Hello all,
I'm trying to implement the SIC scheme proposed in PRB 99, 235139 (2019) by Giustino et al.
The new SIC scheme is a minor modification on the one proposed by Mauri [PRB 71, 205210 (2005)].
Since the Mauri SIC is implemented in CP2K, incorporation of the Giustino scheme should not need
much coding work. The Hartree self-interaction part is similar for all the schemes, so I'm only interested
in the XC part. The implementation of the XC part of the Mauri scheme is coded in qs_vxc.F.
There are two types of SIC functionals for the Mauri scheme: Mauri_SPZ and Mauri_US.
The corresponding SIC corrrected XC functionals are:
Mauri_SPZ: Exc = Exc [ alpha, beta ] - Exc [ alpha - beta, 0 ]
Mauri_US: Exc = Exc [ alpha, beta ] - Exc [ alpha, beta ] + Exc [ beta, beta ]
And the XC potentials are:
Mauri_SPZ: Vxc_up = Vxc_up [ alpha, beta ] - Vxc_up [ alpha - beta, 0 ]
Vxc_dn = Vxc_dn [ alpha, beta ] + Vxc_up [ alpha - beta, 0 ]
Mauri_US: Vxc_up = 0
Vxc_dn = Vxc_up [ beta, beta ] + Vxc_dn [ beta, beta ]
For the Giustino scheme, the XC functional is:
Exc = 0.5*Exc [ alpha, beta ] + Exc [ beta, beta ] - 0.5* Exc [ beta - m, beta ]
where m = alpha - beta. Based on my understanding, the XC potentials are:
Vxc_up = 0.5*Vxc_up [ alpha, beta ] + 0.5*Vxc_up [ beta - m, beta ]
Vxc_dn = 0.5*Vxc_dn [ alpha, beta ] + Vxc_up [ beta, beta ] + Vxc_dn [ beta, beta ]
-0.5*Vxc_dn [ beta - m, beta ] - Vxc_up [ beta - m, beta ]
Please can anyone correct me if my understanding above is wrong.
I implemented the Giustino SIC based on the above equations by slightly modifying the US scheme
as already in CP2K. However, I never get convergence for the SCF calculations (see part of the log
file below). For the same system, the SPZ and US schemes both can easily get convergence.
So I'm wondering if anyone could give me any comments on this?
Best,
Xiaoming
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1 OT CG 0.15E+00 14.2 0.00014039 -8153.9988425820 -8.15E+03
2 OT LS 0.10E+00 5.2 -8154.0035499679
3 OT CG 0.10E+00 10.6 0.00020232 -8154.0032891957 -4.45E-03
4 OT LS 0.46E-01 6.0 -8154.0015689085
5 OT CG 0.46E-01 10.8 0.00009816 -8154.0041296811 -8.40E-04
6 OT LS 0.31E-01 5.1 -8154.0048751897
7 OT CG 0.31E-01 13.1 0.00007670 -8154.0046628243 -5.33E-04
8 OT LS 0.26E-01 5.2 -8154.0051281540
9 OT CG 0.26E-01 12.0 0.00007395 -8154.0050568034 -3.94E-04
10 OT LS 0.21E-01 6.2 -8154.0053917653
11 OT CG 0.21E-01 11.2 0.00007210 -8154.0053264707 -2.70E-04
12 OT LS 0.16E-01 5.3 -8154.0055646935
13 OT CG 0.16E-01 10.4 0.00005042 -8154.0055112362 -1.85E-04
14 OT LS 0.15E-01 5.3 -8154.0056327656
15 OT CG 0.15E-01 11.4 0.00004942 -8154.0056270301 -1.16E-04
16 OT LS 0.14E-01 5.3 -8154.0057343493
17 OT CG 0.14E-01 11.5 0.00004857 -8154.0057262676 -9.92E-05
18 OT LS 0.13E-01 5.4 -8154.0058189369
19 OT CG 0.13E-01 10.7 0.00004785 -8154.0058097707 -8.35E-05
