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Chem 516: Day 20

Computational Chemistry

Goals for today

Understand what people mean when they say “I optimized the structure using B3LYP/6-31G*”

Learn the difference between Hartree-Fock and Density Functional Theory

Know how to read a basis set name and why you care

Basically know enough to be able to learn more on your own

Using O

as an example of molecular orbitals

In freshman chemistry, we all learned how to draw pictures like this: But how to do you tell a computer to do that?

As usual, let’s look at the Hamiltonian

 H = Electron kinetic energy Nuclear kinetic energy Electron-nuclear attraction Electron-electron repulsion Nuclear-nuclear repulsion

Next approximation: MOs are linear

combinations of atomic orbitals (LCAOs)



How do we know what is the best electronic

structure?

 (^) “Variational Principle” says that E(Ψ best ) ≤ E(Ψ trial )  So I can just keep trying different electron configurations until I converge on the best energy I can find. That will be the optimal wavefunction for my molecule  “best subject to all of the approximations I have made”  (^) So our task is to start with some educated guess for the molecular orbitals and occupations, then tweak that guess bit by bit.

Here’s the workflow

Guess initial MOs (coefficients, AOs) Calculate VHF^ for all e-s Calculate E Is the energy difference from the last round ≈0? Change those coefficients a little bit Done! No Yes

Density Functional Theory

Here’s the problem: a molecule like a porphyrin has ~100 electrons. Each has x,y,z coordinates, so that is now 300 variables I need to keep track of.

It’s more efficient to just keep track of the total electron density than to keep track of each individual electron

But now the Hamiltonian isn’t so straightforward: H = T + V + U 11 Kinetic Energy Potential from nuclei e

• -e - interaction energy

Basis Sets



The problem is that you end up needing to

calculate lots of overlap integrals

There’s no analytical equation for this

But there’s not enough electron density at the

nucleus:

The solution is to add up skinny and wide

gaussians

Slater Gaussian 1 Gaussian 2 Gaussian 3 Slater Gaussian 1 Gaussian 2 Gaussian 3 Sum of gaussians

Basis sets can be described as a sum of

gaussians

6-311G

Core electrons are sum of 6 gaussians Valence electrons have more options: c 1 * (^) + c 2 * “split-valence, triple-zeta”

• c 3 *

Polarization functions

Fe Ni H Fe Ni

6-31G

H

6-31G**

d orbs on C,N,etc p orbs on H