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Electronic Spectra ofElectronic Spectra of
Metal ComplexesMetal Complexes
V. Santhanam
Department of Chemistry
SCSVMV
Color of the complexes
Observed
Color
Light
Absorbed
Abs Wavelength /
nm
Colorless UV < 380
Yellow Violet 380-450
Orange Blue 450-490
Red Green 490-550
Violet Yellow 550-580
Blue Orange 580-650
Green Red 650-700
Colorless IR > 700
Use of Electronic spectrum
ā€¢ Electronic spectrum ā€“ due to d-d
transitions.
ā€¢ From the transition energy ā€“ energy of dā€¢ From the transition energy ā€“ energy of d
e- can be got.
ā€¢ The energies of d levels affected by many
complicated factors.
Terms, States and Microstates
ā€¢ Energy levels described by quantum numbers.
ā€“ Principal quantum number ā€“ n
ā€“ Azimuthal quantum number ā€“ l
ā€“ Magnetic quantum number ā€“ mā€“ Magnetic quantum number ā€“ ml
ā€“ Spin quantum number ā€“ ms
ā€¢ But actual conditions are complicated .
ā€¢ Quantum numbers alone are not sufficient
Why ?
Configuration
ā€¢ Arrangement of e-s in an atom or ion
ā€“ The electrons are filled in the increasing
order of energy ā€“ Aufbau principle
ā€“ If more than one orbital is having same
energy, pairing of e- will not take placeenergy, pairing of e- will not take place
until all the orbitals are at least singly
occupied ā€“ Hundā€™s rule
ā€“ No two electrons can have all the four
quantum numbers same ā€“ Pauliā€™s exclusion
principle
Terms
ā€¢ Energy level of an atomic system specified by
an electronic configuration.
ā€¢ Many terms may arise from a configuration
ā€¢ Depends on the intrinsic nature of cofig.ā€¢ Depends on the intrinsic nature of cofig.
ā€¢ Electrons from filled orbitals have no
contribution to energy ā€“ Assumption
ā€¢ Partially filled orbitals decide the energy
terms.
Terms ā€¦ Cont
ā€¢ Partially filled orbitals have two
perturbations
ā€“Inter Electronic Repulsionsā€“Inter Electronic Repulsions
ā€“Spin-Orbit coupling
Inter-electronic repulsions
ā€¢ Energy depends on the arrangement of e-
ā€¢ The electrons in partially filled orbitals repel
each other.
ā€¢ Repulsion splits the energy levels resulting inā€¢ Repulsion splits the energy levels resulting in
many terms.
ā€¢ Energies of electrons within an orbital itself
are slightly different [ Pairing and Exchange
energies].
Inter-electronic repulsions
Racah Parameters (A, B and C)
ļƒ˜Racah parameters were generated as a means to describe
the effects of electron-electron repulsion within the metal
complexes.
ļƒ˜A is ignored because it is roughly the same for any metalļƒ˜A is ignored because it is roughly the same for any metal
center.
ļƒ˜ B is generally approximated as being 4C.
Inter-electronic repulsions
ļƒ˜What B represents is an approximation of the
bond strength between the ligand and metal.
ļƒ˜Comparisons between tabulated free
ion B and B of a coordination complex is called the
nephelauxetic ratio (the effect of reducingnephelauxetic ratio (the effect of reducing
electron-electron repulsion via ligands).
ļƒ˜This effect is what gives rise to the nephelauxetic
series of ligands.
Nephelauxetic Effect
ā€¢ Normally the electron repulsion is found to be weaker
in complexes than in free ion and this means the
value of B for the complex is less than for a free ion.
ā€¢ This is due to the delocalization of the electron over
the ligands away from the metal which separates
them and hence reduces repulsion.them and hence reduces repulsion.
ā€¢ The reduction of B from its free ion is normally
reported in terms of nephelauxetic effet Ī²
Ī² = B' complex
B free ion
ā€¢ Where Ī² is the nephelauxetic parameter and refer to
the electron cloud expansion.
Nephelauxetic series
ā€¢ The values of Ī² depend on the ligand and vary along
the nephelauxetic series. The ligands can be
arranged in a nephelauxetic series as shown below.
This is the order of the ligands ability to cause d
electron cloud expansion.electron cloud expansion.
I- < Br -< Cl- < CN- < NH3 < H2O < F-
ā€¢ The series tell us that a small value of Ī² means that
there is large measure of d- electron delocalization
and a greater covalent character in the complex.
Reasons for e- cloud expansion
ā€¢ This electron cloud expansion effect may occur for
one (or both) of two reasons.
ā€“ One is that 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-reduced by any negative charge on the ligands, the d-
orbitals can expand slightly.
ā€“ The second is the act of overlapping with ligand orbitals
and forming covalent bonds increases orbital size,
because the resulting molecular orbital is formed from
two atomic orbitals
Jorgensen Relation
ā€¢ We know that
ā€¢ C.K.Jogensen derived a relationship for Ī² as
(1-Ī²) = h.k
B
B
ļ¢
ļ€Ŗ
ļ€½
where h- is ligand parameter
k- is metal ion parameter
Ī²* = Ī² ā€“ Ī²h.k
Spin-Orbit coupling
ā€¢ Responsible for fine structure of
spectrum
ā€¢ e- has both spin and orbit angular
moments and associated magneticmoments and associated magnetic
moments.
ā€¢ These magnetic moments interact
weakly to split the energy levels.
Spin-Orbit coupling
ā€¢ Microstates can be visualized through
the vector model of the atom. The
vector model associates angular
momentum with energy.momentum with energy.
ā€¢ Each electron has an orbital angular
momentum l and a spin angular
momentum s.
The single electron orbital angular momentum l (and
hence the total orbital angular momentum L) can only
have certain orientations quantization.
ā€¢ The total orbital
angular momentum
L of a group of
electrons in an atom
is given by a vector
sum of the individualsum of the individual
orbital angular
momenta l.
Spin-orbit coupling / L-S coupling
i) Russel-Saunders for
light atoms:
J = L + S, L + S ā€“1, ā€¦, |L ā€“S|
L = l1 + l2, l1 + l2 ā€“1, ā€¦, |l1-l2|
S = s1 + s2, s1 + s2 ā€“1, ā€¦, |s1 ā€“ s2|
- Couple all individual orbital angular
momenta l to give a resultant total
orbital angular momentum L. (L = Ę© li)
- Couple all individual spin angular
momenta s to give a resultant total
spin angular momentum S. (S = Ę© s )spin angular momentum S. (S = Ę© si)
- Finally couple L and S to give the
total angular momentum J for the
entire atom.
Russel-Saunders
coupling works
well for the light
elements up to
bromine.
Spin-orbit coupling / L-S coupling
ā€¢ The extent to which L and S are coupling is
called ā€œSpin-Orbit Coupling constantā€
ā€¢ The perturbation created by L-S coupling is
ļ€Ø ļ€©ļŗ
ļ€Ø ļ€©sl.ļŗThis value is for
single electron of a ļ€Ø ļ€©sl.ļŗsingle electron of a
configuration and
always positive
Spin-orbit coupling / L-S coupling
ā€¢ For convenience, a parameter characteristic
of a term is used.
ā€¢ L-S coupling constant for a term is
ā€¢ The perturbation of energy of a term is
ļ¬
ļ€Ø ļ€©sl.ļ¬ā€¢ The perturbation of energy of a term is ļ€Ø ļ€©sl.ļ¬
s.2
ļŗ
ļ¬
ļ‚±
ļ€½
ā€¢ The value is positive for less than half
filled and negative if the orbital is greater
than half filled.
ļ¬
L-S Coupling continued
ā€¢ Each term is split in to states by L-S coupling
specified by J values, which differing by unity.
ā€¢ Each L value will have (2L+1) ML components.
ā€¢ Each S value will have (2S+1) M components.ā€¢ Each S value will have (2S+1) MS components.
