[CP2K-user] [CP2K:21990] Questions on small differences in density matrices and Mulliken populations from CP2K single-point calculation
Richard李
scarletlotus009 at gmail.com
Sun Nov 30 12:24:25 UTC 2025
Dear CP2K Developers,
I am writing to ask for your advice regarding some small but systematic
discrepancies I observed in density matrices and Mulliken population
analysis obtained from a single‐point calculation performed using CP2K.
In my test for CO, I compared the following files generated from the same
single-point SCF calculation:
1.
*The MOLDEN file* (CO_molopt_smearing-mos.molden-1_0.molden)
2.
*The Mulliken file* (CO_molopt_smearing-mulliken-1.mulliken)
3.
*The largest iteration AO log file* (e.g.,
CO_molopt_smearing-ao-1_0_12.Log)
4.
*The 1_0 AO log file* (CO_molopt_smearing-ao-1_0.Log)
I found that:
-
The density matrices read from the last AO log file and from the 1_0 AO
file differ by approximately *1×10⁻⁷*, even though they originate from
the same single-point calculation.
-
Constructing Mulliken populations by *element-wise multiplication* of
the density matrix P and the overlap matrix S (i.e., computing PμνSμν
for each pair of atomic orbitals) leads to slightly different values
compared to the *MULLIKEN NET ATOMIC ORBITAL AND OVERLAP POPULATION
MATRIX* reported in CP2K’s Mulliken output file.
-
Additionally, when processing the MOLDEN file using *Multiwfn*, the
computed Mulliken bond orders are again slightly different from those
obtained directly from CP2K.
Before I proceed further, I would like to confirm:
1.
Are these ~1e−7 differences expected due to formatting, truncation,
numerical precision, or different internal representations used when
writing the log files, MOLDEN file, and Mulliken file?
2.
Is there a recommended “most reliable” source of the density matrix for
reproducing CP2K Mulliken results (Mulliken file vs. AO log file vs. MOLDEN
file)?
3.
Are the Mulliken matrices produced by CP2K post‐processed in any
additional way (e.g., symmetrization, thresholding) that could explain
these differences?
4.
Are there known limitations or differences in the basis function
ordering between MOLDEN export and the AO log files?
For reference, I attach (or can provide) the following files:
CO_molopt_smearing.inp
CO_molopt_smearing.out
CO_molopt_smearing-mulliken-1.mulliken
CO_molopt_smearing-mos.molden-1_0.molden
CO_molopt_smearing-ao-1_0.Log
CO_molopt_smearing-ao-1_0_12.Log
Any guidance on how to interpret these discrepancies would be greatly kind
of you. Thank you very much for your time and for your continuous
development of CP2K.
Best regards
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DENSITY MATRIX
1 2
1 1 C 2s 1.687422069764 0.002940113789
2 1 C 3py 0.002940113789 0.305179854579
3 1 C 3pz -0.781630509299 -0.001885193048
4 1 C 3px 0.002460040616 0.000005959307
5 2 O 2s -0.150867369898 -0.000314353831
6 2 O 3py -0.000074704920 0.632928692836
7 2 O 3pz 0.017312810615 0.005153329520
8 2 O 3px -0.000062527043 -0.000016201710
3 4
1 1 C 2s -0.781630509299 0.002460040616
2 1 C 3py -0.001885193048 0.000005959307
3 1 C 3pz 0.804436655129 -0.001577386046
4 1 C 3px -0.001577386046 0.305177105013
5 2 O 2s 0.084652594327 -0.000263018408
6 2 O 3py 0.005147725437 -0.000016201744
7 2 O 3pz -0.736856203735 0.004311867072
8 2 O 3px 0.004307169089 0.632934073736
5 6
1 1 C 2s -0.150867369898 -0.000074704920
