hexaaqua & hexafluoro complexes of the +3 transition metal ions, the interelectronic repulsion energy, sometimes called the the nephelauxetic effect, is large & is required to remove the deviation from a smooth curves through the d0, d5 & d10 values. Why do we care about LFSE ? There are two principal reasons. First, it provides a more quanti- tative approach to the high-spin-low-spin electron configuration, helping predict which configuration will be more likely. Second, it is the basis for our discussion of the spectra of these complexes in Ch 11.
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The nephelauxetic effect (electron cloud expansion) may occur for one (or both) of two reasons: 1. The effective positive charge on the metal has
decreased. Because the positive charge of the metal is reduced by any negative charge on the ligands, the d-orbitals can expand slightly.
2. The act of overlapping with ligand orbitals & forming covalent bonds increases orbital size, because the resulting molecular orbital is formed from two atomic orbitals.
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Nephelauxetic (cloud expanding) effect : It refers to a decrease in the Racah interelectronic repulsion parameter, B, that occurs when a transition metal free ion forms a complex with ligands. The decrease in B indicates that in a complex there is less repul- sion between the two electrons in a given doubly occupied metal d-orbital than there is in the respec- tive Mn+ gaseous metal ion, which in turn implies that the size of the orbital is larger in the complex (metal ion has less effective charge).
Nephelauxetic effect is a measure of the electron repulsion within M-L bonding orbitals.
Nephelauxetic series
F- > H2O > NH3 > en > NCS- > Cl- ~ CN- > Br- >S2- > I-
Larger electronegativity & more electrowithdrawing ⇒ higher delocalization (M→L) [covalent character
increases], reach left.
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10-3-4 π bonding py (L) : for σ bonding px,z (L): for π bonding
or from ligand’s π*
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T1g & T2u (L) : nonbonding T2g (L) : dxy, dyz, dxz (M); available T1u (L) : px, py, pz (M); not available (have been used for σ bonding.
Atomic orbitals of metal ions for π-bonding.
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e-
The electron density of HOMO (3σ) is concentrated on C. ( 2s(C) contributes.)
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M
(a)
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From Figure 10-11(a) : A larger Δo value & increased bonding strength (π acceptor ligands : CN-, CO…). Significant energy stabilization can result from this added π bonding. This metal-to-ligand (M L, MLCT) π bonding is also called π back-bonding, with electrons from d orbitals of the metal donated back to the ligands. e-e-
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From Figure 10-11(b) : A smaller Δo (π donor ligands : F-, Cl-…).
The metal ion d electrons are pushed into the higher t2g* orbital by the ligand electrons. This is described as ligand-to-metal (L M, LMCT) π bonding, with the π electrons from the ligands being donated to the metal ion.
e-e-
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Summary : Empty higher energy π* or d orbitals on the ligands result in M L π bonding & a larger Δo for the complex.
Filled π or p orbitals on ligands (frequently with relatively low energy) result in L M π bonding & a smaller Δo for the complex.
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Ligand-to-metal π bonding usually gives decreased stability for the complex, favoring high-spin configuration.
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Part of the stabilizing effects of π back-bonding is a result of transfer of negative charge away from the metal ion. The metal ion accepts electrons from the ligands to form the σ bonds. The metal is then left with a large negative charge. When the π orbitals can be used to transfer part of this charge back to the ligands, the overall stability is improved (electron neutrality).
10-3-5 Square-planar Complexes
6s 6p
10-4 Angular overlap
Angular overlap model estimates the strength of interaction between individual ligand orbitals & metal d orbitals based on the overlap between them & then combines these values for all ligands & all d orbitals for the complete picture.
The term angular overlap is used because the amount of overlap depends strongly on the angles of the metal orbitals & the angle at which the ligand approaches (orientation).
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1eσ
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Example : [M(NH3)6]n+ (octahedral & with only σ-interaction)
(1) Metal d orbitals : dz2 & dx2-y2; dxy, dyz, dxz (2) Ligand orbitals (pz or hybrid orbital) dz2 : +3eσ dx2-y2 : +3eσ dxy, dyz, dxz : 0 ligand orbitals : -eσ
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Summary :
1. The energy pattern is the same as the LF model. 2. Δo = 3eσ (t2g/eg) 3. The net stabilization is 12eσ for the bonding
pairs; & d electrons in the upper eg level are destabilized by 3eσ for each electrons.
