From owner-chemistry@ccl.net Tue Jul 5 11:08:01 2022 From: "Alan Shusterman alan%%reed.edu" To: CCL Subject: CCL:G: Question about phosphorus in 6-31G basis set Message-Id: <-54744-220702182033-15875-s5v0o54PJJy1zfcd2DecSQ_._server.ccl.net> X-Original-From: Alan Shusterman Content-Type: multipart/alternative; boundary="000000000000de02b505e2d9e87c" Date: Sat, 2 Jul 2022 15:20:14 -0700 MIME-Version: 1.0 Sent to CCL by: Alan Shusterman [alan(-)reed.edu] --000000000000de02b505e2d9e87c Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable A useful description of these Pople basis sets, how they were designed, and the motivations for their design can be found in: *Ab initio Molecular Orbital Theory* by Warren J. Hehre, Leo Radom, Paul von R. Schleyer, John Pople, Wiley (1986), ISBN 978-0-471-81241-8 https://www.wiley.com/en-us/AB+INITIO+Molecular+Orbital+Theory-p-9780471812= 418 I don't have my copy handy, but only a few pages need to be read to answer your questions. Your college/university library probably has a copy on its shelves. Alan On Tue, Jun 28, 2022 at 8:18 PM Cory Pye Cory.Pye+/-smu.ca < owner-chemistry:-:ccl.net> wrote: > Andrew, > > > > I believe that it is because the developers of the basis set strive for a > consistent description across each period of the periodic table. > > I would imagine part of the reason might be that the use of Cartesian D > instead of spherical harmonic d might interact with the s-shell because o= f > the x^2 + y^2 + z^2 combination. The beginning and end members of the > series have the same contraction pattern. > > > > H-He =3D (3S, 1S) > > Li-Ne =3D (6S,3SP,1SP) < note here that Li has SP shells even though its > electron configuration is [He]2s1 . In order to get contraction > coefficients for the P part of the SP shells for Li and Be, they probably > had to optimize them for an excited configuration with at least one > electron in the 2p orbital. > > Na-Ar =3D (6S,6SP,3SP,1SP) =E2=80=93 no occupied d orbitals in any of the= se elements. > > K-Kr =3D (6s,6SP,6SP,3SP,1SP,3D,1D) =E2=80=93 the 3d orbitals start filli= ng in here. > In order to get contraction coefficients for the d orbitals for K and Ca, > one would have to optimize these for some excited configuration with at > least one electron in a d orbital. > > > > -Cory > > > > *From:* owner-chemistry+cory.pye=3D=3Dsmu.ca],[ccl.net > *On Behalf Of *Andrew > DeYoung andrewdaviddeyoung^_^gmail.com > *Sent:* Tuesday, June 28, 2022 2:59 PM > *To:* Cory Pye > *Subject:* CCL:G: Question about phosphorus in 6-31G basis set > > > > Hi, > > > > I am running a geometry optimization in Gaussian 16. One of the ions in > my system contains a phosphorus atom. As an inexpensive starting point, = I > chose the HF/6-31G level of theory, which is built into Gaussian: > > > > # Opt HF/6-31G > > > > Gaussian gives me this warning: > > " Warning! P atom 19 may be hypervalent but has no d functions." > > > > So, I went to the Basis Set Exchange and took a look at the form of the > 6-31 basis set for phosphorus ( > https://www.basissetexchange.org/basis/6-31g/format/gaussian94/?version= =3D1&elements=3D15 > > ) and found that, indeed, there are no d functions: > > > !---------------------------------------------------------------------- > ! Basis Set Exchange > ! Version v0.9 > ! https://www.basissetexchange.org > > !---------------------------------------------------------------------- > ! Basis set: 6-31G > ! Description: 6-31G valence double-zeta > ! Role: orbital > ! Version: 1 (Data from Gaussian 09/GAMESS) > !