# PolarizationOrbital¶

class PolarizationOrbital(base_orbital)

Class for representing the polarization of a confined orbital.

Parameters: base_orbital (ConfinedOrbital) – The confined orbital from which the polarization orbital should be determined.
angularMomentum()
Returns: The angular momentum. int
baseOrbital()
Returns: The confined orbital used for generating the polarization orbital. ConfinedOrbital

## Usage Examples¶

Define a BasisSet for hydrogen:

hydrogen_1s = ConfinedOrbital(
principal_quantum_number=1,
angular_momentum=0,
confinement_strength=20.000*Hartree*Bohr,
)

hydrogen_1s_polarization = PolarizationOrbital(hydrogen_1s)

my_hydrogen_basis = BasisSet(
element=Hydrogen,
orbitals=[hydrogen_1s, hydrogen_1s_polarization],
occupations=[1.0 ,0.0],
pseudopotential=NormConservingPseudoPotential('normconserving/H.LDAPZ.zip'),
)


## Notes¶

The polarization orbital is generated by perturbing the base_orbital ($$\phi_{l}^\text{base}$$ ) by an electric field $$E$$ pointing in the z-direction:

$[\hat{H}_0 + E z] (\phi_{l}^\text{base}+\delta \phi) = \varepsilon_l (\phi_{l}^\text{base}+\delta \phi) .$

The perturbed orbital, $$\delta \phi$$, is calculated by first order perturbation theory and has angular momentum $$l+1$$. The polarization orbital is constructed from $$\delta \phi$$.

Further information about the basis functions can be found in LCAO basis set.