Subject: BOND ORDERS

From: Mike Peterson (System Admin) <[email-masked]>
Date: Fri, 29 Sep 1995 14:50:46 -0400

Errol Lewars wrote:

>Re the question about algorithms for bond orders: Dr Istvan Mayer (Central
>Research Institute, Hungarian Acad. of Sciences) argues that only his
>algorithm really gives correct (sensible?) bond orders.  Thus the
>Mayer bond order of H2+ is 0.5 (a 1-electron bond), but (all?) other
>approaches give 0.25.

Although there is a theoretical basis for the Mayer method given
in the papers, and it gives very sensible bond orders for a wide
range of molecules and basis sets, including the * basis sets,
it can be made to fail. For example, using 3-21+G, you will
get C-C "bond order" results like:

Molecule            Mulliken           Mayer
---------------     --------           -----
Ethane               -0.328            0.566
Benzene              -5.008            2.179
Ethylene              1.169            2.480
Acetylene            -0.109            4.496

I suspect almost any basis set containing diffuse functions will cause
the Mayer method to fail similarly, though it at least still produces
ascending numbers. Note that the Mayer scheme can not produce negative
bond orders due to its formulation.

For 3-21G, you get almost exactly 1.0, 1.5, 2.0 and 3.0 respectively
with the Mayer method, and pretty close to that for 6-31G* as I recall.

Mike.
--
When the chips are down, switch to pretzels.       |  Mike Peterson, SysAdmin
                                                   |  U/Toronto Chemistry
E-mail: [email-masked]               Tel: (416)978-7094
WWW:    http://www.chem.utoronto.ca/                  Fax: (416)978-8775