<div dir="ltr"><div><div>Dear Giuseppe,<br><br></div>You are thinking about coupling between magnetic moments. I just wanted to know if hybrid functional could have non-magnetic ground state, when GGA or LDA has magnetic ground state. I would like to comment on the difference between B3LYP and DFT+U. Basically, DFT+U is DFT+Hartree Fock for selected orbitals and hybrid functional is a mixture of DFT and Hartree. So, it is not surprising, sometimes, they show similar physics. <br>
<br></div>Cheers<br>Jia<br></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Fri, Jan 3, 2014 at 6:12 PM, Giuseppe Mattioli <span dir="ltr"><<a href="mailto:giuseppe.mattioli@ism.cnr.it" target="_blank">giuseppe.mattioli@ism.cnr.it</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br>
Dear Jia<br>
One last (at least for now...) word, which perhaps deserves to be<br>
written. Let us focus on excess electrons in transition metal oxides<br>
(only because I've studied them for long). If you create an O vacancy<br>
in Ti(IV)O2 the missing O atom lets back two excess electrons. If you<br>
perform a conventional DFT (i.e., PBE) calculation the two excess<br>
electrons are delocalized in the conduction band and the total<br>
magnetization is 0 muB. Here the delocalization (self interaction,<br>
double counting, ...) error spread "little pieces of electron" around<br>
all the supercell. Both EXX and DFT+U methods localize the electrons<br>
on two Ti(III) sites neighbouring the missing O because they tend to<br>
linearize the E(N) vs N curve and, therefore, to create a (correct)<br>
derivative discontinuity at integer N values in the E(N) curve. They<br>
also can provide high-spin solutions, and in this regard you are<br>
right: the correction of delocalization errors by EXX can provide high<br>
spin results. Regarding the O vacancy, my DFT+U result is a supercell<br>
with two unpaired electrons on the two Ti(III) sites. They can be<br>
antiferromagnetically (S=1) or ferromagnetically (S=3) coupled,<br>
slightly depending on U values, convergence, ...: in chemical language<br>
they have therefore always the highest multiplicity of electrons, and<br>
the high-spin and broken-symmetry solutions are very close in energy,<br>
so close that I'm not really sure about the lowest one, because I've<br>
not pushed down the forces on nuclei at very very low values. There<br>
are several papers by Pacchioni, Di Valentin and Selloni where the O<br>
vacancy has been investigated by using B3LYP in a periodic GTO<br>
approach. Of course I've not got them here with me, but I (faintly)<br>
remember that the low-spin solution (two electrons coupled on the same<br>
Kohn-Sham orbital shared between the same two Ti(III) centers) was<br>
competitive in energy with the open-shell one far more than in my<br>
DFT+U calculations, and this fact involves the static correlation<br>
problem discussed before. The differences between the DFT+U and B3LYP<br>
total density distributions were minimal, so which is the "correct"<br>
solution? In my opinion these problems are among the most interesting<br>
challenges for dft, and I would be very glad to test some mp2 trick on<br>
correlation like B2PLYP in plane wave calculations...<br>
Sorry for the long answers, and Happy New Year to you!<br>
G.<br>
<span class="HOEnZb"><font color="#888888"><br>
Giuseppe Mattioli<br>
ISM-CNR<br>
Italy<br>
</font></span><div class="HOEnZb"><div class="h5"><br>
Quoting Jia Chen <<a href="mailto:jiachenchem@gmail.com">jiachenchem@gmail.com</a>>:<br>
<br>
> Dear Giuseppe,<br>
><br>
> It is very nice of you to provide so much information! It is certainly much<br>
> more to this question than I thought earlier. Thank you very much and Happy<br>
> New Year.<br>
><br>
> Cheers<br>
> Jia<br>
><br>
><br>
> On Fri, Jan 3, 2014 at 4:27 PM, Giuseppe Mattioli <<br>
