CCL: looking for a parameter to characterize the degree of delocal

 Sent to CCL by: "Youzhao  Lan" [lyzhao:aliyun.com]
 Dear Dr. Cina,
 Thanks for your kind help.
 Multiwfn can do it in terms of its manual.
 Best regards.
 --------------------------------------------------------------------------------
 Youzhao Lan
 > From: Cina Foroutan-Nejad canyslopus]~[yahoo.co.uk
 Date: 2015-03-19 17:26
 To: Lan, Youzhao
 Subject: CCL: looking for a parameter to characterize the degree of
 delocalization
 Dear Youhao,
 There is a straighforward parameter defined within the context of QTAIM (quantum
 theory of atoms in molecules). It is called delocalization index. It measures
 the degree of electron sharing between two topological atoms. Many QTAIM
 programs can define delocalization index between atomic pairs but usually they
 do not partition it into orbital contributions. However, if you want you can
 partition DI into orbital contributions by having overlap matrix for each atom.
 Among AIM programs AIM2000 provides overlap 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) = - 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 orbital. 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 this 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 compare it with total DI to have the
 contribution of mixing too. This type of computation is NOT conventional or
 straightforward and I cannot refer you to a particular paper but theoretically
 is possible. For more information regarding DI you may look at J. Phys. Chem. A,
 1999, 103, 304-314.
 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 "response" 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 Republic
 https://muni.academia.edu/CinaForoutanNejad