AnalyticalSplit

	AnalyticalSplit
DeviceSlaterKosterCalculator	BasisSet

Name

AnalyticalSplit — Class for representing the analytical split of a confined or polarization orbital.

Synopsis

Namespace: NanoLanguage

AnalyticalSplit(
base_orbitial,
split_norm
)

Description

Constructor for the AnalyticalSplit orbital.

AnalyticalSplit Arguments

base_orbitial

The basis orbital from which this orbital should be split.

Type: ConfinedOrbital | PolarizationOrbital

Default:


          None

split_norm

The input orbital will be split at the radius where the input orbital has this given norm (1-split_norm).

Type: 0.0 < float < 1.0

Default:


          None

AnalyticalSplit Methods

A AnalyticalSplit object provides the following methods:

This object supports cloning. See the section called “Cloning of ATK Python objects”.
angularMomentum(): Return the angular momentum.
baseOrbital(): Return the base orbital used for generating this split orbital.
splitNorm(): Return the split norm.

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*Units.Hartree*Units.Bohr,
    radial_step_size = 0.001*Units.Bohr,
    )

hydrogen_1s_split = AnalyticalSplit(hydrogen_1s, split_norm = 0.40)

my_hydrogen_basis = BasisSet(
   element = Hydrogen,
   orbitals = [hydrogen_1s, hydrogen_1s_split],
   occupations = [0.7 , 0.3],
   pseudopotential = NormConservingPseudoPotential('normconserving/H.LDAPZ.zip'),
   )

Notes

The AnalyticalSplit orbital ( $\phi_{l}^\text{split}$ ) is obtained by constructing an analytical orbital that matches the base_orbital ( $\phi_{l}^\text{base}$ ) smoothly at the radius $r^{\text{split}}$ . The functional form used for the AnalyticalSplit orbital is

$\displaystyle \phi_{l}^\text{split}(r) = \begin{cases} r^l(a_l-b_l r^2) & \text{if} \, \, r<r^{\text{split}} \\ \phi_{l}^\text{base}(r) & \text{if} \, \, r \ge r^{\text{split}} \end{cases}$

The radius $r^{\text{split}}$ is determined by specifying the split_norm( $\Delta N$ ) of the base_orbital, which is defined by

$\displaystyle \Delta N = \int_{r^{\text{split}}}^{r^c} r^2 |\phi_{l}^\text{base}(r)|^2 dr$

Further information about the basis functions can be found in the section called “LCAO basis set”


DeviceSlaterKosterCalculator		BasisSet