Lecture 2: Hartree Fock Flashcards
What are operators (functions)?
They act upon the wave function and return observable properties of the system
What is H in the Schrödinger equation?
Hamiltonian operator
What is E in the Schrödinger equation?
The system energy
What is the Hamiltonian operators made up of?
The sum of:
-electrons KE
-Nuclei KE
-electron-nuclei PE
-electron-electron PE
-nuclei-nuclei PE
- other terms
What can the Hamiltonian operator be solved mathematically for?
A hydrogen atom (1 proton, 1 electron)
H2+ molecule (2 protons, 1 electron)
Why do we approximate the Hamiltonian operator for larger systems?
Because we can’t solve it mathematically
What does orthonormal mean?
The unit vectors are perpendicular to each other
What does linear combination of atomic orbitals mean?
The bond orbitals are a sum of atomic orbital contributions
“Schrödinger atom”
What are the two spins?
Alpha=+ ℏ/2 (up)
beta= -ℏ/2 (down)
What is the Pauli exclusion principle?
No two electrons can have the same set of quantum numbers
How many electrons does each spatial MO hold?
Two electrons
For a system of 2N electrons how many MOs will there be?
N
What can a wave function be split into?
The spatial and spin parts
What is the Hartree product made up of?
The products of one-electron eigenfunctions
In Hartree Fock, what are nuclei treated as?
Stationary points
In Hartree Fock theory, what are electrons treated as?
Wave functions
In Hartree Fock theory, what do you do to the electrons?
Integrate them over all space which accounts for interaction of electrons in an average way as a field
How is the Hartree Fock Hamiltonian different to regular Hamiltonian?
-only considers electronic parts
-discards nucleus motion
-nucleus-nucleus interaction is constant
What does the first integral for Hartree Fock represent?
Electron kinetic energy and interaction with nucleus
What does the second integral for Hartree Fock represent?
What is it a combination of?
Electron-electron interactions
Combo of coulomb integral and exchange integral
In Hartree Fock second integral, what is the coulomb integral?
The potential energy of electron i due to charge density or electron j
(Two electrons in same bonding orbital)
In Hartree Fock second integral, what is the exchange integral?
Potential energy of electron i due to the non-indistinguishable nature of electron j
(2 Electrons in separate bonding orbitals)
How do we use HF in comp chem?
-For each electron, treat rest as an average field (self consistent field theory)
-It’s an iterative procedure until it is converged
Limitations of Hartree Fock
-Ignores all electron correlation due to 1-electron nature
-the accuracy of the HF is completely dependent on the basis set- how do we choose the right one?
-there’s lots of 2 electron/4 electron integrals
What is a good analogy for HF?
-An orchestra all guessing the note R to play
-they all play their best guess, the sound is averaged, and then played back to them
-the musicians then adjust the note they play to be closer to the averaged note
-this continues until they converge to the same note
