Chemistry 6440 / 7440

1. Chemistry 6440 / 7440 Potential Energy Surfaces

2. Model Potential Energy Surface

3. Potential Energy Surfaces • Many aspects of chemistry can be reduced to questions about potential energy surfaces (PES) • A PES displays the energy of a molecule as a function of its geometry • Energy is plotted on the vertical axis, geometric coordinates (e.g bond lengths, valence angles, etc.) are plotted on the horizontal axes • A PES can be thought of it as a hilly landscape, with valleys, mountain passes and peaks • Real PES have many dimensions, but key feature can be represented by a 3 dimensional PES

4. Equilibrium molecular structures correspond to the positions of the minima in the valleys on a PES • Energetics of reactions can be calculated from the energies or altitudes of the minima for reactants and products • A reaction path connects reactants and products through a mountain pass • A transition structure is the highest point on the lowest energy path • Reaction rates can be obtained from the height and profile of the potential energy surface around the transition structure

5. The shape of the valley around a minimum determines the vibrational spectrum • Each electronic state of a molecule has a separate potential energy surface, and the separation between these surfaces yields the electronic spectrum • Properties of molecules such as dipole moment, polarizability, NMR shielding, etc. depend on the response of the energy to applied electric and magnetic fields

6. Potential Energy Surfaces and the Born-Oppenheimer Approximation • A PES associates an energy with each geometry of a molecule • Quantum mechanics can be used to calculate the energy as a function of the positions of the nuclei • This assumes that the electronic distribution of the molecule adjusts quickly to any movement of the nuclei • This corresponds to invoking the Born-Oppenheimer approximation in the solution of the Schrödinger equation for a molecular system • Except when potential energy surfaces for different states get too close to each other or cross, the Born-Oppenheimer approximation is usually quite good • Thus a PES arises as a natural consequence of the Born-Oppenheimer approximation

7. PES and Molecular Dynamics • A molecule in motion can be visualized as a ball rolling on a potential energy surface • Dynamics of a molecule can be treated either classically or quantum mechanically • Small amplitude motions correspond to molecular vibrations (treated quantum mechanically) • Large amplitude motions can lead to reactions (treated by classical trajectory calculations) • Statistical mechanics connects the dynamics of an individual molecule with the behavior of macroscopic samples

8. PES Summary • The concept of potential energy surfaces is central to computational chemistry • The structure, energetics, properties, reactivity, spectra and dynamics of molecules can be readily understood in terms of potential energy surfaces • Except in very simple cases, the potential energy surface cannot be obtained from experiment • The field of computational chemistry has developed a wide array of methods for exploring potential energy surface • The challenge for computational chemistry is to explore potential energy surfaces with methods that are efficient and accurate enough to describe the chemistry of interest

9. Asking the Right Questions • molecular modeling can answer some questions easier than others • stability and reactivity are not precise concepts • need to give a specific reaction • similar difficulties with other general concepts: • resonance • nucleophilicity • leaving group ability • VSEPR • etc.

10. Asking the Right Questions • phrase questions in terms of energy differences, energy derivatives, geometries, electron distributions • trends easier than absolute numbers • gas phase much easier than solution • structure and electron distribution easier than energetics • vibrational spectra and NMR easier than electronic spectra • bond energies, IP, EA, activation energies are hard (PA not quite as hard) • excited states much harder than ground states • solvation by polarizable continuum models (very hard by dynamics)