From owner-chemistry@ccl.net Thu Oct 8 05:45:00 2020 From: "Marcel Swart (GMail) marcel.swart##gmail.com" To: CCL Subject: CCL:G: Interaction energy between open-shell systems Message-Id: <-54180-201008054422-25387-R1CsKOF+OEeWbDuDFb9dag=-=server.ccl.net> X-Original-From: "Marcel Swart (GMail)" Content-Type: multipart/alternative; boundary="Apple-Mail=_B1DB9D2D-D13E-4F18-918D-69C30C1E7D64" Date: Thu, 8 Oct 2020 11:44:13 +0200 Mime-Version: 1.0 (Mac OS X Mail 12.4 \(3445.104.17\)) Sent to CCL by: "Marcel Swart (GMail)" [marcel.swart()gmail.com] --Apple-Mail=_B1DB9D2D-D13E-4F18-918D-69C30C1E7D64 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=utf-8 For simple organic radicals, the answer is easy. The correct interaction = energy is the one which is lowest. For transition metals there is a variety of possible spin states, which = is not simple to predict. Metals can have different oxidation states, = different spin states, the ligand can be redox non-innocent, etc. etc. = There is a wealth of publications out there, including the first = textbook that deals entirely with spin states: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118898277 Or you can read a recent book chapter: M. Swart "Dealing with spin states in computational organometallic catalysis" Top. Organomet. Chem. 2020, ASAP http://www.dx.doi.org/10.1007/3418_2020_49 High-spin diiron(III) tend to couple antiferromagnetically, see e.g. http://www.dx.doi.org/10.1021/jacs.9b12081 Much more information and useful literature can be found in the list of = papers resulting from the ECOSTBio COST Action: http://www.ecostbio.eu/publications/index.html MS > On 07 Oct 2020, at 22:24, Radoslaw Kaminski rkaminski85:+:gmail.com = wrote: >=20 > Dear All, >=20 > We frequently do interaction energy computations using Gaussian=20 > (counterpoise keyword etc.). In our case we cut out molecules from the=20= > crystal and compute int. energies between molecules for various = motifs. >=20 > For simple organic molecules this is simple since they are usually=20 > singlets, thus the corresponding spin and multiplicity line looks like=20= > that (assuming all molecules are neutral): >=20 > 0 1 0 1 0 1 >=20 > The situation is much more complex if unpaired electrons are present. = If=20 > molecule has a multiplicity of 2 (one unpaired electron) the total=20 > multiplicity of the system can be both 1 or 3. Thus, two are possible=20= > (again, for neutral molecules): >=20 > 0 1 0 2 0 2 > 0 3 0 2 0 2 >=20 > My question is then what would be the "correct" approach to compute=20 > interactions energies in such case? In this sample example we can = compute=20 > both, and from our tentative results the energies are very mych=20 > different. Which are then the most "correct" ones? >=20 > We plan to compute such int. energies between molecules with = transition=20 > metals such as Fe or Co as well. In such cases the metal can be, for=20= > example, in high-spin state. Computation of int. energies between two = HS=20 > molecules leads to variety of multiplicity states to consider... >=20 > If someone has experience and would be kind enough to provide an = comment=20 > on such problems I would be grateful. Some references would also be of=20= > benefit (I could not easily find any unfortunately). With many thanks = in=20 > advance. >=20 > Regards, >=20 > Radek Kaminski Marcel Swart ICREA Research Professor at University of Girona Director of Institut de Qu=C3=ADmica Computacional i Cat=C3=A0lisi Univ. Girona, Campus Montilivi (Ci=C3=A8ncies) c/ M.A. Capmany 69 17003 Girona, Spain www.marcelswart.eu marcel.swart%%gmail.com vCard addressbook://www.marcelswart.eu/MSwart.vcf = --Apple-Mail=_B1DB9D2D-D13E-4F18-918D-69C30C1E7D64 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=utf-8 For = simple organic radicals, the answer is easy. The correct interaction = energy is the one which is lowest.

