From owner-chemistry@ccl.net Sat Apr 25 01:11:00 2020 From: "Thomas Manz thomasamanz|-|gmail.com" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54032-200425010831-12402-a30U/1Kgv52VGUT1SV7jBQ]=[server.ccl.net> X-Original-From: Thomas Manz Content-Type: multipart/alternative; boundary="000000000000c7647605a4167895" Date: Fri, 24 Apr 2020 23:08:14 -0600 MIME-Version: 1.0 Sent to CCL by: Thomas Manz [thomasamanz(_)gmail.com] --000000000000c7647605a4167895 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Dear Colleagues, While writing a journal manuscript, I encountered the following technical question, to which I do not currently know the answer. Is it known which of the following charge partitioning methods (if any) can sometimes assign a negative electron density value to one (or more) atoms at some position(s) in space? (1) Intrinsic bond orbital (IBO) method by Knizia (J Chem Theory Comput, 2013, 9, 4834=E2=88=924843, DOI: 10.1021/ct400687b) (2) Bickelhaupt method by Bickelhaupt et al. (Organometallics 1996, 15, 2923-2931, DOI: 10.1021/om950966x) (3) Minimal basis set Bickelhaupt (MBSBickelhaupt) method by Cho et al. (ChemPhysChem, 2020, 21, 688-696, DOI:10.1002/cphc.202000040) (4) Natural population analysis (NPA) by Reed, Weinstock, and Weinhold (J Chem Phys, 1985, 83, 735-746, DOI: 10.1063/1.449486) If you have insights into this question, would you be able to provide a specific example, reference, or brief mathematical explanation? Sincerest thanks, Tom Manz --000000000000c7647605a4167895 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Dear Colleagues,

While writing a journal manuscript= , I encountered the following technical question, to which I do not current= ly know the answer.

Is it known which of the following charge partit= ioning methods (if any) can sometimes assign a negative electron density va= lue to one (or more) atoms at some position(s) in space?

(1) Intrins= ic bond orbital (IBO) method by Knizia (J Chem Theory Comput, 2013, 9, 4834= =E2=88=924843, DOI: 10.1021/ct400687b)

(2) Bickelhaupt method by Bic= kelhaupt et al. (Organometallics 1996, 15, 2923-2931, DOI:=C2=A010.1021/om9= 50966x)

(3) Minimal basis set Bickelhaupt (MBSBickelhaupt) method by= Cho et al. (ChemPhysChem, 2020, 21, 688-696, DOI:10.1002/cphc.202000040)
(4) Natural population analysis (NPA) by Reed, Weinstock, and Weinhol= d (J Chem Phys, 1985, 83, 735-746, DOI:=C2=A010.1063/1.449486)

=
If you have insights into this question, would you be able to pr= ovide a specific example, reference, or brief mathematical explanation?

Sincerest thanks,

Tom Manz

<= div>
--000000000000c7647605a4167895-- From owner-chemistry@ccl.net Sat Apr 25 03:45:01 2020 From: "Partha Sengupta anapspsmo%%gmail.com" To: CCL Subject: CCL:G: TD spectra Message-Id: <-54033-200425034342-25734-aatjBOzIlQH45tlR47atXw- -server.ccl.net> X-Original-From: Partha Sengupta Content-Type: multipart/alternative; boundary="000000000000b991ef05a418a34b" Date: Sat, 25 Apr 2020 13:13:17 +0530 MIME-Version: 1.0 Sent to CCL by: Partha Sengupta [anapspsmo-x-gmail.com] --000000000000b991ef05a418a34b Content-Type: text/plain; charset="UTF-8" Sir, Which method in TD works(UV-VIS) relates closest peak values in Gaussian 09w with the experimental peak values. PSSengupta -- *Dr. Partha Sarathi SenguptaAssociate ProfessorVivekananda Mahavidyalaya, Burdwan* --000000000000b991ef05a418a34b Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable

Sir,=C2=A0
Which method i= n TD works(UV-VIS) relates closest peak values in Gaussian 09w with the exp= erimental peak values.
PSSengupta=C2=A0