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d
88
σ-donor only
Ignore s,p
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i.e., halides can act as both a σ & a π donor
(Δo’)
2-?
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In general, in situations involving in ligands that can behave as both π acceptors & π donors (such as CO & CN-), the π-acceptor nature predominates.
Although π-donor ligands cause Δo to decrease, the larger effect of the π-acceptor ligands causes Δo to increase. π-acceptor ligands are better at splitting the d orbitals (causing larger changes in Δo).
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10-4-4 Types of ligands & the spectrochemical series Ligands are frequently classified by their donor & acceptor capability. Some, like σ donors only, with no orbitals of appropriate symmetry for π bonding. The ligand field split, Δ, then depends on the relative energies of the metal ion & ligand orbitals & on the degree of overlap. Ti(III)L6
d1
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(1) en > NH3 : proton basicity (2) F- > Cl- > Br- > I-
F-, Cl- : hard base; Br- : borderline base; I- : soft base (proton basicity / electrostatic interaction)
Spectrochemical Series
(2’) NH3 > H2O > F- > RCO2 - > OH- > Cl- > Br- > I-
Ligands that have occupied p orbitals are potentially π donors. They tend to donate these electrons to the metal along with the σ-bonding electrons (this π-donor interaction decreases Δ).
As a result, most halide complexes have high-spin configurations (OH- below H2O in the series because it has more π-donating tendency).
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(3) CO, CN- > phen(anthroline) > NO2 - > NCS-
π acceptors (when ligands have vacant π* or d orbitals, there is the possibility of π back bonding, & the ligands are π acceptors)
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The covalent bonding character & electrostatic effect are also considered.
The trend is also related to : different metal ions, different charge on the metal ions, ligands with different substituents, & co-ligands present.
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10-4-5 Magnitudes of eσ, eπ, and Δ Changing the ligand or the metal changes the magnitude of eσ & eπ, with resulting changes in Δ & a possible change in the number of unpaired electrons. (1) [Co(H2O)6]2+ v.s. [Co(H2O)6]3+
high-spin low-spin (2) [Fe(H2O)6]3+ v.s. [Fe(CN)6]3-
high-spin low-spin
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Strong back bonding leads to a larger stabilization of t2g orbitals (negative eπ values).
spectrochemical series
• eσ is always larger than eπ (2~9 times).
• The magnitudes of both the σ & π parameters decrease with increasing size & decreasing electronegativity of the halides (F- > Cl- > Br- > I-).
• The metal’s nuclear charge increases σ & π parameters.
103
10-5 The Jahn-Teller effect
The Jahn-Teller theorem states that there cannot be unequal occupation of orbitals with identical energies. To avoid such unequal occupation, the molecule distorts so that these orbitals are no longer degenerate (Cu2+ = d9).
[Cu(OH2)6]2+
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The resulting distortions is most often an elongation along one axis, but compression along one axis is also possible.
105
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The expected Jahn-Teller effects for octahedral coordination are given in the following table
For elongation
α > β
106
Low-spin Cr(II) (d4) : for an octahedral geometry, Oh → D4h. They show two absorption bands, one in the visible & one in the near-infrared region, caused by this distortion.
1 2 -1 2
CrII(d4)
107
Cr(II) also forms dimeric complexes with CrCr quadruple bonds & [Cr2(OAc)4] is nearly diamagnetic.
The quadruple bond between two chromium atoms arises from the overlap of four d-orbitals on each metal with the same orbitals on the other metal : the dz
2 orbitals overlap to give a σ-bonding component, the dxz & dyz orbitals overlap to give two π bonding components, & the dxy orbitals give a δ bond.
108
(1)
Cu2+ forms the most common complexes with signifi- cant Jahn-Teller effects. In most cases, the distortion is an elongation of two bond, but K2CuF4 forms a crystal with two shortened bonds in the octahedron.
109
(2) The formation constant for the addition of a third molecule of en to Cu2+ is much lower than for Ni2+.
[Cu(en)3]2+ v.s. [Ni(en)3]2+
Cu2+ : tetrahedral, square-planar, distorted TBP or SP, but not octahedral.
