What dose DD mean in the log file

[bubble]

Hi, I have three questions
1. In the log file, what dose DD mean?
2. Do the DM(U) and DM (D) represent the spin-up and -down components of density matrix?
3. For a given calculation, we use PBE-SGGA and SZP basis set, even though the basis set is relatively small, for my system the SZP contains, for example, 2s, 2p,3d orbitals. I wonder why in the loge file for a given atom,the  DM(U) and DM (D) are only two numbers rather than matrix?   

Thank you!

[Jess Wellendorff]

1) DD = density matrix on that specific atom.
2) yes, U/D means up/down components
3) see answer 1)

[bubble]

Thank you for your reply.

However, what is the relationship betwenn, DM(U), DM(D) and DD? is there any more related   information?

[Ulrik G. Vej-Hansen]

DM(U) is the Density Matrix for spin Up and DM(D) is the same for spin Down.

DD is the difference between their sum, and the DM for the neutral atom.

[bubble]

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                       |
+------------------------------------------------------------------------------+

[Jess Wellendorff]

1) DM is a partial trace of the density matrix, so for each atom it's basically the Mulliken population.
2) DD is then the difference between DM and the (integer) number of valence electrons in the pseudopotential. So you can use the MullikenPopulation analysis module to compute it.
3) no, such a rule does not exist in general: If it's a bulk system, the system can be nonmagnetic even though the total number of valence electrons is odd. Not so if it's a non-periodic system (a molecule); in that case you will probably need spin-polarization if the number of electrons is odd, e.g. in molecular NO.

[Petr Khomyakov]

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)

You can do spin-polarized calculations in ATK for any kind of material, magnetic or nonmagnetic. Just change the default setting to spin-polarized. I note that this has nothing to do with the basis set type or particular code. For plane-wave and LCAO basis set types, it works in the same way, i.e., it is your choice of whether you do spin-polarized calculations or not.