--
Dr. Partha Sarathi= Sengupta
Associate Professor
Vivekananda Mahavidyalaya, Burdwan
--000000000000b991ef05a418a34b-- From owner-chemistry@ccl.net Sat Apr 25 04:19:00 2020 From: "Susi Lehtola susi.lehtola/a\alumni.helsinki.fi" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54034-200425034727-26475-AH778h4Z10FjPYlXBZQR2A=server.ccl.net> X-Original-From: Susi Lehtola Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Sat, 25 Apr 2020 10:47:20 +0300 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola*o*alumni.helsinki.fi] On 4/25/20 8:08 AM, Thomas Manz thomasamanz|-|gmail.com wrote: > Dear Colleagues, > > While writing a journal manuscript, I encountered the following technical > question, to which I do not currently know the answer. > > Is it known which of the following charge partitioning methods (if any) can > sometimes assign a negative electron density value to one (or more) atoms at > some position(s) in space? > > (1) Intrinsic bond orbital (IBO) method by Knizia (J Chem Theory Comput, 2013, > 9, 4834−4843, DOI: 10.1021/ct400687b) > > (2) Bickelhaupt method by Bickelhaupt et al. (Organometallics 1996, 15, > 2923-2931, DOI: 10.1021/om950966x) > > (3) Minimal basis set Bickelhaupt (MBSBickelhaupt) method by Cho et al. > (ChemPhysChem, 2020, 21, 688-696, DOI:10.1002/cphc.202000040) > > (4) Natural population analysis (NPA) by Reed, Weinstock, and Weinhold (J Chem > Phys, 1985, 83, 735-746, DOI: 10.1063/1.449486) > > If you have insights into this question, would you be able to provide a specific > example, reference, or brief mathematical explanation? Dear Tom, this truly is a technical question. Namely, since the electron density is positive semidefinite, n(r) >= 0 everywhere, a charge partitioning method that assigned a *negative electronic charge* to one or more atoms would necessarily mean grave mathematical problems: any well-based method should yield at least zero electrons for any atom. (1) IBO belongs to the class of generalized Pipek-Mezey methods (10.1021/ct401016x) that produce localized orbitals from a given definition of atomic partial charges. The partial charges in IBO are from the intrinsic atomic orbitals (IAO) from the same paper. The IAOs are just taken as the occupied atomic orbitals for the atomic ground state. Since IAO assigns partial charges by projection (like most of the other usable generalized Pipek-Mezey methods that are mathematically well-defined, unlike the original Pipek-Mezey scheme), it is not possible to get negative electron densities with IAO. Projection operators can only have eigenvalues between 0 and 1; 0 for components that cannot be at all described in the other basis and 1 for components that can be exactly represented in the other basis. (2) It is not clear which method you mean; the Bickelhaupt et al paper uses two > from the literature and describes two methods. The first one defines partial charges by integrating the difference of the molecular electron density and the superposition of atomic densities over the Voronoi cell, and the second is a modification to the Mulliken scheme where off-diagonal elements are also included; like the Mulliken scheme, this one is also mathematically ill-defined since it does not have a basis set limit (10.1021/ct401016x). I have a vague recollection of seeing something similar to the modified Mulliken scheme Bickelhaupt used in much earlier literature. It is not obvious how electron density would be assigned by the Voronoi scheme, since it does not use the nuclear charge at all. (3) This is Bickelhaupt's scheme; one just projects into a minimal basis before performing the Mulliken-style analysis. (4) As far as I know, NPA is also based on projections, and thereby should not have problems with negative densities. Even though the Mulliken scheme is not mathematically well-founded, I don't think it is possible to get negative electron densities with it: if you span the molecular basis with basis functions on a single atom, all electrons will be counted on that center, and the others will have zero electrons each. -- ------------------------------------------------------------------ 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 Sat Apr 25 07:46:01 2020 From: "Wojciech Kolodziejczyk dziecial(a)icnanotox.org" To: CCL Subject: CCL:G: TD spectra Message-Id: <-54035-200425074402-15344-3OlosYFTrHp4KDlVEMzaFw##server.ccl.net> X-Original-From: Wojciech Kolodziejczyk Content-Type: multipart/alternative; boundary="00000000000029997a05a41bffdb" Date: Sat, 25 Apr 2020 06:43:43 -0500 MIME-Version: 1.0 Sent to CCL by: Wojciech Kolodziejczyk [dziecial-#-icnanotox.org] --00000000000029997a05a41bffdb Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable The method as well as basis set depends on system you have sob., 25 kwi 2020, 04:49 u=C5=BCytkownik Partha Sengupta anapspsmo%%gmail.c= om < owner-chemistry,ccl.net> napisa=C5=82: > > Sir, > Which method in TD works(UV-VIS) relates closest peak values in Gaussian > 09w with the experimental peak values. > PSSengupta > > > -- > > > *Dr. Partha Sarathi SenguptaAssociate ProfessorVivekananda Mahavidyalaya, > Burdwan* > --00000000000029997a05a41bffdb Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
The method as well as basis set depends on system you hav= e

