Dear Kuilin,
I haven't noticed there is really something special here until
you bring forward this question.
Yes, you're right, Φ=R_nl*Y_lm. But I think that SIESTA
multiply Y_lm by r^l is only a technique solution. Maybe we could do a
little discussion. For a standard Hydrogen atom solution, as you can
see in http://en.wikipedia.org/wiki/Hydrogen_atom,
\psi_{n\ell m}(r,\vartheta,\varphi) = \sqrt {{\left ( \frac{2}{n a_0}
\right )}^3\frac{(n-\ell-1)!}{2n[(n+\ell)!]} } e^{- \rho / 2}
\rho^{\ell} L_{n-\ell-1}^{2\ell+1}(\rho) \cdot Y_{\ell}^{m}(\vartheta,
\varphi ) ,
there is a \rho^{\ell} in radial part, may be this is left in Siesta's
radial part when generating basis but later be added in spherical
part. I'd been taking it for granted that subroutine phiatm should
have no problem, or else the electron density could not be normalized.
I didn't dig much on this r^l issue. Hope someone correct me if I
made mistake here.
note:
1. The equation I put in this mail is in LaTeX format, You can use
latex software or just an online LaTeX equation editor, i.e.
http://www.codecogs.com/latex/eqneditor.php
Best Wishes,
Kuilin, Lu
[email protected]
On 5/22/11, Guangping Zhang <[email protected]> wrote:
>
>
> Thanks for your kind reply. I will check the codes you mentioned.
>
> Another question I want to ask is the atomic orbital we know is the product
> of radial part and spherical harmonics, i.e Φ=R_nl*Y_lm, my question is in
> SIESTA why do we multiply Y_lm by r^l (where l is angular momentum) before
> we multiply the radial part R_nl.
>
> Best
>
> Guangping
>
> 2011-05-22
>
>
>
> Guangping Zhang
>
>