For transition metals there is a = variety of possible spin states, which is not simple to predict. Metals = can have different oxidation states, different spin states, the ligand = can be redox non-innocent, etc. etc. There is a wealth of publications = out there, including the first textbook that deals entirely with spin = states:

https://onlinelibrary.wiley.com/doi/book/10.1002/9781118898277<= /a>

Or you can = read a recent book chapter:

M. Swart
"Dealing with spin states in computational organometallic = catalysis"
Top. Organomet. = Chem. 2020, ASAP

http://www.dx.doi.org/10.1007/3418_2020_49

High-spin diiron(III) = tend to couple antiferromagnetically, see e.g.

http://www.dx.doi.org/10.1021/jacs.9b12081

Much more information = and useful literature can be found in the list of papers resulting from = the ECOSTBio COST Action:

http://www.ecostbio.eu/publications/index.html

MS

On 07 Oct 2020, at 22:24, Radoslaw Kaminski rkaminski85:+:gmail.com <owner-chemistry%%ccl.net> wrote:

Dear All,

We frequently do interaction = energy computations using Gaussian
(counterpoise keyword etc.). In = our case we cut out molecules from the
crystal and compute int. = energies between molecules for various motifs.

For simple organic molecules = this is simple since they are usually
singlets, thus the corresponding = spin and multiplicity line looks like
that (assuming all molecules are = neutral):

0 1 0 1 0 = 1

The situation = is much more complex if unpaired electrons are present. If
molecule has a multiplicity of 2 = (one unpaired electron) the total
multiplicity of the system can = be both 1 or 3. Thus, two are possible
(again, for neutral = molecules):

0 1 0 2 0 = 2
0 3 0 2 0 = 2

My question = is then what would be the "correct" approach to compute
interactions energies in such = case? In this sample example we can compute
both, and from our tentative = results the energies are very mych
different. Which are then the = most "correct" ones?

We plan to compute such int. energies between molecules with = transition
metals such as Fe or Co as well. = In such cases the metal can be, for
example, in high-spin state. = Computation of int. energies between two HS
molecules leads to variety of = multiplicity states to consider...

If someone has experience and would be kind enough to provide = an comment
on such problems I would be = grateful. Some references would also be of
benefit (I could not easily find = any unfortunately). With many thanks in
advance.

Regards,

Radek = Kaminski

Marcel Swart

ICREA Research = Professor at University of Girona

Director of Institut de Qu=C3=ADmica Computacional = i Cat=C3=A0lisi

Univ. Girona, Campus Montilivi = (Ci=C3=A8ncies)

