Dynamics During Spectroscopic Transitions

In order to understand the dynamics of spectroscopic transitions, it is convenient to review the elementary principles of quantum theory. The treatment that follows differs therefore somewhat in point of view from the one usually presented in a first course in quantum mechanics for chemists. A very straightforward, elegant, and detailed exposition of this material may be found in the book by Fano and Fano [1], as well as in other quantum mechanics textbooks.

Spectroscopy is the study of resonant, reversible exchanges of energy between chromophores (atoms, ions, and molecules) and an oscillating electromagnetic field. In Chap. 2, a theoretical description of the chromophores was presented. The purpose of this chapter is to provide a description of the electromagnetic field. The theoretical description of the chromophores, although elementary and incomplete, adhered strictly to the principles of the theory believed to be rigorously correct for such systems — namely, quantum mechanics. By way of contrast, it is proposed to describe the radiation field in accordance with classical electromagnetic theory, which is known to be only an approximation to the correct theory, with a limited range of validity. A thorough exposition of the classical theory may be found in many standard textbooks (e.g., the one by Stratton [1]).

In Chap. 1 it was stated that atoms, ions, molecules and other quantum systems can absorb and emit electromagnetic radiation. Quantum-mechanical methods for calculating the properties of quantum systems were described in Chap. 2. In Chap. 3 it was explained that the most important method for the exchange of energy between radiation and matter is the exertion of torques by the uniform fields of the former upon the dipole moments of the latter. The purpose of this chapter is to link together the material presented in the first three chapters to produce a unified picture of spectroscopic transitions. Because the dipole moments will be calculated by means of quantum mechanics and the radiation fields by means of classical electromagnetic theory, the resultant description of the interaction process is called the semiclassical (or sometimes neoclassical) theory of quantum transitions [1].

The quantum systems that interact with light waves in spectroscopic experiments have been treated in preceding chapters as if these systems were to be studied one at a time. In practice, however, one ordinarily deals with macroscopic samples of matter, each of which consists of very large numbers (≅ 10²⁰) of microscopic chromophores. Statistical methods must be used in such cases to predict the behavior of the sample, and it is the purpose of this chapter to develop appropriate techniques.

A dissipative system is a system in which energy is dissipated. In the present Chapter our major concern will be focused around this concept. Although we will describe and emphasize concrete applications we will also occupy ourselves with a general view of the fundamental dilemma usually phrased as “why and how does there exist a unique privileged direction of time” and further the immediate consequences for scenarios related to the question of reductionism versus holism. In this context it is also appropriate to discuss the hierarchical character of subdynamics, timescales, entanglement in quantum mechanics, EPR correlations, nonlinear dynamics in non-equilibrium situations, reduced density matrices of complex systems etc.

We will now proceed to discuss some recent applications of the present description of quantum correlation effects of disordered condensed matter using the theoretical development in the previous Chapter, i.e. in terms of coherent dissipative structures. The present view-point has led to the study of resonances in quantum chemistry, e.g. in atomic, molecular and solid state theory but recent emphasis on collective non-linear effects has produced many new surprising and unexpected applications to physical chemistry and the physics of disordered condensed matter. Predictions and theoretical interpretations have been made, see below, and to recapitulate the situation we will start by stressing the following fundamental points:

The spinning charged particle having an angular momentum quantum number of 1/2 was introduced in Chap. 4 to illustrate the quantum-mechanical nature of spectroscopic transitions. This system is particularly suitable for such a purpose because the component of the transition dipole moment in any direction in space can be made an eigenvalue property by choosing an appropriate state. In Chap. 1 it was noted that the ideas presented in this book were historically first discovered and applied in the study of such systems. For these reasons, and because of the remarkable simplicity of the quantum-mechanical calculations in this case, the first detailed application of material developed in the first five chapters will be made to quantum transitions of spin−1/2 particles in a magnetic field (magnetic resonance spectroscopy). Chapter 4 was devoted to magnetic resonance in molecular beams, so that the quantum systems could be studied one at a time. By way of contrast, in this chapter the emphasis will be placed on spin−1/2 particles in bulk samples, and the statistical methods introduced in Chap. 5 must be employed.

An electron possesses a spin of magnitude \( (\sqrt 3/2) \) ħ, just like a proton. Associated with this is a magnetic moment μ _e that is conventionally written as , where S is the operator for the electron spin. As the minus sign shows, μ _e points in the opposite direction as the spin, owing to the negative charge of the electron. The strength of the magnetic moment, which is about 658 times that of a proton, is expressed in terms of the Bohr magneton β of the electron, β = 9.27 × 10⁻²⁶ J/Gauss, and a number g. This so-called g-factor amounts to 2.0023 for a free electron. If the electron is confined in an organic molecule containing no transition elements, g is only slightly higher or lower, usually by much less than one percent. Its value is characteristic for its surroundings. (Actually, g is a tensor, but in liquid solution rapid molecular motions average out all anisotropy effects.)

The promises made in Chaps. 4 and 5 will be fulfilled in this chapter. In the earlier chapters assertions were made about the dynamics of the interactions between matter and radiation that lead to spectroscopic transitions. These assertions were proved for the cases of nuclear and electron magnetic resonance in Chap. 8. The theory used in the magnetic resonance case will now be generalized to cover rotational, vibrational, and electronic transitions. Relaxation processes applicable to microwave, infra-red, and optical spectroscopy will be discussed, as will the optical analogs of coherent transient effects first observed in nuclear magnetic resonance. The first step will be to establish the applicability of the gyroscopic model of the interaction process to electric dipole transitions.

In Chapter 11 a general theory of four-wave mixing (FWM) and the third order nonlinear susceptibility χ(3) was developed. In this Chapter the basics and applications for a special case of a FWM process the so-called transient grating (TG) or forced light scattering will be considered. This method has found wide-spread use in nonlinear laser spectroscopy and serves as an example for the versatility and the detailed understanding a specific technique allows in the study of light-matter interactions and material dynamics A more thorough and exhaustive treatment of this subject can be found in the monograph by Eichler, Günter and Pohl [1].

The last chapter of a textbook normally is not the easiest one hut, hopefully, you will find this one easy. Synchrotron radiation (SR) is a strongly recommendable light source but, unfortunately, you cannot find a description of it in most standard textbooks. In the following chapter, therefore, experimental and technical designs will also be presented; if you are going to use SR as your light source you should be able to understand what the machine operators are doing with that light source.