3.014 Materials Laboratory December 2006 Lab Week 4 – Experiment α2 Delocalization: Optical and Electronic Properties of C-based Molecules Instructor: Benjamin Wunsch OBJECTIVES •Review the Linear Combination of Electronic Orbitals (LCAO) model of electronic structure •Measure the optical absorption spectra of several carbon compounds •Evaluate the anisotropic nature of the conductivity of graphite •Make structure-property connections in terms of LCAO theory QUESTIONS At the end of your time working on this module, you should be able to answer the following questions: 1) How is LCAO related to the HOMO-LUMO gap? 2) How does this gap change as a function of molecule size? 3) What connections can be made between the optical and electronic properties of a material and the delocalization of electrons?3.014 Materials Laboratory December 2006 INTRODUCTION The intent of this lab module is to make connections between the LCAO model of electronic structure and measurable physical properties of a broad variety of carbonaceous compounds. We will be using UV-vis spectroscopy to measure the absorption wavelengths of molecules of increasing size and structural complexity. You should observe what happens to the adsorption wavelength as molecular size changes, and relate it to concepts of electron delocalization and LCAO, which are discussed in brief below. To complement these experiments, we will be measuring the conductivity of single crystalline, highly-ordered pyrolytic graphite (HOPG) as a function of crystal orientation. These measurements will again illustrate the connection between the atomic configuration, electronic structure, and physical properties of a material. LCAO Theory: A Brief Review You have seen in lecture that a linear combination of atomic orbitals can be used as a means of approximating the orbitals of larger clusters of atoms. That is to say, the allowable electronic states of a cluster of atoms are determined by combining the wavefunctions of the individual atoms which constitute the cluster. In planar systems, a matrix detailing the interactions of the atoms making up a molecule can be developed, with one matrix element, α, describing the “coulombic integral”, a value measuring the ability of a given atom to attract electron density. For a given atom in a molecule, α is independent of any other atoms in the system [1]. The second matrix element, β, describes the extent to which an electron can be shared between neighboring atoms. In this model, known as the Hückel approach, it is assumed that atoms further away than nearest-neighbor positions do not contribute to this electron sharing. The result, for a compound with only one unique atom, is two Hamiltonians, Hij, such that Hij = α when i = j and Hij = β, when i and j are neighbors. Consider the case of the benzene ring, which is the building block of many of the compounds you will look at in this experiment. In benzene, the six carbon atoms cannot be differentiated from each other, resulting in the expression: H11 = H22 = H33 =H44 = H55 = H66 = α3.014 Materials Laboratory December 2006 H12 = H23 = H34 =H45 = H56 = H61 = β Linear algebra tells us that nonzero solutions to the matrix derived from the above information exist when the determinant of the matrix (shown below) is zero [1]. α - E β 0 0 0 β β α - E β 0 0 0 0 β α - E β 0 0 0 0 β α - E β 0 0 0 0 β α - E β β 0 0 0 β α - E The solution to the determinant (done in Matlab) is x6 – 6x4 + 9x2 – 4, which results in the roots α + 2β, α - 2β, α + β (twice), and α – β (twice). With β > 0 corresponding to a decrease in energy, this explains both the discretized energy levels (and the degeneracy of two of the levels) shown in Figure 1 (below), which is a slide taken from lecture 12. Figure 1: Formation of bonding and anti-bonding π orbitals as derived from Hückel’s approach. Note that the two bonding orbitals α + β and the antibonding α – β appear twice because their roots do in the solution to the determinant. A physical rendition of their corresponding electron densities is shown at right. (From 3.012 Lecture Slides) Rules for filling molecular orbitals dictate that electrons enter orbitals of the lowest available energy. Each of the six carbon atoms in benzene donates 1 electron to the delocalized π orbitals, resulting in the complete filling of the three bonding orbitals with no electrons free to enter the higher-energy antibonding orbitals. In general, the MO of the highest energy that is occupied by electrons is dubbed HOMO (Highest Occupied Image removed due to copyright restrictions.Source: 3.012 Fall 2005 lecture slides.3.014 Materials Laboratory December 2006 Molecular Orbital), and the MO of lowest energy that is empty and available for electrons to be excited into is referred to as LUMO (Lowest Unoccupied Molecular Orbital). You might think of the energy difference between HOMO and LUMO, commonly referred to as the HOMO-LUMO gap, as the molecular equivalent of the band gap in a semiconductor or insulator. What happens to the molecular orbitals as more atoms are introduced to a molecule? Each atom introduced into the system brings with it an additional bonding and anti-bonding orbital, with energies approaching α. Increasing the number of atoms in a molecule therefore reduces the HOMO-LUMO gap. Benzene derivatives are a choice set of systems to illustrate how increases in electron delocalization lead to changes in the HOMO-LUMO gap. As additional benzene rings are added to a system, so too are additional delocalized electrons. In this lab, you will first consider a class of benzene derivatives known as polycyclic aromatic hydrocarbons (PAHs). These consist of edge-sharing benzene rings. Like benzene, they are planar or near-planar molecules (Can you show why, knowing what you do about hybridization?), a structural feature that further helps facilitate the delocalization of electrons within the system, as π-bonds are known to delocalize above and below the plane of the molecule [2]. Simple structures are shown in Table 1; more complex compounds that you will also look at are shown in Table 2. For the compounds shown in Table 2, give some additional consideration to what impact various bonds in each molecule will have on the delocalization of π bonds. Table 1: Simple Polycyclic Aromatic