- Slater-type orbital
Slater-type orbitals (STOs) are functions used as
atomic orbital s in thelinear combination of atomic orbitals molecular orbital method . They are named after the physicistJohn C. Slater , who introduced them in 1930 [J.C. Slater, "Atomic Shielding Constants", Phys. Rev. vol. 36, p. 57 (1930)] .STOs have the following radial part:
: R(r) = N r^{n-1} e^{-zeta r},where: "n" is a
natural number that plays the role ofprincipal quantum number , "n" = 1,2,...,: "N" is anormalization constant,: "r" is the distance of the electron from theatomic nucleus , and: zeta is a constant related to the effective charge of the nucleus, the nuclear charge being partly shielded by electrons.The normalization constant is computed from the integral:int_0^infty x^n e^{-alpha x} dx = frac{n!}{alpha^{n+1.Hence :N^2 int_0^infty left(r^{n-1}e^{-zeta r} ight)^2 r^2 dr =1 LongrightarrowN= (2zeta)^n sqrt{frac{2zeta}{(2n)!.
It is common to use the real form of
spherical harmonics depending on the polar coordinates θ and φ as the angular part of the Slater orbital.References
ee also
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