From owner-chemistry@ccl.net Thu Mar 19 10:11:00 2015 From: "Youzhao Lan lyzhao.*|*.aliyun.com" To: CCL Subject: CCL: looking for a parameter to characterize the degree of delocal Message-Id: <-51156-150319091325-29018-1CZ4bmYDqnF5HypZCMZUnQ*|*server.ccl.net> X-Original-From: "Youzhao Lan" Date: Thu, 19 Mar 2015 09:13:23 -0400 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