1. Photo-Inorganic Chemistry (21CYT807)
Module 1
Philips Kumar Rai
Malaviya National Institute of Technology, Jaipur
Oct 14, 2022
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
2. Selection Rules
Transition Moment (TM) under some approximations is given by
TM =
Z
φi µ̂φf dτe
Z
si sf dτs
Z
θi θf dτN (1)
Where,
R
φi µ̂φf dτe=Electronic transition moment
R
si sf dτs=Spin overlap intregal
R
θi θf dτN=Nuclear overlap integral
Selection rules are used to predict the intensity of electronic transitions on
the basis of terms appearing in equation (1).
The validity of equation (1) was based on Born Oppenheimer
Approximation, Condon Approximation and Approximation of Electronic
Wavefunctions, i.e., separating the orbital and spin part of one electron
wavefunctions.
TM will be zero if any of the three components of TM (equation 1)
becomes zero and at this condition, the transition is said to be
“forbidden“, whereas in case of TM6=0, the transition will be ”allowed”.
Because of the approximation used, forbidden transition can often be
observed, although with intensities much less than those of allowed
transitions.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
3. Symmetry Selection Rules
It is known that integral over all space of an antisymmetric function of
the coordinates vanishes, whereas the integral over all space of a
symmetric function does not vanish.
The electronic transition moment (
R
φi µ̂φf dτe) is related to the
symmetry of orbitals.
Dipole moment operator (µ̂) can be resolved into three separated
components as follows
Z
φi ˆ
µtotal φf dτe =
Z
φi ˆ
µxφf dτe +
Z
φi ˆ
µy φf dτe +
Z
φi ˆ
µzφf dτe (2)
If all the three components of equation (2) will be zero, the electronic
transition moment becomes zero and transition will be “forbidden“. On
the other hand, if any of the three components in equation (2) will not be
zero, then there will be ”allowed” transition.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
5. Symmetry Selection Rules
In the point group C2v (consider formaldehyde), the three components
ˆ
µx, ˆ
µy and ˆ
µz transform as the symmetry species B1, B2 and A1. For the
n −
→ π∗
transition, the initial orbital (2py ) belongs to the symmetry B2
and the π∗
orbital to B1.
Therefore, the φi ˆ
µxφf integrand has a symmetry generated by the direct
product B2×B1×B1.
The resulting characters of the direct products of the three components
correspond to following irreducible representations
φi ˆ
µxφf =B2×B1×B1=B2 (Antisymmetric)
φi ˆ
µy φf =B2×B2×B1=B1 (Antisymmetric)
φi ˆ
µzφf =B2×A1×B1=A2 (Antisymmetric)
All three components of the electronic transition moment are zero and the
n −
→ π∗
transition is symmetry “forbidden“.
For π −
→ π∗
transition,
φi ˆ
µzφf =B1×A1×B1=A1 (symmetric). Therefore, π −
→ π∗
transition is an
allowed transition but polarized along the z-axis.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
6. Symmetry Selection Rules
An important particular case of the symmetry selection rule is that
concerning molecules that have a center of symmetry (e.g., ethene and
transition metal complexes).
All wave functions are either symmetric or antisymmetric with respect to
the center of symmetry, that is, either gerade (even), g, or ungerade
(odd), u, and all components of the dipole moment vector are of necessity
ungerade.
The totally symmetric representation in the point groups of these
molecules is of course gerade. The product of two functions is ungerade
only if one is gerade and the other ungerade.
g×u=u
u×g=u
g×g=g
u×u=g
Hence, the integrand in Equation (2) can be gerade only if the initial wave
function (φi ) and the final wave function (φf ) have an unequal
gerade/ungerade character.
φi µ̂ φf Final Transition
g u u g Allowed
u u g g Allowed
g u g u Forbidden
u u u u Forbidden
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
7. Spin Selection Rules
The effect of electron spin on transition intensities is given by the factor
R
si sf dτs in the transition moment expression (equation 1).
