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.
Return type:: int

baseOrbital()¶

Returns:: The confined orbital used for generating the polarization orbital.
Return type:: ConfinedOrbital

uniqueString()¶: Return a unique string representing the state of the object.

Usage Examples¶

Define a BasisSet for hydrogen:

hydrogen_1s = ConfinedOrbital(
    principal_quantum_number=1,
    angular_momentum=0,
    radial_cutoff_radius=5.28603678847*Bohr,
    confinement_start_radius=0.8 * 5.28603678847*Bohr,
    additional_charge=0.0,
    confinement_strength=20.000*Hartree*Bohr,
    radial_step_size=0.001*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.