sob., 25 kwi 2020, 04:49 u=C5=BCytkownik Partha Sengupta anapspsmo%%gmail.com <owner-chemistry,ccl.net> napisa=C5=82:

Sir,=C2=A0
Which method in TD works(UV-VIS) relates closest peak values in Gauss= ian 09w with the experimental peak values.
PSSengupta=C2=A0


--
= Dr. Partha Sarathi Sengupta
Associate Professor
Vivekananda= Mahavidyalaya, Burdwan
--00000000000029997a05a41bffdb-- From owner-chemistry@ccl.net Sat Apr 25 08:23:00 2020 From: "Margraf, Johannes johannes.margraf#,#ch.tum.de" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54036-200425082123-28735-kDeTPcOuIF0SDqRuljLqcw[-]server.ccl.net> X-Original-From: "Margraf, Johannes" Content-Language: en-US Content-Type: multipart/alternative; boundary="_000_f555cac309df489cbd7dfc8dcaaa537bchtumde_" Date: Sat, 25 Apr 2020 12:21:12 +0000 MIME-Version: 1.0 Sent to CCL by: "Margraf, Johannes" [johannes.margraf]![ch.tum.de] --_000_f555cac309df489cbd7dfc8dcaaa537bchtumde_ Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: base64 SGksDQoNCg0KSSBhZ3JlZSB3aXRoIFN1c2kuDQoNCg0KSSB3b3VsZCBhZGQsIGhvd2V2ZXIsIHRo YXQgdGhlcmUgbWF5IGJlIHNvbWUgZWRnZSBjYXNlcyB3aGVyZSBuZWdhdGl2ZSBkZW5zaXRpZXMg YXJlIHBvc3NpYmxlIGZvciBtZXRob2RzIHRoYXQgdXNlIHRoZSBvbmUtcGFydGljbGUgZGVuc2l0 eSBtYXRyaXggKGkuZS4gTXVsbGlrZW4gb3IgTkJPKS4gS3VybGFuY2hlZWsgYW5kIEhlYWQtR29y ZG9uIHNob3dlZCAoaHR0cHM6Ly9kb2kub3JnLzEwLjEwODAvMDAyNjg5NzA5MDI4MzU2MzcpIHRo YXQgTVAyIGRlbnNpdHkgbWF0cmljZXMgYmFzZWQgb24gVUhGIG9yYml0YWxzIGNhbiBoYXZlIG5l 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multipart/alternative; boundary="00000000000093d60605a41c4bd9" Date: Sat, 25 Apr 2020 17:35:05 +0530 MIME-Version: 1.0 Sent to CCL by: Raghavendra V [raghav011986%gmail.com] --00000000000093d60605a41c4bd9 Content-Type: text/plain; charset="UTF-8" Hi sir, There is no one particular functional that works for all systems, depends on the chemical system you are using. What is the chemical you are working with? Regards. Raghav On Sat, 25 Apr, 2020, 3:14 PM Partha Sengupta anapspsmo%%gmail.com, < owner-chemistry*o*ccl.net> wrote: > > Sir, > Which method in TD works(UV-VIS) relates closest peak values in Gaussian > 09w with the experimental peak values. > PSSengupta > > > -- > > > *Dr. Partha Sarathi SenguptaAssociate ProfessorVivekananda Mahavidyalaya, > Burdwan* > --00000000000093d60605a41c4bd9 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hi sir,=C2=A0

There is no one particular functional that works for all systems, depends= on the chemical system you=C2=A0are using.