ā€¢ So any term will have a degeneracy of
(2S+1).(2L+1)
L-S coupling in a p2 system
Let us consider p2 configuration
Maximum L value possible is 2
Maximum S value possible is 0
So possible J value is 2
Degeneracy of this state is
((2 x 2)+1) x ((2 x 0)+1) = 5
1D
(9)
J=2
(9)
((2 x 2)+1) x ((2 x 0)+1) = 5
Next maximum L value possible is 1
For this L value maximum S value
possible is 1
Possible J values are 2, 1, 0
Degeneracy of this state is
((2 x 1)+1) x ((2 x 1)+1) = 9
3P
(9)
J=2
(5)
J=1
(3)
J=0
(1)
2Ī»
Ī»
L-S coupling
ā€¢ Each L and S combination is having a particular energy.
ā€¢ Total angular momentum quantum number J
J = |L+S|, |L+S-1|, |L+S-2|,ā€¦ā€¦|L-S|
ā€¢ J values are of unit difference.
ļ› ļ)1()1()1(
2
ļ€«ļ€­ļ€«ļ€­ļ€«ļ€½ SSLLJJE J
ļ¬
ā€¢ J values are of unit difference.
ā€¢ The energy gap between any two successive J values is
ā€¢ For less than half filled, lowest value of J, |L-S| has the
lowest energy. (Normal multiplet)
ā€¢ For more than half filled highest value of J |L+S| has the
lowest energy (Inverted multiplet)
)1(1, ļ€«ļ€½ļ„ ļ€« JE JJ ļ¬
Normal and Inverted Multiplets
Normal Multiplet Inverted MultipletNormal Multiplet Inverted Multiplet
j-j coupling
ā€¢ Couple individual orbital l and spin s angular
momenta first to the complete electron angular
momentum j. (j = l + s)
ā€¢ Couple all j to give the total angular momentum
J. (J = j)J. (J = j)
ā€¢ j-j coupling is much more complicated to treat,
but should be used for elements heavier than
bromine.
ā€¢ For 4d and 5d series of ions.
IER Vs SOC
ā€¢ Both IER and SOC are operating
simultaneously.
ā€¢ Their relative magnitudes are important.
ā€¢ IER is very high than SOC.ā€¢ IER is very high than SOC.
ā€¢ So the IER causes the splitting first, then
splitting by SOC.
ā€¢ Resulting levels may be further split by
magnetic field.
Tackling the Multi-Electron Problem
Start by taking a step back
ā€¢ first we must treat the V3+ ā€˜free ionā€™ with no ligands in a spherically
symmetric environment
ā€¢ since V3+ is d2, we must consider eā€“-eā€“ interactions, spin-spin
interactions, and spin-orbital interactions
Define a few terms
ā€¢ microstate ā€“ a specific valence electron configuration for a multi-ā€¢ microstate ā€“ a specific valence electron configuration for a multi-
electron free ion
ā€¢ atomic state ā€“ a collection of microstates with the same energy
ā€¢ term symbol ā€“ the label for a free ion atomic state
2S+1L
L term symbol label
0 S
1 P
2 D
3 F
4 G
ā€œspin
multiplicityā€
i! 10!
j!ļ€Øi ļ€­ jļ€©! 2!ļ€Ø10 ļ€­ 2ļ€©!
ļ€½ ļ€½ 45# microstatesļ€½
#eā€“
#spaces
Multi-Electron Quantum Numbers
When we learn about atoms and electron configurations, we learn
the one-electron quantum numbers (n, l, ml, ms)
Multi-electron ions need multi-electron quantum numbers
ā€¢ L gives the total orbital angular momentum of an atomic state
(equal to the maximum value of ML)
ā€¢ ML is the z-component of the orbital angular momentum of a microstate
ā€¢ S gives the total spin angular momentum of an atomic state
(equal to the maximum value of MS (for a given L value)
ā€¢ MS is the z-component of the spin angular momentum of a microstate
Spin-Orbit Coupling
So far weā€™ve considered only eā€“-eā€“ (orbital angular momentum) and
spin-spin (spin angular momentum) interactions.
Orbitals and spins can also interact giving rise to spin-orbit
coupling
ā€¢ J is the total angular momentum
So for the 3F ground state of a d2 free ion, we haveSo for the 3F ground state of a d2 free ion, we have
To determine the lowest energy spin-orbit coupled state:
1. For less than half-filled shells, the lowest J is the lowest energy
2. For more than half-filled shells, the highest J is the lowest energy
3. For half-filled shells, only one J is possible
J ļƒž L ļ€« S ļ€½ 4
ļƒž L ļ€­ S ļ€½ 2
so J ļ€½ 4, 3,2
So the 3F ground state
electron configuration of
a d2 free ion splits into
3F4, 3F3, and 3F2.
Number of microstates for a system
)!2(!
!2
xyx
y
N
ļ€­
ļ€½
Where
N= number of microstates possible
y ā€“ number of orbitals
X- number of electrons
Number of microstates ā€“ p1 system
+1 0 -1 y ā€“ number of orbitals - 6
x - number of electrons ā€“ 1
))!16.(2!.(1
)!6.(2
ļ€­
ļ€½N
))!16.(2!.(1 ļ€­
ļ€½N
))5.4.3.2.1(2.(1
)6.5.4.3.2.1.(2
ļ€½N
N = 6
Number of microstates ā€“ p2 system
y ā€“ number of orbitals - 6
x - number of electrons ā€“ 2
)!6.(2
ļ€½N
))!26.(2!.(2 ļ€­
ļ€½N
))4.3.2.1(2).(2.1(
)6.5.4.3.2.1.(2
ļ€½N
N = 15
Term Symbols for p2
ā€¢ Maximum L value possible is 2
ā€“ Possible ML values are -L, -(L+1), ā€¦, 0 , ā€¦, +(L-1), +L
ā€“ i.e. -2 , -1 , 0 , +1 , +2
ā€¢ Maximum S value possible is : 0
ā€“ Possible Ms value is 0
ā€¢ Considering all possible combinations
ML +2 +1 0 -1 -2
Ms 0 0 0 0 0
Term 1D
Term Symbols for p2
ā€¢ Next maximum L value possible is 1
ā€“ Possible ML values are -L, -(L+1), ā€¦, 0 , ā€¦, +(L-1), +L
ā€“ i.e. -1 , 0 , +1
ā€¢ Maximum S value possible is : 1
ā€“ Possible Ms value are +1 , 0 , -1
ā€¢ Considering all possible combinations
MS +1 0 -1
ML +1 0 -1 +1 0 -1 +1 0 -1
Term 3P
Term Symbols for p2
ā€¢ Next L value possible is 0
ā€“ Possible ML value is 0
ā€¢ The only S value possible is : 0
ā€“ Possible Ms value is 0
The term is 1S
MS 0
ML 0
Term
1S
Term Symbols for d2
l1 = 2; l2= 2
L = |l1+l2|, |l1+l2-1|, |l1+l2-2|ā€¦,0,ā€¦, |l1-l2|
So the possible values for L are
L = 4, 3, 2, 1, 0L = 4, 3, 2, 1, 0
s1 = Ā½ ; s2 = Ā½
So the possible values for S are
S = 1, 0
Microstates of d2
Maximum L value is 4
So the possible ML values are +4, +3, +2, +1, 0, -1, -2, -3, -4
Maximum S value possible is 0
So M can be only 0
ML +4 +3 +2 +1 0 -1 -2 -3 -4
MS 0 0 0 0 0 0 0 0 0
Term 1G (9)
So Ms can be only 0
Microstates of d2
Next maximum L value is 3
So the possible ML values are +3, +2, +1, 0, -1, -2, -3
Maximum S value possible is 1
So M can be +1, 0, -1So Ms can be +1, 0, -1
ML +3 +2 +1 0 -1 -2 -3
MS
+1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1
Term 3F (21)
Microstates of d2
Next maximum L value is 2
So the possible ML values are +2, +1, 0, -1, -2
Maximum S value possible is 1
So M can be +1, 0, -1So Ms can be +1, 0, -1
ML +2 +1 0 -1 -2
MS 0 0 0 0 0
Term 1D (5)
Microstates of d2
ā€¢ Next maximum L value possible is 1
ā€“ Possible ML values are +1 , 0 , -1
ā€¢ Maximum S value possible is : 1
ā€“ Possible Ms value are +1 , 0 , -1
ā€¢ Considering all possible combinations
MS +1 0 -1
ML +1 0 -1 +1 0 -1 +1 0 -1
Term 3P (9)
Microstates of p2
ā€¢ Next L value possible is 0
ā€“ Possible ML value is 0
ā€¢ The only S value possible is : 0
ā€“ Possible Ms value is 0
The term is 1S
MS 0
ML 0
Term
1S (1)
Inter-electronic repulsions
The Crystal Field Splitting of
Russell-Saunders terms in weak oh crystal fields
Russell-Saunders Terms Crystal Field Components
S (1) A1g
P (3) T1g
D (5) Eg +T2gD (5) Eg +T2g
F (7) A2g + T1g + T2g
G (9) A1g +Eg + T1g +T2g
H (11) Eg + T1g + T1g+ T2g
I (13) A1g + A2g + Eg + T1g + T2g+T2g
Mulliken Symbols
Mulliken Symbol Explanation
A Non-degenerate orbital; symmetric to principal Cn
B Non-degenerate orbital; unsymmetric to principal Cn
E Doubly degenerate orbital
T Triply degenerate orbital
(subscript) g Symmetric with respect to center of inversion(subscript) g Symmetric with respect to center of inversion
(subscript) u Unsymmetric with respect to center of inversion
(subscript) 1 Symmetric with respect to C2 perp. to principal Cn
(subscript) 2 Unsymmetric with respect to C2 perp. to principal Cn
(superscript) ' Symmetric with respect to Ļƒh
(superscript) " Unsymmetric with respect to Ļƒh
Mulliken Symbols
ā€¢ Examine the correlation diagram for a d2
configuration in an octahedral ligand field.
