Thank you the quantum staffs for replying my question.
However, I have three quesitons
1. I still don't understand why the DM for an atom is only a number rather than matrix. Because I think the dimension of the DM should depend on, e.g., the basis sets etc. am i wrong? (Below is three adjacent SCI-loops in a log file. )
2. How to obtain DD?
3. For a nonmagnetic system, if its total electron number is odd, shoud spin-polarized calculation be included in ATK? (like some other plane-wave-based codes do)
+------------------------------------------------------------------------------+
| Density Matrix Report DM DM[D] DD |
+------------------------------------------------------------------------------+
| 0 Cu [ 0.000 , 0.000 , 0.000 ] 5.77870 5.54062 0.31932 |
| 1 Cu [ 1.278 , 0.000 , -2.068 ] 5.68480 5.28859 -0.02661 |
| 2 Cu [ 0.000 , 2.068 , -1.278 ] 5.68480 5.28859 -0.02661 |
| 3 Cu [ 2.068 , 1.278 , 0.000 ] 5.68480 5.28859 -0.02661 |
| 4 Cu [ 2.068 , -1.278 , 0.000 ] 5.68480 5.28859 -0.02661 |
| 5 Cu [ 0.000 , -2.068 , -1.278 ] 5.68480 5.28859 -0.02661 |
| 6 Cu [ -1.278 , 0.000 , -2.068 ] 5.68480 5.28859 -0.02661 |
| 7 Cu [ -2.068 , 1.278 , 0.000 ] 5.68480 5.28859 -0.02661 |
| 8 Cu [ 0.000 , 2.068 , 1.278 ] 5.68480 5.28859 -0.02661 |
| 9 Cu [ 1.278 , 0.000 , 2.068 ] 5.68480 5.28859 -0.02661 |
| 10 Cu [ 0.000 , -2.068 , 1.278 ] 5.68480 5.28859 -0.02661 |
| 11 Cu [ -2.068 , -1.278 , 0.000 ] 5.68480 5.28859 -0.02661 |
| 12 Cu [ -1.278 , 0.000 , 2.068 ] 5.68480 5.28859 -0.02661 |
+------------------------------------------------------------------------------+
| 1 E = -25.4904 dE = 2.719759e+00 dH = 2.467539e-01 |
+------------------------------------------------------------------------------+
|--------------------------------------------------|
Calculating Eigenvalues : ==================================================
Calculating Density Matrix : ==================================================
+------------------------------------------------------------------------------+
| Density Matrix Report DM DM[D] DD |
+------------------------------------------------------------------------------+
| 0 Cu [ 0.000 , 0.000 , 0.000 ] 5.66884 5.36145 0.03028 |
| 1 Cu [ 1.278 , 0.000 , -2.068 ] 5.69131 5.30617 -0.00252 |
| 2 Cu [ 0.000 , 2.068 , -1.278 ] 5.69131 5.30617 -0.00252 |
| 3 Cu [ 2.068 , 1.278 , 0.000 ] 5.69131 5.30617 -0.00252 |
| 4 Cu [ 2.068 , -1.278 , 0.000 ] 5.69131 5.30617 -0.00252 |
| 5 Cu [ 0.000 , -2.068 , -1.278 ] 5.69131 5.30617 -0.00252 |
| 6 Cu [ -1.278 , 0.000 , -2.068 ] 5.69131 5.30617 -0.00252 |
| 7 Cu [ -2.068 , 1.278 , 0.000 ] 5.69131 5.30617 -0.00252 |
| 8 Cu [ 0.000 , 2.068 , 1.278 ] 5.69131 5.30617 -0.00252 |
| 9 Cu [ 1.278 , 0.000 , 2.068 ] 5.69131 5.30617 -0.00252 |
| 10 Cu [ 0.000 , -2.068 , 1.278 ] 5.69131 5.30617 -0.00252 |
| 11 Cu [ -2.068 , -1.278 , 0.000 ] 5.69131 5.30617 -0.00252 |
| 12 Cu [ -1.278 , 0.000 , 2.068 ] 5.69131 5.30617 -0.00252 |
+------------------------------------------------------------------------------+
| 2 E = -28.2305 dE = 2.740125e+00 dH = 1.336710e-01 |
+------------------------------------------------------------------------------+
|--------------------------------------------------|
Calculating Eigenvalues : ==================================================
Calculating Density Matrix : ==================================================
+------------------------------------------------------------------------------+
| Density Matrix Report DM DM[D] DD |
+------------------------------------------------------------------------------+
| 0 Cu [ 0.000 , 0.000 , 0.000 ] 5.59103 5.26557 -0.14340 |
| 1 Cu [ 1.278 , 0.000 , -2.068 ] 5.69673 5.31522 0.01195 |
| 2 Cu [ 0.000 , 2.068 , -1.278 ] 5.69673 5.31522 0.01195 |
| 3 Cu [ 2.068 , 1.278 , 0.000 ] 5.69673 5.31522 0.01195 |
| 4 Cu [ 2.068 , -1.278 , 0.000 ] 5.69673 5.31522 0.01195 |
| 5 Cu [ 0.000 , -2.068 , -1.278 ] 5.69673 5.31522 0.01195 |
| 6 Cu [ -1.278 , 0.000 , -2.068 ] 5.69673 5.31522 0.01195 |
| 7 Cu [ -2.068 , 1.278 , 0.000 ] 5.69673 5.31522 0.01195 |
| 8 Cu [ 0.000 , 2.068 , 1.278 ] 5.69673 5.31522 0.01195 |
| 9 Cu [ 1.278 , 0.000 , 2.068 ] 5.69673 5.31522 0.01195 |
| 10 Cu [ 0.000 , -2.068 , 1.278 ] 5.69673 5.31522 0.01195 |
| 11 Cu [ -2.068 , -1.278 , 0.000 ] 5.69673 5.31522 0.01195 |
| 12 Cu [ -1.278 , 0.000 , 2.068 ] 5.69673 5.31522 0.01195 |
+------------------------------------------------------------------------------+
| 3 E = -30.0083 dE = 1.777799e+00 dH = 8.903270e-02 |
+------------------------------------------------------------------------------+