From owner-chemistry@ccl.net Thu Oct 25 05:12:00 2018 From: "Ulrike Salzner salzner\a/fen.bilkent.edu.tr" To: CCL Subject: CCL:G: signs of AO coefficients and nodes of orbitals Message-Id: <-53528-181025050933-26466-uo9GktvZG9XVeHaBPXeOMg]-[server.ccl.net> X-Original-From: Ulrike Salzner Content-Type: multipart/alternative; boundary="000000000000ca27bd057909e77c" Date: Thu, 25 Oct 2018 12:04:56 +0300 MIME-Version: 1.0 Sent to CCL by: Ulrike Salzner [salzner..fen.bilkent.edu.tr] --000000000000ca27bd057909e77c Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable Thanks to Per-Ola and Frank. Ulrike Frank Jensen If you plot the radial behavior of the orbital, you will find that there is the correct number of nodes. Remember that the GTO basis functions are continuous functions, and those with small exponents have a significant amplitude across a wide range of distance from the nucleus. GTOs with small coefficients in the AO/MO, positive or negative, thus modifies the shape, but does not necessarily change the sign of the total orbital. Frank > From: Norrby, Per-Ola Per-Ola.Norrby/./astrazeneca.com < owner-chemistry[A]ccl.net> Date: Mon, Oct 22, 2018 at 6:05 PM Subject: CCL: sign of AO coefficients and nodes of orbitals To: Salzner, Ulrike Dear Ulrike, I usually use the same trick myself, but it is really only appropriate with primitive Gaussians, or contracted functions without radial nodes. I believe these contracted functions themselves contain radial nodes=E2=80=A6= In this case, I have no simple trick, just counting them and trusting that the 2s orbital will have only one radial node=E2=80=A6 /Per-Ola *From:* owner-chemistry+per-ola.norrby=3D=3Dastrazeneca.com[A]ccl.net *On Behalf Of= *Ulrike Salzner salzner-,-fen.bilkent.edu.tr *Sent:* den 22 oktober 2018 12:07 *To:* Norrby, Per-Ola *Subject:* CCL: sign of AO coefficients and nodes of orbitals Hello, I always thought that the sign changes of the AO or MO coefficients reflect the nodal structure of the atomic orbitals, e.g one sign change for 2s, two for 3s and so on no matter how many basis functions contribute. This seems to be the case with Pople basis sets. At least that's what I saw for any case that I have looked at so far. With Dunning correlation consistent basis sets, the sign changes seem to have nothing to do with the nature of the orbitals, see for example for Mg 2s below which has two sign changes. My thinking was obviously wrong but how can I figure out what orbital I am dealing with, if the coefficients do not tell me? Thanks for enlightenment, Ulrike 6-31G* Molecular Orbital Coefficients: 1 2 3 4 5 (A1G)--O (A1G)--O (T1U)--O (T1U)--O (T1U)--O Eigenvalues -- -49.01914 -3.76376 -2.27827 -2.27827 -2.27827 1 1 Mg 1S 0.99741 -0.25504 0.00000 0.00000 0.00000 2 2S 0.01078 1.02972 0.00000 0.00000 0.0000= 0 3 2PX 0.00000 0.00000 0.99510 0.00000 0.00000 4 2PY 0.00000 0.00000 0.00000 0.99510 0.00000 5 2PZ 0.00000 0.00000 0.00000 0.00000 0.99510 aug-cc-pvqz Molecular Orbital Coefficients: 1 2 3 4 5 (A1G)--O (A1G)--O (T1U)--O (T1U)--O (T1U)--O Eigenvalues -- -49.03177 -3.76773 -2.28221 -2.28221 -2.28221 1 1 Mg 1S 1.00047 -0.25370 0.00000 0.00000 0.00000 2 2S -0.00346 0.62949 0.00000 0.00000 0.0000= 0 3 3S -0.00165 -0.42495 0.00000 0.00000 0.0000= 0 4 4S -0.00048 0.01639 0.00000 0.00000 0.0000= 0 5 5S 0.00046 -0.01004 0.00000 0.00000 0.0000= 0 6 6S -0.00022 0.00393 0.00000 0.00000 0.0000= 0 7 7S 0.00005 -0.00084 0.00000 0.00000 0.0000= 0 Prof. Ulrike Salzner Department of Chemistry Bilkent University 06800 Bilkent, Ankara Prof. Ulrike Salzner Department of Chemistry Bilkent University 06800 Bilkent, Ankara --000000000000ca27bd057909e77c Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
Thank= s to Per-Ola and Frank.
Ulrike


Frank Jensen <frj[A]chem.au.dk>

If you plot the r= adial behavior of the orbital, you will find that there is the correct numb= er of nodes.

Remember that the GTO basis functions are continuous functions, and those with=20 small exponents have a significant amplitude across a wide range of=20 distance from the nucleus. GTOs with small coefficients in the AO/MO,=20 positive or negative, thus modifies the shape, but does not necessarily=20 change the sign of the total orbital.

