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<div data-externalstyle="false" dir="ltr" style="font-family: 'Meiryo', 'Calibri', 'Segoe UI', 'Microsoft YaHei UI', 'Microsoft JhengHei UI', 'Malgun Gothic', 'sans-serif';font-size:11.4975pt;"><div>Dear Andrea,</div><div><br></div><div>I am developing both Gaussian basis-set software and plane-wave software,</div><div>thus, I am more or less familiar with B3LYP.</div><div>Let me explain VWN functionals in B3LYP.</div><div><br></div><div>The original B3LYP is defined with VWN-5 (A.D.Becke, J. Chem. Phys., 107, 8554 (1997)).</div><div>And almost all of quantum chemical softwares (with Gaussian basis-set) adopt VWN-5.</div><div>However, some softwares use other VWNs.</div><div>For examples, Gaussian09 uses VWN-3, NWChem uses VWN-1-RPA.</div><div><br></div><div>If you want to implement Becke’s 3-parameter formulation,</div><div>I recommend to adopt VWN-5 or some VWNs can be selected.</div><div><br></div><div>Regards,</div><div>Satomichi<br></div><div><br></div><div><br></div><div style="padding-top: 5px; border-top-color: rgb(229, 229, 229); border-top-width: 1px; border-top-style: solid;"><div><font face=" 'Meiryo', 'Calibri', 'Segoe UI', 'Microsoft YaHei UI', 'Microsoft JhengHei UI', 'Malgun Gothic', 'sans-serif'" style='line-height: 15pt; letter-spacing: 0.02em; font-family: "Meiryo", "Calibri", "Segoe UI", "Microsoft YaHei UI", "Microsoft JhengHei UI", "Malgun Gothic", "sans-serif"; font-size: 12pt;'><b>差出人:</b> <a href="mailto:andrea.ferretti@nano.cnr.it" target="_parent">Andrea Ferretti</a><br><b>送信日時:</b> 2015年11月3日 火曜日 8:26<br><b>宛先:</b> <a href="mailto:q-e-developers@qe-forge.org" target="_parent">General discussion list for Quantum ESPRESSO developers</a></font></div></div><div><br></div><div dir=""><div id="readingPaneBodyContent"><br><br>Dear all,<br><br>these days I've addressed a problem that I have been facing for some time, <br>i.e. the validation of B3LYP results obtained by QE.<br>Basically, comparing the restuls of hybrid calculations done with QE (say<br>for a molecule) with other quantum chemistry (localized basis set) codes I<br>was able to get very a good agreement on the results (mostly eigenvalues)<br>for HF and PBE0 (besieds LDA, PBE, etc), but not as good for B3LYP.<br><br>To be more precise, I have looked at small molecules based on light<br>elements (such Cl2, CH4, benzene, etc), and compared with MOLPRO,<br>NWchem, and, to a smaller extent, Gaussian and ORCA (courtesy of Daniele<br>Varsano).<br><br>Common experience was that, when using a rather large basis set (such as <br>aug-cc-pTVZ), the agreement of eigenvalues compared to pp-plane-waves<br>reached few tens of meV (from 0.01 to 0.05 eV in the worst cases, at <br>least for frontier orbitals). This worked across several functionals <br>(local, semilocal, hybrids but B3LYP)<br>Some numbers are listed below.<br><br>All in all, this analysis pointed out a problem localized in the<br>B3LYP.<br>Indeed, looking into the implementation I think that I've found at least a<br>couple of differences wrt the reference paper<br><br>P.J. Stephens,F.J. Devlin,C.F. Chabalowski,M.J. Frisch,<br>J.Phys.Chem 98, 11623 (1994)<br>see Eq. (2)<br><br>as well as the implementations of NWchem and libxc.<br><br>Basically:<br><br>* QE implements vwn lda-correlation according to vwn-1<br> of the vwn paper,<br> S.H.Vosko, L.Wilk, M.Nusair, Can.J.Phys. 58,1200(1980)<br> while vwn-1-rpa has to be used for b3lyp<br><br>* the vwn-1-rpa contribution has to be included with a proper<br> scaling factor and summed to the LYP correlation (both<br> icorr and igcc)<br><br>after these changes have been implemented, the agreement of the QE-b3lyp <br>results with other reference data is much better (of the same order of <br>PBE0 or alike).<br><br>In doing so I've also implemented X3LYP, according to the ref:<br>X. Xu, W.A Goddard III, PNAS 101, 2673 (2004).<br><br>Results are also reported and in the same quantitative agreement with <br>localized basis set codes found for other functionals.<br><br>=========<br><br>In the attachment you can find a tgz file with a patch to few QE files <br>implementing the xc-functionals.<br><br>So far I have not done any commit to the trunk, since I wanted to first <br>hear any comments/suggestions.<br><br>What do you think ?<br><br>take care<br>Andrea<br><br>=========<br><br>Cl2 molecule<br>#========================================================<br># NWCHEM results, AVTZ basis<br>#========================================================<br> HOMO [eV] LUMO [eV] lowest eig [eV]<br>LDA -7.48 -4.65 -23.39<br>VWN-RPA -7.9572 -5.1218 -23.8799<br>PBE -7.36 -4.44 -23.33<br>PBE0 -8.79 -3.36 -26.02<br>HF -12.16 +0.51 -32.98<br><br>X3LYP -8.5772 -3.5198 -25.5847<br>B3LYP -8.52 -3.63 -25.44<br><br>#========================================================<br># QE, plane-waves (this work)<br>#========================================================<br> HOMO [eV] LUMO [eV] lowest eig [eV]<br>LDA -7.45 -4.66 -23.60<br>VWN-RPA -7.9332 -5.1423 -24.0844<br>PBE -7.39 -4.54 -23.52<br>PBE0 -8.82 -3.49 -26.18<br>HF -12.27 >0 -33.11<br><br>X3LYP -8.6243 -3.6022 -25.7891<br><br>B3LYP (FIX) -8.58 -3.72 -25.65<br>B3LYP (WRONG) -8.88 -4.03 -25.96<br><br>===========<br><br>CH4 molecule<br>#========================================================<br># NWCHEM results, AVTZ basis<br>#========================================================<br> HOMO [eV] LUMO [eV] lowest eig [eV]<br>LDA -9.4622 -3.2760 -16.9573<br>PBE -9.4413 -3.6852 -17.0532<br>PBE0 -10.9809 +0.0368 -19.4375<br>HF -14.8200 +0.8104 -25.6458<br><br>X3LYP -10.8204 -0.1998 -19.0752<br>B3LYP -10.7594 -0.2262 -18.9560<br><br><br>#========================================================<br># QE, plane-waves (this work)<br>#========================================================<br> HOMO [eV] LUMO [eV] lowest eig [eV]<br>LDA -9.4896 -0.5150 -16.9666<br>PBE -9.4829 -0.5322 -16.9490<br>PBE0 -11.0220 -0.2528 -19.3512<br>HF -14.8492 0.1920 -25.6397<br><br>X3LYP -10.8440 -0.3028 -19.0213<br><br>B3LYP (FIX) -10.7898 -0.3041 -18.9041<br>B3LYP (WRONG) -11.1000 -0.4030 -19.2163<br><br><br><br>-- <br>Andrea Ferretti, PhD<br>S3 Center, Istituto Nanoscienze, CNR<br>via Campi 213/A, 41125, Modena, Italy<br>Tel: +39 059 2055322; Skype: andrea_ferretti<br>URL: http://www.nano.cnr.it<br></div></div></div>
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