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Because of their extraordinary sensitivity and speed, optical spectroscopic techniques are well suited for addressing a broad range of questions in molecular and cellular biophysics. Photomultipliers sensitive enough to detect a single photon make it possible to measure the fluorescence fromindividual molecules, and lasers providing light pulses with widths of less than 10 s can be used to probe molecular behavior on the time scale of nuclear motions. Spectroscopic properties such as absorbance, fluorescence, and linear and circular dichroism can report on the identities, concentrations, energies, conformations, or dynamics of molecules and can be sensitive to small changes in molecular structure or surroundings. Resonance energy transfer provides a way to probe intermolecular distances. Because they usually are not destructive, spectrophotometric techniques can be used with samples thatmust be recovered after an experiment. They also can provide analytical methods that avoid the need for radioisotopes or hazardous reagents. When combined with genetic engineering and microscopy, they provide windows to the locations, dynamics, and turnover of particular molecules in living cells.

In this chapter we discuss the basic principles of quantum mechanics that underlie optical spectroscopy. More comprehensive treatments are available in the classic text by Pauling and Wilson (1935), a collection of historical papers edited by van der Waerden (1968), and numerous more recent texts such as those by Szabo and Ostlund (1982), Atkins (1983), Simons and Nichols (1997), Jensen (1999), Levine (2000), and Engel (2006). Atkins (1991) is a useful source of leading references and concise discussions of the main ideas.

In this chapter we consider classical and quantum mechanical descriptions of electromagnetic radiation. We develop expressions for the energy density and irradiance of light passing through a homogeneous medium, and we discuss the Planck black-body radiation law and linear and circular polarization. Readers anxious to get on to the interactions of light with matter may skip ahead to Chap. 4 and return to the present chapter as the need arises.

This chapter begins with a discussion of how the oscillating electric field of light can raise amolecule to an excited electronic state. We then explore the factors that determine the wavelength, strength, linear dichroism, and shapes of molecular absorption bands. Our approach is to treat the molecule quantum mechanically with time-dependent perturbation theory (Chap. 2) but to consider light, the perturbation, as a purely classical oscillating electric field. Because many of the phenomena associated with absorption of light can be explained well by this semiclassical approach, we defer considering the quantum nature of light until Chap. 5. Interactions with the magnetic field of light will be discussed in Chap. 9.

We have seen that light can excite molecules from their ground states to states with higher energies and can stimulate downward transitions from excited states to the ground state. But excited molecules also decay to the ground state even when the light intensity is zero. The extra energy of the excited molecule can be radiated as fluorescence, transferred to another molecule, or dissipated to the surroundings as heat. In this chapter we consider fluorescence.

Excitations of molecules to higher vibrational states typically occur in the mid-IR region of the spectrum, between 200 and 5,000 cm ( = 2.5–50μm). In this chapter we consider the main factors that determine the energies and strengths of vibrational excitations and describe several applications of IR spectroscopy to macromolecules. Chapter 12 discusses Raman spectroscopy, in which vibrational transitions accompany the scattering of light at higher frequencies.

One way that an excited molecule can return to the ground state is to transfer the excitation energy to another molecule. This process, , plays a particularly important role in photosynthetic organisms. Extended arrays of pigment–protein complexes in the membranes of plants and photosynthetic bacteria absorb sunlight and transfer energy to the reaction centers, where the energy is trapped in electron-transfer reactions (van Amerongen et al. 2000; Green and Parson 2003). In other organisms, photolyases, which use the energy of blue light to repair UV damage in DNA, contain a pterin or a deazaflavin that transfers energy efficiently to a flavin radical in the active site (Sancar 2003). A similar antenna has been found in cryptochromes, which appear to play a role in circadian rhythms (Saxena et al. 2005). Because the rate of resonance energy transfer depends on the distance between the energy donor and acceptor, the process also is used experimentally to probe intermolecular distances in biophysical systems (van der Meer et al. 1994). Typical applications are to measure the distance between two proteins in a multienzyme complex or between ligands bound at two sites on a protein, or to examine the rate at which components from two membrane vesicles mingle in a fused vesicle. An inquiry into the mechanism of resonance energy transfer also provides a springboard for discussing other time-dependent processes such as electron transfer.

The Förster theory we considered in the last chapter applies to molecules that are far enough apart so that intermolecular interactions are very weak. Jumping of excitations from one molecule to the other is slow relative to the vibrational relaxation and dephasing that determine the homogeneous widths of the absorption bands, and it has little effect on the absorption spectra of the molecules. If the energy donor and acceptor are distinguishable we could examine the overall absorption or stimulated-emission spectrum of the system and, at least in principle, determine which molecule is excited at any given time. But suppose we move the molecules together so that the time required for energy to hop from one molecule to the other becomes shorter and shorter. At some point, it will be impossible to say which molecule is excited. In this situation, we might expect that resonance between multiple excited states could cause the absorption spectrum of an oligomer to differ from the spectra of the individual molecules, and indeed this turns out to be the case.

In our analysis of how an electromagnetic radiation field interacts with electrons, we have, to this point, considered only the oscillating electric field, (). We set aside possible effects of the magnetic field, (), on the grounds that they usually are much smaller than the effects of the electric field. With this assumption we found that the strength of the absorption band for a transition between two states with wavefunctions and depends on the square of the dot product of with the electric dipole matrix element, . There are, however, cases in which the symmetry of the wavefunctions makes zero, and yet the transition still has a measurable dipole strength. The absorption in these cases sometimes results from quadrupole, octupole, or other small terms that we have neglected in using the dipole operator, but in other cases it can be traced to interactions with the magnetic field. In addition, coupled interactions involving both () and () can cause the dipole strength of a transition to be different for left- and right-circularly polarized light. This is .

The time-dependent perturbation theory that we have used to treat resonance energy transfer and absorption of light assumes that we know that a system is in a given state (state 1), so the coefficient associated with this state () is 1, while the coefficient for finding the system in a different state () is zero. The resulting expression for the rate of transitions to state 2 (Eq. (2.58) or Eq. (7.8)) neglects the possibility of a return to state 1. It can continue to hold at later times only if the transition to state 2 is followed by a relaxation that takes the two states out of resonance.