Multiwfn forum

nfbarrera

Member

Registered: 2021-12-15

Posts: 1

How to calculate Tsallis entropy

Dear Prof. Tian Lu,

First of all, thank you very much for developing this amazing software. I am calculating different entropies in my research and now I want to calculate the Tsallis entropy, but the latter is not available in the list of real space functions, so my question is if it is possible to put somehow define the Tsallis entropy inside multiwfn and be able to calculate it? The other entropies I got by modifying the settings.ini in 'iuserfunc ='. Could you please help me?

Thank you very much,
Nicolás Barrera

sobereva

Tian Lu (Multiwfn developer)

From: Beijing

Registered: 2017-09-11

Posts: 1,777

Website

Re: How to calculate Tsallis entropy

Dear Nicolás Barrera,

Tsallis entropy cannot be expressed as integral of a real space function, therefore there is no something like Tsallis entropy density and provided in user-defined function list. However, you can still calculate it via Multiwfn. Tsallis entropy of order n is defined as follows

The key ingredient to evaluate is the integral of ρ^n(r). As can be seen in Section 2.7 of Multiwfn manual, user-defined functions 55 and 56 correspond to ρ^2(r) and ρ^3(r), respectively. Therefore if you want to evaluate Tsallis entropy of order 2, simply set "iuserfunc" to 55, then boot up Multiwfn and load an input file, then enter subfunction 4 of main function 100, choose "100 User-defined function". Then ρ^2(r) will be integrated over the whole space. After that you can manually calculate Tsallis entropy of order 2 by very simple mathematical operations on the integral. Tsallis entropy of order 3 can also be obtained in similar way.

Best regards,

Tian Lu