Slater-type orbital

In quantum chemistry are Slater -type orbitals ( STOs, according to John C. Slater, who in 1930 introduced ) wave functions in spherical coordinates, which are used in the LCAO approximation as atomic orbitals.

Since the calculations with STOs by the integrals to be solved quickly become very expensive, one often tries each Slater function by using multiple Gaussian type orbitals ( GTOs ) to approach. For example, the minimum basic block STO-3G may be used wherein three GTOs for approximating a STO.

Radial part

With

  • The distance r of the electron from the nucleus
  • The principal quantum number n = 1, 2, ...
  • Shielding constants for the effective nuclear charge
  • A normalization constant N.

The normalization constant is calculated from the normalization of the above mentioned equation:

Using the general integral

To

Angle -dependent part

For the angle-dependent part of the STOs, that is, those that depends on θ and φ, are mostly used spherical harmonic functions, which provide the basis of its zeros for the required nodal surfaces.

Linear combination of atomic orbitals Atomic nucleus Slater determinant
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