sisl.Orbital

class sisl.Orbital(R: float | dict | None, q0: float = 0.0, tag: str = '')

Bases: object

Base class for orbital information.

The orbital class is still in an experimental stage and will probably evolve over some time.

Parameters:

R – maximum radius of interaction. In case of a dict the values will be passed to the radial_minimize_range method. Currently allowed arguments are:
- contains: R will be selected such that the integrated function func
  will contain this percentage of the full integral (determined at maxR
- maxR: maximum R to search in, default to 100 Ang
- func: the function that will be integrated and checked for contains
See examples for details. If None the default will be {'contains': 0.9999}. If a negative number is passed, it will be converted to {'contains':-R} A dictionary will only make sense if the class has the _radial function associated.
q0 – initial charge
tag – user defined tag

Examples

>>> orb = Orbital(1)
>>> orb_tag = Orbital(2, tag="range=2")
>>> orb.R == orb_tag.R / 2
True
>>> orbq = Orbital(2, 1)
>>> orbq.q0
1.

Optimizing the R range for the radial function integral \(\int\mathrm dr radial(r)^2 r ^2\) >>> R = { … “contains”: 0.9999, … “func”: lambda radial, r: (radial(r) * r)**2, … “maxR”: 100 … } >>> orb = Orbital(R)

The default dictionary if none is passed will be: dict(contains=0.9999, func=lambda radial, r: abs(radial(r)), maxR=100) The optimization problem depends heavily on the func since the tails are important for real-space quantities.

See also

SphericalOrbital: orbitals with a spherical basis set
AtomicOrbital: specification of n, m, l quantum numbers + a spherical basis set
HydrogenicOrbital: simplistic orbital model of Hydrogenic-like basis sets
GTOrbital: Gaussian-type orbitals
STOrbital: Slater-type orbitals

Methods

`copy`()	Create an exact copy of this object
`equal`(other[, psi, radial])	Compare two orbitals by comparing their radius, and possibly the radial and psi functions
`name`([tex])	Return a named specification of the orbital (`tag`)
`psi`(r, args, *kwargs)	Calculate \(\phi(\mathbf r)\) for Cartesian coordinates
`scale`(scale)	Scale the orbital by extending R by `scale`
`toGrid`([precision, c, R, dtype, atom])	Create a Grid with only this orbital wavefunction on it
`toSphere`([center])	Return a sphere with radius equal to the orbital size

Attributes

`R`	Maxmimum radius of orbital
`q0`	Initial charge
`tag`	Named tag of orbital

copy() → Orbital: Create an exact copy of this object

equal(other, psi: bool = False, radial: bool = False)[source]

Compare two orbitals by comparing their radius, and possibly the radial and psi functions

When comparing two orbital radius they are considered equal with a precision of 1e-4 Ang.

Parameters:

other (Orbital) – comparison orbital
psi – also compare that the full psi are the same
radial – also compare that the radial parts are the same

name(tex=False)[source]: Return a named specification of the orbital (tag)

psi(r, *args, **kwargs)[source]: Calculate \(\phi(\mathbf r)\) for Cartesian coordinates

scale(scale: float) → Orbital: Scale the orbital by extending R by scale

toGrid(precision: float = 0.05, c: float = 1.0, R=None, dtype=np.float64, atom=1)[source]

Create a Grid with only this orbital wavefunction on it

Parameters:

precision (float, optional) – used separation in the Grid between voxels (in Ang)
c (float or complex, optional) – coefficient for the orbital
R (float, optional) – box size of the grid (default to the orbital range)
dtype (numpy.dtype, optional) – the used separation in the Grid between voxels
atom (optional) – atom associated with the grid; either an atom instance or something that Atom(atom) would convert to a proper atom.

toSphere(center=None)[source]

Return a sphere with radius equal to the orbital size

Returns:: Sphere – sphere with a radius equal to the radius of this orbital

property R: Maxmimum radius of orbital

property q0: Initial charge

property tag: Named tag of orbital