From owner-chemistry@ccl.net Sun Apr 26 05:44:00 2020 From: "Susi Lehtola susi.lehtola()alumni.helsinki.fi" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54042-200426053810-6010-MnBHrtrGKrx3ioJ2o5B+3Q a server.ccl.net> X-Original-From: Susi Lehtola Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Sun, 26 Apr 2020 12:37:59 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola~!~alumni.helsinki.fi] On 4/25/20 7:27 PM, Thomas Manz thomasamanz/agmail.com wrote: > Hi Susi and Hannes, > > Thanks for your replies. > > (a) The Mulliken method assigns negative electron orbital populations on some > atoms in materials. This issue was already discussed with examples in Mulliken's > original 1955 paper (see Table V and text discussion in J Chem Phys 23, 1955, > 1833-1840, DOI: 10.1063/1.1740588). Consequently, Mulliken's method assigns > negative electron density to some atoms at some positions in space. I don't think that is the case. Table V is reporting populations on the AOs; the partial charge is obtained as a sum of these. Looking at the AO density matrix or arbitrarily summing over its elements does not mean that there is negative density. There are very good reasons not to use Mulliken; it's basically just a random number generator. (Löwdin's scheme that many people assume is better is actually much, much worse.) > However, my question concerns the electron density value assigned to each atom > for a particular spatial position. It is not a question about net atomic charges > (of course those can be positive, negative, and zero) or about the integrated > number of electrons assigned to an atom (i.e., the populations). For example, if > the electron density at a particular spatial position is 17.1 electrons/bohr^3, > do any of these methods ever assign a negative electron density value (e.g., > -0.35 electrons/bohr^3) to any atom at any spatial position. In this example, > the electron density assigned to the other atoms would thus sum to 17.45 > electrons/bohr^3, to reproduce the electron density value of 17.1 > electrons/bohr^3 when summed over all atoms at this particular spatial position. No partial charge analysis gives you an electron density distribution. The only exceptions are the ones where the partial charges are defined explicitly by a real-space integral of a weight function times the electron density, i.e. Hirshfeld and its extensions such as iterative Hirshfeld and Stockholder analysis; then, you can trivially define the electron density for each atom at a particular spatial position. > This question is an extremely hard one, because it involves the sum of three > terms: the self-term between localized orbital on atom A, the self-term between > localized orbital on atom B, and the corresponding cross term. Only if the > magnitude of the cross term can exceed the self-terms at some location in space > then the assigned electron density distribution may be negative at some spatial > position for some atom. For the four methods mentioned in my email, I am having > trouble figuring out if or when this could occur. ... assuming the basis functions are localized, which is not a given. > (c) The Bickelhaupt method I referred to was intended to mean their modified > Mulliken-like scheme (eqn 11 of their paper). Mulliken's method assigns half of > each localized orbitals cross term each of the two atoms. In the Bickelhaupt > scheme, the cross term for localized orbital i on atom A and localized orbital j > on atom B is divided as follows: > > fraction of i-j cross-term assigned to atom A = proportional to qii/(qii + qjj), > where qii is the self-population of orbital i on atom A > fraction of i-j cross-term assigned to atom B = proportional to qjj/(qii + > qjj), where qjj is the self-population of orbital j on atom B > (These sum to one.) Such a division makes me think that it's not rotationally invariant... > (e) I do not yet fully understand the nature of the projections involved in the > IBO method. Consequently, it is hard for me to completely follow your argument > about why the IBO method is expected to always yield non-negative integrated > populations. I do understand that if the projection operator has all > non-negative eigenvalues then its double contraction with any vector will yield > a non-negative population. (This is a basic property of all positive > semi-definite matrices.) So, I understand the gist of your argument, even if > some of the finer details of the IBO projection are still unclear to me. > Nevertheless, I am particularly interested in whether the IBO method may