Photochemical and Magnetic Properties of Complex and Nuclear Chemistry

• Programme: MSc in Chemistry

• Course Code: MSCHE2001C04

• Course Title: Photochemical and magnetic properties of complex and nuclear chemistry

• Unit: Electronic spectra of coordination compounds

• Course Coordinator: Dr. Jagannath Roy, Associate Professor, Department of Chemistry,

Central University of South Bihar

Note: These materials are only for classroom teaching purpose at Central University of South Bihar. All the data/figures/materials are taken from text books, e-books, research articles, wikipedia and other online resources. 1

Course Objectives: 1. To make students understand structure and propeties of inorganic compounds 2. To accuaint the students with the electronic spectroscopy of coordination compounds 3. To introduce the concepts of magnetochemistry among the students for analysing the properties of complexes. 4. To equip the students with necessary skills in photochemical reaction transition metal complexes 5. To develop knowledge among the students on nuclear and radio chemistry

Learning Outcomes: After completion of the course, learners will be able to: 1. Analyze the optical/electronic spectra of coordination compounds 2. Make use of the photochemical behaviour of complexes in designing solar cells and other applications. 3. Design and perform photochemical reactions of transition metal complexes 4. Analyze the magnetic properties of complexes 5. Explain the various phenomena taking place in the nucleus 6. Understand the working of nuclear reactors

Lecture-1 Lecture Topic- Introduction to the Electronic Spectra of Transition Metal complexes

Crystal field theory (CFT) is ideal for d1 (d9) systems but tends to fail for the more common multi- electron systems. This is because of electron-electron repulsions in addition to the crystal field effects on the repulsion of the metal electrons by the ligand electrons. To deal with this we introduce the concept of an electronic state. The Electronic state refers to energy levels available to a group of electrons, just as electronic configurations refer to the way in which the electrons occupy the d orbitals.

1 When describing electronic configurations, lower case letters are used, eg t2g etc. For electronic states, upper case (CAPITAL) letters are used and by analogy, a T state is triply degenerate and an E state is doubly degenerate. Quantum Numbers: n = Principal quantum numbers l = Azimuthal quantum numbers ml = Magnetic quantum numbers ms = Spin quantum numbers

L 0 1 2 3

Shape of orbital s p d f

No of ml 1 3 5 7

ml is a subset of l, where ml take values from l…. 0….-l.

There are thus (2l +1) values of ml for each l value, i.e. for the 1 s orbital (l = 0), 3 p orbitals (l = 1), 5 d orbitals (l = 2), etc.

Russell-Saunders (R-S) coupling The ways in which the angular momenta associated with the orbital and spin motions in many- electron-atoms can be combined together are many and varied. In spite of this seeming complexity, the results are frequently readily determined for simple atom systems and are used to characterise the electronic states of atoms. The interactions that can occur are of three types: • spin-spin coupling (S) • orbit-orbit coupling (L) • spin-orbit coupling (J) There are two principal coupling schemes used: • Russell-Saunders (or L - S) coupling • j - j coupling.

In the Russell Saunders scheme it is assumed that: • spin-spin coupling > orbit-orbit coupling > spin-orbit coupling. • This is found to give a good approximation for first row transition series where J coupling can generally be ignored, however for elements with atomic number greater than thirty, spin-orbit coupling becomes more significant and the j-j coupling scheme is used.

Spin-Spin coupling S - the resultant spin quantum number for a system of electrons. The overall spin S arises from adding the individual ms together and is as a result of coupling of spin quantum numbers for the separate electrons. The total spin is normally reported as the value of 2S + 1, which is called the multiplicity of the term:

S = 0 ½ 1 3/2 2 5/2

2S + 1 1 2 3 4 5 6

singlet doublet triplet quartet quintet sextet

Orbit-Orbit coupling L - the total orbital angular momentum quantum number defines the energy state for a system of electrons. These states or term letters are represented as follows: By analogy with the notation s, p, d, … for orbitals with l = 0, 1, 2, …, the total orbital angular momentum of an atomic term is denoted by the equivalent upper case letter: Total Orbital Momentum:

L 0 1 2 3 4

S P D F G

Spin-Orbit coupling Coupling occurs between the resultant spin and orbital momenta of an electron which gives rise to J the total angular momentum quantum number. Multiplicity occurs when several levels are close together and is given by the formula (2S+1). The multiplicity is written as a left superscript representing the value of L and the entire label of a term is called a term symbol.