> <a href="mailto:giuseppe.mattioli@ism.cnr.it">giuseppe.mattioli@ism.cnr.it</a>> wrote:<br>
><br>
>><br>
>> Dear Jia<br>
>> Sorry, I'm not at my usual desktop, and I cannot therefore access to<br>
>> the whole of my data base. But I can recall by heart this paper<br>
>> Scherlis, Cococcioni, Sit and Marzari; J. Phys. Chem. B 2007, 111,<br>
>> 7384-7391<br>
>> which investigates the spin states of the well known iron(II)<br>
>> porphyrin and of some of its (Fe(II) and Fe(III)) derivatives. In that<br>
>> case a tendency to stabilize lower-spin states is reported (i.e. in<br>
>> the case of the imidazole or chloride ligated molecules triplet and<br>
>> quartet states arise at the b3lyp level, respectively, as opposite to<br>
>> the expected quintet and sextet states. I've performed calculations<br>
>> (partly unpublished, partly published here,that is, actually, not very<br>
>> visible...)<br>
>> Macroheterocycles 2011 4(3) 161-163<br>
>> on different mono and di-iron porphyrin and phthalocyanine complexes.<br>
>> For instance, in the case of the Fe(III) azide and chloride porphyrins<br>
>> I've obtained a sextet spin-state in the case of DFT+U(Fe=4.0 eV, with<br>
>> Quantum ESPRESSO) and B2PLYP/def2-TZVPP (with the ORCA package), and a<br>
>> quartet spin-state in the case of B3LYP/def2-TZVPP (always with ORCA).<br>
>> More examples: there is an interesting family of Co(III) complexes<br>
>> investigated by several authors (including me). You can find several<br>
>> structures in the supporting information of<br>
>> Li and Siegbahn; J. Am. Chem. Soc. 2013, 135, 13804−13813<br>
>> In the case of the tetranuclear Co(III) complex both B3LYP and<br>
>> DFT+U(Co=5.9 eV,O=2.0 eV) indicate a low spin (S=1) result as the most<br>
>> stable configuration. I've published some results, obtained at a<br>
>> restricted open-shell level on the tetranuclear (something in the SI)<br>
>> and (mainly) on larger complexes here<br>
>> Mattioli et al.; J. Am. Chem. Soc. 2013, 135, 15353−15363<br>
>> The interesting thing (and still under investigation) is that in<br>
>> larger Co(III)-oxo clusters the peripheral Co atoms seem not to couple<br>
>> in a low-spin fashion with the other ones, when investigated at DFT+U<br>
>> level, as opposite to the B3LYP case. If you are interested I can send<br>
>> you some more details offline (after tuesday, however). A very similar<br>
>> tetranuclear Ni-oxo compound has been investigated here<br>
>> Cao et al.; PRL 100, 167206 (2008)<br>
>> And a very complex antiferromagnetically-coupled (or broken-symmetry,<br>
>> if you prefer) high-spin has been spotted by DFT+U(Ni,O), and<br>
>> confirmed by comparison of calculated and measured coupling constants J.<br>
>><br>
>> This said, the world of open shell transition metal complexes is vast,<br>
>> and of course there is something that does not fit in my previous<br>
>> simple solution to Alex's problem. On the other hand, the fact that if<br>
>> you stretch an H2 molecule and use EXX you will obtain overcoupling of<br>
>> electrons is a matter of fact. Anyway, we may discuss again (after<br>
>> next tuesday...) the properties of further compounds.<br>
>><br>
>> All the best<br>
>><br>
>> Giuseppe<br>
>><br>
>> Giuseppe Mattioli<br>
>> ISM-CNR<br>
>> Giuseppe<br>
>><br>
>><br>
>><br>
>><br>
>><br>
>> Quoting Jia Chen <<a href="mailto:jiachenchem@gmail.com">jiachenchem@gmail.com</a>>:<br>
>><br>
>> > Dear Giuseppe Mattioli,<br>
>> ><br>
>> > It is quite surprising for me, that hybrid functional actually<br>
>> > overestimates stability of low-spin solution. I know a compound ,for<br>
>> > which, hybrid functional overestimates stability of high-spin solution.<br>
>> Do<br>
>> > you know any published papers with examples of hybrid functional favours<br>
>> > low-spin? Thank you very much!<br>
>> ><br>