assign > a negative electron density value (at a particular spatial position) to any atom. The point in IAO (IBO is the orbital localization with IAOs!) is that you get the partial charges on the atoms by projecting onto the atomic orbitals. This operation is positive definite. -- ------------------------------------------------------------------ Mr. Susi Lehtola, PhD Junior Fellow, Adjunct Professor susi.lehtola=alumni.helsinki.fi University of Helsinki http://susilehtola.github.io/ Finland ------------------------------------------------------------------ Susi Lehtola, dosentti, FT tutkijatohtori susi.lehtola=alumni.helsinki.fi Helsingin yliopisto http://susilehtola.github.io/ ------------------------------------------------------------------ From owner-chemistry@ccl.net Sun Apr 26 07:19:00 2020 From: "Stefan Grimme grimme ~~ thch.uni-bonn.de" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-mat Message-Id: <-54043-200426071726-21790-S7ujDHKn9m5oX0nAcf9rYw,server.ccl.net> X-Original-From: "Stefan Grimme" Date: Sun, 26 Apr 2020 07:17:24 -0400 Sent to CCL by: "Stefan Grimme" [grimme*thch.uni-bonn.de] Dear Susi Lehtola. regarding your statement "There are very good reasons not to use Mulliken; it's basically just a random number generator." I have to say that this is may be true for extended AO basis sets. But with minimal or even DZ basis sets, the Mulliken scheme gives very reasonable and useful results (and I agree, better than with Lwdin). Note, that the electrostatic energy in modern tight-binding QM methods like DFTB or GFN-xTB is self-consistently computed by a Mulliken partitioning (both, at an atom or shell level). The corresponding total energies (observable) compare well to high-level reference data for many systems and this can hardly be termed "random". Best Stefan Grimme From owner-chemistry@ccl.net Sun Apr 26 08:39:01 2020 From: "Tatiana Korona tania%%tiger.chem.uw.edu.pl" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54044-200426082014-17767-ONel5sH9hD1XfSc5agP58Q^_^server.ccl.net> X-Original-From: Tatiana Korona Content-Type: MULTIPART/MIXED; BOUNDARY="1473576194-1974904447-1587903605=:18363" Date: Sun, 26 Apr 2020 14:20:05 +0200 (CEST) MIME-Version: 1.0 Sent to CCL by: Tatiana Korona [tania[]tiger.chem.uw.edu.pl] This message is in MIME format. The first part should be readable text, while the remaining parts are likely unreadable without MIME-aware tools. --1473576194-1974904447-1587903605=:18363 Content-Type: TEXT/PLAIN; charset=utf-8; format=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE Dear Dr. Lehtola, It is a very interesting reply. I have one question: could you write more o= n=20 your statement that the Loewding's scheme is much worse than Mulliken one? = I=20 among these "many people" who so far have assumed that it is better than=20 Mulliken's scheme :-) Best wishes, Tatiana Korona On Sun, 26 Apr 2020, Susi Lehtola susi.lehtola()alumni.helsinki.fi wrote: > > Sent to CCL by: Susi Lehtola [susi.lehtola~!~alumni.helsinki.fi] > On 4/25/20 7:27 PM, Thomas Manz thomasamanz/agmail.com wrote: >> Hi=C2=A0Susi=C2=A0and Hannes, >> >> Thanks for your replies.=C2=A0 >> >> (a) The Mulliken method assigns negative electron orbital populations on= some >> atoms in materials. This issue was already discussed with examples in Mu= lliken's >> original 1955 paper (see Table V and text discussion in J Chem Phys 23, = 1955, >> 1833-1840, DOI: 10.1063/1.1740588). Consequently, Mulliken's method assi= gns >> negative electron density to some atoms at some positions in space. > > I don't think that is the case. Table V is reporting populations on the A= Os; the > partial charge is obtained as a sum of these. > > Looking at the AO density matrix or arbitrarily summing over its elements= does > not mean that there is negative density. There are very good reasons not = to use > Mulliken; it's basically just a random number generator. (L=C3=B6wdin's = scheme that > many people assume is better is actually much, much worse.) > >> However, my question concerns the electron density value assigned to eac= h atom >> for a particular spatial position. It is not a question about net atomic= charges >> (of course those can be positive, negative, and zero) or about the integ= rated >> number of electrons assigned to an atom (i.e., the populations). For exa= mple, if >> the electron density at a particular spatial position is 17.1 electrons/= bohr^3, >> do any of these methods ever assign a negative electron density value (e= =2Eg., >> -0.35 electrons/bohr^3) to any atom at any spatial position.