Advanced Inorganic Chemistry

A DVANCED

NORGANIC

C HEMISTRY UV visible infrared

3 3 A2g → T2g

3 1 A2g → Eg

2+ [Ni(NH3)6] ?

υ, cm-1

A MOLECULAR ABSORPTION PROCESSES DVANCED

-18

~10 J I NORGANIC • Electronic transitions

• UV and visible wavelengths

C • Molecular vibrations HEMISTRY Increasing energy • Thermal infrared wavelengths

• Molecular rotations • Microwave and far-IR wavelengths -23 ~10 J

• Each of these processes is quantized • Translational kinetic energy of molecules is unquantized

ترمطیفی DVANCED

ELECTRONIC (UV-VISIBLE) SPECTROSCOPY

I NORGANIC

C HEMISTRY

Electronic XPS UPS UV-visible

Ferdowsi University of Mashhad 5

ترمطیفی DVANCED

ELECTRONIC (UV-VISIBLE) SPECTROSCOPY

I NORGANIC

C HEMISTRY

c = n . l With energy of photons E = h . n

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ترمطیفی DVANCED

UV-visible spectroscopy I ligand p* NORGANIC (1) metal-metal (d-d) transition metal d s*

metal-ligand

(2) charge transfer (MLCT) C ligand-metal HEMISTRY (LMCT) metal d n

ligand p n

(3) ligand-centered transition s

s s*, n s*, n p*, and p p*

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ترمطیفی DVANCED

UV-visible spectroscopy I

NORGANIC (1) metal-metal (d-d) transition

metal-ligand

(2) charge transfer (MLCT) C ligand-metal HEMISTRY (LMCT)

(3) ligand-centered transition

s s*, n s*, n p*, and p p*

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A DVANCED

NORGANIC

C HEMISTRY

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There are three types of electronic transitions: DVANCED - p, s, and n electrons

- d and f electrons

NORGANIC - charge transfer electrons

single bonds → sigma (s) orbitals → s electrons HEMISTRY double bond → a sigma (s) orbital and a pi (p) molecular orbital

Pi orbitals are formed by the parallel overlap of atomic p orbitals

Ferdowsi University of Mashhad 10 Selection Rules

1. Spin selection rule: DS = 0 only one electron is involved in any transition allowed transitions: singlet  singlet or triplet  triplet forbidden transitions: singlet  triplet or triplet  singlet Changes in spin multiplicity are forbidden • Spin-forbidden transitions – Transitions involving a change in the spin state of the molecule are forbidden – Strongly obeyed – Relaxed by effects that make spin a poor quantum number (heavy atoms)

Selection rules

2. Laporte selection rule (or parity rule): there must be a change in the parity (symmetry) of the complex DL = ±1

Electric dipole transition can occur only between states of opposite parity.

Laporte-allowed transitions: g  u or u  g

Laporte-forbidden transitions: g  g or u  u

g stands for gerade – compound with a center of symmetry u stands for ungerade – compound without a center of symmetry Selection rules can be relaxed due to:

vibronic coupling (interaction between electron and vibrational modes) spin-orbit coupling geometry relaxation during transition • Symmetry-forbidden transitions – Transitions between states of the same parity are forbidden – Particularly important for centro-symmetric molecules (ethene) – Relaxed by coupling of electronic transitions to vibrational transitions (vibronic coupling)

ترمطیفی selection rules DVANCED

electronic transition e

Laporte allowed (charge transfer) 10000

I NORGANIC (1000—50000) Laporte forbidden (d-d transition)

spin allowed; noncentrosymmetiric 100—200

(200—250) HEMISTRY spin allowed; centrosymmetric 5—100 (20—100) spin forbidden 0.01—1 (< 1)

Ferdowsi University of Mashhad 15 The Selection rules for electronic transitions

Charge-transfer band – Laporte and spin allowed – very intense

3 1 A2g → Eg Laporte and spin forbidden – very weak

a, b, and c, Laporte 2+ a [Ni(H2O)6] forbidden, spin allowed, inter- mediate intensity