ā€“ Far left (absence of ligand field) ā€“ the free-ion
terms. On this side, the ligand field has very
little influence.
Correlation Diagrams
Relating Electron Spectra to Ligand Field Splitting
little influence.
ā€“ Far right (strong ligand field) ā€“ the states are
largely determined by the ligand field.
ā€¢ In real compounds, the situation is somewhere in
the middle.
ā€¢ Correlating the states on both sides is done in
accordance with the so called ā€œ non-crossing rule ā€ .
Orgel Diagram
ā€¢ Used for interpretation of electronic spectra
of metal ion complexes.
ā€¢ Got by plotting the energies of split levels of
a term by increasing ligand field strengtha term by increasing ligand field strength
ā€¢ Only applicable for weak field cases.
ā€¢ Can predict only spin-allowed transitions.
ā€¢ Transitions are assumed to occur from the
lowest energy level.
Orgel Diagram
Energyofterm
10Dq
2D
Energyofterm
Orgel Diagram
d2 oh
d8 oh
Selection Rules for Electronic Spectra
ā€¢ When the molecule absorbs electromagnetic
radiation, it may be due to interaction of
ā€“ electrical dipole or quadruple with the electrical
field of emr ā€“ Electrical dipole transitionsfield of emr ā€“ Electrical dipole transitions
ā€“ the magnetic dipole of the molecule with the
magnetic field of emr ā€“ Magnetic dipole
transitions
Electrical dipole >> Magnetic dipole > Electrical quadruple
Transition Moment Integral
ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM es
ex
gs
ex
ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM es
ey
gs
ey
ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM esgs
ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM es
ez
gs
ez
ā€¢ Probability of any transition is proportional to Mi
2
ā€¢ Allowed transition Mi ā‰  0
ā€¢Forbidden transition Mi = 0
Transition Moment Integral
gs es gs es
i o i o s sM d dļ¹ ļ­ļ¹ ļ“ ļ¹ ļ¹ ļ“ļ€¼ ļ€¾ļ€½ ļƒ² ļƒ²
soe ļ¹ļ¹ļ¹ ļ€½
ā€¢For any allowed electronic transition, the Mi value should be
non-zero.
ā€¢ so either first integral or second one should be zero if Mi is
zero.
ā€¢ The dipole moment operator deals with the displacement of
atoms and associated dipole moment changes, so the spin
part can be isolated.
Odds and evens
Gerade or Ungerade
ļ€Ø ļ€© ļ€Ø ļ€©
1 3 31 3
2
1 1
1 1 1 1 2
3 3 3 3 3 3
x
x dx
ļ€«ļ€«
ļ€­ ļ€­
ļƒ© ļƒ¹ļ€« ļ€­ļƒ© ļƒ¹ ļƒ© ļƒ¹ļ€­ļƒ¦ ļƒ¶
ļ€½ ļ€½ ļ€­ ļ€½ ļ€­ ļ€½ļƒŖ ļƒŗļƒŖ ļƒŗ ļƒ§ ļƒ·ļƒŖ ļƒŗ
ļƒØ ļƒøļƒŖ ļƒŗ ļƒ« ļƒ»ļƒ« ļƒ» ļƒ« ļƒ»
ļƒ²
ļ€Ø ļ€© ļ€Ø ļ€©
1 4 41 4
3
1 1
1 1
0
4 4 4
x
x dx
ļ€«ļ€«
ļ€­ ļ€­
ļƒ© ļƒ¹ļ€« ļ€­ļƒ© ļƒ¹
ļ€½ ļ€½ ļ€­ ļ€½ļƒŖ ļƒŗļƒŖ ļƒŗ
ļƒŖ ļƒŗļƒ« ļƒ» ļƒ« ļƒ»
ļƒ²
( ) ( )f x f xļ€½ ļ€­ ( ) ( )
( ) ( )
f x f x
f x f x
ļ‚¹ ļ€­
ļ€­ ļ€½ ļ€­
f
1 operator f
2 Product
x5 x3 x5 x13 Zero
x5 x3 x2 x10 Non-zero
x2 x3 x5 x10 Non-zero
x2 x3 x2 x7 Zero
ļ€Ø ļ€©productfunction dx
ļ€«ļ‚„
ļ€­ļ‚„
ļƒ²
Ļˆe
gs Āµ Ļˆe
es Product Mi
Odd Odd Odd Odd Zero
Odd Odd Even Even Non-zero
Even Odd Odd Odd Non-zero
Even Odd Even Odd Zero
px-orbital Ungerade (u)
dxy- orbital -gerade(g)
ā€¢ All transitions within the d-shell, such as 3A2gā†’3T2g are
Laporte forbidden, because they are gā†’g.
ā€¢ The intensity of the d-d transitions that give d-block
metal ions their colors are not very intense.
The Laporte Selection Rule
metal ions their colors are not very intense.
ā€¢ Charge transfer bands frequently involve pā†’d or dā†’p
transitions, and so are Laporte-allowed and therefore
very intense.
.
The Selection rules for electronic transitions
Charge-transfer band ā€“ Laporte and spin allowed ā€“ very intense
[Ni(H2O)6]2+a
3A2g ā†’1Eg Laporte and spin forbidden ā€“ very weak
a, b, and c, Laporte
forbidden, spin
allowed, inter-
mediate intensity
b
3A2g ā†’3T2g
c
mediate intensity
Why theā€˜forbiddenā€™ transitions occur?
The orbital selection rule or the Laporte selection
rule may be relaxed by any one of the following
ļƒ˜ Departure from cubic symmetry
ļƒ˜ d-p mixing
ļƒ˜ Vibronic coupling
Departure from cubic symmetry
ā€¢ The orbital selection rule is strictly followed only in
perfect cubic symmetries (Oh and cubic)
ā€¢ If the symmetry is lowered, i.e. centre of symmetry is
removed either permanently or temporarily, then d-d
transitions may become allowed.transitions may become allowed.
ā€¢ Td complexes are having more intense colors, since
the transitions are allowed due to the absence of
center of symmetry.
ā€¢ This mechanism may not greatly relax the selection
rule, but an useful pathway for transition.
Mixing of states
ā€¢ The states in a complex are never pure.
ā€¢ When two states are energetically too close
they may be mixed by thermal vibrations
itself.itself.
ā€¢ Some of the symmetry properties of
neighboring states become mixed.
ā€¢ This makes the transitions partially allowed
which are normally forbidden.
Mixing of states: Comparison of [Ni(H2O)6]2+ and[Ni(en)3]2+:
[Ni(H2O)6]2+
[Ni(en) ]2+
3A2g 2gā†’3T (F)
The spin-forbidden 3A2g ā†’1Eg is close to thespin-allowed
3A2g ā†’3T2g(F) and ā€˜borrowsā€™ intensity by mixing of states
The spin-forbidden 3A2g ā†’1Eg is not close
to any spin allowed band and is very weak
3A2g ā†’1Eg
Note: The two spectra are
drawn on the same graph
for ease of comparison.