What is the chemical you are working with?

Regards.
Ragh= av

On Sat, 25 Apr, 2020, 3:14 PM Partha Sengupta anapspsmo%%gmail.com, <owner-chemistry*o*ccl.net> wrote:

Sir,=C2=A0
Whic= h method in TD works(UV-VIS) relates closest peak values in Gaussian 09w wi= th the experimental peak values.
PSSengupta=C2=A0


--
Dr. Partha Sarathi Sengupta
Associate Professor
Vivekananda Mahavidy= alaya, Burdwan
--00000000000093d60605a41c4bd9-- From owner-chemistry@ccl.net Sat Apr 25 12:22:01 2020 From: "Mezei, Mihaly mihaly.mezei^mssm.edu" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54038-200425122039-26827-bAryKcaXWvkPKcgDcn2Q5w++server.ccl.net> X-Original-From: "Mezei, Mihaly" Content-Language: en-US Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset="utf-8" Date: Sat, 25 Apr 2020 16:20:33 +0000 MIME-Version: 1.0 Sent to CCL by: "Mezei, Mihaly" [mihaly.mezei~~mssm.edu] Greetings, Let me add one more method to the list of density partitioning techniques: Mihaly Mezei and Edwin S. Campbell, Efficient Multipole Expansion: Choice of Order and Density Partitioning Techniques, Theoret. Chim. Acta (Berl.) 43, 227-237 (1977). The corresponding software is available at the URL http://inka.mssm.edu/~mezei/maxwell Mihaly Mezei Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai Voice: (212) 659-5475. Fax: (212) 849-2456 WWW (MSSM home): http://icahn.mssm.edu/profiles/mihaly-mezei WWW (Lab home - software, publications): http://inka.mssm.edu/~mezei ________________________________________ > From: owner-chemistry+mihaly.mezei==mssm.edu]|[ccl.net on behalf of Thomas Manz thomasamanz|-|gmail.com Sent: Saturday, April 25, 2020 1:08:14 AM To: Mezei, Mihaly Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? USE CAUTION: External Message. Dear Colleagues, While writing a journal manuscript, I encountered the following technical question, to which I do not currently know the answer. Is it known which of the following charge partitioning methods (if any) can sometimes assign a negative electron density value to one (or more) atoms at some position(s) in space? (1) Intrinsic bond orbital (IBO) method by Knizia (J Chem Theory Comput, 2013, 9, 4834−4843, DOI: 10.1021/ct400687b) (2) Bickelhaupt method by Bickelhaupt et al. (Organometallics 1996, 15, 2923-2931, DOI: 10.1021/om950966x) (3) Minimal basis set Bickelhaupt (MBSBickelhaupt) method by Cho et al. (ChemPhysChem, 2020, 21, 688-696, DOI:10.1002/cphc.202000040) (4) Natural population analysis (NPA) by Reed, Weinstock, and Weinhold (J Chem Phys, 1985, 83, 735-746, DOI: 10.1063/1.449486) If you have insights into this question, would you be able to provide a specific example, reference, or brief mathematical explanation? Sincerest thanks, Tom Manz From owner-chemistry@ccl.net Sat Apr 25 12:57:00 2020 From: "Thomas Manz thomasamanz/a\gmail.com" To: CCL Subject: CCL: which charge partitioning methods always give non-negative atom-in-material densities? Message-Id: <-54039-200425122732-28789-R6ZlmkVJ/ufpfsUiu+Xppg^server.ccl.net> X-Original-From: Thomas Manz Content-Type: multipart/alternative; boundary="00000000000005c21705a41ff5f4" Date: Sat, 25 Apr 2020 10:27:15 -0600 MIME-Version: 1.0 Sent to CCL by: Thomas Manz [thomasamanz(-)gmail.com] --00000000000005c21705a41ff5f4 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable 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. (b) Because the NPA localized orbitals are orthonormal, and their assigned partial occupancies are non-negative, the overlap or cross term between two localized orbitals integrates to zero (because the localized orbitals are orthonormal) leaving a net non-negative contribution to each atom's integrated population from each localized orbital. 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. 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. The NPA method does not appear to describe a particular protocol for dividing the cross terms between two atoms. Since the NPA cross terms integrate to zero (i.e., the NAO's are orthonormal), the NPA method has not yet concerned itself with a particular protocol for dividing the cross terms. Accordingly, the NPA method yields non-negative integrated populations, but appears to have no specific electron distributions assigned to particular atoms in the material. However, one could easily do that by assuming a cross-term partitioning ala Mulliken (in which each atom gets half the cross term) or Bickelhaupt (in which each cross-term is divided proportionally to the corresponding self-terms) except using the orthonormal NAOs as the basis functions. This would, of course, return the NPA integrated populations, but also assign an electron density distribution to each atom in the material. (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 =3D 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 =3D proportional to qjj/(qii= + qjj), where qjj is the self-population of orbital j on atom B (These sum to one.) (d) I understand the point about MP2 population analysis yielding potentially negative populations, in cases where it yields negative eigenvalues for one of the natural orbitals (eigenstates of MP2 density matrix). This, of course, is an important point. So, let me rephrase or restrict my original question to those cases where the quantum chemistry density is N-representable (i.e., eigenvalues of the natural spin-orbitals are between 0 and 1 inclusive). (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. Sincerely, Tom On Sat, Apr 25, 2020 at 3:08 AM Susi Lehtola susi.lehtola/ aalumni.helsinki.fi wrote: > > Sent to CCL by: Susi Lehtola [susi.lehtola*o*alumni.helsinki.fi] > On 4/25/20 8:08 AM, Thomas Manz thomasamanz|-|gmail.com wrote: > > Dear Colleagues, > > > > While writing a journal manuscript, I encountered the following technic= al > > question, to which I do not currently know the answer. > > > > Is it known which of the following charge partitioning methods (if any) > can > > sometimes assign a negative electron density value to one (or more) > atoms at > > some position(s) in space? > > > > (1) Intrinsic bond orbital (IBO) method by Knizia (J Chem Theory Comput= , > 2013, > > 9, 4834=E2=88=924843, DOI: 10.1021/ct400687b) > > > > (2) Bickelhaupt method by Bickelhaupt et al. (Organometallics 1996, 15, > > 2923-2931, DOI: 10.1021/om950966x) > > > > (3) Minimal basis set Bickelhaupt (MBSBickelhaupt) method by Cho et al. > > (ChemPhysChem, 2020, 21, 688-696, DOI:10.1002/cphc.202000040) > > > > (4) Natural population analysis (NPA) by Reed, Weinstock, and Weinhold > (J Chem > > Phys, 1985, 83, 735-746, DOI: 10.1063/1.449486) > > > > If you have insights into this question, would you be able to provide a > specific > > example, reference, or brief mathematical explanation? > > Dear Tom, > > > this truly is a technical question. Namely, since the electron density is > positive semidefinite, n(r) >=3D 0 everywhere, a charge partitioning meth= od > that > assigned a *negative electronic charge* to one or more atoms would > necessarily > mean grave mathematical problems: any well-based method should yield at > least > zero electrons for any atom. > > (1) IBO belongs to the class of generalized Pipek-Mezey methods > (10.1021/ct401016x) that produce localized orbitals from a given > definition of > atomic partial charges. The partial charges in IBO are from the intrinsic > atomic > orbitals (IAO) from the same paper. The IAOs are just taken as the occupi= ed > atomic orbitals for the atomic ground state. > > Since IAO assigns partial charges by projection (like most of the other > usable > generalized Pipek-Mezey methods that are mathematically well-defined, > unlike the > original Pipek-Mezey scheme), it is not possible to get negative electron > densities with IAO. > > Projection operators can only have eigenvalues between 0 and 1; 0 for > components > that cannot be at all described in the other basis and 1 for components > that can > be exactly represented in the other basis. > > (2) It is not clear which method you mean; the Bickelhaupt et al paper > uses two > > from the literature and describes two methods. The first one defines > partial > charges by integrating the difference of the molecular electron density > and the > superposition of atomic densities over the Voronoi cell, and the second i= s > a > modification to the Mulliken scheme where off-diagonal elements are also > included; like the Mulliken scheme, this one is also mathematically > ill-defined > since it does not have a basis set limit (10.1021/ct401016x). > > I have a vague recollection of seeing something similar to the modified > Mulliken scheme Bickelhaupt used in much earlier literature. It is not > obvious > how electron density would be assigned by the Voronoi scheme, since it > does not > use the nuclear charge at all. > > (3) This is Bickelhaupt's scheme; one just projects into a minimal basis > before > performing the Mulliken-style analysis. > > (4) As far as I know, NPA is also based on projections, and thereby shoul= d > not > have problems with negative densities. > > Even though the Mulliken scheme is not mathematically well-founded, I don= 't > think it is possible to get negative electron densities with it: if you > span the > molecular basis with basis functions on a single atom, all electrons will > be > counted on that center, and the others will have zero electrons each. > -- > ------------------------------------------------------------------ > 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-> > > --00000000000005c21705a41ff5f4 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Hi=C2=A0Susi=C2=A0and Hannes,

