You need to optimize the geometry. Optimized geometry gives you the strain free lattice constants, atomic coordinates, and ground state crystal structure. Comparison with experimental lattice parameters gives the main circumstantial support in favor of the pseudopotential, optimization constraints, and exchange correlation function used in the DFT calculations. As a rule of thumb, if the geometrical optimaization gives you lattice parameters different from the experimental values, try other exchange terms and pseudopotential. Proper pseudopotential, exchange term and optimization constraints usually yied a geometry that shows excellent agreement with the experimental one. If proper optimization is not done then the electronic band structure and therefore, the band gap will not correspond to a relaxed and ground state crystal structure. This is a question of self-consistency.

Dear Rana Hossain,

You have to perform the optimization, otherwise, you would have an electronic structure that would correspond to a system that could be stressed, or would correspond to a system that has a little bit different Wyckoff positions if the calculations would optimize. Regarding the band gap, you should know that band gap values obtained by DFT depend on a lot of the "recipe" used. Hence, I suggest to perform the calculations or make a collaboration with someone with experience in calculations.

Best regards

You need to optimize the geometry. Optimized geometry gives you the strain free lattice constants, atomic coordinates, and ground state crystal structure. Comparison with experimental lattice parameters gives the main circumstantial support in favor of the pseudopotential, optimization constraints, and exchange correlation function used in the DFT calculations. As a rule of thumb, if the geometrical optimaization gives you lattice parameters different from the experimental values, try other exchange terms and pseudopotential. Proper pseudopotential, exchange term and optimization constraints usually yied a geometry that shows excellent agreement with the experimental one. If proper optimization is not done then the electronic band structure and therefore, the band gap will not correspond to a relaxed and ground state crystal structure. This is a question of self-consistency.

Dear Rana,

Professor Lopez and Professor Naqib provided you useful suggestions. Please follow their suggestions and optimize geometry for DFT calculations. I have no idea for theoretical calculations, but I am convinced to read their valuable suggestions. Thank you very much Professor Sinhue Lopez and Professor S. H. Naqib. Best regards, Basith

Dear

Professor Dr. Naqib and Dr. Lopez

Thank you for your valuable suggestions with explanations. Honestly, I never go through the mathematical description of DFT. I do not know how to derive 'Effective potential' and derive 'Kohn-Sham' equations with pen and paper. What I have tried to understand are just the basic flowchart and some very introductory description provided by the code developers. I think it is important to me know that how DFT actually works.

However,

as Dr. Naqib suggested I have done geometry optimization with all XC functional GGA+(PBE, RPBE, WC, PW91, PBEsol) and LDA+ CA-PZ available in CASTEP. As we have not performed neutron diffraction or M-H experiment at low temperature, therefore both ferromagnetic and anti-ferromagnetic order of spin (collinear) were considered. (I have also played with different energy cutoff and k points). For all functionals, anti-ferromagnetic order showed the lowest energy which is consistent with the low-temperature experimental results found in the literature. With GGA+PBE the optimized lattice constant 5.668 A was closest to the experimental 5.632 A .

Regarding the band gap,

as Dr. Lopez mentioned the term "recipe", I have done a series of calculation with GGA+PBE+U for different U to find the band gap so that it can be satisfactorily described with respect to the experimental results.

***I have also calculated the band gap without any geometry optimization.

What is confusing me are the papers I have attached.

They have done combined experimental and computational work. I have carefully read their computational methods and found nothing about geometry optimization or structural relaxation. Let me quote from the papers (I also highlighted the sections in pdf).