3 3 A2g → T2g b c ADVANCED INORGANIC CHEMISTRY

ترمطیفی

DVANCED

NORGANIC

C HEMISTRY

2- [CoCl4]

2+ [Co(H2O)6]

2+ [Mn(H2O)6]

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d-d transition crystal field splitting A DVANCED

I NORGANIC

HEMISTRY

Do size and charge of the metal ion and ligands 4d metal ~50% larger than 3d metal 5d metal ~25% larger than 4d metal 5d > 4d > 3d

d-d transition crystal field splitting A DVANCED

I NORGANIC

HEMISTRY

crystal field stabilization energy (CFSE) spin-pairing energy high-spin/low spin configuration d4 ~ d7 d4

A ترمطیفی Tetrahedral DVANCED

I NORGANIC

Dt = 4/9 Do

tetrahedron octahedron elongated square C octahedron planar HEMISTRY

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ترمطیفی DVANCED

I NORGANIC

C HEMISTRY

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ترمطیفی DVANCED

I NORGANIC

C HEMISTRY

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A DVANCED Crystal Field Theory

 An energy diagram of the orbitals shows all five d orbitals I are higher in energy in the forming complex than in the free NORGANIC metal ion, because of the repulsions from the approaching

ligands

Crystal Field Splitting Energy C HEMISTRY

Forming Complex

Ligand field theory combines an electrostatic model of metal-ligand interactions (crystal field theory) and a covalent model (molecular orbital theory).

24 OH

Octahedral 3d Complexes

Δo ≈ P (pairing energy)

Both low-spin (Δo ≤ P) and high-spin (P ≥ Δo ) complexes are found

Tetrahedral Complexes

ΔTd = 4/9 Δo hence P >> ΔTd and tetrahedral complexes are always high spin ELECTRONIC STRUCTURE OF HIGH-SPIN AND LOW-SPIN OH COMPLEXES NOTE: SOME FACTORS INFLUENCING THE MAGNITUDE OF Δ-SPLITTING

Oxidation State 3+ 2+ Δo (M ) > Δo(M ) e.g. Δo for Fe(III) > Fe(II).

The higher oxidation state is likely to be low-spin

5d > 4d >3d

e.g. Os(II) > Ru(II) > Fe(II)

All 5d and 4d complexes are low-spin.

A DVANCED Crystal Field Theory

I NORGANIC *Crystal Field Splitting Energy - The d orbital energies are “split” with the two dx2-y2 and dz2 orbitals (eg orbital set)

higher in energy than the dxy, dxz, and dyz orbitals (t2g

orbital set) C HEMISTRY

*The energies of the d orbitals in different environments determines the magnetic and electronic spectral properties of transition metal complexes.

*Strong-field ligands, such as CN- lead to larger splitting energy

*Weak-field ligands such as H2O lead to smaller splitting energy

A DVANCED Crystal Field Theory

 Explaining the Colors of Transition Metals I NORGANIC  Diversity in colors is determined by the energy difference (D) between the t2g and eg orbital sets in

complex ions

C HEMISTRY  When the ions absorbs light in the visible range, electrons move from the lower energy t2g level to the higher eg level, i.e., they are “excited” and jump to a higher energy level

D E electron = Ephoton = hv = hc/l  The substance has a “color” because only certain wavelengths of the incoming white light are absorbed

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A DVANCED Crystal Field Theory  Example – Consider the [Ti(H O) ]3+ ion – Purple in

2 6 I aqueous solution NORGANIC  Hydrated Ti3+ is a d1 ion, with the d electron in one of the

three lower energy t2g orbitals

 The energy difference (DA) between the t2g and eg orbitals C corresponds to the energy of photons spanning the green HEMISTRY and yellow range  These colors are absorbed and the electron jumps to one of the eg orbitals  Red, blue, and violet light are transmitted as purple

A DVANCED Crystal Field Theory

 For a given “ligand”, the color depends on the oxidation I NORGANIC state of the metal ion – the number of “d” orbital electrons available 2+