=C2=A0In thi= s example, >> the electron density assigned to the other atoms would thus sum to 17.45 >> electrons/bohr^3, to reproduce the electron density value of 17.1 >> electrons/bohr^3 when summed over all atoms at this particular spatial p= osition. > > No partial charge analysis gives you an electron density distribution. Th= e only > exceptions are the ones where the partial charges are defined explicitly = by a > real-space integral of a weight function times the electron density, i.e. > Hirshfeld and its extensions such as iterative Hirshfeld and Stockholder > analysis; then, you can trivially define the electron density for each at= om at a > particular spatial position. > >> This question is an extremely hard one, because it involves the sum of t= hree >> terms: the self-term between localized orbital on atom A, the self-term = between >> localized orbital on atom B, and the corresponding cross term. Only if t= he >> magnitude of the cross term can exceed the self-terms at some location i= n space >> then the assigned electron density distribution may be negative at some = spatial >> position for some atom. For the four methods mentioned in my email, I am= having >> trouble figuring out if or when this could=C2=A0occur. > > ... assuming the basis functions are localized, which is not a given. > >> (c) The Bickelhaupt method I referred to was intended to mean their modi= fied >> Mulliken-like scheme (eqn 11 of their paper). Mulliken's method assigns = half of >> each localized orbitals cross term each of the two atoms. In the Bickelh= aupt >> scheme, the cross term for localized orbital i on atom A and localized o= rbital j >> on atom B is divided as follows: >> >> fraction of i-j cross-term assigned to atom A =3D proportional to qii/(q= ii=C2=A0+ qjj), >> where qii is the self-population of orbital i=C2=A0on atom A >> fraction of i-j cross-term assigned to atom B =3D=C2=A0 proportional to = qjj/(qii=C2=A0+ >> qjj), where qjj is the self-population of orbital j on atom B >> (These sum to one.) > > Such a division makes me think that it's not rotationally invariant... > >> (e) I do not yet fully understand the nature of the projections involved= in the >> IBO method. Consequently, it is hard for me to completely follow your ar= gument >> about why the IBO method is expected to always yield non-negative integr= ated >> populations. I do understand that if the projection operator has all >> non-negative eigenvalues then its double contraction with any vector wil= l yield >> a non-negative population. (This is a basic property of all positive >> semi-definite matrices.) So, I understand the gist of your argument, eve= n if >> some of the finer details of the IBO projection are still unclear to me. >> Nevertheless, I am particularly interested in whether the IBO method may= assign >> a negative electron density value (at a particular spatial position) to = any atom. > > The point in IAO (IBO is the orbital localization with IAOs!) is that you= get > the partial charges on the atoms by projecting onto the atomic orbitals. = This > operation is positive definite. > --=20 > ------------------------------------------------------------------ > Mr. Susi Lehtola, PhD Junior Fellow, Adjunct Professor > susi.lehtola:alumni.helsinki.fi University of Helsinki > http://susilehtola.github.io/ Finland > ------------------------------------------------------------------ > Susi Lehtola, dosentti, FT tutkijatohtori > susi.lehtola:alumni.helsinki.fi Helsingin yliopisto > http://susilehtola.github.io/ > ------------------------------------------------------------------ > > > > -=3D This is automatically added to each message by the mailing script = =3D-> > Dr. Tatiana Korona http://tiger.chem.uw.edu.pl/staff/tania/tania.html Quantum Chemistry Laboratory, University of Warsaw, Pasteura 1, PL-02-093 W= arsaw, POLAND --1473576194-1974904447-1587903605=:18363-- From owner-chemistry@ccl.net Sun Apr 26 10:05:00 2020 From: "Sebastian Kozuch seb.kozuch%gmail.com" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54045-200426100154-2522-0C8oOgCBaE5cmT2Yvi0XYw^server.ccl.net> X-Original-From: Sebastian Kozuch Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/html; charset=utf-8 Date: Sun, 26 Apr 2020 17:01:46 +0300 MIME-Version: 1.0 Sent to CCL by: Sebastian Kozuch [seb.kozuch]![gmail.com] To all of those with interest in the accuracy of atomic charges, I recommend this article from Jan Martin:
https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cphc.202000040
"The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees"

