sisl.GTOrbital

class sisl.GTOrbital

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.

$$\begin{array}{rl}{Y}_l^m(\theta ,\phi )& =(-1{)}^m\sqrt{\frac{2l+1}{4\pi }\frac{(l-m)!}{(l+m)!}}{e}^{im\theta }{P}_l^m(\cos (\phi ))\\ {\varphi }_{lmn}(\mathbf{r})& =R_l(|\mathbf{r}|)Y_l^m(\theta ,\phi )\\ R_l(|\mathbf{r}|)& =\sum c_i{e}^{-{\alpha }_i{r}^2}\end{array}$$

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 ndarray) – 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 ndarray) – 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 $\varphi (\mathbf{r})$ at a given point (or more points)
psi_spher(r, theta, phi[, cos_phi])	Calculate $\varphi (|\mathbf{r}|,\theta ,\varphi )$ 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()

Create an exact copy of this object

Parameters:

orbital (_ExponentialOrbital)

Return type:

_ExponentialOrbital

equal(other, psi=False, radial=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 (bool) – also compare that the full psi are the same

• radial (bool) – also compare that the radial parts are the same

name(tex=False)

Return a named specification of the orbital (tag)

psi(r)

Calculate $\varphi (\mathbf{r})$ at a given point (or more points)

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

Parameters:

r (ndarray) – the vector from the orbital origin

Returns:

basis function value at point r

Return type:

numpy.ndarray

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

Calculate $\varphi (|\mathbf{r}|,\theta ,\varphi )$ at a given point (in spherical coordinates)

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

Parameters:

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

• theta (ndarray) – azimuthal angle in the $xy$ plane (from $x$)

• phi (ndarray) – polar angle from $z$ axis

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

Returns:

basis function value at point r

Return type:

numpy.ndarray

radial(r, *args, **kwargs)

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

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

Parameters:

• r (ndarray) – radius from the orbital origin

• *args – arguments passed to the radial function

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

Returns:

radial orbital value at point r

Return type:

numpy.ndarray

scale(scale)

Scale the orbital by extending R by scale

Parameters:

• orbital (Orbital)

• scale (float)

Return type:

Orbital

spher(theta, phi, cos_phi=False)

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

Parameters:

• theta (ndarray) – azimuthal angle in the $xy$ plane (from $x$)

• phi (ndarray) – polar angle from $z$ axis

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

Returns:

spherical harmonics at angles $\theta$ and $\varphi$

Return type:

numpy.ndarray

toGrid(precision=0.05, c=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 with a radius equal to the radius of this orbital

Return type:

Sphere

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