# [Pw_forum] problems on spin polarized lowdin charges

Y.M.Qian yuminqian at gmail.com
Tue Nov 24 06:05:38 CET 2009

```Dear PWSCF user

Recently  I am doing calculation to get the magnetic moment of each atom of a given crystal SrCrO3 . I follow the steps of previous mail about " Magnetic moment on each atom " .
1 SCF
2 nscf
3 projwfc

and get the information from the output file

Lowdin Charges:
Atom #   1: total charge =   9.5544, s =  1.9621, p =  6.3724, d =  1.2199,
spin up      =   4.7911, s =  0.9832, p =  3.1883, d =  0.6196,
spin down    =   4.7633, s =  0.9789, p =  3.1841, d =  0.6003,
polarization =   0.0277, s =  0.0043, p =  0.0042, d =  0.0192,
Atom #   2: total charge =  13.4411, s =  2.1863, p =  6.8075, d =  4.4473,
spin up      =   7.6579, s =  1.0967, p =  3.4108, d =  3.1504,
spin down    =   5.7832, s =  1.0896, p =  3.3967, d =  1.2968,
polarization =   1.8748, s =  0.0070, p =  0.0141, d =  1.8536,
Atom #   3: total charge =   6.3147, s =  1.5461, p =  4.7686, d =  0.0000,
spin up      =   3.1680, s =  0.7732, p =  2.3948, d =  0.0000,
spin down    =   3.1466, s =  0.7729, p =  2.3738, d =  0.0000,
polarization =   0.0214, s =  0.0003, p =  0.0210, d =  0.0000,
Atom #   4: total charge =   6.3147, s =  1.5461, p =  4.7686, d =  0.0000,
spin up      =   3.1680, s =  0.7732, p =  2.3948, d =  0.0000,
spin down    =   3.1466, s =  0.7729, p =  2.3738, d =  0.0000,
polarization =   0.0214, s =  0.0003, p =  0.0210, d =  0.0000,
Atom #   5: total charge =   6.3147, s =  1.5461, p =  4.7686, d =  0.0000,
spin up      =   3.1680, s =  0.7732, p =  2.3948, d =  0.0000,
spin down    =   3.1466, s =  0.7729, p =  2.3738, d =  0.0000,
polarization =   0.0214, s =  0.0003, p =  0.0210, d =  0.0000,
Spilling Parameter:   0.0014

The second atom is transition metal Cr , large magnetic moment appears . But according to the
chemical composition of the compound SrCrO3 , there should be two electrons that occupy the
d orbitals . But here  the results shows there are 4.4473 electrons that occupy d orbitals .
1   Why is  so large number of electrons that occupy d orbitals ? Is there any one know how to explain this discrepancy ?

I also read the tips from Frequently Asked Questions (FAQ) and the correspond reference Sanchez-Portal et al., Sol. State Commun. 95, 685 (1995).

Though absolute number of  charge that projected to the d orbitals lack clear physical meaning ,currently  , but the absolute value of difference of spin-up and spin-down charge have clear physical meaning : magnetic moment .  So if the charge on atoms can't be calcualted accurately
2 how to determine the magnetic moment accurately?