Dear Youhao,

There is a straighforward parameter defined within the = context of QTAIM (quantum theory of atoms in molecules). It is called deloc= alization index. It measures the degree of electron sharing between two top= ological atoms. Many QTAIM programs can define delocalization index between= atomic pairs but usually they do not partition it into orbital contributio= ns. However, if you want you can partition DI into orbital contributions by= having overlap matrix for each atom. Among AIM programs AIM2000 provides o= verlap matrix for atoms. I am not sure if Multiwfn can do it or not but you= may ask its developer. Once you have overlap matrix for any atom, you can = measure orbital contributions via a simple equation:

DI(A,B) =3D - Sigma Sigma [Sij(A)Sij(B)]

Where A and B are two atoms, by Sigma as you = may guess I mean summation, and Sij(a and B) are overlap terms for each orb= ital. Please be careful that if you merely focus on pi-orbitals then a part= of DI which is related to partial overlap between pi and sigma or delta...= will be missing. For an ideally symmetric system this must be zero but thi= s is not necessarily true for all systems. So, for non-planar/non-symmetric= systems you may sum up contributions of pi, sigma, etc. together then comp= are it with total DI to have the contribution of mixing too. This type of c= omputation is NOT conventional or straightforward and I cannot refer you to= a particular paper but theoretically is possible. For more information reg= arding DI you may look at J. Phys. Chem. A, 1999, 103, 304-314.

<= /div>

On the other hand, some researchers believe= that measuring current density in the presence of magnetic fields is also = a measure of pi-delocalization. You may check some papers with the keyword = current density but be aware that there is a fundamental difference between= DI and current density. DI is a ground-state property but current density = that is widely believed is a measure of pi electron delocalization is a "re= sponse" property. This means that DI is non-zero in the absence of external= fields but current density is zero in the absence of an external magnetic = field.

Good luck,

Cina

-= ------------------------------------------------------------------------

Cina Foroutan-Nejad, PhD,

CEITEC-Central European Institute of Technology=

Masaryk University, Brno,

Czech Repu= blic

https://mu= ni.academia.edu/CinaForoutanNejad

On Thursday, 19 March 2015, 3:28, Y= ouzhao Lan lyzhao(_)aliyun.com <owner-chemistry.-$-.ccl.net> wrote:
<= /font>

Sent to CCL by: = "Youzhao Lan" [lyzhao]_[aliyun.com]
Dear all,
Is there a calcul= ated parameter or quantity to characterize
the degree of delocalization = of pi-electron?

Any help will be appreciated.

Best regards.Youzhao Lan

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