Thanks for your replies.=C2=A0

(a) The Mul= liken 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, 1= 955, 1833-1840, DOI: 10.1063/1.1740588). Consequently, Mulliken's metho= d assigns negative electron density to some atoms at some positions in spac= e.

(b) Because the=C2=A0NPA localized orbitals are= orthonormal, and their assigned partial occupancies are non-negative, the = overlap or cross term between two localized orbitals integrates to zero (be= cause the localized orbitals are orthonormal) leaving a net non-negative co= ntribution to each atom's integrated population from each localized orb= ital.=C2=A0

However, my question concerns the elec= tron 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 posi= tive, negative, and zero) or about the integrated number of electrons assig= ned to an atom (i.e., the populations). For example, if the electron densit= y at a particular spatial position is 17.1 electrons/bohr^3, do any of thes= e methods ever assign a negative electron density value (e.g., -0.35 electr= ons/bohr^3) to any atom at any spatial position.=C2=A0In this example, the = electron density assigned to the other atoms would thus sum to 17.45 electr= ons/bohr^3, to reproduce the electron density value of 17.1 electrons/bohr^= 3 when summed over all atoms at this 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 c= ross term. Only if the magnitude of the cross term can exceed the self-term= s at some location in space then the assigned electron density distribution= may be negative at some spatial position for some atom. For the four metho= ds mentioned in my email, I am having trouble figuring out if or when this = could=C2=A0occur.

The NPA method does not appe= ar to describe a particular protocol for dividing the cross terms between t= wo atoms. Since the NPA cross terms integrate to zero (i.e., the NAO's = are orthonormal), the NPA method has not yet concerned itself with a partic= ular protocol for dividing the cross terms. Accordingly, the NPA method yie= lds non-negative integrated populations, but appears to have no specific el= ectron distributions assigned to particular atoms in the material. However,= one could easily do that by assuming a cross-term partitioning ala Mullike= n (in which each atom gets half the cross term) or Bickelhaupt (in which ea= ch cross-term is divided proportionally to the corresponding self-terms) ex= cept using the orthonormal NAOs as the basis functions. This would, of cour= se, return the NPA integrated populations, but also assign an electron dens= ity distribution to each atom in the material.

(c)= The Bickelhaupt method I referred to was intended to mean their modified M= ulliken-like scheme (eqn 11 of their paper). Mulliken's method assigns = half of each=20 localized orbitals cross term each of the two atoms. In the Bickelhaupt sch= eme, 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 =3D proportional to qii/(qii=C2=A0+ qjj), w= here qii is the self-population of orbital i=C2=A0on atom A
fract= ion 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 o= rbital j on atom B
(These sum to one.)

(= d) I understand the point about MP2 population analysis yielding potentiall= y negative populations, in cases where it yields negative eigenvalues for o= ne of the natural orbitals (eigenstates of MP2 density matrix). This, of co= urse, is an important point. So, let me rephrase or restrict my original qu= estion to those cases where the quantum chemistry density is N-representabl= e=C2=A0(i.e., eigenvalues of the natural spin-orbitals are between 0 and 1 = inclusive).

