The measurement and interpretation of electronic spectra of molecules is an interesting and important topic in physical chemistry. The nature of the excited state and the processes of absorption and emission are central ideas in modern spectroscopy. Additionally, the discussion of these concepts uses principles from quantum mechanics, thermodynamics, and kinetics (1-4), and thus encompasses a broad range of physical chemistry.Electronic spectra are interpreted by simple models, semiempirical models, or advanced theoretical principles. Some simple models and all semiempirical models are based on parameterization. It is useful for students to learn that parameters are chosen to fit a given set of experimental data. An experiment that integrates both experimental and theoretical aspects of electronic spectra benefits students by developing connections between experiment and theory. For the past few years, students at La Salle University have been performing an experiment of this nature on a series of conjugated dyes.
The Basic ModelA rigorous approach to explain spectral data may use ab initio methods including configuration interaction. Such methods are usually beyond the scope of a first course in physical chemistry. A rudimentary technique using the particle-in-a-box model that is presented in all physical chemistry texts can be used to rationalize the wavelengths of maximum absorption in conjugated molecules. The model, modified by Kuhn (5), is unrealistic and deals only with the π electrons, but predicts trends reasonably well when applied to a series of similar conjugated cyanine dyes (6, 7).Students can readily understand the model, and it can be used to illustrate the process of parameterization of models to yield improved agreement with experimental data.Each conjugated dye (Fig. 1) is approximated as a onedimensional box of length L. The energy levels of this system are given by E n = h 2 n 2 /8mL 2 where n is the quantum number, m is the electron mass, and h is Planck's constant. Each dye will have, of course, a different value for the length. Since the Pauli principle limits the occupation of a nondegenerate energy level to two electrons, a molecule with N electrons has the N/2 lowest levels filled. The longest wavelength transition is, therefore, from level n l = N/2 to level n u = (N/2) +1. The energy change for this transition isThe wavelength of the transition iswhere c is the speed of light. The nitrogen atoms are assumed to be the walls of the box. The number of π electrons and the length of the polymethine chain in each dye (Fig. 1) are related to the number of double bonds between the nitrogen atoms; thus, the wavelength depends on this quantity. For example, pinacyanol has three double bonds between the two nitrogen atoms and has eight π electrons (six from the double bonds and two from the neutral nitrogen). Kuhn allowed the box to extend one bond length past each nitrogen to indicate that the electrons do not stop abruptly at these atoms. With this approximation, the length of the box is (2k +...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.