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6…Excited-State Energies, Electron Transfer, Oxidation, Reduction, Ionisation and Redox Potentials

6…Excited-State Energies, Electron Transfer, Oxidation, Reduction, Ionisation and Redox Potentials

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P. Douglas et al.

Table 1.4 Ionisation energies (potentials) of some atoms and molecules in the gas phase


Ionisation energy/eV







10.16 (adiabatic), 10.85 (vertical)c,d

7.50 (adiabatic), 8.08 (vertical)c,d

7.12 (adiabatic), 7.37 (vertical)c,d

7.57 (adiabatic)c

6.86 (vertical)c

6.39 (vertical)c

6.70 (adiabatic), 6.92 (vertical)c,d












Tetraphenylporphyrin, free base



Taken from Ref. [33]

First ionisation energy


Taken from Ref. [34]


The vertical ionisation energy is the energy required to form the positive ion with the same

geometry as the ground state molecule. In the adiabatic ionisation energy, the positive ion is

formed in its thermally-relaxed vibrational ground state (see Fig. 1.23)


ejected electrons are collected at an appropriate detector. The photoelectron

spectrum relates the number of electrons ejected as a function of the energy carried

by each electron. This gives a measure of the binding energies of all the core-level

electrons in the molecule. The ionisation potentials are normally given in eV.

Some values for typical metal atoms and organic molecules are given in Table 1.4.

In condensed phases (solutions and solids), electrochemical measurements are a

relatively easy way to measure the potential energy difference between two

electron states. Electrochemical methods use volts (V) as the scale of potential

energy. A potential difference of 1 V is equivalent to an energy separation of

electron energy levels of 96.5 kJ mol-1. A convenient electrochemical reference

point is the energy of an electron on a platinum electrode dipping into an acidic

aqueous solution in which the proton concentration is 1 mol dm-3 (more precisely

of unit activity) at equilibrium with an atmosphere of hydrogen gas at a pressure of

1 atmosphere at a temperature of 298 K. This is the Standard Hydrogen Electrode

(SHE), sometimes called the Normal Hydrogen Electrode (NHE). Direct electrochemical comparison of the potential energy of an electron state against the zero

of the SHE is obtained by the measurement of the potential difference, in volts,

between the electron state of interest and the SHE. This gives the potential energy

of the electron state of interest, its redox potential, directly. Conventionally,

electrode potentials are given for the reduction half-reaction, i.e.

M ỵ ne  Mn :


1 Foundations of Photochemistry


Table 1.5 Standard reduction potentials (E0) for ground and excited states of some electrochemical couples in aqueous solution

Lowest excited state


Ground state

E0/V (vs SHE)

E0/V (vs SHE)















bpy is 2,20 -bipyridyl

From Ref. [39]

From Ref. [40]

Older literature sometimes represents the oxidation potentials for the reverse

reaction. These are related simply by changing the sign. Table 1.5 shows the

standard reduction potentials for the ground and excited states of some commonly

investigated electrochemical couples in aqueous solution.

Experimentally, the SHE is not very convenient but there are other reference

electrodes, and a variety of reliable methods which can be used to measure or

estimate the redox potential of electron energy states in many chemical species. In

addition, various attempts have been made to obtain ‘absolute’ standard hydrogen

electrode potentials. Various different definitions have been provided, but one

of the most common is to define this vs a free electron at rest in vacuum. A value

of -4.44 ± 0.02 V has been recommended for the absolute electrode potential of

the standard hydrogen electrode in water at 25 °C. This has been calculated from a

detailed thermodynamical analysis of the various processes involved [35]. This

value can be added to standard electrode potentials of any electrochemical couple

to calculate the absolute potential. Data are also available for the absolute electrode potential of the SHE in a variety of organic solvents. However, it is frequently more convenient in this case to determine oxidation and reduction

potentials by the method of cyclic voltammetry (CV) using a known reference

couple [36]. The ferrocene/ferrocinium (Fc/Fc+) couple is often chosen as the

reference since this is relatively unaffected by environment effects [37]. Absolute

energy level values can be calculated from the electrochemical results using an

appropriate energy for the Fc/Fc+ couple [38].

