Chemistry 700. Lectures. Resources. Grant and Richards, Foresman and Frisch, Exploring Chemistry with Electronic Structure Methods (Gaussian Inc., 1996) Cramer, Jensen, Ostlund and Szabo, Modern Quantum Chemistry (McGraw-Hill, 1982). Why is one interested in computational chemistry?.
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Why is one interested in computational chemistry?
• structure and property prediction is of great value.
1sA + 1sB
FCi = iSCi
1. The Hartree-Fock method (HF)
We want to solve the electronic Schrödinger equation:
For this, we need to make some approximations
These will lead to the Hartree-Fock method (which is
the simplest ab initio method)
Decompose Y into a combination of molecular orbitals (MOs)
MO: one-electron wavefunction (fn)
However, this is not a good wavefunction, as
wavefunctions need to be antisymmetric: swapping the
coordinates of two electrons should lead to sign change
The antisymmetry of the wavefunction can be achieved by
constructing the wavefunction as a Slater Determinant:
fi is a “spinorbital”: contains also the spin of the electron
The Hartree-Fock wavefunction consists
of a single Slater Determinant
(This implies that the electron-electron repulsion
is only included as an average effect => the
Hartree-Fock method neglects electron correlation)
LCAO: Linear Combination of Atomic Orbitals
AO or basis function
The MOs fi are written as linear combinations of
pre-defined one-electron functions (basis functions or AOs)
How to obtain the optimal coefficients cmi?
linear combinations of atomic orbitals
“The energy calculated from an approximation to the true
wavefunction will always be greater than the true energy”
So, just find the coefficients cmi that give the lowest energy!
This leads to the Hartree-Fock equations, which can be
solved by the Self-Consistent Field (SCF) method
Approximations leading to the Hartree-Fock method
imposed by using Slater Determinant wavefunctions
The main weakness of Hartree Fock is that it neglects
In HF theory: each electron moves in an average field
of all the other electrons. Instantaneous electron-electron
repulsions are ignored
Electron correlation: correlation between the spatial
positions of electrons due to Coulomb repulsion
- always attractive!
Post-HF methods include electron correlation
(MP2, MP3, MP4,…)
(CCSD, CCSDT, …)