1. "experimental lattice constants and ionic coordinates obtained from

neutron diffraction studies were used in the calculations without

performing any structural or ionic relaxations.'' (pdf page-2)

2. "The iteration process is continued until calculated total energy and charge density of the crystal converged and becomes less than 0.01 mRy/unit cell and 0.001 e/a.u.3" (pdf page-6)

3. "Crystallographic data, without any relaxation and neutral charge, were used in order to compute the previously mentioned properties." (pdf page-8)

4." For the self-consistent calculation with the plane wave basis, a 4x4x4 Monkhorst Pack k-point mesh is used. The spin polarised GGA exchange-correlation function has been used in the calculations. Initially, the lattice parameters and the atomic positions obtained from the Rietveld refinement are used as the input for the calculations.'' (pdf page-10)

5."Our calculations were carried out within the local (spin) density approximation [L(S)DA] using the Full Potential Local Orbital band-structure package (FPLO). A k mesh of 12 × 12 × 12 k points in the whole Brillouin zone was employed." (pdf page-5)

6."The projector augmented-wave (PAW) potentials were used and the wave functions were expanded in the plane-wave basis with a kinetic-energy cutoff of 500 eV. Reciprocal-space integrations were carried out with a k-space mesh of 8 × 8 × 8." (pdf page-2)

Clearly, there were no conditions in terms of force, stress and displacement in their computational part. I guess they have done single point energy calculations with experimental data first and then computed desired properties.

There are many literatures where they kept lattice parameter fixed and allowed the atomic positions to be minimized and vice-versa. I do not know, may be they have some logical explanations.

Anyway, I have prepared two reports on my material with and without structural optimization. I found both are satisfactory with some little deviation compared to my experimental outcomes.

Now, which one should I submit?

Dear Rana,

From my point of view, always is better to optimize the structures. We know that many articles have been published by using the experimental parameters as input parameters without optimizing the structure. So, I suggest reporting the optimized results. Only one comment, generally, you get a better agreement regarding the experimental lattice parameters if you use PBEsol+U, while the electronic structure is quite similar if you use PBE+U or PBEsol+U.

Best regards

Thank You

Dr. Sinhue Lopez for your constructive, significant and fruitful comment. Your tips are very practical and worthwhile. It will help me immensely.

it is adviseable to optimize the structural parameters

my take is that the total potential is determined by the structure (where the ions are and where electrons follow, so including e-e interactions etc.), thus the correct structure to do anything theoretical in, is the theoretical one, i.e the optimized one (in both cell parameters and ion positions). of course, if you use a lousy pseudopotential or functional the structure will be lousy as well (though at least theoretically consistent). it is a good idea to use functionals that give decent structure, and be mindful that some will occasionally give incorrect electronic structure (see paper attached).

this seems obvious now, but it is a kind of philosophical question people did not want to hear back in the day. it took me a long time as a student to publish a paper where I just said that much (also attached).

Dear Rana,

Thank you for the question. As everyone says that the geometry optimization is necessary and it is true. But I would like to tell you something more. The exchange correlational function and pseudopotential you mentioned above might be not practical to get the actual band gap, I mean compared to experimental. In that case, it would be better to use non local function (HSE) and norm conserving pseudopotential. Please try with it.

Thank You, Dr. Al Helal.

in reference to the last comment, of course having the correct structure does not guarantee the correct gap in semilocal DFT (or indeed any other quantities). For gaps HSE is better than LDA/GGA, GW manybody perturbation theory better still. Other methods such as pSIC also have their merits (see paper I attached previously). Who does best is not always clear, see the attached papers.

From my own experience, it is always advisable to go always for geometry optimization prior to the property calculation in order to maintain the theoretical consistency.

However, in principle it should be ok to go with crystal structure, but technically there are higher chances of not achieving accurate/meaningful results.

So, for majority of cases, the way out from such issues is to calculate the atomic coordinates (at different level) and compare the important structural properties. Thereafter, select the most reasonable level and go for the property calculations.

Dear Rana Hossain

It is advisable to optimise the structure first in DFT to calculate any property. Whatever functional you will use in DFT will never reproduce the experimental values. So it is good practice to perform optimisation calculation to determine the ground state parameters so that your system is not under any artifact force. Then use these optimised parameters to calculate band gap or any other property.

Please how do we perform geometry optimization at a particular hydrostatic pressure and simultaneously derive elastic constants by applying finite strains?

I performed geometry optimization at a particular hydrostatic presssure, after that i took the optimized structure and performed elastic constants on the structure... is this the right way to generate elastic constants at a particular hydrostatic pressure ? or there is way to do both simultaneously.