The Russell Saunders term symbol is then written as: (2S+1)L

Examples: For a d1 configuration: S= +½, hence (2S+1) = 2 ; L=2 and the ground term is written as 2D (doublet dee) For an s1p1 configuration: S= both +½, hence (2S+1) = 3; or paired hence (2S+1) = 1 ; L=0+1=1 and the terms arising from this are 3P (triplet pee) or 1P (singlet pee)

The Ground Terms are deduced by using Hund's Rules 1. The Ground Term will have the maximum multiplicity. 2. If there is more than 1 Term with maximum multipicity, then the Ground Term will have the largest value of L. Thus for a d2 the rules predict 3F < 3P < 1G < 1D < 1S Note the idea of the "hole" approach: Hole formalism in quantum chemistry states that, one may consider systems with e or (n-e), the number of unoccupied sites or “holes”, to be equivalent. A d1 configuration is treated as similar to a d9 configuration. d1 has 1 electron more than d0 and d9 has 1electron less than d10 i.e. a hole. Calculating d-ion Ground Terms

dn 2 1 0 -1 -2 L S Ground Term

d1 ↑ 2 1/2 2D

d2 ↑ ↑ 3 1 3F

d3 ↑ ↑ ↑ 3 3/2 4F

d4 ↑ ↑ ↑ ↑ 2 2 5D

d5 ↑ ↑ ↑ ↑ ↑ 0 5/2 6S

d6 ↑↓ ↑ ↑ ↑ ↑ 2 2 5D

d7 ↑↓ ↑↓ ↑ ↑ ↑ 3 3/2 4F

d8 ↑↓ ↑↓ ↑↓ ↑ ↑ 3 1 3F

d9 ↑↓ ↑↓ ↑↓ ↑↓ ↑ 2 1/2 2D

The overall result shown in the Table is that: 4 configurations (d1, d4, d6, d9) give rise to D ground terms, 4 configurations (d2, d3, d7, d8) give rise to F ground terms d5 configuration gives an S ground term.

Terms for dn free ion configurations The Russell Saunders term symbols for all the free ion configurations are given in the Table below.

The ligand field splitting of Transition Metal complex ground terms So far our discussion refer only to free atoms, we will now take it a step further to the domain of transition metal complex ions.

The treatment will be restricted to complex ions in an Oh crystal field. The ground term energies for transition metal complexes are affected by the influence of a ligand field. The effect of a ligand field is that: d orbitals split into t2g and eg subsets.

By analogy the D ground term states split into T2g and Eg. f orbitals are split to give subsets known as t1g, t2g and a2g.

By analogy, the F ground term when split by a crystal field will give states known as T1g, T2g, and

A2g. S orbitals are never split, hence S ground terms are also not split. Note that whenever the ground state is an F term there will be a P term found at higher energy with the same spin multiplicity.

Lecture-2 Lecture Topic- Spectroscopic ground states and Splitting of dn terms

Splitting of dn terms in an octahedral field is represented in the follwing table:

Term Components in an octahedral field

S A1g

P T1g

D Eg+T2g

F A2g+T1g+T2g

G A1g+Eg+T1g+T2g

H Eg+T1g+T1g+T2g

I A1g+A2g+Eg+T1g+T2g+T2g

d1 and d9 case

Octahedral Crystal Field

The ground state free ion term for this configuration can be calculated as follows:

Total orbital angular momentum value = L = Σml = 2

Total spin angular momentum value = S = Σms = 1/2

Spin multiplicity = (2S+1) = (2(1/2)+1) = 2

Thus the free ion ground state term for d1 and d9 configuration comes out to be 2D.

