<div dir="ltr">Happy new year!<div><br></div><div>Really appreciate if anyone could confirm my derivation of the XC potential.</div><div><br></div><div>Best,</div><div>Xiaoming<br><br>On Friday, December 27, 2019 at 11:50:58 AM UTC-5, Xiaoming Wang wrote:<blockquote class="gmail_quote" style="margin: 0;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div dir="ltr">Hello all,<div><br></div><div>I'm trying to implement the SIC scheme proposed in PRB 99, 235139 (2019) by Giustino et al. </div><div><br></div><div>The new SIC scheme is a minor modification on the one proposed by Mauri [PRB 71, 205210 (2005)]. </div><div><br></div><div>Since the Mauri SIC is implemented in CP2K, incorporation of the Giustino scheme should not need </div><div><br></div><div>much coding work. The Hartree self-interaction part is similar for all the schemes, so I'm only interested</div><div><br></div><div>in the XC part. The implementation of the XC part of the Mauri scheme is coded in qs_vxc.F. </div><div><br></div><div>There are two types of SIC functionals for the Mauri scheme: Mauri_SPZ and Mauri_US. </div><div><br></div><div>The corresponding SIC corrrected XC functionals are:</div><div><br></div><div> Mauri_SPZ: Exc = Exc [ alpha, beta ] - Exc [ alpha - beta, 0 ]</div><div><br></div><div> Mauri_US: Exc = Exc [ alpha, beta ] - Exc [ alpha, beta ] + Exc [ beta, beta ]</div><div><br></div><div>And the XC potentials are:</div><div><br></div><div> Mauri_SPZ: Vxc_up = Vxc_up [ alpha, beta ] - Vxc_up [ alpha - beta, 0 ]</div><div> Vxc_dn = Vxc_dn [ alpha, beta ] + Vxc_up [ alpha - beta, 0 ]</div><div><br></div><div> Mauri_US: Vxc_up = 0</div><div> Vxc_dn = Vxc_up [ beta, beta ] + Vxc_dn [ beta, beta ]</div><div><br></div><div>For the Giustino scheme, the XC functional is:</div><div><br></div><div> Exc = 0.5*Exc [ alpha, beta ] + Exc [ beta, beta ] - 0.5* Exc [ beta - m, beta ]</div><div><br></div><div>where m = alpha - beta. Based on my understanding, the XC potentials are:</div><div><br></div><div> Vxc_up = 0.5*Vxc_up [ alpha, beta ] + 0.5*Vxc_up [ beta - m, beta ]</div><div><br></div><div> Vxc_dn = 0.5*Vxc_dn [ alpha, beta ] + Vxc_up [ beta, beta ] + Vxc_dn [ beta, beta ]</div><div> </div><div> -0.5*Vxc_dn [ beta - m, beta ] - Vxc_up [ beta - m, beta ]</div><div><br></div><div>Please can anyone correct me if my understanding above is wrong. </div><div><br></div><div>I implemented the Giustino SIC based on the above equations by slightly modifying the US scheme </div><div><br></div><div>as already in CP2K. However, I never get convergence for the SCF calculations (see part of the log</div><div><br></div><div>file below). For the same system, the SPZ and US schemes both can easily get convergence.</div><div><br></div><div>So I'm wondering if anyone could give me any comments on this?</div><div><br></div><div><br></div><div><br></div><div>Best,</div><div><br></div><div>Xiaoming</div><div><br></div><div><br></div><div><br></div><div>--</div><div><div> 1 OT CG 0.15E+00 14.2 0.00014039 -8153.9988425820 -8.15E+03</div><div> 2 OT LS 0.10E+00 5.2 -8154.0035499679</div><div> 3 OT CG 0.10E+00 10.6 0.00020232 -8154.0032891957 -4.45E-03</div><div> 4 OT LS 0.46E-01 6.0 -8154.0015689085</div><div> 5 OT CG 0.46E-01 10.8 0.00009816 -8154.0041296811 -8.40E-04</div><div> 6 OT LS 0.31E-01 5.1 -8154.0048751897</div><div> 7 OT CG 0.31E-01 13.1 0.00007670 -8154.0046628243 -5.33E-04</div><div> 8 OT LS 0.26E-01 5.2 -8154.0051281540</div><div> 9 OT CG 0.26E-01 12.0 0.00007395 -8154.0050568034 -3.94E-04</div><div> 10 OT LS 0.21E-01 6.2 -8154.0053917653</div><div> 11 OT CG 0.21E-01 11.2 0.00007210 -8154.0053264707 -2.70E-04</div><div> 12 OT LS 0.16E-01 5.3 -8154.0055646935</div><div> 13 OT CG 0.16E-01 10.4 0.00005042 -8154.0055112362 -1.85E-04</div><div> 14 OT LS 0.15E-01 5.3 -8154.0056327656</div><div> 15 OT CG 0.15E-01 11.4 0.00004942 -8154.0056270301 -1.16E-04</div><div> 