LSDA+U: diagonal elements of the density matrix are larger than 1.0

[xianghjun]

Dear all,
I calculated a 4f system using LSDA+U. From the OUTCAR, I found that
some diagonal elements of the density matrix are larger than 1.0, which seems very strange. Is the result physically correct? I am wondering if the
Pauli exclusion principle is violated.

=====================================
atom = 1 type = 1 l = 3

onsite density matrix

spin component 1

1.0723 0.0000 0.0126 0.0000 0.0335 0.0000 0.0038
0.0000 1.1053 0.0000 -0.0088 0.0000 -0.0251 0.0000
0.0126 0.0000 1.0741 0.0000 0.0287 0.0000 0.0133
0.0000 -0.0088 0.0000 1.0478 0.0000 0.0062 0.0000
0.0335 0.0000 0.0287 0.0000 1.0835 0.0000 -0.0182
0.0000 -0.0251 0.0000 0.0062 0.0000 1.0532 0.0000
0.0038 0.0000 0.0133 0.0000 -0.0182 0.0000 1.0781

spin component 2

0.0226 0.0000 0.0042 0.0000 0.0086 0.0000 0.0016
0.0000 0.0298 0.0000 -0.0029 0.0000 0.0159 0.0000
0.0042 0.0000 0.0231 0.0000 0.0074 0.0000 0.0035
0.0000 -0.0029 0.0000 0.0167 0.0000 -0.0269 0.0000
0.0086 0.0000 0.0074 0.0000 0.0241 0.0000 -0.0033
0.0000 0.0159 0.0000 -0.0269 0.0000 1.0644 0.0000
0.0016 0.0000 0.0035 0.0000 -0.0033 0.0000 0.0236
=====================================


Thank you very much.

Best,
Hongjun Xiang

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