c/ M.A. = Capmany 69
17003 Girona, Spain

www.marcelswart.eu

marcel.swart%%gmail.com

vCard

addressbook://www.marcelswart.eu/MSwart.vcf

= --Apple-Mail=_B1DB9D2D-D13E-4F18-918D-69C30C1E7D64-- From owner-chemistry@ccl.net Thu Oct 8 06:20:01 2020 From: "Mariusz Radon mariusz.radon .. gmail.com" To: CCL Subject: CCL:G: Interaction energy between open-shell systems Message-Id: <-54181-201008055301-28427-LMh7cOshsfzOtwrUoSnr0w(_)server.ccl.net> X-Original-From: Mariusz Radon Content-Type: multipart/alternative; boundary="Apple-Mail=_CC24F753-2D60-4817-8B2E-8D2A8A3C9381" Date: Thu, 8 Oct 2020 11:52:51 +0200 Mime-Version: 1.0 (Mac OS X Mail 13.4 \(3608.120.23.2.4\)) Sent to CCL by: Mariusz Radon [mariusz.radon(!)gmail.com] --Apple-Mail=_CC24F753-2D60-4817-8B2E-8D2A8A3C9381 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=utf-8 > On 7 Oct 2020, at 22:24, Radoslaw Kaminski rkaminski85:+:gmail.com = wrote: >=20 >=20 > Sent to CCL by: "Radoslaw Kaminski" [rkaminski85^gmail.com] > Dear All, >=20 > We frequently do interaction energy computations using Gaussian=20 > (counterpoise keyword etc.). In our case we cut out molecules from the=20= > crystal and compute int. energies between molecules for various = motifs. >=20 > For simple organic molecules this is simple since they are usually=20 > singlets, thus the corresponding spin and multiplicity line looks like=20= > that (assuming all molecules are neutral): >=20 > 0 1 0 1 0 1 >=20 > The situation is much more complex if unpaired electrons are present. = If=20 > molecule has a multiplicity of 2 (one unpaired electron) the total=20 > multiplicity of the system can be both 1 or 3. Thus, two are possible=20= > (again, for neutral molecules): >=20 > 0 1 0 2 0 2 > 0 3 0 2 0 2 >=20 > My question is then what would be the "correct" approach to compute=20 > interactions energies in such case? In this sample example we can = compute=20 > both, and from our tentative results the energies are very mych=20 > different. Which are then the most "correct" ones? Dear Radek: The two possibilities correspond to different total spin states of the = entire system: either triplet or singlet. The total triplet state (0 3) = correspond to ferromagnetic whereas the singlet state (0 1) to = antiferromagnetic coupling between the spins of the two subsystems.=20 In principle you should pick the spin state which correspond to lower = energy because it is thermodynamically more stable. If the energy = difference between the two total spin state is small, the choice is not = that important (because the energy difference is small anyway), but you = said the energies are =E2=80=9Cvery much different=E2=80=9D. This simply = means that one of the total spin states is energetically very = unfavorable compared with the other one. This being said, watch out for the following: 1). At the DFT level the spin state energetics can be very inaccurate. = It is recommended to check at least two different functionals (hybrids = with different %HF or hybrid vs GGA, hybrid vs double-hybrid, etc). 2). You should look at the value of the total singlet state. There = are good chances that your calculations converge to spin-restricted = solution =3D0 (or maybe even Gaussian enforced it when you set =E2=80=9C= 0 1=E2=80=9D?), whereas there might exist a lower energy open-shell = singlet solution with grater than 0. If this is the case of course = you should choose the lower energy open-shell solution. 3). If you indeed obtain an open-shell singlet solution with grater = than 0 and energy below the closed-shell singlet solution, keep in mind = that the open-shell solution is is contaminated with the triplet state = (probably the same one you compute also with =E2=80=9C0 3=E2=80=9D = settings); this causes the value to differ from 0. In other words = these are broken-symmetry calculations. It is possible to correct the = energy for spin contamination using the Yamaguschi=E2=80=99s or = Noodleman=E2=80=99s approximate projection method (you can easily find = these formulas in the literature) 4). If you obtain closed-shell single, try using unrestricted initial = guess or perform stability analysis with Stable(RUHF,Opt). 5). I recommend you to clearly inspect not only the values for both = total spin states, but also their natural orbitals or natural spin = density orbitals of both solutions to make sure that they correspond to = what you expect (as far as I understand, some kind of radical coupling = of two open-shell fragment). 6). You may also consider to include ZPE or thermochemical corrections = to judge the relative thermochemical stabilities of your spin states = more accurately. Best wishes, Mariusz --=20 Mariusz Radon, Ph.D., D.Sc. Assistant Professor Faculty of Chemistry, Jagiellonian University Address: Gronostajowa 2, 30-387 Krakow, Poland Room C1-06, Phone: 48-12-686-24-89 E-mail: mradon++chemia.uj.edu.pl = (mariusz.radon++uj.edu.pl ) Web: http://www.chemia.uj.edu.pl/~mradon = ORCID: https://orcid.org/0000-0002-1901-8521 = = --Apple-Mail=_CC24F753-2D60-4817-8B2E-8D2A8A3C9381 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=utf-8

On 7 = Oct 2020, at 22:24, Radoslaw Kaminski rkaminski85:+:gmail.com <owner-chemistry++ccl.net> wrote:

Sent to CCL by: "Radoslaw Kaminski" = [rkaminski85^gmail.com]
Dear All,

We frequently do = interaction energy computations using Gaussian
(counterpoise = keyword etc.). In our case we cut out molecules from the
crystal and = compute int. energies between molecules for various motifs.