(e) I do not yet fully understand the = nature of the projections involved in the IBO method. Consequently, it is h= ard for me to completely follow your argument about why the IBO method is e= xpected to always yield non-negative integrated populations. I do understan= d 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 und= erstand 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 in= terested in whether the IBO method may assign a negative electron density v= alue (at a particular spatial position) to any atom.

Sincerely,

Tom


O= n Sat, Apr 25, 2020 at 3:08 AM Susi Lehtola susi.lehtola/aalumni.helsinki.fi <owner-chemistry]-[ccl.n= et> wrote:
alumni.helsinki.fi]
On 4/25/20 8:08 AM, Thomas Manz thomasamanz|-|gmail.com wrote:
> Dear Colleagues,
>
> While writing a journal manuscript, I encountered the following techni= cal
> question, to which I do not currently know the answer.
>
> Is it known which of the following charge partitioning methods (if any= ) can
> sometimes assign a negative electron density value to one (or more) at= oms at
> some position(s) in space?
>
> (1) Intrinsic bond orbital (IBO) method by Knizia (J Chem Theory Compu= t, 2013,
> 9, 4834=E2=88=924843, DOI: 10.1021/ct400687b)
>
> (2) Bickelhaupt method by Bickelhaupt et al. (Organometallics 1996, 15= ,
> 2923-2931, DOI:=C2=A010.1021/om950966x)
>
> (3) Minimal basis set Bickelhaupt (MBSBickelhaupt) method by Cho et al= .
> (ChemPhysChem, 2020, 21, 688-696, DOI:10.1002/cphc.202000040)
>
> (4) Natural population analysis (NPA) by Reed, Weinstock, and Weinhold= (J Chem
> Phys, 1985, 83, 735-746, DOI:=C2=A010.1063/1.449486)
>
> If you have insights into this question, would you be able to provide = a specific
> example, reference, or brief mathematical explanation?

Dear Tom,


this truly is a technical question. Namely, since the electron density is positive semidefinite, n(r) >=3D 0 everywhere, a charge partitioning met= hod that
assigned a *negative electronic charge* to one or more atoms would necessar= ily
mean grave mathematical problems: any well-based method should yield at lea= st
zero electrons for any atom.

(1) IBO belongs to the class of generalized Pipek-Mezey methods
(10.1021/ct401016x) that produce localized orbitals from a given definition= of
atomic partial charges. The partial charges in IBO are from the intrinsic a= tomic
orbitals (IAO) from the same paper. The IAOs are just taken as the occupied=
atomic orbitals for the atomic ground state.

Since IAO assigns partial charges by projection (like most of the other usa= ble
generalized Pipek-Mezey methods that are mathematically well-defined, unlik= e the
original Pipek-Mezey scheme), it is not possible to get negative electron densities with IAO.

Projection operators can only have eigenvalues between 0 and 1; 0 for compo= nents
that cannot be at all described in the other basis and 1 for components tha= t can
be exactly represented in the other basis.

(2) It is not clear which method you mean; the Bickelhaupt et al paper uses= two
> from the literature and describes two methods. The first one defines p= artial
charges by integrating the difference of the molecular electron density and= the
superposition of atomic densities over the Voronoi cell, and the second is = a
modification to the Mulliken scheme where off-diagonal elements are also included; like the Mulliken scheme, this one is also mathematically ill-def= ined
since it does not have a basis set limit (10.1021/ct401016x).

I have a vague recollection of seeing something similar to the=C2=A0 modifi= ed
Mulliken scheme Bickelhaupt used in much earlier literature. It is not obvi= ous
how electron density would be assigned by the Voronoi scheme, since it does= not
use the nuclear charge at all.

(3) This is Bickelhaupt's scheme; one just projects into a minimal basi= s before
performing the Mulliken-style analysis.

(4) As far as I know, NPA is also based on projections, and thereby should = not
have problems with negative densities.