[Ni(en)3]2+
3A2g ā†’3T2g
ā€¢ Electronic transitions are always very broad
because they are coupled to vibrations.
ā€¢ The transitions are thus from ground states
plus several vibrational states to excited states
plus several vibrational states.
ā€¢ so the ā€˜electronicā€™ band is actually a composite
of electronic plus vibrational transitions
Vibronic Coupling
ā€¢ The vibrational
states may be of
opposite parity to
the electronic
g
u
g
the electronic
states, and so help
overcome the
Laporte selection
rule.
g
g
Symmetry of vibrational states, and their
coupling to electronic states:
observed
spectrum
E- Ļ…1
E- Ļ…2
E- Ļ…3
1E + Ļ… ā€™ E
E + Ļ…2ā€™
E + Ļ…3ā€™
T1u
symmetry
vibration
A1g
symmetry
vibration
(symbols have same meaning for
vibrations: A = non-degenerate,
T = triply degenerate, g = gerade,
u = ungerade, etc.)
The band one sees in the
UV-visible spectrum is the
sum of bands due to transitions
to coupled electronic (E) and
vibrational energy levels (Ļ…1, Ļ…2, Ļ…3)
Td vs Oh
ā€¢ A tetrahedron has no center of symmetry,
and so orbitals in such symmetry cannot
be gerade. Hence the d-levels in a
tetrahedral complex are e and t2.
ā€¢ This largely overcomes the Laporteā€¢ This largely overcomes the Laporte
selection rules, so that tetrahedral
complexes tend to be very intense in color.
ā€¢ Dissolving CoCl2 in water produces a
pale pink solution of [Co(H2O)6]2+, but in
alcohol forms, which is a tetrahedral
[CoCl4]2- having very intense blue color.
[Co(H2O)6]2+ and [CoCl4]2-
[CoCl4]2-
The spectra at left
show the very intense
d-d bands in the blue
tetrahedral complex
[CoCl4]2-, as compared
with the much weaker
[Co(H2O)6]2+
with the much weaker
band in the pink
octahedral complex
[Co(H2O)6]2+. This
difference arises
because the T com-d
plex has no center of
symmetry, helping to
overcome the gā†’g
Laporte selection rule.
Shape of Electronic bands
ā€¢ Variation of 10Dq
ā€¢ Lower symmetry components
ā€¢ Vibrational structure & F.C Principle
ā€¢ Jahn-Teller distortion
ā€¢ Spin-Orbit coupling
Variation of 10Dq
ā€¢ The Dq value is very sensitive to the M-L
bond distance.
ā€¢ When the complex molecule vibrates M-L
bond length continuously changes, and hencebond length continuously changes, and hence
the Dq.
ā€¢ Since transition energy is a function of Dq,
the transition occurs over a range of energy,
i.e the line broadens.
Variation of 10Dq
Ī”Ī•C
Ex.state : C
Ī”Ī•B Ex.state : B
Ī”Dq
Gr.state : A
Lower symmetry components
Perfect Oh
Pseudo Oh
Lower symmetry components
ā€¢ Selection rules strictly obeyed in perfect cubic
symmetry.
ā€¢ When the ligands are substituted, there is an
effective Oh symmetry but not true Oheffective Oh symmetry but not true Oh
ā€¢ This may resolve the electronic states, if the
energy gap is more two distinct peaks will
appear.
ā€¢ In the case of lesser energy difference broad
peaks due to overlap of two lines, may appear.
Jahn -Teller distortion
ā€¢ In 1937, Hermann Jahn and Edward Teller postulated
a theorem stating that "stability and degeneracy are
not possible simultaneously unless the molecule is a
linear one," in regards to its electronic state.
ā€¢ This leads to a break in degeneracy which stabilizesā€¢ This leads to a break in degeneracy which stabilizes
the molecule and by consequence, reduces its
symmetry.
ā€¢ ā€œAny non-linear molecular system in a degenerate
electronic state will be unstable and will undergo
distortion to form a system of lower symmetry and
lower energy, thereby removing the degeneracy."
Jahn-Teller distortion
Jahn -Teller distortion
Spectra got if energies of
transitions are too close
[CuF6]4-
transitions are too close
Vibrational structure
&
Franck-Condon principle
ā€¢ During an electronic transition, many
vibrational transitions may also be
simultaneously activated.
ā€¢ This lead to many closely packed vibrationalā€¢ This lead to many closely packed vibrational
peak to appear, which make a broad band.
ā€¢ Under normal temperature many vibartional
levels are populated, hence vibartional
coarse structure is very common in electronic
spectra
Spin-Orbit coupling
ā€¢ Generally spin-orbit coupling is considered as
a small perturbation when compared to
crystal field. ( at least for 3d series).
ā€¢ But n higher elements, the L-S coupling mayā€¢ But n higher elements, the L-S coupling may
be stronger, which mix the levels of different
spins.
ā€¢ Now S is not a valid quantum number, and
many spin-forbidden bands appear leading to
broader absorptions.
ā€¢Charge-transfer band arise from the movement
of electrons between orbitals that are
predominantly ligand in character and orbitals
that are predominantly metal in character.
Charge-Transfer Bands
ā€¢These transitions are identified by their high
intensity and the sensitivity of their energies to
solvent polarity.
ā€¢Absorption for charge transfer transition is
more intense than dā€“d transitions.
(ʐd-d=20 L mol-1 cm-1 or less, ʐcharge-transfer =50,000 L mol-1 cm-1 or
greater)
Charge-Transfer transition is classified into:
ļƒ˜Ligand-to-Metal Charge-Transfer transition.
(LMCT transition)
If themigration of the electron is from
theligand to the metal.
ļƒ˜Metal-to-Ligand Charge-Transfer transition.
(MLCT transition)
If themigration of the electron is from
themetal to the ligand .
ā€¢Ligands possess Ļƒ, Ļƒ*, Ļ€, Ļ€*, and nonbonding (n) molecular orbitals.
ā€¢If the ligand molecular orbitals are full, charge transfer may occur
from the ligand molecular orbitals to the empty or partially filled metal
d-orbitals.
ā€¢LMCT transitions result in intense bands. Forbidden d-d transitions
may also take place giving rise to weak absorptions.
ā€¢ Ligand to metal charge transfer results in the reduction of the metal.
MLCT
ā€¢If the metal is in a low oxidation state (electron rich) and
the ligand possesses low-lying empty orbitals (e.g., CO or
CN āˆ’ ).
ā€¢LMCT transitions are common for coordination
compounds having Ļ€-acceptor ligands.
ā€¢ Upon the absorption of light, electrons in the metalā€¢ Upon the absorption of light, electrons in the metal
orbitals are excited to the ligand Ļ€* orbitals.
ā€¢MLCT transitions result in intense bands. Forbidden d ā€“ d
transitions may also occur.
ā€¢ This transition results in the oxidation of the metal.
Metal-to-Ligand Charge-
Transfer transition.
Effect of Solvent Polarity on CT Spectra
You are preparing a sample for a UV/Vis experiment and you decide
to use a polar solvent. Is a shift in wavelength observed when:
ļƒ¼ Both the ground state and the excited state are neutral .