2 1 C 3py -0.000314353831 0.632928692836
3 1 C 3pz 0.084652594327 0.005147725437
4 1 C 3px -0.000263018408 -0.000016201744
5 2 O 2s 1.876110654430 -0.001801644168
6 2 O 3py -0.001801644168 1.312775783744
7 2 O 3pz 0.480800977555 -0.000106947449
8 2 O 3px -0.001507448664 0.000000358928
7 8
1 1 C 2s 0.017312810615 -0.000062527043
2 1 C 3py 0.005153329520 -0.000016201710
3 1 C 3pz -0.736856203735 0.004307169089
4 1 C 3px 0.004311867072 0.632934073736
5 2 O 2s 0.480800977555 -0.001507448664
6 2 O 3py -0.000106947449 0.000000358928
7 2 O 3pz 1.338937084860 -0.000089497486
8 2 O 3px -0.000089497486 1.312776526243
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OVERLAP MATRIX
1 2
1 1 C 2s 1.000000000000 0.000000000000
2 1 C 3py 0.000000000000 1.000000000000
3 1 C 3pz 0.000000000000 0.000000000000
4 1 C 3px -0.000000000000 0.000000000000
5 2 O 2s 0.394694632283 -0.001802284625
6 2 O 3py 0.001603057429 0.301795926111
7 2 O 3pz -0.425854788917 0.002019430158
8 2 O 3px 0.001341304028 -0.000006360548
3 4
1 1 C 2s 0.000000000000 -0.000000000000
2 1 C 3py 0.000000000000 0.000000000000
3 1 C 3pz 1.000000000000 0.000000000000
4 1 C 3px 0.000000000000 1.000000000000
5 2 O 2s 0.478779814619 -0.001508000639
6 2 O 3py 0.002019430158 -0.000006360548
7 2 O 3pz -0.234661347418 0.001689689812
8 2 O 3px 0.001689689812 0.301798205936
5 6
1 1 C 2s 0.394694632283 0.001603057429
2 1 C 3py -0.001802284625 0.301795926111
3 1 C 3pz 0.478779814619 0.002019430158
4 1 C 3px -0.001508000639 -0.000006360548
5 2 O 2s 1.000000000000 0.000000000000
6 2 O 3py 0.000000000000 1.000000000000
7 2 O 3pz -0.000000000000 0.000000000000
8 2 O 3px 0.000000000000 0.000000000000
7 8
1 1 C 2s -0.425854788917 0.001341304028
2 1 C 3py 0.002019430158 -0.000006360548
3 1 C 3pz -0.234661347418 0.001689689812
4 1 C 3px 0.001689689812 0.301798205936
5 2 O 2s -0.000000000000 0.000000000000
6 2 O 3py 0.000000000000 0.000000000000
7 2 O 3pz 1.000000000000 0.000000000000
8 2 O 3px 0.000000000000 1.000000000000
DENSITY MATRIX
1 2
1 1 C 2s 1.687418715947 0.002939823576
2 1 C 3py 0.002939823576 0.305179093549
3 1 C 3pz -0.781631120176 -0.001885051625
4 1 C 3px 0.002459795242 0.000005958214
5 2 O 2s -0.150867979622 -0.000314295961
6 2 O 3py -0.000074513860 0.632928165533
7 2 O 3pz 0.017309636288 0.005153268375
8 2 O 3px -0.000062366669 -0.000016201210
3 4
1 1 C 2s -0.781631120176 0.002459795242
2 1 C 3py -0.001885051625 0.000005958214
3 1 C 3pz 0.804439657498 -0.001577267862
4 1 C 3px -0.001577267862 0.305176344518
5 2 O 2s 0.084648620838 -0.000262968144
6 2 O 3py 0.005147594918 -0.000016201252
7 2 O 3pz -0.736856749300 0.004311816801
8 2 O 3px 0.004307058573 0.632933546355
5 6
1 1 C 2s -0.150867979622 -0.000074513860
2 1 C 3py -0.000314295961 0.632928165533
3 1 C 3pz 0.084648620838 0.005147594918
4 1 C 3px -0.000262968144 -0.000016201252
5 2 O 2s 1.876115340524 -0.001801649861
6 2 O 3py -0.001801649861 1.312776862152
7 2 O 3pz 0.480800360109 -0.000106910347
8 2 O 3px -0.001507453439 0.000000358972
7 8
1 1 C 2s 0.017309636288 -0.000062366669
2 1 C 3py 0.005153268375 -0.000016201210
3 1 C 3pz -0.736856749300 0.004307058573
4 1 C 3px 0.004311816801 0.632933546355
5 2 O 2s 0.480800360109 -0.001507453439
6 2 O 3py -0.000106910347 0.000000358972
7 2 O 3pz 1.338934078873 -0.000089468230
8 2 O 3px -0.000089468230 1.312777604448
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