---------------------------------------------------------------------- > > P 0 > S 6 1.00 > 0.1941330000D+05 0.1851598923D-02 > 0.2909420000D+04 0.1420619174D-01 > 0.6613640000D+03 0.6999945928D-01 > 0.1857590000D+03 0.2400788603D+00 > 0.5919430000D+02 0.4847617180D+00 > 0.2003100000D+02 0.3351998050D+00 > SP 6 1.00 > 0.3394780000D+03 -0.2782170105D-02 0.4564616191D-02 > 0.8101010000D+02 -0.3604990135D-01 0.3369357188D-01 > 0.2587800000D+02 -0.1166310044D+00 0.1397548834D+00 > 0.9452210000D+01 0.9683280364D-01 0.3393617168D+00 > 0.3665660000D+01 0.6144180231D+00 0.4509206237D+00 > 0.1467460000D+01 0.4037980152D+00 0.2385858009D+00 > SP 3 1.00 > 0.2156230000D+01 -0.2529241139D+00 -0.1776531273D-01 > 0.7489970000D+00 0.3285184468D-01 0.2740581964D+00 > 0.2831450000D+00 0.1081254762D+01 0.7854215630D+00 > SP 1 1.00 > 0.9983170000D-01 0.1000000000D+01 0.1000000000D+01 > > **** > > > > On the other hand, 6-31G*, alias 6-31G(d), not surprisingly, does have a = d > function ( > https://www.basissetexchange.org/basis/6-31g_st_/format/gaussian94/?versi= on=3D1&elements=3D15 > > ): > > > > !---------------------------------------------------------------------- > ! Basis Set Exchange > ! Version v0.9 > ! https://www.basissetexchange.org > > !---------------------------------------------------------------------- > ! Basis set: 6-31G* > ! Description: 6-31G + polarization on heavy atoms > ! Role: orbital > ! Version: 1 (Data from Gaussian 09/GAMESS) > !---------------------------------------------------------------------- > > P 0 > S 6 1.00 > 0.1941330000D+05 0.1851598923D-02 > 0.2909420000D+04 0.1420619174D-01 > 0.6613640000D+03 0.6999945928D-01 > 0.1857590000D+03 0.2400788603D+00 > 0.5919430000D+02 0.4847617180D+00 > 0.2003100000D+02 0.3351998050D+00 > SP 6 1.00 > 0.3394780000D+03 -0.2782170105D-02 0.4564616191D-02 > 0.8101010000D+02 -0.3604990135D-01 0.3369357188D-01 > 0.2587800000D+02 -0.1166310044D+00 0.1397548834D+00 > 0.9452210000D+01 0.9683280364D-01 0.3393617168D+00 > 0.3665660000D+01 0.6144180231D+00 0.4509206237D+00 > 0.1467460000D+01 0.4037980152D+00 0.2385858009D+00 > SP 3 1.00 > 0.2156230000D+01 -0.2529241139D+00 -0.1776531273D-01 > 0.7489970000D+00 0.3285184468D-01 0.2740581964D+00 > 0.2831450000D+00 0.1081254762D+01 0.7854215630D+00 > SP 1 1.00 > 0.9983170000D-01 0.1000000000D+01 0.1000000000D+01 > D 1 1.00 > 0.5500000000D+00 1.0000000 > **** > > > > I am new to quantum chemical calculations, so please forgive me if this i= s > an extremely basic question with an obvious answer. Why doesn't phosphor= us > have d functions in 6-31G, while atoms such as potassium and calcium do? > (See, for example, > https://www.basissetexchange.org/basis/6-31g/format/gaussian94/?version= =3D1&elements=3D19,20 > > .) I realize that phosphorus ([Ne] 3s^2 3p^3) doesn't have d electrons, > but neither do potassium ([Ar] 4s^1) or calcium ([Ar] 4s^2) and yet their > 6-31G basis functions do include d functions ([Ar] =3D [Ne] 3s^2 3p^6 and > [Ne] =3D 1s^2 2s^2 2p^6). > > > > Thanks so much for your help, and thanks for your patience with a probabl= y > very basic question, > > Andrew > --=20 Alan Shusterman Professor Emeritus Chemistry Department Reed College 3203 SE Woodstock Blvd Portland, OR 97202-8199 http://blogs.reed.edu/alan/ "Patience, persistence, and a sense of humor." Dave Barrett (1956-2017, Reed College '77) --000000000000de02b505e2d9e87c Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
A useful description of these Pople basis sets, how t= hey were designed, and the motivations for their design can be found in:
Ab initio Molecular Orbital Theory by Warren J. Hehre, Leo Radom, Paul von R. Schleyer, John Pople, Wiley (1986), ISBN= 978-0-471-81241-8

