## Potential energy surfaces, Model chemistries, Asking the right questions

#### Potential energy surfaces

- Born-Oppenheimer approx. allows us to separate electronic and nuclear
motion
- when nuclei move, the electrons re-adjust quickly
- energy of molecule is a function of the positions of the nuclei
- potential energy surface describes energy of a molecule in terms of
its structure
- Figure from 'Geometry Optimization' article in Encyclopedia of Computational
Chemistry
#### Structure

- determined from the potential energy surface
- minimum corresponds to an equilibrium structure
- first order saddle point corresponds to a transition state for a reaction
- a reaction path is the steepest descent path connecting a transition
state to minima
#### Dynamics

- molecules move on the potential energy surface
- dynamics can be treated classically or quantum mechanically
- small amplitude motions - normal modes of vibration
- large amplitude motions - trajectories, wave packets, reactions
- statistical mechanics to connect microscopic to macroscopic

#### Model chemistries

Schrödinger equation and stat. mech. provide a mathematical model
of chemistry
cannot solve equations exactly, except for trivial problems
need to make approximations
model chemistry - approximate mathematical model
models need to be validated
types of models: molecular mechanics, semi-empirical, ab initio
#### Asking the right questions

molecular modeling can answer some questions easier than others
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)
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.