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Log Mesh of PAO
Date: 2009/11/18 02:28
Name: Liao Chen   <>

Dear Prof.T.Ozaki and OPENMX users,

I find that the pseudo-atomic basis functions are generated on Log-mesh,
which has form r(i)=exp(xmin + i*dx), and that xmin are -7 for all elements
while dx and number of mesh grids are different for each elements.

I wonder:
1. why xmin are taken as -7?
2. how to determine dx and number of mesh grids for each element.

Another Question:

As far as I know, evaluating two-centre integral in reciprocal space needs to
calculate spherical Bessel transform(SBT):

g(k) = int r**2 jl(r) f(r) dr

I performed SBT using Method proposed by Talman, which calculates SBT
on log mesh kappa = ln(k) and the array of values returned also on log mesh:

k(i) = exp(kappa_min + i * dkappa);

Constraints are dkappa = dx. How to choose kappa_min in order to continue calculation
using values of SBT accurately? I think it should be not too large or too small.

Hope for your advice.

Sincerely, Liao Chen
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Re: Log Mesh of PAO ( No.1 )
Date: 2009/12/01 13:19
Name: Masayuki Toyoda  <>


As for the latter question, I can give you some infomation.

I'm working on computation of two-electron integrals and also having
difficulities in finding optimum parameters for SBT.
Basically, I choose parameters simply by trial and error.
Note that errors can be estimated by performinig direct and inverse SBT.

From my experience, when using N=1024 points, rho0 = kappa0 = -10
(where r[i]=exp(rho0+drho*i) and k[j]=exp(kappa0+dkappa*j)) seems to
yield good results.

My articles are posted on the following page, a part of which relates
to this issue and I hope helps you:

Best regards,

Masayuki Toyoda

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