110
10.6 Four- and six-coordinate preferences
Angular overlap calculations of the energies expected for different numbers of d electrons & different geometries can give us some indication of relative stabilities (i.e., octahedral, square planar, & tetrahedral).
10-7 Other shapes (TBP)
Any successful theory of bonding in coordination complexes must be consistent with experimental data regarding their behavior. This chapter provides a review of some of the types of experimental observations that have been made on coordination complexes, then describes theories of electronic structure & bonding that have been used to account for their properties.
3
10-1-1 Thermodynamic data (enthalpy & free energy)
One of the primary goals of a bonding theory must be to explain the energies of compounds. Experimentally, the energy is frequently not determined directly, but from thermodynamic measurements.
4
Stability constants (K, formation constants) can be as indicators of bonding strengths. The large stability constants indicate that bonding with the incoming ligand is much more favorable than bonding with water.
5
K : stability constants (formation constants) ΔG = -RT lnK = ΔH - TΔS
6
In practice, thermodynamic values alone are rarely sufficient to predict other properties of coordination complexes or their structures or formulas. But, it is more valuable in considering relationship among similar complexes.
7
Hard-Soft Acid Base concept Such qualitative descriptions are useful, but it is difficult to completely rationalize data such as these without extensive theoretical calculations.
Ag+ is softer, while Cu2+ is a borderline cation.
(2,000) (17,000)
(entropy effect dominates))
10-1-2 Magnetic susceptibility ( )
Hund’s rule : maximum multiplicity (maximum number of unpaired electrons) When there are unpaired electrons, the compound is paramagnetic, & is attracted into a magnetic field. The measure of this magnetism is called the magnetic susceptibility (electrons behave as tiny magnets).
no field weak field strong field
10
♦ Diamagnetism - spin-paired state (or zero unpaired electron) is very weakly repelled by the magnetic field. ♦ Paramagnetism - with unpaired electron(s) is attracted into the magnetic field. The spins are lining up together under an external magnetic field but are not aligned in the crystal in the absence of the external field (random).
pyrolytic graphite ( ) : A very diamagnetic material.
11
♦ Ferromagnetism - The spins are aligned in the crystal even without an external magnetic field.
♦ Antiferromagnetism -The spins are anti-aligned in the crystal even without an external magnetic field.
12
14
16
The magnetic susceptibility, χ, of noninteracting spins can be modeled by the
Curie Law : χ = C/T, C = Ng2μB
2S(S+1)/3kB
where μB is the Bohr magneton (magnetic moment), N is Avogadro’s number, kB the Boltzmann constant, & g the Landé g Value.
17
Interacting spins either reduce or enhance the susceptibility & can be modeled by the
Curie-Weiss Law :
χ = C/(T− θ)
where θ > 0 signifies an enhanced susceptibility or ferromagnetic (↑↑), & θ < 0 signifies a reduced susceptibility or antiferromagnetic (↑↓).
antiferromagnetic interaction
θ < 0
θ > 0
Diamagnetic : repel each other Paramagnetic : attract each other Gouy balance (Louis Georges Gouy)
⇒ Magnetic susceptibility “χ” (unit: cm3/mole) Effective magnetic moment (μeff) : μeff = 2.828(χT)1/2 [χ = C/T, C = Ng2μB
2S(S+1)/3kB] μeff (spin only) : The unit of magnetic moment is Bohr magneton: μB = 9.27 x 10-24 JT-1 (joules/tesla). Tesla = 104 Gauss (SI magnetic flux density)
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Spin magnetic moment is characterized by S, spin quantum number (maximum total spin) (electron spin, ms = +1/2, -1/2) Orbital angular momentum, characterized by the quantum number, L (the maximum possible sum of the ml values, results in an additional orbital magnetic momentum).
Quantum Mechanics of Magnetism
S = 1 (1/2+1/2+1/2-1/2) L =1 (+1+0-1+1)
L-S coupling [J = total angular momentum = (L-S) ~ (L+S)]
(spin-spin, orbital-orbital, & spin-orbital interactions)
l = +1 0 -1
(1) L-S (Russell-Saunders) coupling scheme For multi-electron atoms where the spin-orbit coupling is weak,
it can be presumed that the orbital angular momenta of the individual electrons add to form a resultant orbital angular momentum L. Likewise, the individual spin angular momenta are presumed to couple to produce a resultant spin angular momentum S. Then L & S combine to form the total angular momentum J = L + S. This gives good agreement with the observed spectral details for many light atoms (Z ≤ 30).