ļƒ¼ The excited state is polar, but the ground state is neutralļƒ¼ The excited state is polar, but the ground state is neutral
ļƒ¼ The ground state and excited state is polar
ļƒ¼ The ground state is polar and the excited state is neutral
The excited state is polar, but the
ground state is neutral
The ground state and excited state
is polar
The ground state is polar and the
excited state is neutral
The MO view of electronic transitions in an
octahedral complex
t *1u
a1g*
4p
t2gā†’t1u*
Mā†’L Charge transfer
Laporte and spin
allowed
t2gā†’eg
dā†’d transition
Laporte forbidden
Spin-allowed or
forbidden
eg*
t2g
4s
eg
a1g
t1u
3d
t1uā†’t2g
Lā†’M Charge transfer
Laporte and spin
allowed
The eg level in CFT
is an eg* in MO
In CFT we consider
only the eg and t2g
levels, which are a
portion of the over-
all MO diagram
Ļƒ-donor orbitals
of six ligands
Electronic spectra of metal complexes-1

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Electronic spectra of metal complexes-1

  • 1. Electronic Spectra ofElectronic Spectra of Metal ComplexesMetal Complexes V. Santhanam Department of Chemistry SCSVMV
  • 2. Color of the complexes
  • 3. Observed Color Light Absorbed Abs Wavelength / nm Colorless UV < 380 Yellow Violet 380-450 Orange Blue 450-490 Red Green 490-550 Violet Yellow 550-580 Blue Orange 580-650 Green Red 650-700 Colorless IR > 700
  • 4. Use of Electronic spectrum ā€¢ Electronic spectrum ā€“ due to d-d transitions. ā€¢ From the transition energy ā€“ energy of dā€¢ From the transition energy ā€“ energy of d e- can be got. ā€¢ The energies of d levels affected by many complicated factors.
  • 5. Terms, States and Microstates ā€¢ Energy levels described by quantum numbers. ā€“ Principal quantum number ā€“ n ā€“ Azimuthal quantum number ā€“ l ā€“ Magnetic quantum number ā€“ mā€“ Magnetic quantum number ā€“ ml ā€“ Spin quantum number ā€“ ms ā€¢ But actual conditions are complicated . ā€¢ Quantum numbers alone are not sufficient Why ?
  • 6. Configuration ā€¢ Arrangement of e-s in an atom or ion ā€“ The electrons are filled in the increasing order of energy ā€“ Aufbau principle ā€“ If more than one orbital is having same energy, pairing of e- will not take placeenergy, pairing of e- will not take place until all the orbitals are at least singly occupied ā€“ Hundā€™s rule ā€“ No two electrons can have all the four quantum numbers same ā€“ Pauliā€™s exclusion principle
  • 7.
  • 8.
  • 9. Terms ā€¢ Energy level of an atomic system specified by an electronic configuration. ā€¢ Many terms may arise from a configuration ā€¢ Depends on the intrinsic nature of cofig.ā€¢ Depends on the intrinsic nature of cofig. ā€¢ Electrons from filled orbitals have no contribution to energy ā€“ Assumption ā€¢ Partially filled orbitals decide the energy terms.
  • 10. Terms ā€¦ Cont ā€¢ Partially filled orbitals have two perturbations ā€“Inter Electronic Repulsionsā€“Inter Electronic Repulsions ā€“Spin-Orbit coupling
  • 11. Inter-electronic repulsions ā€¢ Energy depends on the arrangement of e- ā€¢ The electrons in partially filled orbitals repel each other. ā€¢ Repulsion splits the energy levels resulting inā€¢ Repulsion splits the energy levels resulting in many terms. ā€¢ Energies of electrons within an orbital itself are slightly different [ Pairing and Exchange energies].
  • 12. Inter-electronic repulsions Racah Parameters (A, B and C) ļƒ˜Racah parameters were generated as a means to describe the effects of electron-electron repulsion within the metal complexes. ļƒ˜A is ignored because it is roughly the same for any metalļƒ˜A is ignored because it is roughly the same for any metal center. ļƒ˜ B is generally approximated as being 4C.
  • 13. Inter-electronic repulsions ļƒ˜What B represents is an approximation of the bond strength between the ligand and metal. ļƒ˜Comparisons between tabulated free ion B and B of a coordination complex is called the nephelauxetic ratio (the effect of reducingnephelauxetic ratio (the effect of reducing electron-electron repulsion via ligands). ļƒ˜This effect is what gives rise to the nephelauxetic series of ligands.
  • 14. Nephelauxetic Effect ā€¢ Normally the electron repulsion is found to be weaker in complexes than in free ion and this means the value of B for the complex is less than for a free ion. ā€¢ This is due to the delocalization of the electron over the ligands away from the metal which separates them and hence reduces repulsion.them and hence reduces repulsion. ā€¢ The reduction of B from its free ion is normally reported in terms of nephelauxetic effet Ī² Ī² = B' complex B free ion ā€¢ Where Ī² is the nephelauxetic parameter and refer to the electron cloud expansion.
  • 15. Nephelauxetic series ā€¢ The values of Ī² depend on the ligand and vary along the nephelauxetic series. The ligands can be arranged in a nephelauxetic series as shown below. This is the order of the ligands ability to cause d electron cloud expansion.electron cloud expansion. I- < Br -< Cl- < CN- < NH3 < H2O < F- ā€¢ The series tell us that a small value of Ī² means that there is large measure of d- electron delocalization and a greater covalent character in the complex.
  • 16. Reasons for e- cloud expansion ā€¢ This electron cloud expansion effect may occur for one (or both) of two reasons. ā€“ One is that 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-reduced by any negative charge on the ligands, the d- orbitals can expand slightly. ā€“ The second is the act of overlapping with ligand orbitals and forming covalent bonds increases orbital size, because the resulting molecular orbital is formed from two atomic orbitals
  • 17. Jorgensen Relation ā€¢ We know that ā€¢ C.K.Jogensen derived a relationship for Ī² as (1-Ī²) = h.k B B ļ¢ ļ€Ŗ ļ€½ where h- is ligand parameter k- is metal ion parameter Ī²* = Ī² ā€“ Ī²h.k
  • 18.
  • 19. Spin-Orbit coupling ā€¢ Responsible for fine structure of spectrum ā€¢ e- has both spin and orbit angular moments and associated magneticmoments and associated magnetic moments. ā€¢ These magnetic moments interact weakly to split the energy levels.
  • 20. Spin-Orbit coupling ā€¢ Microstates can be visualized through the vector model of the atom. The vector model associates angular momentum with energy.momentum with energy. ā€¢ Each electron has an orbital angular momentum l and a spin angular momentum s.
  • 21. The single electron orbital angular momentum l (and hence the total orbital angular momentum L) can only have certain orientations quantization.
  • 22. ā€¢ The total orbital angular momentum L of a group of electrons in an atom is given by a vector sum of the individualsum of the individual orbital angular momenta l.
  • 23.
  • 24. Spin-orbit coupling / L-S coupling i) Russel-Saunders for light atoms: J = L + S, L + S ā€“1, ā€¦, |L ā€“S| L = l1 + l2, l1 + l2 ā€“1, ā€¦, |l1-l2| S = s1 + s2, s1 + s2 ā€“1, ā€¦, |s1 ā€“ s2| - Couple all individual orbital angular momenta l to give a resultant total orbital angular momentum L. (L = Ę© li) - Couple all individual spin angular momenta s to give a resultant total spin angular momentum S. (S = Ę© s )spin angular momentum S. (S = Ę© si) - Finally couple L and S to give the total angular momentum J for the entire atom. Russel-Saunders coupling works well for the light elements up to bromine.