I don't have my copy handy, but only a few pages need to be= read to answer your questions. Your college/university library probably ha= s a copy on its shelves.

Alan

<= div class=3D"gmail_quote">
On Tue, Jun= 28, 2022 at 8:18 PM Cory Pye Cory.Pye+/-smu.ca <owner-chemistry:-:ccl.net> wrote:

Andrew,

=C2=A0

I believe that it is because the developers of the b= asis set strive for a consistent description across each period of the peri= odic table.

I would imagine part of the reason might be that the= use of Cartesian D instead of spherical harmonic d might interact with the= s-shell because of the x^2 + y^2 + z^2 combination. The beginning and end = members of the series have the same contraction pattern.

=C2=A0

H-He =3D (3S, 1S)

Li-Ne =3D (6S,3SP,1SP) < note here that Li has SP= shells even though its electron configuration is [He]2s1 . In order to get= contraction coefficients for the P part of the SP shells for Li and Be, th= ey probably had to optimize them for an excited configuration with at least one electron in the 2p orbital.=

Na-Ar =3D (6S,6SP,3SP,1SP) =E2=80=93 no occupied d o= rbitals in any of these elements.

K-Kr =3D (6s,6SP,6SP,3SP,1SP,3D,1D) =E2=80=93 the 3d= orbitals start filling in here. In order to get contraction coefficients f= or the d orbitals for K and Ca, one would have to optimize these for some e= xcited configuration with at least one electron in a d orbital.

=C2=A0

-Cory

=C2=A0

From: owner-chemistry+cory.pye=3D=3Dsmu.ca],[ccl.n= et <owner-chemistry+cory.pye=3D=3Dsmu.ca],[ccl.n= et> On Behalf Of Andrew DeYoung andrewdaviddeyoung^_^gmail.com
Sent: Tuesday, June 28, 2022 2:59 PM
To: Cory Pye <Cory.Pye],[smu.ca>
Subject: CCL:G: Question about phosphorus in 6-31G basis set<= u>

=C2=A0

Hi,

=C2=A0

I am running a geometry optimization in Gaussian 16.= =C2=A0 One of the ions in my system contains a phosphorus atom.=C2=A0 As an= inexpensive starting point, I chose the HF/6-31G level of theory, which is= built into Gaussian:

=C2=A0

# Opt HF/6-31G

=C2=A0

Gaussian gives me this warning:

" Warning!=C2=A0 P =C2=A0atom =C2=A0 19 may be = hypervalent but has no d functions."

=C2=A0

So, I went to the Basis Set Exchange and took a look= at the form of the 6-31 basis set for phosphorus ( https://www.basissetexchange.org/basis/6-31g/format/gaussian94/?version=3D1= &elements=3D15 ) and found that, indeed, there are no d functions:<= u>


!----------------------------------------------------------------------
! Basis Set Exchange
! Version v0.9
! https://www.basissetexchange.org
!----------------------------------------------------------------------
! =C2=A0 Basis set: 6-31G
! Description: 6-31G valence double-zeta
! =C2=A0 =C2=A0 =C2=A0 =C2=A0Role: orbital
! =C2=A0 =C2=A0 Version: 1 =C2=A0(Data from Gaussian 09/GAMESS)
!----------------------------------------------------------------------