22
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Splitting between terms with different values of J is typically small & occurs only in a magnetic field.
in magnetic field
mJ l +1 0 -1
Ground state term: L = 1, S = 1, J = 0, 1, 2
Zeeman splitting
electron configuration
Spin-orbit coupling
(2) Spin-Orbital coupling scheme
In heavier atoms, the orbital & spin angular momentum of individual electrons first couple, giving a resultant j for each electron; we say that spin-orbital coupling is energetically important. The individual j’s then couple (J-J coupling), produce an overall J.
25
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Experimentally, μeff can be measured.
27
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1010--2 Theories of electronic structure2 Theories of electronic structure 10-2-1 Terminology (I) Valence bond theory : This method describes bonding using hybrid orbitals & electron pairs, as an extension of the electron-dot & hybrid orbital methods used for simple molecules.
29
(II) Crystal field theory : This is an electrostatic approach, used to describe the split in metal d- orbital energies. It provides an approximate description of the electronic energy levels that determine the ultraviolet & visible (UV-VIS) spectra, but does not describe the bonding.
(III) Ligand field theory : This is a more complete description of bonding in terms of the electronic energy levels of the frontier orbitals. It used some of the terminology of crystal field theory but includes the bonding orbitals.
ex. Cl- ex. CO π*
30
31
(IV) Angular overlap theory : This is a method of estimating the relative magnitudes of the orbital energies in a molecular orbital calculation.
It explicitly takes into account the bonding energy as well as the relative orientation of the frontier orbitals.
32
10-2-2 Historical background valence bond theory The valence bond theory, originally proposed by Pauling in the 1930s, used the hybridization ideas. For octahedral complexes, d2sp3 hybrids of the metal orbitals are required. However, the d orbitals used by the first-row transition metals could be either 3d or 4d.
3d 4s 4p 4d
33
34
The valence bond theory was of great importance in the development of bonding theory for coordin- ation compounds. Although it provides a set of orbitals for bonding, the use of the high energy 4d orbitals seems unlikely, & the results do not lend themselves to a good explanation of the electronic spectra of complexes.
35
Crystal field theory : the split in metal d-orbital energies by the electrostatic field.
Spherical field Oh field
eg
t2g
36
When the d orbitals of a metal ion are placed in an octahedral field of ligand electron pairs, any elec- trons in them are repelled by the field. As a result, the dx2-y2 & dz2 orbitals, which are directed at the surrounding ligands, are raised in energy. The dxy, dxz, & dyz orbitals, which are directed between the surrounding ions, are relatively unaffected by the field.
This approach provides a simple means of identify- ing the d-orbital splitting found in coordination complexes. The chief drawbacks are in its concept of the repulsion of orbitals by the ligands & its lack of any explanation for bonding in coordination complexes. The purely electrostatic approach does not allow for the lower (bonding) molecular orbitals & thus fails to provide a complete picture of the electronic structure.
37
38
10-3 Ligand field theory
Crystal field theory does not consider the effect of molecular bonding & fails to explain many cases. For example, why CO is a strong-field ligand & Cl- a weak one ?
The electrostatic crystal field theory & the molecular orbital theory were combined into a more complete theory called ligand field theory, described qualitatively by Griffith & Orgel.
39
Simple MO treatment
dx2-y2, dz2 : bonding orbitals dxy, dxz, dyz : nonbonding orbitals
The six ligand σ-donor orbitals collectively form a reducible representation Γ in the point group Oh. Γ = A1g + T1u + Eg
4s, 4px, 4py, 4pz, 3dz2 & 3dx2-y2Metal orbitals used for σ-bonding: 40
41
The six ligand σdonor orbitals (p orbitals or hybrid orbitals with the same symmetry) match the symmetries of the 4s, 4px, 4py, 4pz, 3dz2 & 3dx2-y2
metal orbitals.
