1. Potential Energy Surfaces
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)