Best,
Sebastian

On 26/4/20 3:20 PM, Tatiana Korona tania%%tiger.chem.uw.edu.pl wrote:

Dear Dr. Lehtola,

It is a very interesting reply. I have one question: could you write more on your statement that the Loewding's scheme is much worse than Mulliken one? I among these "many people" who so far have assumed that it is better than Mulliken's scheme :-)

Best wishes,

Tatiana Korona

On Sun, 26 Apr 2020, Susi Lehtola susi.lehtola()alumni.helsinki.fi wrote:

Sent to CCL by: Susi Lehtola [susi.lehtola~!~alumni.helsinki.fi]
On 4/25/20 7:27 PM, Thomas Manz thomasamanz/agmail.com wrote:

Hi Susi and Hannes,

Thanks for your replies.

(a) The Mulliken method assigns negative electron orbital populations on some
atoms in materials. This issue was already discussed with examples in Mulliken's
original 1955 paper (see Table V and text discussion in J Chem Phys 23, 1955,
1833-1840, DOI: 10.1063/1.1740588). Consequently, Mulliken's method assigns
negative electron density to some atoms at some positions in space.

I don't think that is the case. Table V is reporting populations on the AOs; the
partial charge is obtained as a sum of these.

Looking at the AO density matrix or arbitrarily summing over its elements does
not mean that there is negative density. There are very good reasons not to use
Mulliken; it's basically just a random number generator. (Löwdin's scheme that
many people assume is better is actually much, much worse.)

However, my question concerns the electron density value assigned to each atom
for a particular spatial position. It is not a question about net atomic charges
(of course those can be positive, negative, and zero) or about the integrated
number of electrons assigned to an atom (i.e., the populations). For example, if
the electron density at a particular spatial position is 17.1 electrons/bohr^3,
do any of these methods ever assign a negative electron density value (e.g.,
-0.35 electrons/bohr^3) to any atom at any spatial position. In this example,
the electron density assigned to the other atoms would thus sum to 17.45
electrons/bohr^3, to reproduce the electron density value of 17.1
electrons/bohr^3 when summed over all atoms at this particular spatial position.

No partial charge analysis gives you an electron density distribution. The only
exceptions are the ones where the partial charges are defined explicitly by a
real-space integral of a weight function times the electron density, i.e.
Hirshfeld and its extensions such as iterative Hirshfeld and Stockholder
analysis; then, you can trivially define the electron density for each atom at a
particular spatial position.

This question is an extremely hard one, because it involves the sum of three
terms: the self-term between localized orbital on atom A, the self-term between
localized orbital on atom B, and the corresponding cross term. Only if the
magnitude of the cross term can exceed the self-terms at some location in space
then the assigned electron density distribution may be negative at some spatial
position for some atom. For the four methods mentioned in my email, I am having
trouble figuring out if or when this could occur.

... assuming the basis functions are localized, which is not a given.

