1s Slater-type function

A normalized 1s Slater-type function is a function which is used in the descriptions of atoms and in a broader way in the description of atoms in molecules. It is particularly important as the accurate quantum theory description of the smallest free atom, hydrogen. It has the form

ψ
 
 1
 s
 
 
 (
 ζ
 ,
 
 r
 −
 R
 
 )
 =
 
 
 (
 
 
 
 ζ
 
 3
 
 
 π
 
 
 )
 
 
 
 1
 2
 
 
 
 
 
 e
 
 −
 ζ
 
 |
 
 
 r
 −
 R
 
 
 |
 
 
 
 .
 
 
 {\displaystyle \psi _{1s}(\zeta ,\mathbf {r-R} )=\left({\frac {\zeta ^{3}}{\pi }}\right)^{1 \over 2}\,e^{-\zeta |\mathbf {r-R} |}.}
 
<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a>
It is a particular case of a <a href="/facts/Slater-type_orbital/jPPIkkUQ">Slater-type orbital</a> (STO) in which the <a href="/facts/Principal_quantum_number/8SzSWV6w">principal quantum number</a> n is 1. The parameter 
 
 
 
 ζ
 
 
 {\displaystyle \zeta }
 
 is called the Slater orbital exponent. Related sets of functions can be used to construct <a href="/facts/STO-nG_basis_sets/ezoyYlGC">STO-nG basis sets</a> which are used in <a href="/facts/Quantum_chemistry/H9AXV0lx">quantum chemistry</a>.

1s Slater-type function open-in-new

1s Slater-type function