Advanced Inorganic Chemistry - Reza Takjoor.takjoo.profcms.um.ac.ir/imagesm/1006/stories/advanced/modern 10-1... · Crystal Field Theory *Crystal Field Splitting Energy - The d orbital

Advanced Inorganic Chemistry

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3A2g →3T2g

3A2g →1Eg

υ, cm-1

UV

[Ni(NH3)6]2+

visible infrared

?

MOLECULAR ABSORPTION PROCESSES

• Electronic transitions • UV and visible wavelengths

• Molecular vibrations • Thermal infrared wavelengths

• Molecular rotations

• Microwave and far-IR wavelengths

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

Increasing energy

~10-18 J

~10-23 J

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Ferdowsi University of Mashhad

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ELECTRONIC (UV-VISIBLE) SPECTROSCOPY

XPS UPS UV-visible

Electronic

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ELECTRONIC (UV-VISIBLE) SPECTROSCOPY

c = n . l

With energy of photons

E = h . n

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UV-visible spectroscopy (1) metal-metal (d-d) transition metal-ligand (2) charge transfer (MLCT) ligand-metal (LMCT) (3) ligand-centered transition

s

ligand p*

metal d s*

metal d n

ligand p

s s*, n s*, n p*, and p p*

n

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UV-visible spectroscopy (1) metal-metal (d-d) transition metal-ligand (2) charge transfer (MLCT) ligand-metal (LMCT) (3) ligand-centered transition

s s*, n s*, n p*, and p p*

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There are three types of electronic transitions:

- p, s, and n electrons

- d and f electrons

- charge transfer electrons

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

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

Selection Rules

1. Spin selection rule: DS = 0

allowed transitions: singlet singlet or triplet triplet forbidden transitions: singlet triplet or triplet singlet

Changes in spin multiplicity are forbidden

only one electron is involved in any transition

• 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

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

DL = ±1

• 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)

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electronic transition e Laporte allowed (charge transfer) 10000 (1000—50000) Laporte forbidden (d-d transition) spin allowed; noncentrosymmetiric 100—200 (200—250) spin allowed; centrosymmetric 5—100 (20—100) spin forbidden 0.01—1 (< 1)

The Selection rules for electronic transitions

3A2g →3T2g

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

[Ni(H2O)6]2+ a

b c

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

a, b, and c, Laporte forbidden, spin allowed, inter- mediate intensity

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[Co(H2O)6]2+

[CoCl4]2-

[Mn(H2O)6]2+

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d-d transition crystal field splitting

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

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d-d transition crystal field splitting

crystal field stabilization energy (CFSE)

spin-pairing energy

high-spin/low spin configuration d4 ~ d7

d4

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Tetrahedral

Dt = 4/9 Do

tetrahedron octahedron elongated square octahedron planar

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Crystal Field Theory

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

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Crystal Field Splitting Energy

Forming Complex

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

OH

TD

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 Δo (M3+) > Δo(M2+) 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.


*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)

*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

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Explaining the Colors of Transition Metals

Diversity in colors is determined by the energy difference (D) between the t2g and eg orbital sets in complex ions

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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Example – Consider the [Ti(H2O)6]3+ ion – Purple in

aqueous solution

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 corresponds to the energy of photons spanning the green 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

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

A solution of [V(H2O)6]2+ ion is violet

A solution of [V(H2O)6]3+ ion is yellow

For a given “metal”, the color depends on the ligand

[Cr(NH3)6]3+ (yellow-orange)

[Cr(NH3)5]2+ (Purple)

Even a single ligand is enough to change the color

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Spectrochemical Series

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

For a given ligand, the color depends on the oxidation state of the metal ion

For a given metal ion, the color depends on the ligand

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

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The splitting of energy levels influence magnetic properties

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

According to Hund’s rules, electrons occupy orbitals one at a time as long as orbitals of “equal energy” are available

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

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The occupancy of “d” orbitals, in turn, determines the number of unpaired electrons, thus, the paramagnetic 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

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)

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Explanation of Magnetic Properties

Weak-Field ligands and High-Spin complexes

Ex. [Mn(H2O)6]2+ Mn2+ ([Ar] 3d5)

A weak-field ligand, such as H2O, has a “small” crystal field splitting energy (D)

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

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ITION

ELEM

E

NTS &

TH

EIR C

OO

R

DIN

ATI

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CO

MP

OU

ND

S


Explanation of Magnetic Properties

Strong-Field Ligands and Low-Spin Complexes

Ex. [Mn(CN)6]4-

Strong-Field Ligands, such CN-, cause large crystal field splitting of the d-orbital energies, i.e., higher (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

Strong-Field ligands create low-spin complexes, i.e., those with fewer unpaired electrons

Generally Diamagnetic

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Fewer unpaired electrons

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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

With three “lower” energy t2g orbitals available, the d1, 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)

The two t2g orbitals must have either two d8 or one d9 unpaired electron

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Explaining Magnetic Properties

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high spin: weak-field

ligand

low spin: strong-field

ligand

high spin: weak-field

ligand

low spin: strong-field

ligand

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d5 d6d7

d4

HighSpin

LowSpin

n = 4

s = 4.90 n = 5

s = 5.92 n = 4

s = 4.90 n = 3

s = 3.87

n = 2

s = 2.83 n = 1

s = 1.73

n = 0

s =0

n = 1

s = 1.73

* *

* *

P > D

D > P

* Some additional orbital contribution to magnetic moment expected

Magnetic moments of high-spin and low-spin states d4-d7

[V(H2O)6]Cl3 = 3.10

[Co(NH3)6]Br2 = 4.55

K4[Fe(CN)6] = 0

Account for the magnetic moments of the following complexes

PR

AC

TICE P

RO

BLEM

Iron(II) forms an essential complex in hemoglobin

For each of the two octahedral complex ions

[Fe(H2O)6]2+ [Fe(CN)6]

4-

Draw an orbital splitting diagram, predict the number of

unpaired electrons, and identify the ion as low-spin or high

spin

Ans:

Fe2+ has the [Ar] 3d6 configuration

H2O produces smaller crystal field splitting (D) than CN-

The [Fe(H2O)6]2+ has 4 unpaired electrons (high spin)

The [Fe(CN)6]4- has no unpaired electrons (low spin)

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Four electron groups about the central atom

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 “square planar” arrangement

Tetrahedral – AX4

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

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

Splitting of d-orbital energies by a tetrahedral field of ligands

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Crystal Field Theory (Splitting)

Tetrahedral Complexes

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, 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)

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Crystal Field Theory (Splitting)

Square Planar Complexes

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 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

D8 metals ions such as [PdCl4]2- have 4 pairs of the

electrons filling the lowest energy levels and are thus, “diamagentic”

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Advanced Inorganic Chemistry - Reza Takjoor.takjoo.profcms.um.ac.ir/imagesm/1006/stories/advanced/modern 10-1... · Crystal Field Theory *Crystal Field Splitting Energy - The d orbital