2.8 Solvent Effects on Absorption and Emission Spectra
75
In acidic media the heteroatom that provides the n orbital may be protonated: in that
limiting case the lone pair is not anymore available and the n → π
∗ band disappears.
Of course, charge transfer transitions are strongly affected by the interaction with a
polar solvent, due to the large difference between the ground and the excited state
polarity, see Table 2.5. The Reichardt’s dye of Fig. 2.10, thanks to its impressive
solvatochromism, can be used as a polarity probe.
2.9 Computational Note: The Determination of Electronic
Excited States
This short section is devoted to readers that are at least minimally acquainted with
quantum chemistry methods. Excellent textbooks, both at introductory level [4, 31]
and more advanced [7, 32], can be consulted for a deeper understanding of theory and
techniques. Here we shall be concerned with the application of quantum chemistry
to the determination of the properties of excited states and in particular of their PESs
and spectra.
The simplest approximate method to solve the time-independent Schrödinger
equation ˆ
H el ϕ = U ϕ for the electronic ground state of a molecular system is represented by the Hartree–Fock self consistent field (SCF) theory, where ϕ is written in
the form of a single Slater determinant. Usually, the SCF method provides a good
qualitative description of the ground state of organic molecules near to their equilibrium geometry. One could extend the SCF theory to excited states, however we
know from Sect. 2.6 that in most cases an excited state cannot be represented by just
one Slater determinant, so the Hartree–Fock approximation is normally qualitatively
wrong for excited states. For the same reason, the SCF method cannot be used to
obtain a potential energy surface: in fact, it behaves incorrectly at dissociation (see
Sect. 2.6.2), close to a transition state, and in general in degeneracy situations, where
it is mandatory to consider more than one Slater determinant.
The methods which build on the SCF determinant Φ 0 to obtain a more refined
(ground state) wavefunction are called single-reference. Examples are singlereference configurations interaction (CI) and coupled cluster (CC). In most cases
it is possible to obtain from these methods excited state wavefunctions and/or energies. However, the description is clearly biased in favor of the ground state (e.g., the
molecular orbitals are optimized for it). Moreover, problems are expected in regions
where the single determinant approximation is not valid.
To have a balanced treatment of ground and excited states one has to rely on
multireference methods, which also allow for full PES exploration. In particular, the
most used version of multiconfigurational SCF (MCSCF) is complete active space
SCF (CASSCF), in which a set of active electrons and orbitals is defined, and a full
CI within that set is performed. This is effective from the computational point of
view and simplifies the choice of the configurations to include in the wavefunction.
However, in many cases a valence CASSCF calculation gives too high S 0 → S n
75
In acidic media the heteroatom that provides the n orbital may be protonated: in that
limiting case the lone pair is not anymore available and the n → π
∗ band disappears.
Of course, charge transfer transitions are strongly affected by the interaction with a
polar solvent, due to the large difference between the ground and the excited state
polarity, see Table 2.5. The Reichardt’s dye of Fig. 2.10, thanks to its impressive
solvatochromism, can be used as a polarity probe.
2.9 Computational Note: The Determination of Electronic
Excited States
This short section is devoted to readers that are at least minimally acquainted with
quantum chemistry methods. Excellent textbooks, both at introductory level [4, 31]
and more advanced [7, 32], can be consulted for a deeper understanding of theory and
techniques. Here we shall be concerned with the application of quantum chemistry
to the determination of the properties of excited states and in particular of their PESs
and spectra.
The simplest approximate method to solve the time-independent Schrödinger
equation ˆ
H el ϕ = U ϕ for the electronic ground state of a molecular system is represented by the Hartree–Fock self consistent field (SCF) theory, where ϕ is written in
the form of a single Slater determinant. Usually, the SCF method provides a good
qualitative description of the ground state of organic molecules near to their equilibrium geometry. One could extend the SCF theory to excited states, however we
know from Sect. 2.6 that in most cases an excited state cannot be represented by just
one Slater determinant, so the Hartree–Fock approximation is normally qualitatively
wrong for excited states. For the same reason, the SCF method cannot be used to
obtain a potential energy surface: in fact, it behaves incorrectly at dissociation (see
Sect. 2.6.2), close to a transition state, and in general in degeneracy situations, where
it is mandatory to consider more than one Slater determinant.
The methods which build on the SCF determinant Φ 0 to obtain a more refined
(ground state) wavefunction are called single-reference. Examples are singlereference configurations interaction (CI) and coupled cluster (CC). In most cases
it is possible to obtain from these methods excited state wavefunctions and/or energies. However, the description is clearly biased in favor of the ground state (e.g., the
molecular orbitals are optimized for it). Moreover, problems are expected in regions
where the single determinant approximation is not valid.
To have a balanced treatment of ground and excited states one has to rely on
multireference methods, which also allow for full PES exploration. In particular, the
most used version of multiconfigurational SCF (MCSCF) is complete active space
SCF (CASSCF), in which a set of active electrons and orbitals is defined, and a full
CI within that set is performed. This is effective from the computational point of
view and simplifies the choice of the configurations to include in the wavefunction.
However, in many cases a valence CASSCF calculation gives too high S 0 → S n