A solution of [V(H O) ] ion is violet 2 6 C 3+ HEMISTRY A solution of [V(H2O)6] ion is yellow  For a given “metal”, the color depends on the ligand 3+ [Cr(NH3)6] (yellow-orange) 2+ [Cr(NH3)5] (Purple) Even a single ligand is enough to change the color

A DVANCED Crystal Field Theory

 Spectrochemical Series

I  The Spectrochemical Series is a ranking of ligands with NORGANIC regard to their ability to split d-orbital energies

 For a given ligand, the color depends on the oxidation

state of the metal ion C  For a given metal ion, the color depends on the ligand HEMISTRY  As the crystal field strength of the ligand increases, the splitting energy (D) increases (shorter wavelengths of light must be absorbed to excite the electrons

MAGNETIC PROPERTIES OF TRANSITION METAL COMPLEXES

A DVANCED  The splitting of energy levels influence magnetic

properties

I  Affects the number of unpaired electrons in the metal ion NORGANIC “d” orbitals

 According to Hund’s rules, electrons occupy orbitals one at

a time as long as orbitals of “equal energy” are available C HEMISTRY  When “all” lower energy orbitals are “half-filled (all +½ spin state)”, the next electron can  Enter a half-filled orbital and pair up (with a –½ spin state electron) by overcoming a repulsive pairing energy (Epairing) or  Enter an empty, higher energy orbital by overcoming the crystal field splitting energy (D)

 The relative sizes of Epairing and (D) determine the occupancy of the d orbitals 36

MAGNETIC PROPERTIES OF TRANSITION METAL COMPLEXES

A DVANCED

 The occupancy of “d” orbitals, in turn, determines the

I number of unpaired electrons, thus, the paramagnetic NORGANIC behavior of the ion  Ex. Mn2+ ion ([Ar] 3d5) has 5 unpaired electrons in 3d

orbitals of equal energy

 In an octahedral field of ligands, the orbital energies split HEMISTRY  The orbital occupancy is affected in two ways:  Weak-Field ligands (low D) and High-Spin complexes  Strong-Field ligands (high D) and Low-Spin complexes (from spectrochemical series)

A DVANCED Crystal Field Theory

 Explanation of Magnetic Properties

I  Weak -Field ligands and High-Spin complexes NORGANIC

2+ 2+ 5  Ex. [Mn(H2O)6] Mn ([Ar] 3d )

 A weak-field ligand, such as H2O, has a “small” crystal

field splitting energy (D) C HEMISTRY  It takes less energy for “d” electrons to move to the “eg” set (remaining unpaired) rather than pairing up in the “t2g” set with its higher repulsive pairing energy (Epairing)  Thus, the number of unpaired electrons in a weak-field ligand complex is the same as in the free ion  Weak-Field Ligands create high-spin complexes, those with a maximum of unpaired electrons  Generally Paramagnetic

T C C E T OUNDS ON DINATI NTS ITION

HEIR LEME RANS

OMP OOR

& &

DVANCED Crystal Field Theory 

Explanation of Magnetic Properties

I NORGANIC  Strong -Field Ligands and Low-Spin Complexes

4-  Ex. [Mn(CN)6]  -

Strong-Field Ligands, such CN , cause large crystal C

field splitting of the d-orbital energies, i.e., higher HEMISTRY (D)

 (D) is larger than (Epairing)  Thus, it takes less energy to pair up in the “t2g“ set than would be required to move up to the “eg” set  The number of unpaired electrons in a Strong-Field Ligand complex is less than in the free ion Fewer  Strong-Field ligands create low-spin complexes, unpaired electrons i.e., those with fewer unpaired electrons  Generally Diamagnetic 39 Crystal Field Theory  Explaining Magnetic Properties

 Orbital diagrams for the d1 through d9 ions in octahedral complexes show that both high-spin and low-spin options are possible only for: d4 d5 d6 d7 ions 1  With three “lower” energy t2g orbitals available, the d , d2, d3 ions always form high-spin (unpaired) complexes because there is no need to pair up  Similarly, d8 & d9 ions always form high-spin complexes because the 3 orbital t2g set is filled with 6 electrons (3 pairs) 8 9 The two t2g orbitals must have either two d or one d unpaired electron