Using a combination of electrochemical and spectroscopic measurements, MO

calculations and other methods, energy level diagrams, such as the one shown for

benzene in Fig. 1.15, have been obtained for many chemical species. Even for

species where precise measurements are not available, such diagrams illustrate the

theoretical relationship between electrochemical and spectroscopic measurements

and the MOs of the species of interest. Note that, because of the high energy

electron in the LUMO and the electron vacancy in the HOMO, the excited-state is

simultaneously both a better reductant and a better oxidant than the ground-state

by an energy corresponding to the excitation energy.


P. Douglas et al.

Fig. 1.15 Electronic energy levels of singlet and triplet states of benzene, with ‘‘absolute’’

values relative to the vacuum level (the Fermi limit) obtained from photoelectron spectra and

relative values (with reference to the ground state) obtained experimentally from UV/Vis

absorption and photoluminescence spectra. The absolute values are based on Koopmans’ theorem

[41], that the energy of the highest occupied molecular orbital (HOMO) is the first vertical

ionisation energy of a molecule. The energy of the HOMO level is obtained from the vertical

ionisation energy of benzene in Ref. [42] and the energies of the excited states are from Ref. [43].

Assignment of the symmetry of the S2 (1B1u) state is from Ref. [44]

1.7 Molecular Energies: Vibrations and Rotations

The formation of chemical species more complex than atoms introduces two new

types of energy into the system—vibrational and rotational. In the same way that

the moving electron has a wave associated with it, the solutions of which are

obtained by the Schrödinger equation, the moving nuclei in vibrations, and rotations of the whole molecule in space, also have waves associated with them, and

the wavefunctions for these motions can also be obtained using the Schrödinger

wave equation. As in the case of the electron constrained within the atom, the

time-independent solutions for vibrations and rotations allows only certain stable

waves, of fixed, quantised energies, giving rise to discrete vibrational and rotational energy states associated with each electronic energy level. Electronic spectra

of molecules often show features arising from simultaneous electronic, vibrational,

and for gas phase samples, rotational transitions.

The potential energy (PE) of multi-atomic species varies with intermolecular

distances. Fig. 1.16 shows the generic one-dimensional PE curve for a diatomic

molecule. A triatomic molecule would require a two-dimensional surface, and

polyatomics a multi-dimensional surface; but the key features can be illustrated by

reference to the diatomic PE curve. Vibrational energy spacings are in the order of

100–4000 cm-1, much smaller than electronic energy spacings, and transitions

between vibrational levels can be induced by IR and NIR photons. Strong bonds

1 Foundations of Photochemistry


Fig. 1.16 A one-dimensional potential energy curve for a diatomic molecule, indicating possible

electronic, vibrational, vibrational–rotational and rotational transitions

involving hydrogen, e.g. O–H, N–H, C–H, give high energy, high frequency

vibrations (*4000–3000 cm-1), strong/moderate bonds between moderately heavy

atoms, e.g. C–C, C = O, give rise to moderate frequency vibrations (*2000–

1000 cm-1), and bonds between heavy atoms, e.g. metal–ligand; C-halogen; I2;

give low frequency vibrations of a few hundred cm-1. Molecular vibrations are

very important in photochemistry for two main reasons. Firstly, because of the

perturbing effects molecular distortions have on the symmetry of chemical structures, which allow processes that may not, in an otherwise rigidly symmetrical

system, be expected to occur. Secondly, vibrations are a route for rapid deactivation

of energy both internally within the molecule, and externally to the surrounding,

such that in solution and solid phases energy can be transferred from the system of

interest to surrounding molecules within the timescale of molecular vibrations, i.e.

picoseconds (10-12 s) or less. Rotational energy spacings are much smaller than

vibrational energy spacings, in the range *20–200 cm-1, and transitions between

rotational energy levels are caused by microwave photons. Rotational energy is

generally less important in condensed phase photochemistry, since in solution and

solid phases contact with neighbouring molecules dampens or completely stops free

rotation so the energy levels are either not quantised or non-existent.

1.8 Energy Levels in Atoms, Molecules and Crystal


Due to the difference in masses of electrons and nuclei it is possible, and very

convenient, to consider as a very good approximation, the energy of the electron to

be separate from the energy of nuclear motions, i.e. vibrations and rotations.

Furthermore, it is also possible to treat vibrations and rotations separately. Thus,

we can consider the energy of a molecule to be made up of the sum of distinct

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6…Excited-State Energies, Electron Transfer, Oxidation, Reduction, Ionisation and Redox Potentials

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