Even though the Mulliken scheme is not mathematically well-founded, I don&#= 39;t
think it is possible to get negative electron densities with it: if you spa= n the
molecular basis with basis functions on a single atom, all electrons will b= e
counted on that center, and the others will have zero electrons each.
--
------------------------------------------------------------------
Mr. Susi Lehtola, PhD=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Junior= Fellow, Adjunct Professor
susi.lehtola##alumni.helsinki.fi=C2=A0 =C2=A0University of Helsinki
http://susilehtola.github.io/=C2=A0 =C2=A0 =C2=A0Finland
------------------------------------------------------------------
Susi Lehtola, dosentti, FT=C2=A0 =C2=A0 =C2=A0 =C2=A0 tutkijatohtori
susi.lehtola##alumni.helsinki.fi=C2=A0 =C2=A0Helsingin yliopisto
http://susilehtola.github.io/
------------------------------------------------------------------



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--00000000000005c21705a41ff5f4-- From owner-chemistry@ccl.net Sat Apr 25 13:37:00 2020 From: "Partha Sengupta anapspsmo{}gmail.com" To: CCL Subject: CCL:G: TD spectra Message-Id: <-54040-200425111556-18687-tcVvgveEkyQWMrPBBYS+vQ()server.ccl.net> X-Original-From: Partha Sengupta Content-Type: multipart/alternative; boundary="0000000000000eca1605a41ef5b1" Date: Sat, 25 Apr 2020 20:45:30 +0530 MIME-Version: 1.0 Sent to CCL by: Partha Sengupta [anapspsmo]=[gmail.com] --0000000000000eca1605a41ef5b1 Content-Type: text/plain; charset="UTF-8" I am working with some nickel and copper complexes. Partha On Sat, Apr 25, 2020 at 8:20 PM Raghavendra V raghav011986],[gmail.com < owner-chemistry _ ccl.net> wrote: > Hi sir, > > There is no one particular functional that works for all systems, depends > on the chemical system you are using. > > What is the chemical you are working with? > > Regards. > Raghav > > On Sat, 25 Apr, 2020, 3:14 PM Partha Sengupta anapspsmo%%gmail.com, < > owner-chemistry[#]ccl.net> wrote: > >> >> Sir, >> Which method in TD works(UV-VIS) relates closest peak values in Gaussian >> 09w with the experimental peak values. >> PSSengupta >> >> >> -- >> >> >> *Dr. Partha Sarathi SenguptaAssociate ProfessorVivekananda Mahavidyalaya, >> Burdwan* >> > -- *Dr. Partha Sarathi SenguptaAssociate ProfessorVivekananda Mahavidyalaya, Burdwan* --0000000000000eca1605a41ef5b1 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
I am working with some nickel and copper complexes.
Pa= rtha

On Sat, Apr 25, 2020 at 8:20 PM Raghavendra V raghav011986],[gmail.com <owner-chemistry _ ccl.net> wrote:
Hi sir,=C2=A0

There is no one particular functional= that works for all systems, depends on the chemical system you=C2=A0are us= ing.

What is the chemica= l you are working with?

= Regards.
Raghav

On Sat, 25 Apr, 2020, 3:14 PM P= artha Sengupta anapspsmo%%gm= ail.com, <owner-chemistry[#]ccl.net> wrote:

Sir,= =C2=A0
Which method in TD works(UV-VIS) relates closest peak valu= es in Gaussian 09w with the experimental peak values.
PSSengupta=C2=A0<= font color=3D"#888888">


--
Dr. Partha Sara= thi Sengupta
Associate Professor
Vivekananda Mahavidyalaya, Burdwan


--
Dr. Partha Sarat= hi Sengupta
Associate Professor
Vivekananda Mahavidyalaya, Burdwan
--0000000000000eca1605a41ef5b1-- From owner-chemistry@ccl.net Sat Apr 25 23:39:00 2020 From: "Bruno Andrade bandrade]_[uesb.edu.br" To: CCL Subject: CCL: Gromacs protein unfolding tutorial Message-Id: <-54041-200425231806-26351-hrfNMfZCsEKmIOksq6l77w]_[server.ccl.net> X-Original-From: "Bruno Andrade" Date: Sat, 25 Apr 2020 23:18:03 -0400 Sent to CCL by: "Bruno Andrade" [bandrade-#-uesb.edu.br] Dear CCL colleagues, Could you indicate any Gromacs tutorial for protein unfolding simulations? Thank you, Bruno Andrade.