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FFT of atomic orbitals Date: 2014/08/20 08:00 Name: M. Chen   <chen59@uwm.edu> Dear Prof. Dr. T. Ozaki, I have a question regarding *.pao file. I am wandering if one could get coefficients of plane waves from LCAO method as implemented in openmx. Suppose that we already have coefficients of atomic orbitals obtained from the LCAO calculations, the coefficients of plane waves are given by the following: a_{n,k}(G) = sum_{j} c_{n,k}^j 1/sqrt(N) sum_{R} e^{i k R} int e^{i (k+G) r} |phi_{j}(r-R-t)> where |phi_{j}(r-R-t)> represents an atomic orbital. The integral can be obtained from a FFT of the atomic orbital (phase factor has to be taken into account for atoms at different postions). And the FFT can be easily performed with numerical atomic orbitals like those for openmx. However, by inspecting *.pao I found that there are only some numbers for each angular momentum (begin with <pseudo.atomic.orbitals.L= xxx). Why are they not given for each l,m but instead l only? Do you have any better idea for calculating the coefficients of plane waves or calculating the integration as shown above? Thanks a lot. Best regards, M. Chen

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Re: FFT of atomic orbitals ( No.1 ) Date: 2014/08/20 09:25 Name: T. Ozaki Hi, > Why are they not given for each l,m but instead l only? PAO is the product of Rl and Ylm, where R and Y are the radial and real spherical functions, respectively. Thus, we do not need to store R for m. > Do you have any better idea for calculating the coefficients of plane waves > or calculating the integration as shown above? Thanks a lot. The cube files for one-particle wave functions are available. Just performing FFT for the cube data gives us coefficients in the plane wave expansion. Regards, TO

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