Therefore, splitting of d9 case is just the inverse of d1 case in octahedral crystal field

d2 and d8 case

Octahedral Crystal Field

The ground state free ion term for this configuration can be calculated as follows:

Total orbital angular momentum value = L = Σml = 2+1 =3

Total spin angular momentum value = S = Σms =2 x ½= 1

Spin multiplicity = (2S+1) = (2 x 1+1) = 3

Thus the free ion ground state term for d2 and d8 configuration comes out to be 3F.

Therefore, splitting of d8 case is just the inverse of d2 case in octahedral crystal field.

d3 and d7 case

Octahedral Crystal Field

The ground state free ion term for this configuration can be calculated as follows:

Total orbital angular momentum value = L = Σml = 2+1+0=3

Total spin angular momentum value = S = Σms =3 x ½= 3/2

Spin multiplicity = (2S+1) = (2 x 3/2 +1) = 4

Thus the free ion ground state term for d3 and d7 configuration comes out to be 4F.

Therefore, splitting of d7 case is just the inverse of d3 case in octahedral crystal field.

d4 and d6 case

Octahedral Crystal Field

The ground state free ion term for this configuration can be calculated as follows:

Total orbital angular momentum value = L = Σml = 2+1+0-1=2

Total spin angular momentum value = S = Σms =4x ½= 2

Spin multiplicity = (2S+1) = (2 x 2 +1) = 5

Thus the free ion ground state term for d4 and d6 configuration comes out to be 5D.

Therefore, splitting of d6 case is just the inverse of d4 case in octahedral crystal field.

Tetrahedral Crystal Field

A tetrahedral crystal field is in effect, a negative octahedral field. So we can expect the inverse relationship between the two symmetries. So the diagrams will be:

Tetrahedral Crystal Field

A tetrahedral crystal field is in effect, a negative octahedral field. So we can expect the inverse relationship between the two symmetries. So the diagrams will be:

Octahedral-Tetrahedral inversion

Note the idea of the "hole" approach:

A d1 configuration is treated as similar to a d9 configuration. d1 has 1 electron more than d0 and d9 has 1electron less than d10 i.e. a hole.

The octahedral-tetrahedral inversion can be summarised as:

Octahedral (dn) Tetrahedral (d10-n) d1 d9 d2 d8 d3 d7 d4 d6 d6 d4 d7 d3 d8 d2 d9 d1

Splitting of d5 terms

Octahedral Crystal Field

For d5, The lowest energy term for the free ion is 6S.

Total orbital angular momentum value = L = Σml = 2+1+0-1-2=0

Total spin angular momentum value = S = Σms = 5 x 1/2 =5/2

Spin multiplicity = (2S+1) = (2(5/2)+1) = 6

6 6 In a weak octahedral field, this S splits to give A1g as the ground state.

2 At an intermediate field, the ground state becomes T2

At this level electrons are paired up.

Number of unpaired electron = 1

Total orbital angular momentum value = L = Σml = 2

Total spin angular momentum value = S = Σms = 1/2

Spin multiplicity = (2S+1) = (2(1/2)+1) = 2

2 2 2 The term symbol will be D which splits into T2g (ground state) and Eg (excited state).

So the change in spin multiplicity from six to two corresponds to a decrease in the number of

unpaired electrons from five to one;

when there is a transition from high to low spin.

The ground states of octahedral d1, d2, d3, d8 and d9 complexes remain the same under all field

strengths.