(c) The Bickelhaupt method I referred to was intended to mean their modified
Mulliken-like scheme (eqn 11 of their paper). Mulliken's method assigns half of
each localized orbitals cross term each of the two atoms. In the Bickelhaupt
scheme, the cross term for localized orbital i on atom A and localized orbital j
on atom B is divided as follows:

fraction of i-j cross-term assigned to atom A = proportional to qii/(qii + qjj),
where qii is the self-population of orbital i on atom A
fraction of i-j cross-term assigned to atom B = proportional to qjj/(qii +
qjj), where qjj is the self-population of orbital j on atom B
(These sum to one.)

Such a division makes me think that it's not rotationally invariant...

(e) I do not yet fully understand the nature of the projections involved in the
IBO method. Consequently, it is hard for me to completely follow your argument
about why the IBO method is expected to always yield non-negative integrated
populations. I do understand that if the projection operator has all
non-negative eigenvalues then its double contraction with any vector will yield
a non-negative population. (This is a basic property of all positive
semi-definite matrices.) So, I understand the gist of your argument, even if
some of the finer details of the IBO projection are still unclear to me.
Nevertheless, I am particularly interested in whether the IBO method may assign
a negative electron density value (at a particular spatial position) to any atom.

The point in IAO (IBO is the orbital localization with IAOs!) is that you get
the partial charges on the atoms by projecting onto the atomic orbitals. This
operation is positive definite.
--
------------------------------------------------------------------
Mr. Susi Lehtola, PhD             Junior Fellow, Adjunct Professor
susi.lehtola:alumni.helsinki.fi   University of Helsinki
http://susilehtola.github.io/     Finland
------------------------------------------------------------------
Susi Lehtola, dosentti, FT        tutkijatohtori
susi.lehtola:alumni.helsinki.fi   Helsingin yliopisto
http://susilehtola.github.io/
------------------------------------------------------------------

Dr. Tatiana Korona http://tiger.chem.uw.edu.pl/staff/tania/tania.html
Quantum Chemistry Laboratory, University of Warsaw, Pasteura 1, PL-02-093 Warsaw, POLAND

-- 
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
.........Sebastian Kozuch.........
......Department of Chemistry.....
Ben-Gurion University of the Negev
.........kozuch+/-bgu.ac.il.........
......www.bgu.ac.il/~kozuch/......
˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭˭

