It is impossible to calculate coefficient of an atom in an orbital, because in practical calculation, each atom carries multiple basis functions, each of which corresponds to a coefficient. You can only say composition of an atom in an orbital. To calculate this information, see Section 4.8 of Multiwfn manual for example.If you just need coefficients of basis functions in specific orbital, you should use a file containing basis function information as input file (such as fch/molden/mwfn, see Section 2.5 of manual), then enter main function 6, select subfunction 4 and then input the orbital index.
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