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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