>> > Bests<br>
>> > Jia<br>
>> ><br>
>> ><br>
>> > On Fri, Jan 3, 2014 at 2:13 PM, Giuseppe Mattioli <<br>
>> > <a href="mailto:giuseppe.mattioli@ism.cnr.it">giuseppe.mattioli@ism.cnr.it</a>> wrote:<br>
>> ><br>
>> >><br>
>> >> Dear Alex<br>
>> >> Paolo is right, of course. Check the convergence on the Re PP first.<br>
>> >> I would add a few words anyway. Hybrid DFT/HF functionals like B3LYP<br>
>> >> are pretty useful, but in the case of open-shell systems there are<br>
>> >> some known limitations. See the very interesting paper by Cohen<br>
>> >> (Science Vol. 321 no. 5890 pp. 792-794). The HF exchange term added to<br>
>> >> the DFT xc kernel leads to an overcoupling of electron pairs and,<br>
>> >> therefore, to an overestimate of the stability of low-spin solutions.<br>
>> >> Chemists usually call it a "static correlation" error. As we could<br>
>> >> spend years in discussing such an issue, I feel to suggest two simple<br>
>> >> tests: try to perform a B2PLYP calculation (if you can afford it) with<br>
>> >> your GTO package. The MP2 treatment of B3LYP correlation is supposed<br>
>> >> to correct part of the static correlation error. Otherwise, try to<br>
>> >> perform a DFT+U calculation with the U correction applied (possibly in<br>
>> >> a self-consistent fashion, see the many related papers by Cococcioni,<br>
>> >> De Gironcoli, Kulik, Marzari, and mine) to the Re 5d shell (I did<br>
>> >> never use Re... Are the 4f electrons embedded in the pseudo?). The<br>
>> >> on-site DFT+U method is supposed to be free from sce, or, better, less<br>
>> >> affected than its parent DFT functional. If you obtain a high-spin<br>
>> >> solution with one of these methods, there are sound reasons, in my<br>
>> >> opinion, to trust that it is a stable solution...<br>
>> >> HTH<br>
>> >> Giuseppe<br>
>> >><br>
>> >> Giuseppe Mattioli<br>
>> >> ISM-CNR<br>
>> >> Italy<br>
>> >><br>
>> >> Quoting Alex Granov <<a href="mailto:alex.granov@outlook.com">alex.granov@outlook.com</a>>:<br>
>> >><br>
>> >> > Hi<br>
>> >> > We are studying an organo-metallic compound which contains 3 Benzene<br>
>> >> > rings, phosphorous, oxygen, Iodine, and rhenium atoms.Our quantum<br>
>> >> > chemistry study using B3LYP/6-31+G* (Gaussian basis set) shows that<br>
>> >> > the ground state of the system is singlet (spin -unpolarized). We<br>
>> >> > attempted to optimize this structure using quantum espresso to<br>
>> >> > calculate some other electronic properties. Then surprisingly we<br>
>> >> > found that the spin-polarized system is more stable than the<br>
>> >> > spin-unpolarized one in contrast with our quantum chemistry study.<br>
>> >> > In the following you can see my input file and I wonder whether<br>
>> >> > there is something wrong in the input that made the very noticeable<br>
>> >> > contrast. I appreciate your comments to understand the issue and<br>
>> >> > solve it in advance.<br>
>> >> > q/e input:&control calculation='relax',<br>
>> >> > restart_mode='from_scratch', prefix='Re-Be', pseudo_dir =<br>
>> >> > './pseudo/', outdir='./tmp/', tprnfor=.t. ,<br>
>> >> > etot_conv_thr=1.0D-4, forc_conv_thr=1.0D-3, nstep=300,<br>
>> >> > dt=10, / &system ibrav= 8, a=20, b=20, c=20, nat=37, ntyp=6,<br>
>> >> > ecutwfc = 30, ecutrho = 300, occupations='smearing',<br>
>> >> > smearing='marzari-vanderbilt', degauss=0.005, nspin=2 ,<br>
>> >> > starting_magnetization(1)=1 ,starting_magnetization(2)=1 ,<br>
>> >> > starting_magnetization(3)=1 , starting_magnetization(4)=1 ,<br>
>> >> > starting_magnetization(5)=1 , starting_magnetization(6)=1 , /<br>
>> >> > &electrons conv_thr = 1.0d-6, mixing_beta=0.2,<br>
>> >> > mixing_mode=local-TF, / &IONS ion_dynamics="bfgs", upscale=100.0D0<br>
>> >> > ,/ATOMIC_SPECIESRe 186.207 Re.pbe-hgh.UPFO 15.999<br>
>> >> > O.pbe-rrkjus.UPFC 12.000 C.pbe-rrkjus.UPFH 1.000<br>