For simple organic molecules this is simple = since they are usually
singlets, = thus the corresponding spin and multiplicity line looks like
that = (assuming all molecules are neutral):

0 1 0 = 1 0 1

The situation is much more complex if = unpaired electrons are present. If
molecule has = a multiplicity of 2 (one unpaired electron) the total
multiplicity = of the system can be both 1 or 3. Thus, two are possible
(again, for = neutral molecules):

0 1 0 2 0 2
0 3 0 2 0 2

My question is then = what would be the "correct" approach to compute
interactions = energies in such case? In this sample example we can compute
both, and = > from our tentative results the energies are very mych
different. = Which are then the most "correct" ones?

Dear Radek:

The two possibilities correspond to = different total spin states of the entire system: either triplet or = singlet. The total triplet state (0 3) correspond to ferromagnetic = whereas the singlet state (0 1) to antiferromagnetic coupling between = the spins of the two subsystems.

In principle you should pick the = spin state which correspond to lower energy because it is = thermodynamically more stable. If the energy difference between the two = total spin state is small, the choice is not that important (because the = energy difference is small anyway), but you said the energies are = =E2=80=9Cvery much different=E2=80=9D. This simply means that one of the = total spin states is energetically very unfavorable compared with the = other one.

This being said, watch out for the = following:

1). At the DFT level the spin state = energetics can be very inaccurate. It is recommended to check at least = two different functionals (hybrids with different %HF or hybrid vs GGA, = hybrid vs double-hybrid, etc).

2). You should look at the = <S2> value of the total singlet state. There are good chances that = your calculations converge to spin-restricted solution <S2>=3D0 = (or maybe even Gaussian enforced it when you set =E2=80=9C0 1=E2=80=9D?), = whereas there might exist a lower energy open-shell singlet solution = with <S2> grater than 0. If this is the case of course you should = choose the lower energy open-shell solution.

3). If you indeed obtain an = open-shell singlet solution with <S2> grater than 0 and = energy below the closed-shell singlet solution, keep in mind that the = open-shell solution is is contaminated with the triplet state = (probably the same one you compute also with =E2=80=9C0 3=E2=80=9D = settings); this causes the <S2> value to differ from 0. In other = words these are broken-symmetry calculations. It is possible to correct = the energy for spin contamination using the Yamaguschi=E2=80=99s or = Noodleman=E2=80=99s approximate projection method (you can easily find = these formulas in the literature)

4). If you obtain closed-shell = single, try using unrestricted initial guess or perform stability = analysis with Stable(RUHF,Opt).

5). I recommend you to clearly = inspect not only the <S2> values for both total spin states, but = also their natural orbitals or natural spin density orbitals of both = solutions to make sure that they correspond to what you expect (as far = as I understand, some kind of radical coupling of two open-shell = fragment).

6). You may also consider to = include ZPE or thermochemical corrections to judge the relative = thermochemical stabilities of your spin states more = accurately.

Best wishes,
Mariusz

--
Mariusz Radon, Ph.D., = D.Sc.
Assistant Professor
Faculty of Chemistry, Jagiellonian = University

Address: Gronostajowa 2, 30-387 = Krakow, Poland
Room C1-06, Phone: = 48-12-686-24-89
E-mail: mradon++chemia.uj.edu.pl (mariusz.radon++uj.edu.pl)
Web: http://www.chemia.uj.edu.pl/~mradon
ORCID: https://orcid.org/0000-0002-1901-8521= --Apple-Mail=_CC24F753-2D60-4817-8B2E-8D2A8A3C9381--