Subject: Summary - How to find the molecular multiplicity?

From: "TELKUNI" <[email-masked]>
Date: Wed, 13 Jun 2001 21:00:34 +0900

Hello! CCLers

  Earlier this week, I posted a question about molecular multiplicity.

Original question:
>   I am using Gaussian98W and have basic question of quantum chemistry.
>
>   Starting with the G98 calculation, we must set the Charge and Multiplicity,
> but I don't know the practical method to find the each molecular multiplicity.
>
>   I have read books and chemical articles which are describing the multiplicity
> and its numerical expression. But I can't find the other methods except the
> numerical expression.
>
>   Does any chemical researcher always calculate the molecular multiplicity with
> such numerical expression in his brain?  Or is there any other method?
>
>   I will summarize the answers for novice quantum chemistry researcher, just like me!

 I have received very useful replies and summarize them. Reading these replies, I aware
that there are something easy rules to find the molecular multiplicity. If you like to get in
touch with replyers, please let me know.
 
 I hope this summary will be helpful to some others.

 Thanks a lot!

**** 1) from Alan Shusterman ****
In most cases the multiplicity can be set according to the following rules:

All electrons in pairs --> singlet (multiplicity = 1)
One unpaired electron (free radical) --> doublet (multiplicity = 2)

Two unpaired electrons (diradical) -->
and unpaired electrons have opposite spin --> singlet (multiplicity = 1)

or

and unpaired electrons have same spin --> triplet (multiplicity = 3)

Multiplicity is the number of degenerate spin eigenfunctions that can be attached 
to the spatial part of the wavefunction.

**** 2) from David Shobe ****
First of all, for closed shell molecules--including most of the isolable
organic molecules--the multiplicity is 1, no further questions needed.
Essentially "closed shell" means that the molecule follows the octet rule.  

Molecular fragments such as radicals and carbenes may have multiplicity >1.
Organic radicals can be assumed to have multiplicity 2 (with very rare
exceptions).  Carbenes can be either 1 or 3 (singlet or triplet), as can
biradicals such as tetramethylene and "trimethylenemethane"
(2-methylene-1,3-propanediyl).  If the multiplicity is unknown, you have to
try both.

The d-block elements and some of the f-block elements are trickiest.  You
may recall the "high-spin" and "low-spin" states from ligand field theory.
Even worse, the multiplicity tends to become blurred when relativistic
effects (spin-orbit coupling) are taken into account.  Again, in cases of
unknown multiplicity, one has to try two or more options, each of which is a
separate calculation.

Generally, instead of using the formula in the quantum textbooks, I just add
1 to the number of unpaired electrons (singly-occupied orbitals).  The
textbook formula is very useful, however, in determining what S**2 should
be.  This is important as a multiplicity=3  calculation is not guaranteed to
yield the correct S**2 value of 2.000.  This is known as spin contamination,
as it involves mixing-in of higher spin states.

**** 3) from Mary O'Connor ****
Hello--
     A general guideline (or so I have read), is that most organic molecules in the
ground states are closed shells, and thus, have a multiplicity of one and no
charge. Since multiplicity only means the number of ways that an electron can
orient itself to a magnetic field, no unpaired electrons means it can only be in
one orientation. I thonk the formula is 2J + 1 for spin states, where J is +/- 1/2.
For closed shells this sums to 1. Then feed any unpaired electrons into the
formula. I suppose this could be done by drawing Lewis structures to find the
number of unshared electrons. Sometimes, knowing the charge will preset your
options for multiplicity in Gaussian. My first instinct is to go with the lowest
multiplicity choice offered to you, as this will probably be either the correct
one, or the first excited state. I'm fairly new with Gaussian myself, but these are
the ideas I keep in mind. I will be interested in the other replies that you get.
  Good luck!

**** 4) from Wang Dongqi ****
Dear Telkuni,
There is an easy way to find the multiplicity. Just to find the number of
the unpair electron, so you will get the multiplicity=2S+1.(S=n*1/2, n is
the number of unpair electron), that is, to molecules and ions, S=0, while
to radical, S=n*1/2. OK?

Wish this is useful for you.

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       Telkuni Tsuru     [email-masked]