>> >> > H.pbe-rrkjus.UPFI 126.90 I.pbe-n-rrkjus_psl.0.2.UPFP 30.9737<br>
>> >> > P.pbe-n-van.UPFK_POINTS {gamma}<br>
>> >> ><br>
>> >> > -------------------------------------------------Alex<br>
>> >> > GranovМосковский физико-технический институт (MIPT)Moscow, Russia<br>
>> >><br>
>> >><br>
>> >> --<br>
>> >> ********************************************************<br>
>> >> - Article premier - Les hommes naissent et demeurent<br>
>> >> libres et ègaux en droits. Les distinctions sociales<br>
>> >> ne peuvent être fondèes que sur l'utilitè commune<br>
>> >> - Article 2 - Le but de toute association politique<br>
>> >> est la conservation des droits naturels et<br>
>> >> imprescriptibles de l'homme. Ces droits sont la libertè,<br>
>> >> la propriètè, la sùretè et la rèsistance à l'oppression.<br>
>> >> ********************************************************<br>
>> >><br>
>> >> Giuseppe Mattioli<br>
>> >> CNR - ISTITUTO DI STRUTTURA DELLA MATERIA<br>
>> >> v. Salaria Km 29,300 - C.P. 10<br>
>> >> I 00015 - Monterotondo Stazione (RM)<br>
>> >> Tel + 39 06 90672836 - Fax +39 06 90672316<br>
>> >> E-mail: <<a href="mailto:giuseppe.mattioli@ism.cnr.it">giuseppe.mattioli@ism.cnr.it</a>><br>
>> >><br>
>> >> _______________________________________________<br>
>> >> Pw_forum mailing list<br>
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>> >><br>
>> ><br>
>> ><br>
>> ><br>
>> > --<br>
>> > Jia Chen<br>
>><br>
>><br>
>> --<br>
>> ********************************************************<br>
>> - Article premier - Les hommes naissent et demeurent<br>
>> libres et ègaux en droits. Les distinctions sociales<br>
>> ne peuvent être fondèes que sur l'utilitè commune<br>
>> - Article 2 - Le but de toute association politique<br>
>> est la conservation des droits naturels et<br>
>> imprescriptibles de l'homme. Ces droits sont la libertè,<br>
>> la propriètè, la sùretè et la rèsistance à l'oppression.<br>
>> ********************************************************<br>
>><br>
>> Giuseppe Mattioli<br>
>> CNR - ISTITUTO DI STRUTTURA DELLA MATERIA<br>
>> v. Salaria Km 29,300 - C.P. 10<br>
>> I 00015 - Monterotondo Stazione (RM)<br>
>> Tel <a href="tel:%2B%2039%2006%2090672836" value="+390690672836">+ 39 06 90672836</a> - Fax <a href="tel:%2B39%2006%2090672316" value="+390690672316">+39 06 90672316</a><br>
>> E-mail: <<a href="mailto:giuseppe.mattioli@ism.cnr.it">giuseppe.mattioli@ism.cnr.it</a>><br>
>><br>
>> _______________________________________________<br>
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>><br>
><br>
><br>
><br>
> --<br>
> Jia Chen<br>
<br>
<br>
--<br>
********************************************************<br>
- Article premier - Les hommes naissent et demeurent<br>
libres et ègaux en droits. Les distinctions sociales<br>
ne peuvent être fondèes que sur l'utilitè commune<br>
- Article 2 - Le but de toute association politique<br>
est la conservation des droits naturels et<br>
imprescriptibles de l'homme. Ces droits sont la libertè,<br>
la propriètè, la sùretè et la rèsistance à l'oppression.<br>
********************************************************<br>
<br>
Giuseppe Mattioli<br>
CNR - ISTITUTO DI STRUTTURA DELLA MATERIA<br>
v. Salaria Km 29,300 - C.P. 10<br>
I 00015 - Monterotondo Stazione (RM)<br>
Tel <a href="tel:%2B%2039%2006%2090672836" value="+390690672836">+ 39 06 90672836</a> - Fax <a href="tel:%2B39%2006%2090672316" value="+390690672316">+39 06 90672316</a><br>
E-mail: <<a href="mailto:giuseppe.mattioli@ism.cnr.it">giuseppe.mattioli@ism.cnr.it</a>><br>
<br>
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<a href="http://pwscf.org/mailman/listinfo/pw_forum" target="_blank">http://pwscf.org/mailman/listinfo/pw_forum</a></div></div></blockquote></div><br><br clear="all"><br>-- <br><div dir="ltr">Jia Chen<br><div><br></div></div>
</div>