P =C2=A0 =C2=A0 0
S =C2=A0 =C2=A06 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.1941330000D+05 =C2=A0 =C2=A0 =C2=A0 0.1851598923D-02=
=C2=A0 =C2=A0 =C2=A0 0.2909420000D+04 =C2=A0 =C2=A0 =C2=A0 0.1420619174D-01=
=C2=A0 =C2=A0 =C2=A0 0.6613640000D+03 =C2=A0 =C2=A0 =C2=A0 0.6999945928D-01=
=C2=A0 =C2=A0 =C2=A0 0.1857590000D+03 =C2=A0 =C2=A0 =C2=A0 0.2400788603D+00=
=C2=A0 =C2=A0 =C2=A0 0.5919430000D+02 =C2=A0 =C2=A0 =C2=A0 0.4847617180D+00=
=C2=A0 =C2=A0 =C2=A0 0.2003100000D+02 =C2=A0 =C2=A0 =C2=A0 0.3351998050D+00=
SP =C2=A0 6 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.3394780000D+03 =C2=A0 =C2=A0 =C2=A0-0.2782170105D-02= =C2=A0 =C2=A0 =C2=A0 0.4564616191D-02
=C2=A0 =C2=A0 =C2=A0 0.8101010000D+02 =C2=A0 =C2=A0 =C2=A0-0.3604990135D-01= =C2=A0 =C2=A0 =C2=A0 0.3369357188D-01
=C2=A0 =C2=A0 =C2=A0 0.2587800000D+02 =C2=A0 =C2=A0 =C2=A0-0.1166310044D+00= =C2=A0 =C2=A0 =C2=A0 0.1397548834D+00
=C2=A0 =C2=A0 =C2=A0 0.9452210000D+01 =C2=A0 =C2=A0 =C2=A0 0.9683280364D-01= =C2=A0 =C2=A0 =C2=A0 0.3393617168D+00
=C2=A0 =C2=A0 =C2=A0 0.3665660000D+01 =C2=A0 =C2=A0 =C2=A0 0.6144180231D+00= =C2=A0 =C2=A0 =C2=A0 0.4509206237D+00
=C2=A0 =C2=A0 =C2=A0 0.1467460000D+01 =C2=A0 =C2=A0 =C2=A0 0.4037980152D+00= =C2=A0 =C2=A0 =C2=A0 0.2385858009D+00
SP =C2=A0 3 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.2156230000D+01 =C2=A0 =C2=A0 =C2=A0-0.2529241139D+00= =C2=A0 =C2=A0 =C2=A0-0.1776531273D-01
=C2=A0 =C2=A0 =C2=A0 0.7489970000D+00 =C2=A0 =C2=A0 =C2=A0 0.3285184468D-01= =C2=A0 =C2=A0 =C2=A0 0.2740581964D+00
=C2=A0 =C2=A0 =C2=A0 0.2831450000D+00 =C2=A0 =C2=A0 =C2=A0 0.1081254762D+01= =C2=A0 =C2=A0 =C2=A0 0.7854215630D+00
SP =C2=A0 1 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.9983170000D-01 =C2=A0 =C2=A0 =C2=A0 0.1000000000D+01= =C2=A0 =C2=A0 =C2=A0 0.1000000000D+01

****

=C2=A0

On the other hand, 6-31G*, alias 6-31G(d), not surpr= isingly, does have a d function ( https://www.basissetexchange.org/basis/6-31g_st_/format/gaussian94/?version= =3D1&elements=3D15 ):

=C2=A0

!---------------------------------------------------= -------------------
! Basis Set Exchange
! Version v0.9
! https://www.basissetexchange.org
!----------------------------------------------------------------------
! =C2=A0 Basis set: 6-31G*
! Description: 6-31G + polarization on heavy atoms
! =C2=A0 =C2=A0 =C2=A0 =C2=A0Role: orbital
! =C2=A0 =C2=A0 Version: 1 =C2=A0(Data from Gaussian 09/GAMESS)
!----------------------------------------------------------------------

