SlaterOrbital

	SlaterOrbital
SingleContourIntegralParameters	SlaterKosterTable

Name

SlaterOrbital — Class for representing a Slater orbital.

Synopsis

Namespace: NanoLanguage

SlaterOrbital(
principal_quantum_number,
angular_momentum,
slater_coefficients,
weights
)

Description

Constructor for the Slater orbitals.

SlaterOrbital Arguments

principal_quantum_number

The Principal quantum number (n) of the orbital.

Type: Positive integer.

angular_momentum

The Azimuthal quantum number (l) of the orbital.

Type: Positive integer.

slater_coefficients

The Slater coefficients as inverse length

Type: A single value or array of strictly positive PhysicalQuantity instances with a unit of inverse length, e.g. 0.3*Bohr**(-1) or [0.3, 0.4]*Bohr**(-1).

weights

The weight for each of the Slater coefficients.

Type: A single value or array of strictly positive dimensionless values, with each value corresponding to a given Slater coefficient, e.g. 0.1 or [0.3, 0.5].

SlaterOrbital Methods

A SlaterOrbital object provides the following methods:

angularMomentum(): Return the angular momentum for the orbital.

Usage Examples

Define a 1s Slater orbital from a single exponential function

carbon_2s = SlaterOrbital(
    principal_quantum_number=2,
    angular_momentum=0,
    slater_coefficients=[ 2.0249*1/Bohr ],
    weights=[ 0.76422]
    )

Define a 2p Slater orbital as superposition of two exponential functions

carbon_2p = SlaterOrbital(
    principal_quantum_number=2,
    angular_momentum=1,
    slater_coefficients=[ 1.62412*1/Bohr , 2.17687*1/Bohr ],
    weights=[ 0.27152, 0.73886]
    )

Notes

Within the extended-Hückel Model, the electronic structure is expanded in a basis of local atomic orbitals (LCAO's)

$\displaystyle \phi_{nlm}({\bf r}) = R_{nl}(r) Y_{lm}(\hat{r}),$

where $Y_{lm}$ is a spherical harmonic and $R_{nl}$ is a Slater orbital

$\displaystyle R_{nl}(r) = \frac{r^{n-1}}{\sqrt{(2n)!}} \left[C_1 (2 \eta_1)^{n+\frac{1}{2}} e^{-\eta_1 \, r}+C_2 (2 \eta_2)^{n+\frac{1}{2}} e^{-\eta_2 \, r} \right].$

The Slater orbital is described by the adjustable parameters $\eta_1, \eta_2 , C_1$ , and $C_2$ . These parameters must be defined for each angular shell of valence orbitals for each element.

Table 26: Slater orbital parameters

Symbol	SlaterOrbital parameters
$n$	principal_quantum_number
$l$	angular_momentum
$\eta$	slater_coefficients
$C$	weights

In the current version we provide a Hoffmann parameter set which is appropriate for organic molecules. The parameter set is available with the keyword HoffmannHuckelParameters.ElementName, where ElementName is the name of the element. For crystal parameters, we refer to the website of J. Cerda. and his paper [11].


SingleContourIntegralParameters		SlaterKosterTable