=C2=A0

Frank

=C2=A0




From: Norrby, Per-Ola Per-Ola.Norrby/./astrazeneca.com <owner-chemistry[A]ccl.net>
Date: Mon, Oct 22, 2018 at 6:= 05 PM
Subject: CCL: sign of AO coefficients and nodes of orbitals
To:= Salzner, Ulrike <salzner[A]fen.bilkent.edu.tr>


Dear Ulrike,

=C2=A0

I usually use the same trick myself, but it is=20 really only appropriate with primitive Gaussians, or contracted=20 functions without radial nodes. I believe these contracted functions=20 themselves contain radial nodes=E2=80=A6 In this case, I have no simple trick, just counting them and trusting that the 2s orbital will=20 have only one radial node=E2=80=A6

=C2=A0

/Per-Ola

=C2=A0

From: owner-chemistry+per-ola.norrby=3D=3Dastrazeneca.com[A]c= cl.net <owner-chemistry+per-ola.norrby=3D=3Dastrazeneca.com[A]ccl.net> On Behalf Of Ulrike Salzner salzner-,-fen.bilkent.edu.tr
Sent: den 22 oktober 2018 12:07
To: Norrby, Per-Ola <Per-Ola.Norrby[A]astrazeneca.com>
Subject: CCL: sign of AO coefficients and nodes of orbitals

=C2=A0

Hello,

I always thought that the sign changes of the AO or MO coefficients=20 reflect the nodal structure of the atomic orbitals, e.g one sign change=20 for 2s, two for 3s and so on no matter how many basis functions contribute. This seems to be the case with Pople basis sets.=20 At least that's what I saw for any case that I have looked at so far.= =20 With Dunning correlation consistent basis sets, the sign changes seem to have nothing to do with the nature of the orbitals, see for example for Mg 2s below which has two sign changes.=20 My thinking was obviously wrong but how can I figure out what orbital I=20 am dealing with, if the coefficients do not tell me?

Thanks for enlightenment,

Ulrike

=C2=A0

6-31G*

=C2=A0=C2=A0=C2=A0=C2=A0 Molecular Orbi= tal Coefficients:
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2= =A0 =C2=A0 =C2=A0=C2=A0 =C2=A0 1=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 = =C2=A0 =C2=A0 =C2=A0 2=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0 =C2= =A0 3=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0=C2=A0=C2=A0 4=C2=A0=C2=A0= =C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0=C2=A0 5
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 = =C2=A0 (A1G)--O=C2=A0 (A1G)--O=C2=A0 (T1U)--O=C2=A0 (T1U)--O=C2=A0 (T1U)--O=
=C2=A0=C2=A0=C2=A0=C2=A0 Eigenvalues --=C2=A0=C2=A0 -49.01914=C2=A0 -3.7637= 6=C2=A0 -2.27827=C2=A0 -2.27827=C2=A0 -2.27827
=C2=A0=C2=A0 1 1=C2=A0=C2=A0 Mg 1S=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0 =C2=A0=C2=A0 0.99741=C2=A0 -0.25504=C2=A0=C2=A0 0.00000=C2=A0=C2= =A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 2=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.01078=C2=A0=C2=A0 = 1.02972=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 3=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2PX=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000= =C2=A0=C2=A0 0.99510=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 4=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2PY=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2= =A0=C2=A0 0.00000=C2=A0=C2=A0 0.99510=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 5=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2PZ=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2= =A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.99510

aug-cc-pvqz

=C2=A0

=C2=A0=C2=A0=C2=A0 Molecular Orbital Coefficients:
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0= =C2=A0=C2=A0=C2=A0=C2=A0 1=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0= =C2=A0=C2=A0 2=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 3= =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0=C2=A0 4=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0=C2=A0 5
=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0= =C2=A0 (A1G)--O=C2=A0 (A1G)--O=C2=A0 (T1U)--O=C2=A0 (T1U)--O=C2=A0 (T1U)--O=
=C2=A0=C2=A0=C2=A0=C2=A0 Eigenvalues --=C2=A0=C2=A0 -49.03177=C2=A0 -3.7677= 3=C2=A0 -2.28221=C2=A0 -2.28221=C2=A0 -2.28221
=C2=A0=C2=A0 1 1=C2=A0=C2=A0 Mg 1S=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0 1.00047 =C2=A0=C2=A0 -0.25370=C2=A0=C2=A0 0.00000=C2=A0=C2= =A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 2=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 2S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 -0.00346 =C2=A0=C2=A0 =C2=A0 = 0.62949=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 3=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 3S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 -0.00165 =C2=A0 =C2=A0 -0.42495=C2=A0= =C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 4=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 4S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 -0.00048 =C2=A0 =C2=A0=C2=A0 0.01639=C2= =A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 5=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 5S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 =C2=A0 0.00046 =C2=A0=C2=A0 -0.01004=C2= =A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 6=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 6S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 -0.00022=C2=A0 =C2=A0 =C2=A0 0.00393=C2= =A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000
=C2=A0=C2=A0 7=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 7S=C2=A0=C2=A0=C2= =A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 =C2=A0 =C2=A0 0.00005 =C2=A0=C2=A0 -0.000= 84=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000=C2=A0=C2=A0 0.00000


Prof. Ulrike Salzner
Department of Chemistry
Bilkent University
06800 Bilkent, Ankara


Prof. Ulrike Salzner<= br>Department of Chemistry
Bilkent University
06800 Bilkent, Ankara
--000000000000ca27bd057909e77c--