[Pw_forum] Calculation of Helmholtz free energy at a finite temperature

[Krishnendu Mukherjee]

Dear Dr. Lorenzo Paulatto,

 Thank you for your reply regarding how to find out the value for 'E(a)'
that is the ground state energy or energy of static lattice as a function
of cell parameters.

Today I have a question regarding calculation of Helmholtz free energy at a
finite temperature.

 I was going through an article titled, "Ab initio study of the
thermodynamic properties of nonmagnetic elementary fcc metals:
Exchange-correlation-related error bars and chemical trends", in Physical
Review B 76, 024309 (2007), authored by Naugebauer et al. In their method
of calculation of Helmholtz free energy there are two terms: Electronic
free energy and vibrational free energy. The electronic free energy is
composed of total energy E-total(V) at absolute temperature T=0 and a
remaining part F-el (V,T) with a 'linear dependence on V most suitable:'

F-el(V,T) = a (T) + b (T) V


Now, in Physical Review B 71, 205214 (2005) , Marzari et al. has mentioned
in Equation 7,
 Helmholtz free energy F(a, T)=E(a) + Fvib(T)
where, 'a' is geometrical degrees of freedom, 'T' is temperature, 'Fvib' is
vibrational free energy, and 'E(a)' is the ground state energy or energy of
static lattice as a function of cell parameters.

So, my question is whether the term F-el(V,T) is neglected in the Quantum
Espresso formulation of Helmholtz free energy ? In the methodology reported
by Neugebauer et al. in the above mentioned PRB (2007) article, in section
IIIA, it is mentioned that the electronic free energy was calculated using
the finite temperature formulation of DFT by Mermin. So, my other question
would be if the finite temperature formulation of DFT is included in
calculating the Helmholtz free energy in Quantum Espresso.

I should admit that as a beginner I am unable to differentiate the
methodology of quantifying vibrational free energy in the two above
mentioned publications. May be the temperature effect on electron free
energy is included in the vibrational energy formulation of QE as mentioned
in the paper of Marzari et al. (PRB 71, 205214 (2005)).

I hope I am able to explain my question.

Thanking you,
Yours sincerely,
Krishnendu

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Message: 10
Date: Thu, 23 Nov 2017 08:01:09 +0100
From: Lorenzo Paulatto <paulatz at gmail.com>
Subject: Re: [Pw_forum] Calculation of ground state energy
To: PWSCF Forum <pw_forum at pwscf.org>
Message-ID:
        <CAG+GtJd-0iiMF7k-8iL7c-b=2v-ZeZjYSGOnwyNTkyvQC=XzMQ at mail.gmail.com>
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It is just the "total energy", printed by pw.x, of course it depends on
lattice parameter

Kibd regards

--
Lorenzo Paulatto
Written on a virtual keyboard with real fingers

On 23 Nov 2017 2:17 am, "Krishnendu Mukherjee" <
krishnendu.mukherjee789 at gmail.com> wrote:


Respected Experts,

 In the article PRB 71, 205214 (2005) authored by Nicolas Mounet and Nicola
Marzari, in equation 7, it is mentioned that,

Helmholtz free energy F(a, T)=E(a) + Fvib(T)

where, 'a' is geometrical degrees of freedom, 'T' is temperature, 'Fvib' is
vibrational free energy, and 'E(a)' is the ground state energy or energy of
static lattice as a function of cell parameters.

Can you please guide me how to calculate E(a)? Is there an example of it in
qe-6.2-examples?

Also I take this opportunity to thank Dr. Lorenzo Paulatto who guided me to
the appropriate examples in qe-6.2-examples to calculate the Fvib.

Thanking you,
Yours sincerely,
Krishnendu


-- 
Dr. Krishnendu Mukherjee,

Principal Scientist,
CSIR-NML,
Jamshedpur.
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