Module 1 : Ab-initio Methods

Lecture 8 : Benchmarking of Geometry Optimization

Nomenclature

C

molecular orbital expansion coefficient

D

Slater determinant of orbitals

E

Energy

Exc[ρ]

exchange correlation energy

E

electronic charge

Fock operator

Kohn-Sham operator

One-electron operator

Two-electron operator

Hamiltonian operator

Jij

Coulomb integral

Coulomb operator

Kij

exchange integral

exchange operator

L

angular momentum

me

mass of electron

N

normalization constant

R

radial location of electron, separation distance

U

spin orbital

V

Potential

Vxc

exchange correlation potential

x, y, z

Coordinates

Z

nuclear charge

Greek symbols


Α

Atom

Ε

orbital energy

Ρ

electron probability density

Σ

Exponent

Δ2 

Laplacian

Φ

basis function, orbital, electrostatic potential

Ψ

wave function