From owner-chemistry@ccl.net Sun Apr 26 10:48:00 2020 From: "Susi Lehtola susi.lehtola . alumni.helsinki.fi" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54046-200426104454-21111-RTpmKYpVBIzbRUz+YFky1g .. server.ccl.net> X-Original-From: Susi Lehtola Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Sun, 26 Apr 2020 17:44:44 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola=-=alumni.helsinki.fi] On 4/26/20 3:20 PM, Tatiana Korona tania%%tiger.chem.uw.edu.pl wrote: > Dear Dr. Lehtola, > > It is a very interesting reply. I have one question: could you write more on > your statement that the Loewding's scheme is much worse than Mulliken one? I > among these "many people" who so far have assumed that it is better than > Mulliken's scheme :-) For a demonstration e.g. Table I in our paper "Pipek−Mezey Orbital Localization Using Various Partial Charge Estimates", J. Chem. Theory Comput. 2014, 10, 642−649. doi: 10.1021/ct401016x While Mulliken is already sensitive to the basis set, the basis set sensitivity is over 10 times bigger in the Löwdin scheme. Löwdin predicts oxygen in water to have a positive partial charge of +0.367e already in cc-pVTZ; if you go to aug-cc-pVTZ you get a whopping +1.028e. For Mulliken, the numbers are -0.476e and -0.420e; for IAO -0.739e and -0.750e. -- ------------------------------------------------------------------ Mr. Susi Lehtola, PhD Junior Fellow, Adjunct Professor susi.lehtola^alumni.helsinki.fi University of Helsinki http://susilehtola.github.io/ Finland ------------------------------------------------------------------ Susi Lehtola, dosentti, FT tutkijatohtori susi.lehtola^alumni.helsinki.fi Helsingin yliopisto http://susilehtola.github.io/ ------------------------------------------------------------------ From owner-chemistry@ccl.net Sun Apr 26 11:23:00 2020 From: "Susi Lehtola susi.lehtola]=[alumni.helsinki.fi" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-mat Message-Id: <-54047-200426104733-22729-n8/Nkx2NybmKubXNkwYYmw..server.ccl.net> X-Original-From: Susi Lehtola Content-Language: en-US Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=utf-8 Date: Sun, 26 Apr 2020 17:47:25 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola()alumni.helsinki.fi] On 4/26/20 2:17 PM, Stefan Grimme grimme ~~ thch.uni-bonn.de wrote: > > Sent to CCL by: "Stefan Grimme" [grimme*thch.uni-bonn.de] Dear Susi > Lehtola. regarding your statement > > "There are very good reasons not to use Mulliken; it's basically just a > random number generator." > > I have to say that this is may be true for extended AO basis sets. But with > minimal or even DZ basis sets, the Mulliken scheme gives very reasonable and > useful results (and I agree, better than with Lwdin). Note, that the > electrostatic energy in modern tight-binding QM methods like DFTB or GFN-xTB > is self-consistently computed by a Mulliken partitioning (both, at an atom > or shell level). The corresponding total energies (observable) compare well > to high-level reference data for many systems and this can hardly be termed > "random". This is of course true, but says a lot more about the basis set than the Mulliken method. A good rule of thumb is not to use it, since alternatives like IAO that lack its deficiencies are available. -- ------------------------------------------------------------------ Mr. Susi Lehtola, PhD Junior Fellow, Adjunct Professor susi.lehtola- -alumni.helsinki.fi University of Helsinki http://susilehtola.github.io/ Finland ------------------------------------------------------------------ Susi Lehtola, dosentti, FT tutkijatohtori susi.lehtola- -alumni.helsinki.fi Helsingin yliopisto http://susilehtola.github.io/ ------------------------------------------------------------------ From owner-chemistry@ccl.net Sun Apr 26 12:33:01 2020 From: "Pierre Archirel pierre.archirel|-|universite-paris-saclay.fr" To: CCL Subject: CCL: TDDFT for UV-visible spectra Message-Id: <-54048-200426031156-27595-6q54XbAhjGgBeRMKYwqxMA+*+server.ccl.net> X-Original-From: "Pierre Archirel" Date: Sun, 26 Apr 2020 03:11:53 -0400 Sent to CCL by: "Pierre Archirel" [pierre.archirel(0)universite-paris-saclay.fr] This is an answer to Partha Sarathi Sengupta, Dear colleague, Your short question raises three main difficulties: 1- the TDDFT line at the equilibrium geometry generally does not coincide with the maximum of the absorption band. 2- I guess you are using DFT, which is fast and often efficient, but many functionals are available, choosing the best one requires many tests. 3- if your system is in solution you must model the solvent Since you mention Cu and Ni complexes, I may advertize my work on the Ag(CN)2^2- system in water, where I simulated with success absorption spectra with the TDDFT method, the B3LYP functional and the SMD solvent: P. Archirel et al. PCCP, 2017, 19 23068 But note that B3LYP often yield poor results, in this case I recommend the 'long range corrected' functional lc-wPBE where the w parameter can be optimised, so as to reproduce high level quantum results on little model systems. Allow me again to advertise my work on absorption spectra of peptides: P. Archirel et al. J. Phys. Chem. B 2019, 123, 90879097 In any case fast choices and calculations can yield poor results! Best wishes, Pierre Archirel ICP Universite Paris-Saclay, Orsay, France pierre.archirel&universite-paris-saclay.fr