  • 25. Spin-orbit coupling / L-S coupling ā€¢ The extent to which L and S are coupling is called ā€œSpin-Orbit Coupling constantā€ ā€¢ The perturbation created by L-S coupling is ļ€Ø ļ€©ļŗ ļ€Ø ļ€©sl.ļŗThis value is for single electron of a ļ€Ø ļ€©sl.ļŗsingle electron of a configuration and always positive
  • 26. Spin-orbit coupling / L-S coupling ā€¢ For convenience, a parameter characteristic of a term is used. ā€¢ L-S coupling constant for a term is ā€¢ The perturbation of energy of a term is ļ¬ ļ€Ø ļ€©sl.ļ¬ā€¢ The perturbation of energy of a term is ļ€Ø ļ€©sl.ļ¬ s.2 ļŗ ļ¬ ļ‚± ļ€½ ā€¢ The value is positive for less than half filled and negative if the orbital is greater than half filled. ļ¬
  • 27. L-S Coupling continued ā€¢ Each term is split in to states by L-S coupling specified by J values, which differing by unity. ā€¢ Each L value will have (2L+1) ML components. ā€¢ Each S value will have (2S+1) M components.ā€¢ Each S value will have (2S+1) MS components. ā€¢ So any term will have a degeneracy of (2S+1).(2L+1)
  • 28. L-S coupling in a p2 system Let us consider p2 configuration Maximum L value possible is 2 Maximum S value possible is 0 So possible J value is 2 Degeneracy of this state is ((2 x 2)+1) x ((2 x 0)+1) = 5 1D (9) J=2 (9) ((2 x 2)+1) x ((2 x 0)+1) = 5 Next maximum L value possible is 1 For this L value maximum S value possible is 1 Possible J values are 2, 1, 0 Degeneracy of this state is ((2 x 1)+1) x ((2 x 1)+1) = 9 3P (9) J=2 (5) J=1 (3) J=0 (1) 2Ī» Ī»
  • 29. L-S coupling ā€¢ Each L and S combination is having a particular energy. ā€¢ Total angular momentum quantum number J J = |L+S|, |L+S-1|, |L+S-2|,ā€¦ā€¦|L-S| ā€¢ J values are of unit difference. ļ› ļ)1()1()1( 2 ļ€«ļ€­ļ€«ļ€­ļ€«ļ€½ SSLLJJE J ļ¬ ā€¢ J values are of unit difference. ā€¢ The energy gap between any two successive J values is ā€¢ For less than half filled, lowest value of J, |L-S| has the lowest energy. (Normal multiplet) ā€¢ For more than half filled highest value of J |L+S| has the lowest energy (Inverted multiplet) )1(1, ļ€«ļ€½ļ„ ļ€« JE JJ ļ¬
  • 30. Normal and Inverted Multiplets Normal Multiplet Inverted MultipletNormal Multiplet Inverted Multiplet
  • 31. j-j coupling ā€¢ Couple individual orbital l and spin s angular momenta first to the complete electron angular momentum j. (j = l + s) ā€¢ Couple all j to give the total angular momentum J. (J = j)J. (J = j) ā€¢ j-j coupling is much more complicated to treat, but should be used for elements heavier than bromine. ā€¢ For 4d and 5d series of ions.
  • 32. IER Vs SOC ā€¢ Both IER and SOC are operating simultaneously. ā€¢ Their relative magnitudes are important. ā€¢ IER is very high than SOC.ā€¢ IER is very high than SOC. ā€¢ So the IER causes the splitting first, then splitting by SOC. ā€¢ Resulting levels may be further split by magnetic field.
  • 33.
  • 34. Tackling the Multi-Electron Problem Start by taking a step back ā€¢ first we must treat the V3+ ā€˜free ionā€™ with no ligands in a spherically symmetric environment ā€¢ since V3+ is d2, we must consider eā€“-eā€“ interactions, spin-spin interactions, and spin-orbital interactions Define a few terms ā€¢ microstate ā€“ a specific valence electron configuration for a multi-ā€¢ microstate ā€“ a specific valence electron configuration for a multi- electron free ion ā€¢ atomic state ā€“ a collection of microstates with the same energy ā€¢ term symbol ā€“ the label for a free ion atomic state 2S+1L L term symbol label 0 S 1 P 2 D 3 F 4 G ā€œspin multiplicityā€ i! 10! j!ļ€Øi ļ€­ jļ€©! 2!ļ€Ø10 ļ€­ 2ļ€©! ļ€½ ļ€½ 45# microstatesļ€½ #eā€“ #spaces
  • 35. Multi-Electron Quantum Numbers When we learn about atoms and electron configurations, we learn the one-electron quantum numbers (n, l, ml, ms) Multi-electron ions need multi-electron quantum numbers ā€¢ L gives the total orbital angular momentum of an atomic state (equal to the maximum value of ML) ā€¢ ML is the z-component of the orbital angular momentum of a microstate ā€¢ S gives the total spin angular momentum of an atomic state (equal to the maximum value of MS (for a given L value) ā€¢ MS is the z-component of the spin angular momentum of a microstate
  • 36. Spin-Orbit Coupling So far weā€™ve considered only eā€“-eā€“ (orbital angular momentum) and spin-spin (spin angular momentum) interactions. Orbitals and spins can also interact giving rise to spin-orbit coupling ā€¢ J is the total angular momentum So for the 3F ground state of a d2 free ion, we haveSo for the 3F ground state of a d2 free ion, we have To determine the lowest energy spin-orbit coupled state: 1. For less than half-filled shells, the lowest J is the lowest energy 2. For more than half-filled shells, the highest J is the lowest energy 3. For half-filled shells, only one J is possible J ļƒž L ļ€« S ļ€½ 4 ļƒž L ļ€­ S ļ€½ 2 so J ļ€½ 4, 3,2 So the 3F ground state electron configuration of a d2 free ion splits into 3F4, 3F3, and 3F2.
  • 37. Number of microstates for a system )!2(! !2 xyx y N ļ€­ ļ€½ Where N= number of microstates possible y ā€“ number of orbitals X- number of electrons
  • 38. Number of microstates ā€“ p1 system +1 0 -1 y ā€“ number of orbitals - 6 x - number of electrons ā€“ 1 ))!16.(2!.(1 )!6.(2 ļ€­ ļ€½N ))!16.(2!.(1 ļ€­ ļ€½N ))5.4.3.2.1(2.(1 )6.5.4.3.2.1.(2 ļ€½N N = 6
  • 39. Number of microstates ā€“ p2 system y ā€“ number of orbitals - 6 x - number of electrons ā€“ 2 )!6.(2 ļ€½N ))!26.(2!.(2 ļ€­ ļ€½N ))4.3.2.1(2).(2.1( )6.5.4.3.2.1.(2 ļ€½N N = 15
  • 40. Term Symbols for p2 ā€¢ Maximum L value possible is 2 ā€“ Possible ML values are -L, -(L+1), ā€¦, 0 , ā€¦, +(L-1), +L ā€“ i.e. -2 , -1 , 0 , +1 , +2 ā€¢ Maximum S value possible is : 0 ā€“ Possible Ms value is 0 ā€¢ Considering all possible combinations ML +2 +1 0 -1 -2 Ms 0 0 0 0 0 Term 1D
  • 41. Term Symbols for p2 ā€¢ Next maximum L value possible is 1 ā€“ Possible ML values are -L, -(L+1), ā€¦, 0 , ā€¦, +(L-1), +L ā€“ i.e. -1 , 0 , +1 ā€¢ Maximum S value possible is : 1 ā€“ Possible Ms value are +1 , 0 , -1 ā€¢ Considering all possible combinations MS +1 0 -1 ML +1 0 -1 +1 0 -1 +1 0 -1 Term 3P
  • 42. Term Symbols for p2 ā€¢ Next L value possible is 0 ā€“ Possible ML value is 0 ā€¢ The only S value possible is : 0 ā€“ Possible Ms value is 0 The term is 1S MS 0 ML 0 Term 1S
  • 43. Term Symbols for d2 l1 = 2; l2= 2 L = |l1+l2|, |l1+l2-1|, |l1+l2-2|ā€¦,0,ā€¦, |l1-l2| So the possible values for L are L = 4, 3, 2, 1, 0L = 4, 3, 2, 1, 0 s1 = Ā½ ; s2 = Ā½ So the possible values for S are S = 1, 0
  • 44. Microstates of d2 Maximum L value is 4 So the possible ML values are +4, +3, +2, +1, 0, -1, -2, -3, -4 Maximum S value possible is 0 So M can be only 0 ML +4 +3 +2 +1 0 -1 -2 -3 -4 MS 0 0 0 0 0 0 0 0 0 Term 1G (9) So Ms can be only 0
  • 45. Microstates of d2 Next maximum L value is 3 So the possible ML values are +3, +2, +1, 0, -1, -2, -3 Maximum S value possible is 1 So M can be +1, 0, -1So Ms can be +1, 0, -1 ML +3 +2 +1 0 -1 -2 -3 MS +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 +1 0 -1 Term 3F (21)
  • 46. Microstates of d2 Next maximum L value is 2 So the possible ML values are +2, +1, 0, -1, -2 Maximum S value possible is 1 So M can be +1, 0, -1So Ms can be +1, 0, -1 ML +2 +1 0 -1 -2 MS 0 0 0 0 0 Term 1D (5)
  • 47. Microstates of d2 ā€¢ Next maximum L value possible is 1 ā€“ Possible ML values are +1 , 0 , -1 ā€¢ Maximum S value possible is : 1 ā€“ Possible Ms value are +1 , 0 , -1 ā€¢ Considering all possible combinations MS +1 0 -1 ML +1 0 -1 +1 0 -1 +1 0 -1 Term 3P (9)
  • 48. Microstates of p2 ā€¢ Next L value possible is 0 ā€“ Possible ML value is 0 ā€¢ The only S value possible is : 0 ā€“ Possible Ms value is 0 The term is 1S MS 0 ML 0 Term 1S (1)
  • 49.