16 OT LS 0.14E-01 5.3 -8154.0057343493</div><div> 17 OT CG 0.14E-01 11.5 0.00004857 -8154.0057262676 -9.92E-05</div><div> 18 OT LS 0.13E-01 5.4 -8154.0058189369</div><div> 19 OT CG 0.13E-01 10.7 0.00004785 -8154.0058097707 -8.35E-05</div><div> 20 OT LS 0.11E-01 5.0 -8154.0058883901</div><div> ------------------------------<wbr>----- OT ------------------------------<wbr>---------</div><div> ------------------------------<wbr>----- OT ------------------------------<wbr>---------</div><div> 1 OT CG 0.15E+00 21.8 0.00004727 -8154.0058790748 -6.93E-05</div><div> 2 OT LS 0.11E+00 4.7 -8154.0065750586</div><div> 3 OT CG 0.11E+00 10.9 0.00004074 -8154.0064374937 -5.58E-04</div><div> 4 OT LS 0.13E+00 5.4 -8154.0072008089</div><div> 5 OT CG 0.13E+00 11.3 0.00002783 -8154.0072885701 -8.51E-04</div><div> 6 OT LS 0.51E+00 5.5 -8154.0078327851</div><div> 7 OT CG 0.51E+00 11.1 0.00007874 -8154.0089341020 -1.65E-03</div><div> 8 OT LS 0.21E+00 5.2 -8154.0051598661</div><div> 9 OT CG 0.21E+00 11.3 0.00017344 -8154.0086760074 2.58E-04</div><div> 10 OT LS 0.98E-01 5.3 -8154.0049564999</div><div> 11 OT CG 0.98E-01 11.2 0.00006510 -8154.0082092588 4.67E-04</div><div> 12 OT LS 0.58E-01 5.7 -8154.0086320114</div><div> 13 OT CG 0.58E-01 10.8 0.00003585 -8154.0085028738 -2.94E-04</div><div> 14 OT LS 0.10E+00 5.3 -8154.0088394530</div><div> 15 OT CG 0.10E+00 12.0 0.00007085 -8154.0090772735 -5.74E-04</div><div> 16 OT LS 0.44E-01 5.4 -8154.0084763907</div><div> 17 OT CG 0.44E-01 11.1 0.00003408 -8154.0088708613 2.06E-04</div><div> 18 OT LS 0.72E-01 5.3 -8154.0090917387</div><div> 19 OT CG 0.72E-01 11.4 0.00005874 -8154.0092230991 -3.52E-04</div><div> 20 OT LS 0.30E-01 5.5 -8154.0089057509</div><div> ------------------------------<wbr>----- OT ------------------------------<wbr>---------</div><div> ------------------------------<wbr>----- OT ------------------------------<wbr>---------</div><div> 1 OT CG 0.15E+00 22.0 0.00001421 -8154.0091066057 1.16E-04</div><div> 2 OT LS 0.18E+00 5.9 -8154.0092180076</div><div> 3 OT CG 0.18E+00 10.7 0.00005904 -8154.0092398262 -1.33E-04</div><div> 4 OT LS 0.96E-01 5.5 -8154.0094065127</div><div> 5 OT CG 0.96E-01 11.2 0.00007661 -8154.0094075743 -1.68E-04</div><div> 6 OT LS 0.42E-01 5.6 -8154.0088928557</div><div> 7 OT CG 0.42E-01 10.9 0.00001444 -8154.0092323658 1.75E-04</div><div> 8 OT LS 0.57E-01 5.1 -8154.0092666992</div><div> 9 OT CG 0.57E-01 11.2 0.00001390 -8154.0092787816 -4.64E-05</div><div> 10 OT LS 0.68E-01 5.2 -8154.0093186446</div><div> 11 OT CG 0.68E-01 10.5 0.00002940 -8154.0093259578 -4.72E-05</div><div> 12 OT LS 0.26E-01 5.0 -8154.0092084126</div><div> 13 OT CG 0.26E-01 11.0 0.00001386 -8154.0092843540 4.16E-05</div><div> 14 OT LS 0.13E-01 5.4 -8154.0092839420</div><div> 15 OT CG 0.13E-01 11.0 0.00001387 -8154.0092841905 1.64E-07</div><div> 16 OT LS 0.16E-01 5.4 -8154.0092934733</div><div> 17 OT CG 0.16E-01 11.0 0.00001375 -8154.0092962332 -1.20E-05</div><div> 18 OT LS 0.20E-01 5.4 -8154.0093077912</div><div> 19 OT CG 0.20E-01 10.4 0.00001362 -8154.0093106170 -1.44E-05</div><div> 20 OT LS 0.24E-01 5.3 -8154.0093242773</div><div> ------------------------------<wbr>----- OT ------------------------------<wbr>---------</div><div> ------------------------------<wbr>----- OT ------------------------------<wbr>---------</div><div> 1 OT CG 0.15E+00 22.4 0.00001343 -8154.0093267803 -1.62E-05</div><div> 2 OT LS 0.15E+00 5.4 -8154.0094121812</div><div> 3 OT CG 0.15E+00 11.6 0.00007460 -8154.0094132278 -8.64E-05</div><div> 4 OT LS 0.74E-01 5.3 -8154.0093027278</div><div> 5 OT CG 0.74E-01 10.9 0.00007707 -8154.0094484130 -3.52E-05</div><div> 6 OT LS 0.33E-01 5.6 -8154.0090697156</div><div> 7 OT CG 0.33E-01 14.3 0.00001494 -8154.0093119312 1.36E-04</div><div> 8 OT LS 0.46E-01 6.5 -8154.0093411677</div></div><div><br></div><div>--</div><div><br></div><div><br></div><div><br></div></div></blockquote></div></div>