[QE-users] Speed of valence electrons

[KRISHNENDU MUKHERJEE]

Dear Stefano, 

Thank you for your explanation. It is very helpful for us. 

Regards, 
Krishnendu 


From: degironc at sissa.it 
To: users at lists.quantum-espresso.org 
Sent: Thursday, November 7, 2024 3:26:55 PM 
Subject: Re: [QE-users] Speed of valence electrons 



Dear Krishnendu, 

the group velocity of an electron associated to a given band is related to the derivative of the energy band w.r.t. the k-vector, which is roughly proportional to band-width and lattice parameters which for valence electrons do not depend strongly on the elements involved. 


Assuming a simple dispersion like e(k) = -A*cos(k*a) -> v_g = 1/\hbar d e(k)/ d k = A a/ \hbar * sen(k*a) 


so max v_g ~ A a / \hbar . if you take A ~ 5 eV and a ~ 5 \AA, then max v_g ~ 3 10^7 m/s ~ 0.1 c 


The behavior of the electrons close to the nuclei is of course affected by relativistic effects for heavy elements, this is why one should use relativistic pseudopotentials. 


stefano 
On 07/11/24 06:57, KRISHNENDU MUKHERJEE via users wrote: 




Hello everyone, 

Does the valence electrons (those electrons for which the wave function is solved in Quantum Espresso) have non-relativistic speed ? 

Thanking you, 
Regards, 
Krishnendu 


_______________________________________________
The Quantum ESPRESSO community stands by the Ukrainian
people and expresses its concerns about the devastating
effects that the Russian military offensive has on their
country and on the free and peaceful scientific, cultural,
and economic cooperation amongst peoples
_______________________________________________
Quantum ESPRESSO is supported by MaX ( [ http://www.max-centre.eu/ | www.max-centre.eu ] )
users mailing list [ mailto:users at lists.quantum-espresso.org | users at lists.quantum-espresso.org ] [ https://lists.quantum-espresso.org/mailman/listinfo/users | https://lists.quantum-espresso.org/mailman/listinfo/users ] 



_______________________________________________ 
The Quantum ESPRESSO community stands by the Ukrainian 
people and expresses its concerns about the devastating 
effects that the Russian military offensive has on their 
country and on the free and peaceful scientific, cultural, 
and economic cooperation amongst peoples 
_______________________________________________ 
Quantum ESPRESSO is supported by MaX (www.max-centre.eu) 
users mailing list users at lists.quantum-espresso.org 
https://lists.quantum-espresso.org/mailman/listinfo/users 
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20241109/394dc5ca/attachment.html>