We have already studied the energy level diagrams of diatomics in earlier lectures.   It was pointed out in the beginning of this lecture that  ΔE_electronic ≈10³   ΔE_vibrational   ≈ 10⁶  ΔE _rotational. Although the electronic transition energies are much larger than vibrational and rotational energies, the vibrational “fine” structure is often seen in electronic spectra. We want to summarise the main features of molecular electronic spectroscopy here.

Let us consider the electronic spectrum of molecular hydrogen. Since the molecule has an axis of symmetry (which is the molecular axis; if we rotate the molecule by any angle with respect to this axis, the new molecular orientation or configuration is indistinguishable from the earlier one), the axial component of angular momentum plays an important role. Denoting this by λ, the values that λ can take are 0 (denoted by symbol σ),  1(π), 2 (δ),  3(φ),  and other positive integer values.  States with λ > 0 are doubly degenerate because the projection of the angular momentum on the molecular axis can be positive or negative. The angular momenta of two or more electrons can be added by rules similar to the rules for adding L and S.

In H₂, the ground state is  (1sσ_g )^{2   1}Σ_g⁺.  The   meaning of the symbol is that there are two electrons (superscript 2) occupying a σ orbital (the orbital having cylindrical symmetry) formed by the overlap of two 1s orbitals.  The subscript g refers to “gerade”, which means that the wavefunction (the bonding MO in the present case) is symmetric with respect to the center of symmetry of the molecule.  1sσ orbital is gerade while   1sσ* is ungerade, denoted by subscript u.  In  ¹Σ_g⁺ ,  the + sign refers to symmetry with respect to the reflection across a molecular plane and  Σ refers to the total  angular momentum of orbital part plus spin part of  ½ + (-½ ) = 0    for the two electrons.

There are a large number of empty or bitals in H₂  into which the excited electron can be placed.

 The three possible excited states of H₂  are

(1sσ_g  2 sσ_g ) ¹Σ_g⁺, (1sσ_g  2 sσ_g ) ¹Σ_u⁺ and   (1sσ_g  2p π_u) ¹Π_u. The quantities in parenthesis refer to the orbital contributions.  In the first case, the total axial angular momentum is zero since λ₁ =  λ₂  (the axial angular momentum of each electron) and both are zero. Total angular momentum Λ =  λ₁ +  λ₂ = 0, the total spin S = 0 and hence the   Σ   state.  In the third case, λ₂ = 1 and hence the Π  state.  The energy ordering of these excited states is found to be

¹Σ_u⁺ < ¹ Π_u  < ¹Σ_g+

The selection rules for electronic transitions in diatomics are

ΔΛ = 0, ±  1

ΔS = 0

ΔΩ= 0, ± 1

Σ⁺  ↔ Σ⁺, Σ^- ↔ Σ^-,  Σ⁺ ≠ Σ^-

g ↔ u,  g ≠ g,  u ≠  u                                                                                   (12.17)

Using these, it is seen that the first two lines of the electronic energy spectrum in H₂ are  ¹Σ_g⁺ → ¹Σ_u+ and  ¹Σ_g+ → ¹Π_u . In Eq.(12.17), Λ  refers to the total axial angular momentum  λ₁ + λ₂ , S refers to the total spin S₁ + S₂,  and Ω refers to the total Λ + S.

As we go to polyatomics, a simpler way to approach electronic spectra is to consider electronic excitations from various localized orbitals.  On excitation, orbital shapes as well as molecular shapes can change significantly.  For example, CO₂  becomes bent and H – C  ≡  C − H   becomes  zig-zag.   Among organic groups, common frequencies for excitations of  -C = C-, > C = O, > C = N-  bonds have been observed.  In these molecules which contain double bonds, π → π* and n →  π*  transitions are observed.  The n →  π*  transitions resulting from the excitation of a non-bonding electron is weak with a low value of extinction coefficient.   The σ → σ* transitions require a lot of energy and occur in the far ultraviolet region (wavelength 100 nm) of the electromagnetic spectrum.  The n →  π*  transitions in conjugated ketones may occur in the visible region (400 to 700 nm).  The π →  π*   transitions for C = O, C = C, C  ≡  C and C = N-    occur at 166, 170, 170 and 190 nm respectively.  The  n  → π* transitions in C = O and  C = N-  occur at 280 and 300 nm respectively.  The extinction coefficients of  π →  π*  transitions are in the order of ten to thirty thousand while those for  n  → π* are small.  On conjugation, the wavelength of transitions increase.  For example,   -C=C-C=C and –C=C-C=C-C=C-    have π  → π*  transitions at 220 and 260 nm respectively.  Substituted conjugated systems have been studied extensively in the UV – visible region and contributions of substituent groups to the changes in peak positions of  π → π*  transitions have been quantified and can be used for structural analysis.