[Wien] Comparison between ab inito calculation and "measurement" result

[pieper]

Dear Seongiae,

my two cents on this:
Physics in general is about modeling some situation with as few and as 
simple assumptions, approximations and parameters as possible.

If the model works, that is if the model behaves similar to the real 
thing, fine. As you observed: The confidence in the model increases, 
people tend to conclude that the assumptions were correct and the 
approximations are accurate. Neither of which is necessarily true since 
the nice result might be pure coincidence, but as long as nothing points 
in that direction this is usually considered good enough until something 
actually goes wrong.

If the model description does not work you go looking for which 
assumptions or what approximations are responsible for the trouble.

The advantage of DFT calculations is that they start from generally 
accepted assumptions of quantum theory ('first principles') and 
introduce relatively few assumptions and more or less controlled 
approximations. This hopefully allowes you to pin down what goes wrong 
in your model and you even might be able to fix it. At least it improves 
the chances to do so. After that one can go back and look how earlier 
calculations might have been affected or why the problem did not show up 
there.

The first principles are something like assigning operators to 
observables you are interested in, define the states they act upon, and 
write down some Hamiltionian corresponding to the internal energy 
observable. DFT is then about finding the ground state of this 
Hamiltonian in terms of a single electron density. Personally, I am not 
happy with the term 'first principles' since working on the basis of 
some valid first principles implies a lack of freedom to do something 
wrong. However, one should be aware of the fact that things can go 
sideways already at this stage. The selection of both, the states taken 
into account and the Hamiltonian obviously may influence the outcome.

The Hamiltonian involves by necessity certain approximations. For 
example, the spin-orbit interaction is treated in Wien2k only optionally 
and then with additional approximations. Another prominent problem is 
that one needs a single electron density Hamiltonian to keep the 
computations (barely) manageable. While a single electron density 
corresponding to the ground state of the true many particle Hamiltonian 
is guaranteed to exist, the proof of its existance is not constructive. 
To find it in the space of single electron density wave functions one 
approximates the (two particle) exchange contributions by potentials 
with acronyms like PBE, mBJ, ... I am no expert but I understand 
improving these potentials is a major current research effort.

Even if the Hamiltonian is beyond doubt the result of a calculation can 
be ambiguous. As you noted, the ground state determines only the 
properties at 0 K. If excitations with different values for the 
observables are within the range of the thermal energy this has to be 
taken into account - usually with additional approximations and 
assumptions involved depending on which properties one is interested in 
(phonon package, BolzTrap for transport, Optic ...). It might be 
difficult to even determine that ground state. Especially if additional 
internal degrees of freedom like atomic positions or spins are important 
a plethora of states representing local energy minima can appear with 
very similar energies but very different macroscopic properties.

So in my opinion the foundation for believing that a DFT model 
accurately represents some physical situation at 300 K would be that it 
actually works in lot of cases. When it does not work one usually can 
find fairly specific reasons for the failure (low lying excitations, 
structural phase transitions ...) and improve things from there in a 
systematic way.

Best regards,

Martin


---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564


Am 28.01.2016 05:16, schrieb Seongjae Cho:
> Dear group,
> 
> As an engineering researcher with great lack in understanding the ab
> initio calculations,
> 
> I have basically believed that the first-principle calculation results
> demonatrate rather
> 
> "ideal" values presumably obtained at "0 K" and they need to be
> adjusted by proper mathematical
> 
> models formulated as a function of temperature for reachiing the more
> practical values at non-0 K values.
> 
> However, in many pieces of literature, they are trying to compare the
> ab initio calculation
> 
> results and the measurement results at non-0 K, particularly at room
> temperature.
> 
> I'm wondering what sort of foundation is required for believing that
> the simulation results
> 
> can be treated as those obtained at 300 K. In other words, what models
> or equations can be
> 
> adopted for taking the exact band structures and related parameters
> (Eg, effective mass, etc.)
> 
> in hand in performing the first-principle simulations?
> 
> It will be appreciated if you fix my fault and share some wisdom. Many
> thanks.
> 
> - Sincerely, Seongjae.
> 
> 
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