Spectroscopic Methods in Organic Chemistry (eBook)

1.1Theoretical Introduction

1.2Sample Preparation and Measurement of Spectra

1.3Chromophores

1.4Applications of UV/Vis Spectroscopy

1.5Derivative Spectroscopy

1.6Chiroptical Methods

1 UV/Vis Spectroscopy

1.1 Theoretical Introduction

1.1.1 Electromagnetic Waves and Electron Transitions in Molecules

Electromagnetic radiation is characterized by the wavelength λ or the frequency v. These values are connected with each other by the equation:

v · λ = c

where c is the velocity of light (in vacuum ≈ 2.99 ·1010 cm × s–1). A quantum of light with frequency v has the energy

E = hv

Planck’s constant h has the value ≈ 6.63·1034 J·s. The interaction of electromagnetic waves and molecules leads, in the case of absorption of ultraviolet (UV) and visible light (seldom near-infrared [NIR]), to the excitation of electrons, generally valence electrons. Fig. 1.1 illustrates the relevant regions of the electromagnetic spectrum. The region of light visible to the human eye (Vis) is followed below λ = 400 nm by the UV region. Based on the different biological activities, a subdivision is made into UV-A (400-320 nm), UV-B (320-280 nm), and UV-C (280-10 nm). The IR region starts at 750 nm with the NIR. Sunlight consists on average of 44% IR, 52% Vis, and 4% UV-A. The portion of UV-B is in the o/oo range. The terahertz (THz) region (100 μm ≤ λ ≤ 1 mm, 100 cm–1 ≥ ṽ = 1/λ ≥ 10 cm-1, 3 · 1012 Hz ≥ v ≥ 3 × 1011 Hz) is located at the long-wavelength end of the IR. It is followed by the microwave region (1 mm ≤ λ ≤ 30 cm) and the radio wave region (λ ≥ 30 cm). Spectroscopy of molecules is performed in all these wavelength regions. Apart from UV/Vis spectra in Chapter 1, IR spectra (Chapter 2) and in particular nuclear magnetic resonance (NMR) spectra (Chapter 3) are important for the structure determination of organic compounds. NMR is performed in magnetic fields by applying radio waves.

When visible light of a particular spectral color is absorbed, the human eye recognizes the complementary color:

In the past the wavelength was frequently given in Ångström, nowadays nanometer (nm) is usually used (1 nm = 10–9 m = 107 cm). Instead of giving frequencies in s–1, it is customary to quote the wavenumber ṽ in cm–1.

If the energy is based on a quantum or an individual atomic or molecular process, the customary unit is the electron volt (eV). For a mole, i.e., 6.02 x 1023 quanta of light, the energy is given in kJ. Energy and wavenumber are directly proportional to each other. For conversions the following relationships are recommended:

1 eV ≅ 23 kcal·mol–1 = 96.5 kJ·mol–1 ≅ 8,066 cm-1

1,000 cm–1 ≅ 12 kJ·mol–1

1 kJ·mol–1 ≅ 84 cm–1

If light with the appropriate frequency v meets a molecule in the ground state ψ0, it can be absorbed and will raise the molecule to an electronically excited state ψ1. By spontaneous emission or by stimulated emission, caused by the light rays, the system can return to the ground state. The word “can” in these sentences expresses the transition probability of the two radiative processes, absorption and emission (Fig. 1.2).

The connection with the orbitals involved in the electronic transition is shown in Fig. 1.3. Taking Koopmans’ theorem for granted, the energy of the highest occupied molecular orbital (HOMO) corresponds to the negative ionization potential (IP) and the energy of the lowest unoccupied molecular orbital (LUMO) to the negative electron affinity (EA). The orbital energies used here are related to one-electron configurations:

E (LUMO) − E (HOMO) = IP − EA.

According to Fig. 1.3, the following equation applies for the energy difference of the states:

E (S1) − E (S0) = hv = IP − EA − J + 2K.

The difference in energy between LUMO and HOMO is considerably greater than the excitation energy A for the transition from the singlet ground state S0 to the first excited singlet state S1. The difference arises from the different electronic interactions (Coulomb term J, exchange term 2K ).The singlet-triplet splitting in this approximation is 2K. Since K > 0 the lowest triplet state T1 is always below S1. Molecules, which have the same HOMO-LUMO gap, can have quite different excitation energies. The colorless anthracene represents a classical example, it has the same HOMO-LUMO energy difference as the blue azulene. As a further result of the configurational interaction, the HOMO-LUMO transition is not necessarily the lowest transition S0 → S1 (cf. Fig. 1.21, p. 16). Modern density functional theory (DFT) calculations avoid the problem of additional terms for the configuration interaction and quote HOMO and LUMO levels, which correspond to those obtained, for example, from redox potentials determined by cyclic voltammetry. The measured spectrum can be directly compared with the energy of the electron transitions, when time-dependent DFT (TD-DFT) calculations are performed. Some explicit examples will be given in sections 1.3.3 and 1.3.4.

A measure for the transition probability is the oscillator strength f01, a dimensionless quantity which classically represents the fraction of negative charge (electrons) that brings about the transition (by oscillation). The quantum mechanical equivalent of f is the vector of the transition moment M01, which represents the change of the dipole moment during the transition. The dipole strength D01 = |M01|2 is directly proportional to f01. If D01 = |M01| =f01 = 0 then, even if the resonance condition ∆E = hv is fulfilled, no transition is possible. When the f value is small the term forbidden transition is used, if the f value is close to 1 the term allowed transition is used.

For diatomic or linear polyatomic molecules, as with atoms, selection rules for the allowed transitions between two different electronic states can be established based on the rule of the conservation of angular momentum. For other molecules, which constitute the overwhelming majority, these rules result in transition exclusions.

The spin exclusion rule states that the total spin S and the multiplicity M = 2S + 1 may not change during a transition, i.e., singlet states, for example, may undergo transitions to singlet states by absorption or emission, but not to triplet states. M01 can also be zero because of the symmetry of the orbitals (which are described by the wave functions φ0 and φ1 and represent the electronic part of the total wave functions ψ0 and ψ1). This is described as a symmetry exclusion. An easily comprehensible special case occurs for molecules containing a center of symmetry, whose wave functions are either symmetric (g, gerade = even) or antisymmetric (u, ungerade = odd). The symmetry exclusion states in such cases that electronic transitions between orbitals of the same parity are forbidden (parity exclusion, Laporte’s rule):

Movement of nuclei can reduce the symmetry, so that symmetry-forbidden transitions can, in fact, be seen. (An example of a vibrationally allowed transition is the long-wavelength absorption band of benzene; cf. p. 18.)

An important possible cause for the disappearance of the electronic transition moment is the so-called overlap exclusion, a special case of the symmetry exclusion. This takes effect when the two orbitals which are taking part in the electronic transition overlap poorly or not at all. That is quite clearly the case in an intermolecular charge-transfer (CT) transition where the electronic transition takes place from the donor to the acceptor molecule. There are also numerous intramolecular examples of the overlap exclusion (cf. intramolecular charge transfer [ICT] or the n...