P =C2=A0 =C2=A0 0
S =C2=A0 =C2=A06 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.1941330000D+05 =C2=A0 =C2=A0 =C2=A0 0.1851598923D-02=
=C2=A0 =C2=A0 =C2=A0 0.2909420000D+04 =C2=A0 =C2=A0 =C2=A0 0.1420619174D-01=
=C2=A0 =C2=A0 =C2=A0 0.6613640000D+03 =C2=A0 =C2=A0 =C2=A0 0.6999945928D-01=
=C2=A0 =C2=A0 =C2=A0 0.1857590000D+03 =C2=A0 =C2=A0 =C2=A0 0.2400788603D+00=
=C2=A0 =C2=A0 =C2=A0 0.5919430000D+02 =C2=A0 =C2=A0 =C2=A0 0.4847617180D+00=
=C2=A0 =C2=A0 =C2=A0 0.2003100000D+02 =C2=A0 =C2=A0 =C2=A0 0.3351998050D+00=
SP =C2=A0 6 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.3394780000D+03 =C2=A0 =C2=A0 =C2=A0-0.2782170105D-02= =C2=A0 =C2=A0 =C2=A0 0.4564616191D-02
=C2=A0 =C2=A0 =C2=A0 0.8101010000D+02 =C2=A0 =C2=A0 =C2=A0-0.3604990135D-01= =C2=A0 =C2=A0 =C2=A0 0.3369357188D-01
=C2=A0 =C2=A0 =C2=A0 0.2587800000D+02 =C2=A0 =C2=A0 =C2=A0-0.1166310044D+00= =C2=A0 =C2=A0 =C2=A0 0.1397548834D+00
=C2=A0 =C2=A0 =C2=A0 0.9452210000D+01 =C2=A0 =C2=A0 =C2=A0 0.9683280364D-01= =C2=A0 =C2=A0 =C2=A0 0.3393617168D+00
=C2=A0 =C2=A0 =C2=A0 0.3665660000D+01 =C2=A0 =C2=A0 =C2=A0 0.6144180231D+00= =C2=A0 =C2=A0 =C2=A0 0.4509206237D+00
=C2=A0 =C2=A0 =C2=A0 0.1467460000D+01 =C2=A0 =C2=A0 =C2=A0 0.4037980152D+00= =C2=A0 =C2=A0 =C2=A0 0.2385858009D+00
SP =C2=A0 3 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.2156230000D+01 =C2=A0 =C2=A0 =C2=A0-0.2529241139D+00= =C2=A0 =C2=A0 =C2=A0-0.1776531273D-01
=C2=A0 =C2=A0 =C2=A0 0.7489970000D+00 =C2=A0 =C2=A0 =C2=A0 0.3285184468D-01= =C2=A0 =C2=A0 =C2=A0 0.2740581964D+00
=C2=A0 =C2=A0 =C2=A0 0.2831450000D+00 =C2=A0 =C2=A0 =C2=A0 0.1081254762D+01= =C2=A0 =C2=A0 =C2=A0 0.7854215630D+00
SP =C2=A0 1 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.9983170000D-01 =C2=A0 =C2=A0 =C2=A0 0.1000000000D+01= =C2=A0 =C2=A0 =C2=A0 0.1000000000D+01
D =C2=A0 =C2=A01 =C2=A0 1.00
=C2=A0 =C2=A0 =C2=A0 0.5500000000D+00 =C2=A0 =C2=A0 =C2=A0 1.0000000
****

=C2=A0

I am new to quantum chemical calculations, so please= forgive me if this is an extremely basic question with an obvious answer.= =C2=A0 Why doesn't phosphorus have d functions in 6-31G, while atoms su= ch as potassium and calcium do?=C2=A0 (See, for example, https://www.basissetexchange.org/basis/6-31g/format/gaussian94/?version=3D1= &elements=3D19,20 .)=C2=A0 I realize that phosphorus ([Ne] 3s^2 3p^= 3) doesn't have d electrons, but neither do potassium ([Ar] 4s^1) or ca= lcium ([Ar] 4s^2) and yet their 6-31G basis functions do include d functions ([Ar] =3D [Ne] 3s^2 3p^6 and [Ne] =3D 1s^2 2s^2 2p^= 6).=C2=A0

