sisl.GTOrbital

class sisl.GTOrbital(*args, **kwargs)

Bases: _ExponentialOrbital

Gaussian type orbital

The GTOrbital uses contraction factors and coefficients.

The Gaussian type orbital consists of a gaussian radial part and a spherical harmonic part that only depends on angles.

\[\begin{split}Y^m_l(\theta,\varphi) &= (-1)^m\sqrt{\frac{2l+1}{4\pi} \frac{(l-m)!}{(l+m)!}} e^{i m \theta} P^m_l(\cos(\varphi)) \\ \phi_{lmn}(\mathbf r) &= R_l(|\mathbf r|) Y^m_l(\theta, \varphi) \\ R_l(|\mathbf r|) &= \sum c_i e^{-\alpha_i r^2}\end{split}\]

Notes

This class is opted for significant changes based on user feedback. If you use it, please give feedback.

Parameters:

• n (int, optional) – principal quantum number, default to l + 1

• l (int) – azimuthal quantum number

• m (int, optional for l == 0) – magnetic quantum number

• alpha (float or array_like) – coefficients for the exponential (in 1/Ang^2) Generally the coefficients are given in atomic units, so a conversion from online tables is necessary.

• coeff (float or array_like) – contraction factors

• R – See Orbital for details.

• q0 (float, optional) – initial charge

• tag (str, optional) – user defined tag

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)	Calculate \(\phi(\mathbf r)\) at a given point (or more points)
psi_spher(r, theta, phi[, cos_phi])	Calculate \(\phi(|\mathbf r|, \theta, \phi)\) at a given point (in spherical coordinates)
radial(r, *args, **kwargs)	Calculate the radial part of spherical orbital \(R(\mathbf r)\)
scale(scale)	Scale the orbital by extending R by scale
spher(theta, phi[, cos_phi])	Calculate the spherical harmonics of this orbital at a given point (in spherical coordinates)
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
alpha	\(\alpha\) factors
coeff	\(c\) contraction factors
l	\(l\) quantum number
m	\(m\) quantum number
n	\(n\) quantum number
q0	Initial charge
tag	Named tag of orbital

copy() → _ExponentialOrbital

Create an exact copy of this object

equal(other, psi: bool = False, radial: bool = False)

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)

Return a named specification of the orbital (tag)

psi(r)

Calculate \(\phi(\mathbf r)\) at a given point (or more points)

The position r is a vector from the origin of this orbital.

Parameters:

r (array_like) – the vector from the orbital origin

Returns:

numpy.ndarray – basis function value at point r

psi_spher(r, theta, phi, cos_phi: bool = False)

Calculate \(\phi(|\mathbf r|, \theta, \phi)\) at a given point (in spherical coordinates)

This is equivalent to psi however, the input is given in spherical coordinates.

Parameters:

• r (array_like) – the radius from the orbital origin

• theta (array_like) – azimuthal angle in the \(xy\) plane (from \(x\))

• phi (array_like) – polar angle from \(z\) axis

• cos_phi – whether phi is actually \(cos(\phi)\) which will be faster because cos is not necessary to call.

Returns:

numpy.ndarray – basis function value at point r

radial(r, *args, **kwargs) → ndarray

Calculate the radial part of spherical orbital \(R(\mathbf r)\)

The position r is a vector from the origin of this orbital.

Parameters:

• r (array_like) – radius from the orbital origin

• *args – arguments passed to the radial function

• **args – keyword arguments passed to the radial function

Returns:

numpy.ndarray – radial orbital value at point r

scale(scale: float) → Orbital

Scale the orbital by extending R by scale

spher(theta, phi, cos_phi: bool = False)

Calculate the spherical harmonics of this orbital at a given point (in spherical coordinates)

Parameters:

• theta (array_like) – azimuthal angle in the \(xy\) plane (from \(x\))

• phi (array_like) – polar angle from \(z\) axis

• cos_phi – whether phi is actually \(cos(\phi)\) which will be faster because cos is not necessary to call.

Returns:

numpy.ndarray – spherical harmonics at angles \(\theta\) and \(\phi\)

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

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)

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 alpha

\(\alpha\) factors

property coeff

\(c\) contraction factors

property l

\(l\) quantum number

property m

\(m\) quantum number

property n

\(n\) quantum number

property q0

Initial charge

property tag

Named tag of orbital