SlaterOrbital¶
- class SlaterOrbital(principal_quantum_number, angular_momentum, slater_coefficients, weights)¶
Constructor for the Slater orbitals.
- Parameters:
principal_quantum_number (positive int) – The Principal quantum number (n) of the orbital.
angular_momentum (non-negative int) – The Azimuthal quantum number (l) of the orbital.
slater_coefficients (PhysicalQuantity of type inverse length) – The Slater coefficients as inverse length. Maximum two coefficients can be given. Every entry must be positive.
weights (
numpy.array
) – The weight for each of the Slater coefficients. Each entry should be positive.
- angularMomentum()¶
- Returns:
The angular momentum for the orbital.
- Return type:
int
- principalQuantumNumber()¶
- Returns:
The principal quantum number n for the orbital.
- Return type:
int
- slaterCoefficients()¶
- Returns:
The Slater coefficients as inverse length.
- Return type:
list of PhysicalQuantity of type inverse length
Usage Examples¶
Define a 1s SlaterOrbital 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 SlaterOrbital 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 [1], the electronic structure is expanded in a basis formed by a linear combination of atomic orbitals (LCAO)
where \(Y_{lm}\) is a spherical harmonic and \(R_{nl}\) is a Slater orbital
The SlaterOrbital 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.
Symbol |
SlaterOrbital parameters |
---|---|
\(n\) |
|
\(l\) |
|
\(\eta\) |
|
\(C\) |
|
In the current version QuantumATK comes with built-in Hoffmann and Müller parameter sets which are appropriate for organic molecules, and Cerda parameters [2] which are appropriate for crystals. The parameter set are available with the keyword HoffmannHuckelParameters.ElementName
, MullerHuckelParameters.ElementName
and CerdaHuckelParameters.ElementName
, where ElementName
is the name of the element.
Reference¶