The document discusses electronic spectroscopy of diatomic molecules, focusing on the Born-Oppenheimer approximation and the contributions of electronic, vibrational, and rotational energies to molecular spectra. It explains the Franck-Condon principle affecting the intensity of vibronic spectra and introduces molecular orbital theory, detailing the formation of molecular orbitals and their implications for bonding. Additionally, it covers the electronic structures and configurations of molecules such as hydrogen, highlighting selection rules and energy levels.

1. Electronic Spectroscopy of Molecules
Dipak Palit

2. Electronic Spectroscopy of Diatomic Molecules
The Born – Oppenheimer Approximation: Etotal = Eelectronic + Evibration + Erotation.
A Change in the total energy of the molecule may be written as:
DEtotal =DEelectronic + DEvibration + DErotation Joule
Or, Detotal =Deelectronic + Devibration + Derotation cm-1
The approximate orders of magnitude of these changes are: Deelectronic  Devibration x 103
 Derotation x 106
So, we see that vibrational changes will produce a ‘coarse structure’ and rotational changes a ‘fine structure’ on
the spectra of electronic transitions.
We have seen that pure rotation spectra are shown by molecules possessing a permanent dipole moment and
vibrational transitions require a change in dipole moment during vibration. However, electronic spectra are given
by all molecules, since changes in the electron distribution in a molecule are always accompanied by a dipole
change.
This means that homonuclear molecules, which show no rotation or vibration – rotation spectra, do give an
electronic spectrum and show vibrational and rotational structure in their spectra from which rotational constant
and bond vibration frequencies may be derived.

3. Vibrational course structure : Progressions
Initially, let us ignore the rotational fine structure and discuss the appearance of the vibrational coarse structure of
the spectra. So, etotal = eelectronic + evibration cm-1
𝜺𝒕𝒐𝒕𝒂𝒍=𝜺𝒆𝒍𝒆𝒄 +(𝒗+
𝟏
𝟐)𝝂𝒆 − 𝒙𝒆(𝒗+
𝟏
𝟐)
𝟐
𝝂𝒆(𝒗=𝟎,𝟏,𝟐,…….)
The energy levels of this equation are shown in this figure
Cm-1
The spacing between the upper vibrational levels is
deliberately shown to be rather smaller than that
between the lower; this is the normal situation, since an
excited electronic state usually corresponds to a weaker
bond in the molecule and hence a smaller vibrational
wavenumber, .
There is essentially no selection rule for v, when a
molecule undergoes electronic transition, i.e. every
transition v’  v” has some probability and hence a great
many spectral lines would therefore, be expected.
However, in case of the absorption spectrum, virtually all
the molecules exist in v’’ = 0, and so the only transitions
to be observed originating from this state.

4. Intensity of Vibrational – Electronic (vibronic) Spectra: The Franck – Condon Principle
Although quantum mechanics imposes no restrictions on the change in the vibrational quantum number during an
electronic transition, the vibrational lines in a progression are not all observed to be of the same intensity. In some
spectra the (0, 0) transition is the strongest, in others the intensity increases to a maximum at some value of v’,
while in yet others, only a few vibrational lines with high v’ are seen followed by a continuum.
All these types of spectrum are readily explicable in terms of
Franck – Condon principle, which states that an electronic
transitions takes place so rapidly that a vibrating molecule does
not change its intermolecular distance appreciably during the
transition.

6. Excited state has a nuclear configuration
close to that of the ground state.

8. Electronic spectra of diatomic molecule
Molecular Orbital Theory: Formation of molecules (or molecular orbitals) from atoms (or atomic orbitals).
Without going into the details of solving the Schrodinger equation, a very good qualitative idea of the approximate
shape of the MOs may be obtained from the sums and differences of the atomic orbitals of the constituent atoms. It
is the so-called ‘linear combination of atomic orbitals’ (LCAO) approximation.
For a diatomic molecule, we could imagine the formation of two different molecular orbitals whose wavefunctions
would be:
𝝍 𝑴𝑶 =𝝍𝟏 +𝝍 𝟐 𝒐𝒓 𝝍 𝑴𝑶 =𝝍𝟏 −𝝍𝟐
Here, y1 and y2 are two atomic orbitals associated with formation of MOs.
It is important to note that is identical with because it is , which is represents the probability of finding the
electron of finding an electron in a particular place.

9. Consider formation of MOs of the hydrogen molecule from two 1s atomic orbitals of hydrogen atoms. The first case
Now, we know that value of y1s is positive everywhere in the space and hence the value of yH2 will be increased
where the atomic orbitals overlap (Figure a). This and suggests that concentration of electronic charge increases
between the nuclei and keep the nuclei together. This is called bonding orbital and designated as 1ss.
The second case, , the value of will be smaller or zero where the two orbital overlap and they cancel each other
(Fig. b). Shape of the MO shows that the electronic charge between the nuceli is zero hence no binding energy
between the nuceli, rather nuclear repulsion is enhanced and the orbital is described as antibonding and is
labelled as 1ss*.

10. Formation of MOs using p orbitals
(1) Sigma (s) - bonds (2) Pi (p) --bonds

11. 1ssg
2

12. 8
O : 1s2
2s2
2px
2
2py
1
2pz
1

14. bonding e-
lost
antibonding e-
lost
MO Theory Explains Bonding and stability?
Ground state is the triplet state
• Bond Order =( # bonding e-
– # antibonding e-
)
• Higher bond order = stronger bond
• Molecular electron configurations
• Highest Occupied Molecular Orbital = HOMO
• Lowest Unoccupied Molecular Orbital = LUMO

15. Spectrum of Molecular Hydrogen
(1) Electronic configuration of the ground electronic state of Hydrogen molecule is (1ssg)2.
Both electrons are s electrons with l1 = l2 = 0 and L = l1 + l2 = 0 and it is a S state.
Two electrons are in the same MO and hence the spins are paired. So S = 0 and 2S + 1 = 1.
The MO has a centre of inversion and hence its symmetry is gerade or ‘g’.
Also the MO has a plane of symmetry passing through both the atoms.
Therefore, the term symbol of the ground state of Hydrogen atom is: 𝟏𝜮𝒈
+¿¿
(2) The lowest energy excited state of hydrogen molecule has the electronic configuration is
(1ssg)1
(2psg)1
Here also both the elctrons are in s orbitals, so L =0 and hence the S state. if the spins of
the electrons are opposite, then it is a singlet state with 2S + 1 = 1.
Now, if we think that one of two electrons from a hydrogen atom in the even 1s state and
the other from an odd 2p state – combination of an odd and an even states leads to an
overall odd state. Thus the term symbol for the state (1ssg)1
is .
(4) The next higher excited state with the electronic configuration (1ssg)1
(2ssg)1
is
(3) The next higher state has the electronic configuration (1ssg)1
(2ppu)1
L = l1 + l2 = 0 + 1 = 1, so it is a P state. If it is a singlet state state 2S + 1 = 1.
One electron from 1s and the other from 2p.Therefore, the term symbol for the state (1ssg)1
(2ppu)1
is
𝟏𝜮𝒈
+¿¿

16. 𝟏𝜮𝒈
+¿¿ 𝟏𝚷𝒖
Selection rules:
𝟏 𝜮
+¿¿
𝟏𝚷𝒖
𝟏 𝜮𝒈
+¿¿

17. Electronic spectrum of Oxygen molecule
300-190 nm
200-175 nm
300-242 nm
1270 nm