When the transition occurs with no change in multiplicity,
R
si sf dτs=1.Therefore, singlet-singlet and triplet-triplet transitions are
spin allowed.
As the ground state of molecules is usually a singlet, singlet-singlet
transitions are very common. In fact, they account for most of the
absorption bands observed for molecules that have a singlet ground state.
Because of the orthogonality of spin wave functions, the
R
si sf dτs integral
vanishes whenever the initial and final states have different spin
multiplicity, and the corresponding electronic transitions are called spin
forbidden. Therefore, singlet-triplet transitions are spin forbidden.
This spin selection rule is valid to the extent to which spin and orbital
functions can be separated rigorously. Departures from this approximation
can be dealt with in terms of a perturbation called spin-orbit coupling, by
which states of different spin multiplicity can be mixed.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
8. Radiationless Deactivation and Sayed rules
Radiationless transitions occur between isoenergetic vibrational levels of
different electronic states.
As there is no change in the total energy of the system, no photon is
emitted and the process is represented by a horizontal wavy line in the
Jablonski diagram.
Radiationless transitions are essentially irreversible processes because they
are associated with an entropy increase and because the vibrational
relaxation within the lower excited state is very fast.
The rate constant of the isoenergetic radiationless transition is given,
according to perturbation theory, by Fermi’s golden rule
knr =
4π2
h
hφi Si |Ĥ0
|φf Sf i2
Σhφi,0|φf ,ni2
(3)
Here,H
0
is an appropriate perturbation that promotes the transition.
Radiationless transitions between states of equal or different spin
multiplicity are called internal conversion (i.c.) and intersystem crossing
(i.s.c.), respectively.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
9. Radiationless Deactivation and Sayed rules
For internal conversion, the electronic matrix element=hφi | ˆ
Hic|φf i, where
Hic is the nuclear kinetic energy operator, which belongs to the totally
symmetric irreducible representation. Therefore, the integrand will be
totally symmetric and the matrix element nonzero only if φi and φf
belong to the same irreducible representation.
It follows that, in principle, only states of the same symmetry should
undergo internal conversion. As S1 and S0 must have different
symmetries, the S1-S0 internal conversion is forbidden.
For intersystem crossing, H
0
is the spin-orbit operator (say HSO).
In the absence of heavy atoms, spin-orbit coupling may be very weak and,
as a consequence, intersystem crossing may be forbidden. In organic
molecules, the low-energy excited states most often result from n −
→ π∗
or π −
→ π∗
transitions.
HSO can be resolved into three perpendicular components which
transform like rotation Rx, Ry and Rz in the group character table.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
10. Sayed rules
For 1
(n,π∗
) −
→ 3
(n,π∗
), both states belong to the same excited
configuration, they have the same spatial wave function, φ. Therefore,
direct product φ×φ will belong to the totally symmetric irreducible
representation.
But, in the point groups corresponding to most molecules, rotations do
not belong to the totally symmetric irreducible representation, so that the
integrand will not be totally symmetric and its value will be zero.
The same result is obtained on examination of the 1
(n,π∗
) −
→ 3
(π,π∗
)
intersystem crossing. However,for the 1
(n,π∗
) −
→ 3
(π,π∗
) intersystem
crossing, the direct product φ1×φ2 is not totally symmetric, so that this
process may be allowed.
Sayed rules can be concluded as
1
(n,π∗
) −
→ 3
(π,π∗
)=Allowed
3
(n,π∗
) −
→ 1
(π,π∗
)=Allowed
1
(n,π∗
) −
→ 3
(n,π∗
)=Forbidden
1
(π,π∗
) −
→ 3
(π,π∗
)=Forbidden
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
11. Reference
Balzani, V., Ceroni, P. and Juris, A., 2014. Photochemistry and
photophysics: concepts, research, applications. John Wiley Sons.
Philips Kumar Rai Photo-Inorganic Chemistry (21CYT807)