Lecture-3 Lecture Topic- Introduction to the Electronic Spectra of Transition Metal complexes

The Selection Rules governing transitions between electronic energy levels of transition metal complexes are:

1. The Orbital Rule (Laporte) (Δl = +/- 1)

2. The Spin Rule (ΔS = 0)

The first rule states that allowed transitions must involve the promotion of electrons without a change in their spin. Eg antiparallel pair of electrons cannot be converted to a parallel pair , so a singlet (S=0) cannot under a transition to a triplet state (S=1).

The second rule states that if the molecule has a centre of symmetry, transitions within a given set of s, p or d orbitals are forbidden. That is s-s, p-p, d-d and f-f transitions are forbidden, but s-p, p-d, and d-f transitions are allowed. This rule applies to Oh complexes but not Td.

Laporte selection rules for electronic spectra of transition metal

Laporte rule states that transition between states of same symmetry labels are forbidden while transitions between states of different symmetry labels are allowed.

d-d transitions in octahedral complexes are Laporte forbidden: All d orbitals have gerade (g) symmetry in centrosymmetric molecules.

Some transitions are not allowed, it does not mean that such transition will never occur. Various mechanisms have been applied by which selection rules can be relaxed for the transition to occur.

But such transition have low intensities.

Unsymmetrical vibrations of octahedral complex can temporarily destroy its center of symmetry and allow transitions which Laporte forbidden. Such vibronic (vibrational – electronic) transition will be observable, though weak.

Molar absorptivities for octahedral complexes are in the range of 1 to 102 L mol-1 cm-1. If a 0.10 M solution of a typical ML6 complex is prepared and UV/visible spectrum is taken, the d-d transition is expected to be observable.

Tetrahedral complexes have no center of symmetry and thus orbitals have no ‘g’ or ‘u’ designation.

From the MO diagram, it is observed that energy difference between non bonding ‘e’ and

* antibonding t2 gives the measure of ∆t value.

The nonbonding ‘e’ orbitals are purely metal ‘d’ orbitals and hence retain their ‘g’ character even in the complex.

The t2 Mos, on the other hand, are formed from atomic d (gerade) and p (ungerade) orbitals.

Through this d-p mixing, which imparts some ‘u’ character to the t2 level in the complex, hence the

Laporte selection rule is relaxed.

As a result, extinction coefficients for tetrahedral complexes are about 102 greater than thos for octahedral complexes, ranging from 102 to 103 L mol-1 cm-1.

Spin selection rules for electronic spectra of transition metal

The Spin Rule ΔS = 0

According to this rule, in order to be allowed, a transition must involve no change in the spin state.

Let us consider d2 configuration in an octahedral field

Configuration Ground Terms Excited Terms

2 3 1 1 1 d 3F P, G, D, S

Note that the ground state has a multiplicity of 3 (S=1, 3F) and that there excited states with the

3 3 3 3 same multiplicity: T2g, A2g and T1g (from P). So three spin allowed transitions are:

3 3 T1g → T2g

3 3 T1g → A2g

3 3 T1g → T1g (P)

3 2 Transitions from T1g (F) to any of the singlet excited states are spin forbidden. A d octahedral complex should, therefore, give rise to an electronic spectrum consisting of three absorptions. This will be true whether the filed is strong or weak.

However, it should be observed that as the field strength increases, the separation between the triplet ground and excited states becomes larger.

Thus with increasing field strength, transition energies become higher and spectral band are shifted toward the UV region.

3+ Ex: For blue [V(H2O)6] , two of the three expected absorptions are observed in the visible region.

3 3 -1 3 3 -1 The transition T1g → T2g occurs at 17,200 cm and T1g → T1g (P) occurs at 25,700 cm . 23

3 3 -1 The transition of T1g → A2g occurs at 36,000 cm . , but because it is low intensity and is in the

3+ high energy portion of the spectrum, it is not observed. In the solid state (V /Al2O3), , this transition is seen at 38,000 cm-1.

5 6 In case of d , the ground state ( A1g) is the only state with a multiplicity of 6. This means that for a d5 octahedral complex, all transitions are not only Laporte forbidden but also spin forbidden.

