[Wien] Query Regarding f-Orbital Density Matrix Representation in DFT+U Calculations

Peter Blaha peter.blaha at tuwien.ac.at
Thu Jul 2 16:44:36 CEST 2026


The density matrices are given in the basis of complex spherical 
harmonics, running from m=-l ... l


Am 02.07.2026 um 12:47 schrieb Roopam Pandey:
> Dear All,
> 
> I am working on PrAlGe, which crystallizes in a body-centered tetragonal 
> structure. I intend to perform DFT+U calculations to explore possible 
> local and global energy minima by  manipulating case.dmatup/dn files to 
> initialize different occupations of the Pr 4f states.
> 
> While I understand that, for f orbitals, these files contain a 7 × 7 
> complex density matrix, I am unsure about the ordering of the basis 
> functions. Specifically:
> 
> 1. I would like to know whether the rows and columns correspond directly 
> to the spherical harmonic basis |(l,m)>, i.e., ((3,-3), (3,-2), ..., 
> (3,3)), or whether they are expressed in terms of real-spherical 
> harmonic such as (f_{xyz}), (f_{z^3}), etc. If yes for real- 
> sphercial harmonics, what will be the order of the f-orbitals?
> 
> 2. Additionally, is there a way to have the code write the |case.dmatup/ 
> dn| files explicitly in the (Y_{lm}) (spherical harmonic) basis instead 
> of the default representation?
> 
> I would greatly appreciate any clarification or suggestions.
> 
> 
> 
> 
> 
> 
> 
> /Thanks & Regards//,/
> /Roopam Pandey/
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> /"A fool thinks himself to be wise, but a wise man knows himself to be a 
> fool"/
> 
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Peter Blaha,  Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna
Email: peter.blaha at tuwien.ac.at
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