The combination of the ligand & metal orbitals form six bonding & six antibonding orbitals with a1g, eg & t1u symmetries. The six bonding orbitals are filled by electrons donated by the ligands.
42
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The metal t2g orbitals (dxy, dxz & dyz) do not have appropriate symmetry to interact with the ligands & are nonbonding.
Electrons of the metal occupy these nonbonding orbitals (t2g) & the higher energy antibonding orbitals (eg).
44
Δο (10Dq)
From σ donor ligands (all π interactions are ignored here)
Metal Ligand
Figure 10-6
45
Most of the discussion of octahedral ligand fields is concentrated on the t2g & higher orbitals (eg). Electrons in bonding orbitals provide the potential energy that holds molecules together, & electrons in the higher levels affected by ligand field effects help determine the details of the structure, magnetic properties, & electronic spectrum.
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10-3-2 Orbital splitting & electron spin
In octahedral complexes, electrons from the ligands fill all six bonding MOs, & any electrons from the metal ion occupy the nonbonding (t2g) & antibonding (eg) orbitals.
The splitting between these two sets of orbitals (t2g & eg) is called Δo (10 Dq, o for octahedral).
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Strong-field ligands : ligands whose orbitals interact strongly with the metal orbitals (large Δo). Weak-field ligands : ligands with weak inter- actions (small Δo).
* d0, d3, d8, d10 : only one electron configuration * d4-7 : high-spin & low-spin states
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49
50
Strong ligand field large Δo low spin Weak ligand field small Δo high spin
Electron configurations depend on Πc, Πe, & Δο. Δo : Π (Πc + Πe)
Πc: Coulombic energy Πe: Exchange energy
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Example (p349): Determine the exchange energies for high-spin & low-spin d6 ions in an octahedral complex.
4 Πe
6 Πe
4-5, 1-2, 1-3, 2-3
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[Co(H2O)6]3+ is the only low-spin aqueous complex. Π ~ Δo
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From Table 10-6 1. Δo for 3+ ions is larger than Δo for 2+ ions with
the same number of electrons. Π ? 2. Most of the first-row transition metals require a
stronger field ligand than H2O to give low-spin complexes.
3. Second- & third-row transition metals forms low-spin complexes.
*** Δo > Π : low-spin; Δo < Π : high-spin ***
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Why 2nd, 3rd transition series favor low-spin ? (1) The greater overlap between the larger 4d &
5d orbitals & the ligand orbitals, giving larger Δo (major) - smaller L-L repulsion
(2) A decreased pairing energy Π due to the larger volume available for electrons in the 4d & 5d orbitals compared with 3d orbitals. (minor)
Δo > Π : low-spin
10-3-3 Ligand field stabilization energy (LFSE)
The LFSE represents the stabilization of the d electrons because of the metal-ligand environment.
Δo = 10 Dq
(aq)
Ions with spherical symmetry should have ΔH becoming increasingly exothermic (more negative) continuously across the transition series due to the decreasing radius of the ions with increasing nuclear charge & corresponding increase in electrostatic attraction for the ligands.
Enthalpy of hydration of transition metal ions Effects of LFSE
ΔH increases (< 0)
The almost linear curve of the “corrected” enthalpies is expected for ions with decreasing radius.
Experimental curve
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The differences between the “corrected” & double- humped () experimental values are approxi mately equal to :
(1) LFSE values (for high-spin complexes : weak- field ligands, H2O)
(2) Spin-orbit splittings (0 to 16 kJ/mol) * H-bonding interactions : 1 ~ 40 kJ/mol
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(3) A relaxation effect caused by contraction of the metal-ligand distance (0 to 24 kJ/mol)
(4) An interelectronic repulsion energy that depends on the exchange interactions with the same spin (0 to -19 kJ/mol for M2+, 0 to -156 kJ/mol for M3+)
(2) ~ (4) are less important than LFSE, but they improve the shape of the curve for the corrected values significantly.
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In the case of the hexaaqua & hexafluoro complexes of the +3 transition metal ions, the interelectronic repulsion energy, sometimes called the the nephelauxetic effect, is large & is required to remove the deviation from a smooth curves through the d0, d5 & d10 values. Why do we care about LFSE ? There are two principal reasons. First, it provides a more quanti- tative approach to the high-spin-low-spin electron configuration, helping predict which configuration will be more likely. Second, it is the basis for our discussion of the spectra of these complexes in Ch 11.