=C2=A0

Thanks so much for your help, and thanks for your pa= tience with a probably very basic question,

Andrew



--
Alan Shusterman
Professor Emeritus
Chemistry Department
Reed College
3203 SE Woodstock Blvd
Por= tland, OR 97202-8199
http://blogs.reed.edu/alan/
"Patience, persistence, and = a sense of humor." Dave Barrett (1956-2017, Reed College '77)
<= /div>
--000000000000de02b505e2d9e87c-- From owner-chemistry@ccl.net Tue Jul 5 13:52:00 2022 From: "Susi Lehtola susi.lehtola a alumni.helsinki.fi" To: CCL Subject: CCL:G: Question about phosphorus in 6-31G basis set Message-Id: <-54745-220705134259-360-pMUmdF+K05594+/FXDvQWw%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: Tue, 5 Jul 2022 13:42:48 -0400 MIME-Version: 1.0 Sent to CCL by: Susi Lehtola [susi.lehtola|-|alumni.helsinki.fi] On 6/28/22 13:59, Andrew DeYoung andrewdaviddeyoung^_^gmail.com wrote: > Hi, > > I am running a geometry optimization in Gaussian 16.  One of the ions in > my system contains a phosphorus atom.  As an inexpensive starting point, > I chose the HF/6-31G level of theory, which is built into Gaussian: > > # Opt HF/6-31G While revolutionary in their day, the Pople sets are nowadays obsolete. The sets are only available for a small portion of the periodic table, their definition is a mess (e.g. the mixed use of cartesian D functions + spherical F functions), and they do not form systematic sequences in accuracy. My recommendation is to use the Karlsruhe def2 basis sets by Ahlrichs and coworkers. They are available for the whole periodic table up to Rn (Z=86) and relativistic effects are included cost-efficiently through the use of effective core potentials. The family comes in a number of sizes. For exploratory calculations, one can either use the non-polarized split-valence (def2-SV) basis set, or include polarization either only on heavy atoms (def2-SV(P)) or all atoms (def2-SVP). For quantitative accuracy, there are polarized triple-zeta (def2-TZVP) and quadruple-zeta (def2-QZVP) basis sets. For calculations with anions or long-range interactions, diffuse functions can be added by the D suffix (e.g. def2-SVPD). For post-HF calculations like MP2 or CCSD, one needs to insert a second set of polarization functions (def2-TZVPP and def2-QZVPP). > I am new to quantum chemical calculations, so please forgive me if > this is an extremely basic question with an obvious answer. Why > doesn't phosphorus have d functions in 6-31G, while atoms such as > potassium and calcium do? > I realize that phosphorus ([Ne] 3s^2 3p^3) doesn't have d electrons, > but neither do potassium ([Ar] 4s^1) or calcium ([Ar] 4s^2) and yet > their 6-31G basis functions do include d functions ([Ar] = [Ne] 3s^2 > 3p^6 and [Ne] = 1s^2 2s^2 2p^6).> If I remember correctly, the d orbitals are occupied in low-lying excited states of at least Ca. This is the same reason that minimal Li and Be basis sets often include P functions, even though formally only S orbitals are occupied in the ground state. If you have very low-lying excited states, they can play a role in chemical bonding which is why they are often included in the basis. -- ------------------------------------------------------------------ Mr. Susi Lehtola, PhD Adjunct Professor susi.lehtola|-|alumni.helsinki.fi University of Helsinki http://susilehtola.github.io/ Finland ------------------------------------------------------------------ Susi Lehtola, FT dosentti susi.lehtola|-|alumni.helsinki.fi Helsingin yliopisto http://susilehtola.github.io/ ------------------------------------------------------------------