2.6 Electronic States of Polyatomics and Photoreactivity
61
Rydberg states form series converging to the energy of the cation and can be fitted
by the following formula
E n IP −
Ry
(n − δ) 2
(2.134)
where IP is the ionization potential, Ry = m e α
2 c
2
/2 is the Rydberg energy, n is
the principal quantum number of the singly occupied hydrogen-like orbital, and δ is
the so-called quantum defect, which takes into account the deviation from the point
charge model. Often the first σ → Ry Rydberg states are found at lower energies with
respect to σ → σ
∗ , but they usually show quite low radiative transition probabilities,
rapidly decreasing with n, because of the small overlap of the Rydberg orbitals with
the MO occupied in the ground state. For the same reason, the exchange integral
K σ,Ry is expected to be small, and therefore the energetic splitting between the
singlet and triplet states sharing the same σ → Ry configuration is normally small
(see Eq. (2.93)). Usually the potential energy surface of a Rydberg state looks like
that of the corresponding cation, as the electron in the Rydberg orbital is weekly
affected by changes in the molecular geometry. Large molecules, which cannot be
approximated as point charges, do not show well-characterized Rydberg states.
2.6.3 Excited States n → σ ∗
According to the energetic ordering of molecular orbitals referred above, in molecules containing σ bonds and lone pairs, such as water, ammonia, alcohols, ethers, the
frontier orbitals are n and σ
∗ . Then, the first excited states are normally of n → σ
∗
character (or n → Ry in small molecules). At variance with σ → σ
∗ , the excited
singlet n → σ
∗ has a homolytic dissociation, giving rise to two neutral fragments,
like S 0 . In fact, if A is the atom containing the lone pair n, when the A-B bond
is broken, A will have two nonbonding orbitals (n 1 and n 2 , probably very close
in energy). It will be therefore possible to place the unpaired electron in n 1 or n 2 ,
producing two degenerate or quasi-degenerate singlets.
As a simple example we consider the water photolysis [18, 19]. The first excited
singlet state of water has a mixed valence/Rydberg character (i.e., it can be represented as a combination of the n → σ
∗ and n → 3s configurations). The corresponding absorption band, with a maximum at 166 nm, has a weak intensity and is a
continuum, which is the signature of a dissociative potential energy surface. In fact,
the n → σ
∗ configuration has a repulsive potential energy surface and the S 1 state,
which has a substantial Rydberg character at the S 0 equilibrium geometry, evolves
to become a valence n → σ
∗ state when the O-H bond is stretched. The orbital correlation diagram of Fig. 2.7 shows that the ground state and the n → σ
∗ singlet are
degenerate at dissociation, where two equivalent configurations may be produced
placing the unpaired electron on the OH moiety in one of the two degenerate p
orbitals of the oxygen atom. This simple description is also suited to the dissociation
of O-H and O-C bonds in alcohols and ethers.
61
Rydberg states form series converging to the energy of the cation and can be fitted
by the following formula
E n IP −
Ry
(n − δ) 2
(2.134)
where IP is the ionization potential, Ry = m e α
2 c
2
/2 is the Rydberg energy, n is
the principal quantum number of the singly occupied hydrogen-like orbital, and δ is
the so-called quantum defect, which takes into account the deviation from the point
charge model. Often the first σ → Ry Rydberg states are found at lower energies with
respect to σ → σ
∗ , but they usually show quite low radiative transition probabilities,
rapidly decreasing with n, because of the small overlap of the Rydberg orbitals with
the MO occupied in the ground state. For the same reason, the exchange integral
K σ,Ry is expected to be small, and therefore the energetic splitting between the
singlet and triplet states sharing the same σ → Ry configuration is normally small
(see Eq. (2.93)). Usually the potential energy surface of a Rydberg state looks like
that of the corresponding cation, as the electron in the Rydberg orbital is weekly
affected by changes in the molecular geometry. Large molecules, which cannot be
approximated as point charges, do not show well-characterized Rydberg states.
2.6.3 Excited States n → σ ∗
According to the energetic ordering of molecular orbitals referred above, in molecules containing σ bonds and lone pairs, such as water, ammonia, alcohols, ethers, the
frontier orbitals are n and σ
∗ . Then, the first excited states are normally of n → σ
∗
character (or n → Ry in small molecules). At variance with σ → σ
∗ , the excited
singlet n → σ
∗ has a homolytic dissociation, giving rise to two neutral fragments,
like S 0 . In fact, if A is the atom containing the lone pair n, when the A-B bond
is broken, A will have two nonbonding orbitals (n 1 and n 2 , probably very close
in energy). It will be therefore possible to place the unpaired electron in n 1 or n 2 ,
producing two degenerate or quasi-degenerate singlets.
As a simple example we consider the water photolysis [18, 19]. The first excited
singlet state of water has a mixed valence/Rydberg character (i.e., it can be represented as a combination of the n → σ
∗ and n → 3s configurations). The corresponding absorption band, with a maximum at 166 nm, has a weak intensity and is a
continuum, which is the signature of a dissociative potential energy surface. In fact,
the n → σ
∗ configuration has a repulsive potential energy surface and the S 1 state,
which has a substantial Rydberg character at the S 0 equilibrium geometry, evolves
to become a valence n → σ
∗ state when the O-H bond is stretched. The orbital correlation diagram of Fig. 2.7 shows that the ground state and the n → σ
∗ singlet are
degenerate at dissociation, where two equivalent configurations may be produced
placing the unpaired electron on the OH moiety in one of the two degenerate p
orbitals of the oxygen atom. This simple description is also suited to the dissociation
of O-H and O-C bonds in alcohols and ethers.