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The nephelauxetic effect (electron cloud expansion) may occur for one (or both) of two reasons: 1. The effective positive charge on the metal has
decreased. Because the positive charge of the metal is reduced by any negative charge on the ligands, the d-orbitals can expand slightly.
2. The act of overlapping with ligand orbitals & forming covalent bonds increases orbital size, because the resulting molecular orbital is formed from two atomic orbitals.
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Nephelauxetic (cloud expanding) effect : It refers to a decrease in the Racah interelectronic repulsion parameter, B, that occurs when a transition metal free ion forms a complex with ligands. The decrease in B indicates that in a complex there is less repul- sion between the two electrons in a given doubly occupied metal d-orbital than there is in the respec- tive Mn+ gaseous metal ion, which in turn implies that the size of the orbital is larger in the complex (metal ion has less effective charge).
Nephelauxetic effect is a measure of the electron repulsion within M-L bonding orbitals.
Nephelauxetic series
F- > H2O > NH3 > en > NCS- > Cl- ~ CN- > Br- >S2- > I-
Larger electronegativity & more electrowithdrawing ⇒ higher delocalization (M→L) [covalent character
increases], reach left.
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10-3-4 π bonding py (L) : for σ bonding px,z (L): for π bonding
or from ligand’s π*
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T1g & T2u (L) : nonbonding T2g (L) : dxy, dyz, dxz (M); available T1u (L) : px, py, pz (M); not available (have been used for σ bonding.
Atomic orbitals of metal ions for π-bonding.
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e-
The electron density of HOMO (3σ) is concentrated on C. ( 2s(C) contributes.)
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M
(a)
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From Figure 10-11(a) : A larger Δo value & increased bonding strength (π acceptor ligands : CN-, CO…). Significant energy stabilization can result from this added π bonding. This metal-to-ligand (M L, MLCT) π bonding is also called π back-bonding, with electrons from d orbitals of the metal donated back to the ligands. e-e-
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From Figure 10-11(b) : A smaller Δo (π donor ligands : F-, Cl-…).
The metal ion d electrons are pushed into the higher t2g* orbital by the ligand electrons. This is described as ligand-to-metal (L M, LMCT) π bonding, with the π electrons from the ligands being donated to the metal ion.
e-e-
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Summary : Empty higher energy π* or d orbitals on the ligands result in M L π bonding & a larger Δo for the complex.
Filled π or p orbitals on ligands (frequently with relatively low energy) result in L M π bonding & a smaller Δo for the complex.
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Ligand-to-metal π bonding usually gives decreased stability for the complex, favoring high-spin configuration.
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Part of the stabilizing effects of π back-bonding is a result of transfer of negative charge away from the metal ion. The metal ion accepts electrons from the ligands to form the σ bonds. The metal is then left with a large negative charge. When the π orbitals can be used to transfer part of this charge back to the ligands, the overall stability is improved (electron neutrality).
10-3-5 Square-planar Complexes
6s 6p
10-4 Angular overlap
Angular overlap model estimates the strength of interaction between individual ligand orbitals & metal d orbitals based on the overlap between them & then combines these values for all ligands & all d orbitals for the complete picture.
The term angular overlap is used because the amount of overlap depends strongly on the angles of the metal orbitals & the angle at which the ligand approaches (orientation).
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1eσ
84
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Example : [M(NH3)6]n+ (octahedral & with only σ-interaction)
(1) Metal d orbitals : dz2 & dx2-y2; dxy, dyz, dxz (2) Ligand orbitals (pz or hybrid orbital) dz2 : +3eσ dx2-y2 : +3eσ dxy, dyz, dxz : 0 ligand orbitals : -eσ
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Summary :
1. The energy pattern is the same as the LF model. 2. Δo = 3eσ (t2g/eg) 3. The net stabilization is 12eσ for the bonding
pairs; & d electrons in the upper eg level are destabilized by 3eσ for each electrons.
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d
88
σ-donor only
Ignore s,p
91
i.e., halides can act as both a σ & a π donor
(Δo’)
2-?
