[Pw_forum] Re: Understanding "eband" & "deband" in "total energy"

[Guido Fratesi]

The one-electron contribution is the kinetic + ionic term:

\sum <psi| (-\nabla^2) |psi>  +  Integral[rho(r)*V_ion(r),dr]


This contribution is computed as (eband+deband), since:

1) the sum of the eigenvalues (eband) gives (from KS equations):

\sum eig = \sum <psi| (-\nabla^2) |psi>  +  Integral[rho(r)*V_ion(r),dr]
            + Integral[rho(r)*(V_H(r)+V_XC(r)),dr]

2) deband is defined as:

deband = -Integral[rho(r)*(V_H(r)+V_XC(r)),dr]

Guido

> From: Mousumi Upadhyay Kahaly <mousumi at jncasr.ac.in>
> Date: July 5, 2005 5:43:40 AM GMT+02:00
> To: pw_forum at pwscf.org
> Subject: [Pw_forum] Understanding "eband" & "deband" in "total energy"
> Reply-To: pw_forum at pwscf.org
> 
> 
> 
> This is a resubmission of my last mail, since I'm in real need of help.
> =========================================================================
> 
> Dear All,
> 
>        I wanted to know how the final "total energy" is calculated for the
>  PWSCF output file and what each of those terms line "one-electron
> contribution" etc meant.
> 
>        As the source code "electrons.f90" in PW directory shows,
> 
>        etot    = eband + ( etxc - etxcc ) + ewld + ehart + deband + demet
> 
>        After writing "etot", also other terms like "one-electron
> contribution", "hartree contribution" etc are written by,
> "
>         WRITE( stdout, 9060 ) &
>             eband, ( eband + deband ), ehart, ( etxc - etxcc ), ewld "
> 
>        I am having problem to understand the terms "eband" and "deband".
> How the "deband" value is assigned? When we solve the Kohn-Sham
> equation, the
> energy eigen values obtained are band energies, right? From K-S
> equation how do I obtain all above terms?
> 
>        May I please know (1) from where can I find the details of all
> these terms and their explanations and (2) how each of them will
> contribute to the cohesive energy of a system?
> 
>        Best regards,   mousumi.
> 
> 
> 
> 
>> On Tuesday 28 June 2005 10:14, Mousumi Upadhyay Kahaly wrote:
>> 
>>> [...] total energy is being obtained if we add other terms except "band
>>> 
> energy sum" i.e. total energy = "one-electron contribution" + "hartree
> contribution" + "xc contribution" + "ewald contribution" + "correction for
> metals ".
> 
>>>        Any help to understand this is appreciated.  regards. mousumi.
>>> 
>> For the definiiton of the various terms, see
>>   http://www.democritos.it/pipermail/pw_forum/2003-May/000291.html
>> and
>>   http://www.democritos.it/pipermail/pw_forum/2003-May/000293.html
>> Paolo
>> --
>> Paolo Giannozzi             e-mail:  giannozz at nest.sns.it
>> Scuola Normale Superiore    Phone:   +39/050-509876, Fax:-563513 Piazza
>> 
> dei Cavalieri 7      I-56126 Pisa, Italy
> 
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