Absorptions associated with doubly forbidden transitions are extremely weak with extinction coefficients several hundred times smaller than those for singly forbidden transitions.

Ex: Dilute solutions of Mn (II) are colorless and only with a substantial increase in concentration, a faint pink color is observable.

The spin selection rule breaks down somewhat in complexes that exhibit spin-orbit coupling. This behaviour is particularly common for complexes of the heavier transition elements with the result that bands associated with formally spin forbidden transition (generally limited to ∆S = ±1) gain enough intensity to be observed. Following table summarizes band intensities for various types of electronic transitions, including fully allowed charge transfer absorptions.

Only to predict the number of spin-allowed transitions expected for a complex, a complete correlation diagram is not needed. It is only necessary to know the number of excited states having the same multiplicity as the ground state.

Following table summarizes this information for weak filed octahedral and tetrahedral complexes.

Octahedral complexes having d1, d4, d6 and d9 configurations and weak filed ligands give one absorption correspond to ∆o.

Configurations d2, d3, d7 and d8 in weak octahedral fields have three spin allowed transitions. In each case ∆o is the energy difference between adjacent A2g and T2g terms.

There are no spin allowed transitions for d5 octahedral complexes having weak field strength.

But spin-orbit coupling and Jahn-Teller distortions often lead to more complex spectra than predicted with the spin selection rule.

Three important features in interpreting electronic spectra of transition metal complexes are—

1. The number of spectral lines

2. Intensities of spectral lines

3. Width of spectral lines

The width of the absorption can be attributed mainly to the fact that the complex is not a rigid, static structure. Rather, the metal ligand bonds are constantly vibrating, with the result that an absorption peak is integrated over a collection of molecules with slightly different molecular structures and ∆o values.

Such ligand motions will be exaggerated through molecular collisions in solution. In the

Solid state, however, it is sometimes possible to resolve spectral bands into their vibrational components.

Sharp peaks also occur in solution spectra when the transitions involve ground and excited states that are either insensitive to changes in ∆o, or are affected identically by the changes.

These terms will appear on energy level diagrams as parallel lines, which will be horizontal in the event that energies are independent of ∆o.

Two additional factors that can contribute to line breadth and shape are spin-orbit coupling, which is particularly prevalent in complexes of the heavier transition metals is the Jahn-Teller effect.

Lecture-4 Lecture Topic- Orgel diagram

Orgel diagram is a correlation diagram which show the relative energies of electronic terms in transition metal complexes. It is much simpler than other correlation diagrams because excited states of multiplicities different from that of the ground state are omitted, i.e. this diagram only show the symmetry states of the highest spin multiplicity instead of all possible terms. This diagram is restricted to show only the weak field (i.e. high spin) cases and offer no information about strong field (low spin) cases. These diagrams are qualitative, no energy calculations can be performed from these diagrams.

Observations:

1. Inverse relationship between the two symmetries, which arises because a tetrahedral field is,

in effect, a negative octahedral field.

2. Mixing of terms: general rule is that,

• terms having identical symmetry will mix,

• extent of mixing will be inversely proportional to the energy difference between them,

• mixing of terms exactly parallels as mixing of molecular orbitals and it leads to an identical

results: the upper level is raised in energy while the lower level falls.

4 4 (this is shown as diverging lines for the pairs of T1g and T1 levels)

Observations:

3. Extent of mixing is greater for tetrahedral complexes

(In the following diagram, the condition of no mixing is shown as dashed lines)

4 For the tetrahedral case, in the absence of mixing, the two T1 terms gradually approach each other as the field strength increases but this is not true for octahedral complexes. So the extent of mixing is greater for tetrahedral complexes.

Orgel diagrams provide a convenient means of predicting the number of spin allowed absorption bands which can be expected to observe in a UV/visible spectrum for a complex.

From the following Orgel diagram of Co2+ (or any other d7 ion), we can expect a spectrum with three absorptions.