Dear Peter, Thanks for your reminder.
That's very useful for me. Best Guangping 2011-05-23 Guangping Zhang 发件人: Peter Koval <[email protected]> 发送时间: 2011-05-23 17:33 主 题: Re: Re: Re: Re: Re: Re: [SIESTA-L] reconstruct the wavefunctions 收件人: [email protected] Dear asking person, please, consider also that harmonics must real spherical harmonics. However, in SIESTA, a different convention is used as in the attached paper. I do not know a right reference for this. Best regards, Peter On Mon, May 23, 2011 at 3:56 AM, Guangping Zhang <[email protected]> wrote: Dear Kuilin, I think you are right. I think in siesta, the r^l part is multiplied to the Y_lm not in the radial part. Thank you very much. Best Guangping 2011-05-23 Guangping Zhang 发件人: kuilin lu <[email protected]> 发送时间: 2011-05-22 23:24 主 题: Re: Re: Re: Re: Re: [SIESTA-L] reconstruct the wavefunctions 收件人: [email protected] 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 > > -- Dr. Peter Koval inet: http://sites.google.com/site/kovalpeter/ phone: +34 943 01 8770
