Pseudopotentials

Javier Junquera

CORE

VALENCE CORE

localized around the nuclei

Atomic Si

Atomic Si localized around the nuclei

Core electrons…

highly localized

very depth energy

… are chemically inert

All electron calculation for an isolated N atom

Core charge density Valence charge density

All electron calculation for an isolated N atom

Core charge density Valence charge density

All electron calculation for an isolated N atom

Core charge density Valence charge density

Although there are drastic modifications in the valence charge density

The core charge density remains

unperturbed Peak due to the 2s all-electron orbitals of N,

(they have a node to be ortogonal with the 1s)

Valence wave functions must be orthogonal

to the core wave functions

Atomic Si Core electrons…

highly localized

very depth energy

… are chemically inert

Fourier expansion of a valence wave function has a great contribution of short-wave length

To get a good approximation we would have to use a large number of plane waves.

Pseudopotential idea:

Core electrons are chemically inert

(only valence electrons involved in bonding)

Core electrons make the calculation more expensive more electrons to deal with

orthogonality with valence ? poor convergence in PW Core electrons main effect: screen nuclear potential

Idea:

Ignore the dynamics of the core electrons (freeze them) And replace their effects by an effective potential

core region

Idea, eliminate the core electrons by ironing out the nodes

Ab-initio pseudopotential method:

fit the valence properties calculated from the atom