20 OT LS 0.11E-01 5.0 -8154.0058883901
----------------------------------- OT ---------------------------------------
----------------------------------- OT ---------------------------------------
1 OT CG 0.15E+00 21.8 0.00004727 -8154.0058790748 -6.93E-05
2 OT LS 0.11E+00 4.7 -8154.0065750586
3 OT CG 0.11E+00 10.9 0.00004074 -8154.0064374937 -5.58E-04
4 OT LS 0.13E+00 5.4 -8154.0072008089
5 OT CG 0.13E+00 11.3 0.00002783 -8154.0072885701 -8.51E-04
6 OT LS 0.51E+00 5.5 -8154.0078327851
7 OT CG 0.51E+00 11.1 0.00007874 -8154.0089341020 -1.65E-03
8 OT LS 0.21E+00 5.2 -8154.0051598661
9 OT CG 0.21E+00 11.3 0.00017344 -8154.0086760074 2.58E-04
10 OT LS 0.98E-01 5.3 -8154.0049564999
11 OT CG 0.98E-01 11.2 0.00006510 -8154.0082092588 4.67E-04
12 OT LS 0.58E-01 5.7 -8154.0086320114
13 OT CG 0.58E-01 10.8 0.00003585 -8154.0085028738 -2.94E-04
14 OT LS 0.10E+00 5.3 -8154.0088394530
15 OT CG 0.10E+00 12.0 0.00007085 -8154.0090772735 -5.74E-04
16 OT LS 0.44E-01 5.4 -8154.0084763907
17 OT CG 0.44E-01 11.1 0.00003408 -8154.0088708613 2.06E-04
18 OT LS 0.72E-01 5.3 -8154.0090917387
19 OT CG 0.72E-01 11.4 0.00005874 -8154.0092230991 -3.52E-04
20 OT LS 0.30E-01 5.5 -8154.0089057509
----------------------------------- OT ---------------------------------------
----------------------------------- OT ---------------------------------------
1 OT CG 0.15E+00 22.0 0.00001421 -8154.0091066057 1.16E-04
2 OT LS 0.18E+00 5.9 -8154.0092180076
3 OT CG 0.18E+00 10.7 0.00005904 -8154.0092398262 -1.33E-04
4 OT LS 0.96E-01 5.5 -8154.0094065127
5 OT CG 0.96E-01 11.2 0.00007661 -8154.0094075743 -1.68E-04
6 OT LS 0.42E-01 5.6 -8154.0088928557
7 OT CG 0.42E-01 10.9 0.00001444 -8154.0092323658 1.75E-04
8 OT LS 0.57E-01 5.1 -8154.0092666992
9 OT CG 0.57E-01 11.2 0.00001390 -8154.0092787816 -4.64E-05
10 OT LS 0.68E-01 5.2 -8154.0093186446
11 OT CG 0.68E-01 10.5 0.00002940 -8154.0093259578 -4.72E-05
12 OT LS 0.26E-01 5.0 -8154.0092084126
13 OT CG 0.26E-01 11.0 0.00001386 -8154.0092843540 4.16E-05
14 OT LS 0.13E-01 5.4 -8154.0092839420
15 OT CG 0.13E-01 11.0 0.00001387 -8154.0092841905 1.64E-07
16 OT LS 0.16E-01 5.4 -8154.0092934733
17 OT CG 0.16E-01 11.0 0.00001375 -8154.0092962332 -1.20E-05
18 OT LS 0.20E-01 5.4 -8154.0093077912
19 OT CG 0.20E-01 10.4 0.00001362 -8154.0093106170 -1.44E-05
20 OT LS 0.24E-01 5.3 -8154.0093242773
----------------------------------- OT ---------------------------------------
----------------------------------- OT ---------------------------------------
1 OT CG 0.15E+00 22.4 0.00001343 -8154.0093267803 -1.62E-05
2 OT LS 0.15E+00 5.4 -8154.0094121812
3 OT CG 0.15E+00 11.6 0.00007460 -8154.0094132278 -8.64E-05
4 OT LS 0.74E-01 5.3 -8154.0093027278
5 OT CG 0.74E-01 10.9 0.00007707 -8154.0094484130 -3.52E-05
6 OT LS 0.33E-01 5.6 -8154.0090697156
7 OT CG 0.33E-01 14.3 0.00001494 -8154.0093119312 1.36E-04
8 OT LS 0.46E-01 6.5 -8154.0093411677
--