1. PURPOSE OF THE EXPERIMENT This project will further your exposure to PC-Spartan for modeling molecular properties. In particular, you will investigate the electronic structure of polyenes and porphyrins and will learn how to use results of molecular orbital calculations to predict the (qualitative) spectroscopic properties of molecules. 2. A(nother) BRIEF TOUR OF COMPUTATIONAL CHEMISTRY METHODS It is now possible to predict the structure and reactivity of small and large molecules with computers. Computational chemists often work very closely with experimental chemists to develop better theoretical tools with better predictive power. The synergy between theory and experiment is very important: it is often the case that a computer model may explain a puzzling experimental result. In the pharmaceutical industry, computational chemists are often asked to predict the structural features that lead to an efficient drug by considering the nature of a receptor site. Then, organic chemists synthesize the proposed molecules, which are in turn tested by biochemists for efficiency. The process is often iterative, with experimental results feeding back into the calculations, which in turn generate new proposals for efficient molecules, and so on. As a result, computer-aided molecular modeling is a tool with which every well-educated chemist should be acquainted. Molecular models are mathematical entities generated via the application of the laws of physics to chemical systems. The chemist is often asked to choose between classical and quantum mechanical models. Molecular mechanics and molecular dynamics methods use Newtonian mechanics. The molecule is seen as a collection of hard spheres (the nuclei) connected by flexible springs (the chemical bonds). Electrons are not taken into account explicitly and, as a result, thermochemical properties such as the heat of formation, ∆Hfo, cannot be calculated. The preferred structure of a molecule is obtained by minimizing the so-called steric energy, which is a measure of steric repulsion between spheres or between springs. Therefore, these classical models are only useful for comparing conformational isomers of a given molecule. Molecular mechanics and dynamics are very fast methods that use minimal computer resources. They are still viable tools for the study of very large molecules such as proteins and nucleic acids. Quantum mechanical models are generated via semi-empirical or ab initio methods. They solve the Schrödinger equation for the entire molecule by making different approximations. Semi-empirical methods (such as the AM1 and AM1-SM2 methods) make use of experimental data to characterize mathematically atoms of MOLECULAR ORBITAL CALCULATIONS OFPORPHRINS AND METALLOPORPHRINSMolecu1ar orbital calculations page 2 different elements. The results are reliable to the extent that these parameters do not change from molecule to molecule and to the extent that the experimental data are reliable. Ab initio methods do not depend on empirical parameters. Much of the work in developing these methods comes from developing appropriate mathematical forms for the atomic orbitals of different elements. The goal is to generate molecular structures that agree with experiment. Because the electronic structure of the compound is calculated explicitly, quantum mechanical methods lead to reasonable predictions of structure and thermochemical properties. Semi-empirical methods are a bit less accurate than but are faster than ab initio methods. When used judiciously, semi-empirical methods (e.g., AM1) can give great insight into structure and reactivity of even moderately large molecules. Furthermore, there exist good semi-empirical methods (e.g., AM1-SM2) for the simulation of solvent effects on structure and reactivity. We will use the AM1 and AM1-SM2 semi-empirical methods and (occasionally) the 3-21G ab initio method in this course because they are relatively fast and versatile. Chemists and computer scientists are constantly working on new molecular modeling methods. For example, hybrid methods that take advantage of the best features of classical and quantum mechanical methods are currently being developed to increase the accuracy and speed of simulations of large molecules such as proteins. At the same time, computers are getting faster and better. There are already prototype virtual reality systems that allow chemists to manipulate (literally) molecules in a three-dimensional virtual molecular environment. Indeed, computational chemistry is a field with a great future! 3. PREDICTING THERMODYNAMIC AND KINETIC PROPERTIES FROM MOLECULAR MODELS Although we will not investigate thermodynamic and kinetic properties in these experiments, it is useful to know how molecular modeling can be used to predict such important reaction parameters as enthalpy changes, equilibrium constants, and rate constants. Semi-empirical methods can calculate the heat of formation of a molecule directly, often in units of kcal/mol. As a result, the enthalpy changes of reactions may also be predicted by subtracting the total enthalpy contribution due to reactants from the total enthalpy contribution due to products. Ab initio methods calculate the total energy: the energy of a hypothetical reaction that forms a molecule from a collection of nuclei and electrons. Total energies are always negative and are expressed in atomic units (a.u.). The conversion factors are: 1 au = 627.5 kcal/mol = 2625 kJ/mol (1) The energy change of a reaction may be calculated as: ∆Ereaction = Eproduct1 + Eproduct2 + …….. – Ereactant1 – Ereactant2 - …….. (2) It is also possible to estimate the equilibrium constant, K, of reactions according to the following procedures. First, we express K in terms of the standard free energy change ∆Greaction: K = exp (-∆Greaction/RT) (3)Molecu1ar orbital calculations page 3 where R is the gas constant and T is the absolute temperature. At room temperature (298 K) and for ∆Greaction in a.u., we have: K = exp (-1060 ∆Greaction) (4) In turn, ∆Greaction is given by: ∆Greaction = ∆Hreaction - T∆Sreaction (5) For reactions where the change in entropy may be neglected and where ∆Hreaction ≈ ∆Ereaction, we can write:1 K = exp (-1060 ∆Ereaction) (6) Total energies may be used to calculate energies of activation of reactions: ∆E‡ = Etransition