# AnalyticalSplit¶

class AnalyticalSplit(base_orbital=None, split_norm=None, base_orbitial=None)

Class for representing the analytical split of a confined or polarization orbital,

Parameters: base_orbital (ConfinedOrbital | PolarizationOrbital) – The basis orbital from which this orbital should be split. split_norm (float between 0 and 1) – The input orbital will be split at the radius where the input orbital has this given norm (1 - split_norm). base_orbitial –
angularMomentum()
Returns: The angular momentum. int
baseOrbital()
Returns: The base orbital used for generating this split orbital. ConfinedOrbital | PolarizationOrbital
baseOrbitial()
Returns: The base orbital used for generating this split orbital. ConfinedOrbital | PolarizationOrbital
splitNorm()
Returns: The split norm. float

## 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_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

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

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

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

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