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A DVANCED Crystal Field Theory

Explaining Magnetic Properties  I NORGANIC

high spin: low spin: high spin: low spin: weak-field strong-field weak-field strong-field

ligand ligand ligand ligand

C HEMISTRY

11/21/2012 41 Magnetic moments of high-spin and low-spin states d4-d7

5 6 7 d4 d d d

High Spin P > D

n = 4 n = 5 n = 4 n = 3 s = 4.90 s = 5.92 s = 4.90 * s = 3.87 *

Low Spin D > P

n = 2 n = 1 n = 0 n = 1  = 2.83 * * s s = 1.73 s =0 s = 1.73

* Some additional orbital contribution to magnetic moment expected Account for the magnetic moments of the following complexes

[V(H2O)6]Cl3  = 3.10

[Co(NH3)6]Br2  = 4.55

K4[Fe(CN)6]  = 0 P RACTICEADVANCED PROBLEM INORGANIC CHEMISTRY

2012 - /

21 / 11

spin or high spin or high - ) than CN ) than - 4 ] D 6

[Fe(CN)

+ 2 unpaired electrons (high spin) (high electrons unpaired ] 6 4 configuration

6 O) 2 d has has no unpaired electrons (low spin) electrons has no unpaired 3

2 - ] 4 6 ] [Fe(H 6 O) 2 has the [Ar] has the [Ar]

[Fe(H

+ O produces smaller crystal field splitting ( splitting field crystal smaller O produces 2

2 :

The [Fe(CN) The Fe H unpaired electrons, and identify the ion as low ion the and identify electrons, unpaired spin Draw an orbital splitting diagram, predict the number of the number predict diagram, splitting orbital Draw an

Ans

For each of the two octahedral complex ions complex octahedral two of the each For Iron(II) forms an essential complex in hemoglobin in complex an forms essential Iron(II)

A DVANCED Crystal Field Theory

 Four electron groups about the central atom I NORGANIC  Four ligands around a metal ion also cause d-orbital splitting, but the magnitude and pattern of the splitting

depend on the whether the ligands are in a “tetrahedral” or C

“square planar” arrangement HEMISTRY

 Tetrahedral – AX4

 Octahedral – AX4E2 (2 ligands along “z” axis removed)

Splitting of d-orbital energies by a Splitting of d-orbital energies by tetrahedral field of ligands a square planar field of ligands. 45

A DVANCED Crystal Field Theory (Splitting) 

Tetrahedral Complexes

I NORGANIC  Ligands approach corners of a tetrahedron

 None of the five metal ion “d” orbitals is directly in the

path of the approaching ligands

 Minimal repulsions arise if ligands approach the dxy, dyz, HEMISTRY and dyz orbitals closer than if they approach the dx2-y2 and dz2 orbitals (opposite of octahedral case)  Thus, the dxy, dyz, and dyz orbitals experience more electron repulsion and become higher energy  Splitting energy of d-orbital energies is “less” in a tetrahedral complex than in an octahedral complex

Dtetrahedral < Doctahedral  Only high-spin tetrahedral complexes are known because the magnitude of (D) is small (weak)

A DVANCED Crystal Field Theory (Splitting) 

Square Planar Complexes

I NORGANIC  Consider an Ocatahedral geometry with the two z axis ligands removed, no z-axis interactions take place

 Thus, the dz2, dxz an dyz orbital energies decrease

 The two ‘d” orbitals in the xy plane (dxy, dx2-y2) interact HEMISTRY most strongly with the approaching ligands

 The (dxy, dx2-y2) orbital has its lobes directly on the x,y axis and thus has a higher energy than the dxy orbital  Square Planar complexes are generally strong field – low spin and generally diamagnetic 8 2-  D metals ions such as [PdCl4] have 4 pairs of the electrons filling the lowest energy levels and are thus, “diamagentic”