92
In general, in situations involving in ligands that can behave as both π acceptors & π donors (such as CO & CN-), the π-acceptor nature predominates.
Although π-donor ligands cause Δo to decrease, the larger effect of the π-acceptor ligands causes Δo to increase. π-acceptor ligands are better at splitting the d orbitals (causing larger changes in Δo).
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10-4-4 Types of ligands & the spectrochemical series Ligands are frequently classified by their donor & acceptor capability. Some, like σ donors only, with no orbitals of appropriate symmetry for π bonding. The ligand field split, Δ, then depends on the relative energies of the metal ion & ligand orbitals & on the degree of overlap. Ti(III)L6
d1
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(1) en > NH3 : proton basicity (2) F- > Cl- > Br- > I-
F-, Cl- : hard base; Br- : borderline base; I- : soft base (proton basicity / electrostatic interaction)
Spectrochemical Series
(2’) NH3 > H2O > F- > RCO2 - > OH- > Cl- > Br- > I-
Ligands that have occupied p orbitals are potentially π donors. They tend to donate these electrons to the metal along with the σ-bonding electrons (this π-donor interaction decreases Δ).
As a result, most halide complexes have high-spin configurations (OH- below H2O in the series because it has more π-donating tendency).
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(3) CO, CN- > phen(anthroline) > NO2 - > NCS-
π acceptors (when ligands have vacant π* or d orbitals, there is the possibility of π back bonding, & the ligands are π acceptors)
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The covalent bonding character & electrostatic effect are also considered.
The trend is also related to : different metal ions, different charge on the metal ions, ligands with different substituents, & co-ligands present.
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10-4-5 Magnitudes of eσ, eπ, and Δ Changing the ligand or the metal changes the magnitude of eσ & eπ, with resulting changes in Δ & a possible change in the number of unpaired electrons. (1) [Co(H2O)6]2+ v.s. [Co(H2O)6]3+
high-spin low-spin (2) [Fe(H2O)6]3+ v.s. [Fe(CN)6]3-
high-spin low-spin
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100
Strong back bonding leads to a larger stabilization of t2g orbitals (negative eπ values).
spectrochemical series
• eσ is always larger than eπ (2~9 times).
• The magnitudes of both the σ & π parameters decrease with increasing size & decreasing electronegativity of the halides (F- > Cl- > Br- > I-).
• The metal’s nuclear charge increases σ & π parameters.
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10-5 The Jahn-Teller effect
The Jahn-Teller theorem states that there cannot be unequal occupation of orbitals with identical energies. To avoid such unequal occupation, the molecule distorts so that these orbitals are no longer degenerate (Cu2+ = d9).
[Cu(OH2)6]2+
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The resulting distortions is most often an elongation along one axis, but compression along one axis is also possible.
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The expected Jahn-Teller effects for octahedral coordination are given in the following table
For elongation
α > β
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Low-spin Cr(II) (d4) : for an octahedral geometry, Oh → D4h. They show two absorption bands, one in the visible & one in the near-infrared region, caused by this distortion.
1 2 -1 2
CrII(d4)
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Cr(II) also forms dimeric complexes with CrCr quadruple bonds & [Cr2(OAc)4] is nearly diamagnetic.
The quadruple bond between two chromium atoms arises from the overlap of four d-orbitals on each metal with the same orbitals on the other metal : the dz
2 orbitals overlap to give a σ-bonding component, the dxz & dyz orbitals overlap to give two π bonding components, & the dxy orbitals give a δ bond.
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(1)
Cu2+ forms the most common complexes with signifi- cant Jahn-Teller effects. In most cases, the distortion is an elongation of two bond, but K2CuF4 forms a crystal with two shortened bonds in the octahedron.
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(2) The formation constant for the addition of a third molecule of en to Cu2+ is much lower than for Ni2+.
[Cu(en)3]2+ v.s. [Ni(en)3]2+
Cu2+ : tetrahedral, square-planar, distorted TBP or SP, but not octahedral.
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10.6 Four- and six-coordinate preferences
Angular overlap calculations of the energies expected for different numbers of d electrons & different geometries can give us some indication of relative stabilities (i.e., octahedral, square planar, & tetrahedral).
10-7 Other shapes (TBP)
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