  • 50.
  • 52.
  • 53.
  • 54.
  • 55.
  • 56. The Crystal Field Splitting of Russell-Saunders terms in weak oh crystal fields Russell-Saunders Terms Crystal Field Components S (1) A1g P (3) T1g D (5) Eg +T2gD (5) Eg +T2g F (7) A2g + T1g + T2g G (9) A1g +Eg + T1g +T2g H (11) Eg + T1g + T1g+ T2g I (13) A1g + A2g + Eg + T1g + T2g+T2g
  • 57. Mulliken Symbols Mulliken Symbol Explanation A Non-degenerate orbital; symmetric to principal Cn B Non-degenerate orbital; unsymmetric to principal Cn E Doubly degenerate orbital T Triply degenerate orbital (subscript) g Symmetric with respect to center of inversion(subscript) g Symmetric with respect to center of inversion (subscript) u Unsymmetric with respect to center of inversion (subscript) 1 Symmetric with respect to C2 perp. to principal Cn (subscript) 2 Unsymmetric with respect to C2 perp. to principal Cn (superscript) ' Symmetric with respect to Ļƒh (superscript) " Unsymmetric with respect to Ļƒh
  • 59.
  • 60.
  • 61.
  • 62. ā€¢ Examine the correlation diagram for a d2 configuration in an octahedral ligand field. ā€“ Far left (absence of ligand field) ā€“ the free-ion terms. On this side, the ligand field has very little influence. Correlation Diagrams Relating Electron Spectra to Ligand Field Splitting little influence. ā€“ Far right (strong ligand field) ā€“ the states are largely determined by the ligand field. ā€¢ In real compounds, the situation is somewhere in the middle. ā€¢ Correlating the states on both sides is done in accordance with the so called ā€œ non-crossing rule ā€ .
  • 63.
  • 64.
  • 65. Orgel Diagram ā€¢ Used for interpretation of electronic spectra of metal ion complexes. ā€¢ Got by plotting the energies of split levels of a term by increasing ligand field strengtha term by increasing ligand field strength ā€¢ Only applicable for weak field cases. ā€¢ Can predict only spin-allowed transitions. ā€¢ Transitions are assumed to occur from the lowest energy level.
  • 68.
  • 69.
  • 70.
  • 72.
  • 73.
  • 74. Selection Rules for Electronic Spectra ā€¢ When the molecule absorbs electromagnetic radiation, it may be due to interaction of ā€“ electrical dipole or quadruple with the electrical field of emr ā€“ Electrical dipole transitionsfield of emr ā€“ Electrical dipole transitions ā€“ the magnetic dipole of the molecule with the magnetic field of emr ā€“ Magnetic dipole transitions Electrical dipole >> Magnetic dipole > Electrical quadruple
  • 75. Transition Moment Integral ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM es ex gs ex ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM es ey gs ey ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM esgs ļƒ²ļ€¾ļ€½ļ€¼ ļ“ļ¹ļ­ļ¹ dM es ez gs ez ā€¢ Probability of any transition is proportional to Mi 2 ā€¢ Allowed transition Mi ā‰  0 ā€¢Forbidden transition Mi = 0
  • 76. Transition Moment Integral gs es gs es i o i o s sM d dļ¹ ļ­ļ¹ ļ“ ļ¹ ļ¹ ļ“ļ€¼ ļ€¾ļ€½ ļƒ² ļƒ² soe ļ¹ļ¹ļ¹ ļ€½ ā€¢For any allowed electronic transition, the Mi value should be non-zero. ā€¢ so either first integral or second one should be zero if Mi is zero. ā€¢ The dipole moment operator deals with the displacement of atoms and associated dipole moment changes, so the spin part can be isolated.
  • 77. Odds and evens Gerade or Ungerade ļ€Ø ļ€© ļ€Ø ļ€© 1 3 31 3 2 1 1 1 1 1 1 2 3 3 3 3 3 3 x x dx ļ€«ļ€« ļ€­ ļ€­ ļƒ© ļƒ¹ļ€« ļ€­ļƒ© ļƒ¹ ļƒ© ļƒ¹ļ€­ļƒ¦ ļƒ¶ ļ€½ ļ€½ ļ€­ ļ€½ ļ€­ ļ€½ļƒŖ ļƒŗļƒŖ ļƒŗ ļƒ§ ļƒ·ļƒŖ ļƒŗ ļƒØ ļƒøļƒŖ ļƒŗ ļƒ« ļƒ»ļƒ« ļƒ» ļƒ« ļƒ» ļƒ² ļ€Ø ļ€© ļ€Ø ļ€© 1 4 41 4 3 1 1 1 1 0 4 4 4 x x dx ļ€«ļ€« ļ€­ ļ€­ ļƒ© ļƒ¹ļ€« ļ€­ļƒ© ļƒ¹ ļ€½ ļ€½ ļ€­ ļ€½ļƒŖ ļƒŗļƒŖ ļƒŗ ļƒŖ ļƒŗļƒ« ļƒ» ļƒ« ļƒ» ļƒ²
  • 78. ( ) ( )f x f xļ€½ ļ€­ ( ) ( ) ( ) ( ) f x f x f x f x ļ‚¹ ļ€­ ļ€­ ļ€½ ļ€­
  • 79. f 1 operator f 2 Product x5 x3 x5 x13 Zero x5 x3 x2 x10 Non-zero x2 x3 x5 x10 Non-zero x2 x3 x2 x7 Zero ļ€Ø ļ€©productfunction dx ļ€«ļ‚„ ļ€­ļ‚„ ļƒ² Ļˆe gs Āµ Ļˆe es Product Mi Odd Odd Odd Odd Zero Odd Odd Even Even Non-zero Even Odd Odd Odd Non-zero Even Odd Even Odd Zero
  • 80. px-orbital Ungerade (u) dxy- orbital -gerade(g)
  • 81. ā€¢ All transitions within the d-shell, such as 3A2gā†’3T2g are Laporte forbidden, because they are gā†’g. ā€¢ The intensity of the d-d transitions that give d-block metal ions their colors are not very intense. The Laporte Selection Rule metal ions their colors are not very intense. ā€¢ Charge transfer bands frequently involve pā†’d or dā†’p transitions, and so are Laporte-allowed and therefore very intense. .
  • 82. The Selection rules for electronic transitions Charge-transfer band ā€“ Laporte and spin allowed ā€“ very intense [Ni(H2O)6]2+a 3A2g ā†’1Eg Laporte and spin forbidden ā€“ very weak a, b, and c, Laporte forbidden, spin allowed, inter- mediate intensity b 3A2g ā†’3T2g c mediate intensity
  • 83. Why theā€˜forbiddenā€™ transitions occur? The orbital selection rule or the Laporte selection rule may be relaxed by any one of the following ļƒ˜ Departure from cubic symmetry ļƒ˜ d-p mixing ļƒ˜ Vibronic coupling
  • 84. Departure from cubic symmetry ā€¢ The orbital selection rule is strictly followed only in perfect cubic symmetries (Oh and cubic) ā€¢ If the symmetry is lowered, i.e. centre of symmetry is removed either permanently or temporarily, then d-d transitions may become allowed.transitions may become allowed. ā€¢ Td complexes are having more intense colors, since the transitions are allowed due to the absence of center of symmetry. ā€¢ This mechanism may not greatly relax the selection rule, but an useful pathway for transition.
  • 85.
  • 86. Mixing of states ā€¢ The states in a complex are never pure. ā€¢ When two states are energetically too close they may be mixed by thermal vibrations itself.itself. ā€¢ Some of the symmetry properties of neighboring states become mixed. ā€¢ This makes the transitions partially allowed which are normally forbidden.
