Subject: size of s,p,d orbitals

From: Ulrike Salzner <[email-masked]>
Date: Thu, 4 Oct 2001 15:03:19 +0300 (EET DST)

Dear Collegues,
until 1 hour ago, I firmly believed that p-orbitals are larger than s-
orbitals for atoms that are in the same row of the periodic table. Only
for the second row the sizes were about same. This conviction is mainly
due to a paper by Werner Kutzelnigg, Angew. Chem. 1984, 96, 262-286. I
further believed that s electrons are attracted stronger by the nuclei
because they have no node at the position of the nucleus and that the
similar size of s- and p-orbitals in the second row is due to the lack of
1p orbitals and therefore cancellation of two effects: less attraction of
p electrons due to the node and lack of repulsion between 2p and a lower
shell p-orbital. This is also what I kept telling our first year students.

Today a collegue approached me who teaches inorganic chemistry to our
third year students. She told me that she was surprized that the students
did not know that the order according to decreasing size is s > p > d
within the same row. After admitting that this was to be blamed on me, she
showed me the Inorganic Chemistry textbook by Huhee. There are plots of
radial distribution times r square, clearly indicating that the maximum
shifts to smaller values from s to p to d. Huhee quotes Herberg's "Atomic
Spectra and Atomic Structure" from 1944. In Kutzelniggs article the
average distance of electrons from the nucleus was used not radial
distribution times r square.

The question now is: Do the two ways to determine the size of the orbitals
lead to different conclusions? Is there a mistake somewhere? Is there
newer information? Which orbitals are bigger? What is best method to
determine the size to explain bonding, hybridization, or lack thereof and
so on? 

Thanks in advance for suggestions,
Ulrike Salzner
===================================================================

Dr. Ulrike Salzner
Associate Professor
Department of Chemistry		Tel.: (312) 290-2122
Bilkent University		Fax.: (312) 266-5097
06533 Bilkent, Ankara 		e-mail: [email-masked]
Turkey

====================================================================

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From: Mikael Johansson <[email-masked]>
Date: Thu, 4 Oct 2001 19:26:33 +0300 (EET DST)

Hello Ulrike and All!

> orbitals for atoms that are in the same row of the periodic table. Only
[...]
> did not know that the order according to decreasing size is s > p > d
[...]
> determine the size to explain bonding, hybridization, or lack thereof and

This was an interesting question, succeeding in diverting me from things I
should be doing :-)

Without taking a stand on what method is the "best" I made a quick
calculation on the argon-atom and compared the "sizes" of the 2s/2p and
3s/3p orbitals. Below is reported the radius of a spherical boundary
around the atom which contains 90% resp. 95% of the electron density of
the orbital in question: (the calculation was made on B3LYP/TZVP level,
for no specific reason)

    90%   95%
2s  0.65  0.74 a.u.
2p  0.63  0.72
3s  2.14  2.44
3p  2.64  3.06

So according to the above the 2s/2p-orbitals are about as big, whereas
the 3s is smaller than the 3p.

Other comments on the subject would be very welcome!

Have a nice day,
    Mikael Johansson
    University of Helsinki
    Department of Chemistry
    [email-masked]
    Phone: +358-9-191 50185
    FAX  : +358-9-191 50169

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From: "Robert E. Harris" <[email-masked]>
Date: Thu, 4 Oct 2001 13:39:13 -0500

The discussion given in Chs. 8 and 9 of Slater's Quantum Theory of Atomic
Structure, v. I still seems to me one of the clearest on the subject.

John C. Slater, Quantum Theory of Atomic Structure, v. I, McGraw Hill, New
York, Toronto, London, 1960.

REH

>Thanks in advance for suggestions,
Robert E. Harris  Phone: 573-882-3274.  Fax:  573-882-2754
Department of Chemistry, University of Missouri-Columbia
Columbia, Missouri, USA 65211

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From: John Bushnell <[email-masked]>
Date: Thu, 4 Oct 2001 18:17:06 -0700 (PDT)

Regarding the argument about "the lack of repulsion between
the 2p orbital and a lower shell p-orbital", I would think
that this would not be an issue.  If there was such a thing
as a "1p" orbital, it would be spherically symmetric when
filled.  Thus I wouldn't expect any inherently p-specific
repulsion to such a filled subshell, if it existed.  That
is, the s orbital would also experience such a "lack of
repulsion" :-)

        - John          [email-masked]

On Thu, 4 Oct 2001, Ulrike Salzner wrote:

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