Transcript Chemistry 6440 / 7440 - Department of Chemistry, Wayne

Chemistry 6440 / 7440
Potential Energy Surfaces
Model Potential Energy Surface
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
• 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
• 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
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 BornOppenheimer approximation
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
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
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.
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)