  • 87. Mixing of states: Comparison of [Ni(H2O)6]2+ and[Ni(en)3]2+: [Ni(H2O)6]2+ [Ni(en) ]2+ 3A2g 2gā†’3T (F) The spin-forbidden 3A2g ā†’1Eg is close to thespin-allowed 3A2g ā†’3T2g(F) and ā€˜borrowsā€™ intensity by mixing of states The spin-forbidden 3A2g ā†’1Eg is not close to any spin allowed band and is very weak 3A2g ā†’1Eg Note: The two spectra are drawn on the same graph for ease of comparison. [Ni(en)3]2+ 3A2g ā†’3T2g
  • 88. ā€¢ Electronic transitions are always very broad because they are coupled to vibrations. ā€¢ The transitions are thus from ground states plus several vibrational states to excited states plus several vibrational states. ā€¢ so the ā€˜electronicā€™ band is actually a composite of electronic plus vibrational transitions
  • 89. Vibronic Coupling ā€¢ The vibrational states may be of opposite parity to the electronic g u g the electronic states, and so help overcome the Laporte selection rule. g g
  • 90. Symmetry of vibrational states, and their coupling to electronic states: observed spectrum E- Ļ…1 E- Ļ…2 E- Ļ…3 1E + Ļ… ā€™ E E + Ļ…2ā€™ E + Ļ…3ā€™ T1u symmetry vibration A1g symmetry vibration (symbols have same meaning for vibrations: A = non-degenerate, T = triply degenerate, g = gerade, u = ungerade, etc.) The band one sees in the UV-visible spectrum is the sum of bands due to transitions to coupled electronic (E) and vibrational energy levels (Ļ…1, Ļ…2, Ļ…3)
  • 91. Td vs Oh ā€¢ A tetrahedron has no center of symmetry, and so orbitals in such symmetry cannot be gerade. Hence the d-levels in a tetrahedral complex are e and t2. ā€¢ This largely overcomes the Laporteā€¢ This largely overcomes the Laporte selection rules, so that tetrahedral complexes tend to be very intense in color. ā€¢ Dissolving CoCl2 in water produces a pale pink solution of [Co(H2O)6]2+, but in alcohol forms, which is a tetrahedral [CoCl4]2- having very intense blue color.
  • 92. [Co(H2O)6]2+ and [CoCl4]2- [CoCl4]2- The spectra at left show the very intense d-d bands in the blue tetrahedral complex [CoCl4]2-, as compared with the much weaker [Co(H2O)6]2+ with the much weaker band in the pink octahedral complex [Co(H2O)6]2+. This difference arises because the T com-d plex has no center of symmetry, helping to overcome the gā†’g Laporte selection rule.
  • 93. Shape of Electronic bands ā€¢ Variation of 10Dq ā€¢ Lower symmetry components ā€¢ Vibrational structure & F.C Principle ā€¢ Jahn-Teller distortion ā€¢ Spin-Orbit coupling
  • 94. Variation of 10Dq ā€¢ The Dq value is very sensitive to the M-L bond distance. ā€¢ When the complex molecule vibrates M-L bond length continuously changes, and hencebond length continuously changes, and hence the Dq. ā€¢ Since transition energy is a function of Dq, the transition occurs over a range of energy, i.e the line broadens.
  • 95. Variation of 10Dq Ī”Ī•C Ex.state : C Ī”Ī•B Ex.state : B Ī”Dq Gr.state : A
  • 97. Lower symmetry components ā€¢ Selection rules strictly obeyed in perfect cubic symmetry. ā€¢ When the ligands are substituted, there is an effective Oh symmetry but not true Oheffective Oh symmetry but not true Oh ā€¢ This may resolve the electronic states, if the energy gap is more two distinct peaks will appear. ā€¢ In the case of lesser energy difference broad peaks due to overlap of two lines, may appear.
  • 98.
  • 99. Jahn -Teller distortion ā€¢ In 1937, Hermann Jahn and Edward Teller postulated a theorem stating that "stability and degeneracy are not possible simultaneously unless the molecule is a linear one," in regards to its electronic state. ā€¢ This leads to a break in degeneracy which stabilizesā€¢ This leads to a break in degeneracy which stabilizes the molecule and by consequence, reduces its symmetry. ā€¢ ā€œAny non-linear molecular system in a degenerate electronic state will be unstable and will undergo distortion to form a system of lower symmetry and lower energy, thereby removing the degeneracy."
  • 101. Jahn -Teller distortion Spectra got if energies of transitions are too close [CuF6]4- transitions are too close
  • 102. Vibrational structure & Franck-Condon principle ā€¢ During an electronic transition, many vibrational transitions may also be simultaneously activated. ā€¢ This lead to many closely packed vibrationalā€¢ This lead to many closely packed vibrational peak to appear, which make a broad band. ā€¢ Under normal temperature many vibartional levels are populated, hence vibartional coarse structure is very common in electronic spectra
  • 103.
  • 104. Spin-Orbit coupling ā€¢ Generally spin-orbit coupling is considered as a small perturbation when compared to crystal field. ( at least for 3d series). ā€¢ But n higher elements, the L-S coupling mayā€¢ But n higher elements, the L-S coupling may be stronger, which mix the levels of different spins. ā€¢ Now S is not a valid quantum number, and many spin-forbidden bands appear leading to broader absorptions.
  • 105. ā€¢Charge-transfer band arise from the movement of electrons between orbitals that are predominantly ligand in character and orbitals that are predominantly metal in character. Charge-Transfer Bands ā€¢These transitions are identified by their high intensity and the sensitivity of their energies to solvent polarity. ā€¢Absorption for charge transfer transition is more intense than dā€“d transitions. (ʐd-d=20 L mol-1 cm-1 or less, ʐcharge-transfer =50,000 L mol-1 cm-1 or greater)
  • 106. Charge-Transfer transition is classified into: ļƒ˜Ligand-to-Metal Charge-Transfer transition. (LMCT transition) If themigration of the electron is from theligand to the metal. ļƒ˜Metal-to-Ligand Charge-Transfer transition. (MLCT transition) If themigration of the electron is from themetal to the ligand .
  • 107. ā€¢Ligands possess Ļƒ, Ļƒ*, Ļ€, Ļ€*, and nonbonding (n) molecular orbitals. ā€¢If the ligand molecular orbitals are full, charge transfer may occur from the ligand molecular orbitals to the empty or partially filled metal d-orbitals. ā€¢LMCT transitions result in intense bands. Forbidden d-d transitions may also take place giving rise to weak absorptions. ā€¢ Ligand to metal charge transfer results in the reduction of the metal.
  • 108. MLCT ā€¢If the metal is in a low oxidation state (electron rich) and the ligand possesses low-lying empty orbitals (e.g., CO or CN āˆ’ ). ā€¢LMCT transitions are common for coordination compounds having Ļ€-acceptor ligands. ā€¢ Upon the absorption of light, electrons in the metalā€¢ Upon the absorption of light, electrons in the metal orbitals are excited to the ligand Ļ€* orbitals. ā€¢MLCT transitions result in intense bands. Forbidden d ā€“ d transitions may also occur. ā€¢ This transition results in the oxidation of the metal.
  • 110.
  • 111. Effect of Solvent Polarity on CT Spectra You are preparing a sample for a UV/Vis experiment and you decide to use a polar solvent. Is a shift in wavelength observed when: ļƒ¼ Both the ground state and the excited state are neutral . ļƒ¼ The excited state is polar, but the ground state is neutralļƒ¼ The excited state is polar, but the ground state is neutral ļƒ¼ The ground state and excited state is polar ļƒ¼ The ground state is polar and the excited state is neutral
  • 112. The excited state is polar, but the ground state is neutral
  • 113. The ground state and excited state is polar
  • 114. The ground state is polar and the excited state is neutral
  • 115. The MO view of electronic transitions in an octahedral complex t *1u a1g* 4p t2gā†’t1u* Mā†’L Charge transfer Laporte and spin allowed t2gā†’eg dā†’d transition Laporte forbidden Spin-allowed or forbidden eg* t2g 4s eg a1g t1u 3d t1uā†’t2g Lā†’M Charge transfer Laporte and spin allowed The eg level in CFT is an eg* in MO In CFT we consider only the eg and t2g levels, which are a portion of the over- all MO diagram Ļƒ-donor orbitals of six ligands