Hi all,

the situation is yet a bit more complicated. I don't know what your value of d2E/dk2 is and how it was determined but if you just take the plain values from KPOINTS/EIGENVAL it's still a long way to arrive at the correct value (and I guess your value is just a kind of "plain" derivative without really thinking about crystallography and units). Be aware that either your k points are given in reciprocal coordinates (multiples of the reciprocal lattice vectors) or if you have chosen "cartesian" (which would be the the more easy and more wise decision if you have non-cartesian lattice vectors) in units of 2*pi/lattice constant. You still have to re-scale the value correctly (because first of all a factor of 2*pi is always omitted for the reciprocal coordinates and all has to be scaled by (2*pi)^2 then) and by the length (square) of the reciprocal vectors (or 1/SCALE^2 with SCALE being the scaling factor appearing in the second line of POSCAR -- this is the proper scaling if using cartesian coordinates; but really care about that you plot/fit E versus |k-k_0| in the corresponding k direction). In addition you also have to re-scale all by 1/Rydberg/bohr^2 (1/13.605826/0.529177249^2) in order to transform from eV/Angstroem units to atomic units (with a free electron reference mass m_e=1). Just then you arrive with some 1/m_eff in 1/m_e units which can be inverted (and maybe gives a value more or less close to 0.6 after inversion). If you need a full tensor in the case of low-symmetry systems you have to take derivatives in different directions (most conveniently in x-, y-, z-direction and for monoclinic/triclinic also xy, yz, zx). So, re-think carefully the proper scaling and units (because the "plain" derivatives are anything else but the final answer ...).

Of course, effective masses in DFT (but also with hybrids etc.) are never exact (you may always have deviations of 10-20% or even more and usually also hole masses have larger errors than electron masses). But at least the correct order of magnitude (in you case maybe something in the range 0.5-0.7 should be reproduced correctly (unless DFT fails completely, e.g., due to to wrong band ordering or whatever other reason ...).

I hope these comments help a bit ...

Juergen

Dear Tuhin, As you may be aware, the effective mass is derived using the curvature of the dispersion curve at the extrema, and thus evaluated using the second derivative you have specified in your query. A small effective mass occurs with large curvatures and vice versa. However effective mass is dependent on its anisotropic attributes and therefore relies on the location of the k-point. In VASP, you may need to plot the band diagram in more than one direction, and use a general fitting equation in three dimension. In simple cases, the effective mass tensor is directly evaluated using the longitudinal mass and the transverse mass. However there are self-interaction errors to consider, and in the GW approximation (see https://en.wikipedia.org/wiki/GW_approximation), where VASP employs the projector-augmented-wave (PAW) method, there is the inherent problem of accurate prediction of effective masses. In some instances, empirical adjustments of the self-energy operator is needed. I hope this answer is of partial help, its best to go back to the VASP manual once again to check your input parameters and script.

Hi all,

the situation is yet a bit more complicated. I don't know what your value of d2E/dk2 is and how it was determined but if you just take the plain values from KPOINTS/EIGENVAL it's still a long way to arrive at the correct value (and I guess your value is just a kind of "plain" derivative without really thinking about crystallography and units). Be aware that either your k points are given in reciprocal coordinates (multiples of the reciprocal lattice vectors) or if you have chosen "cartesian" (which would be the the more easy and more wise decision if you have non-cartesian lattice vectors) in units of 2*pi/lattice constant. You still have to re-scale the value correctly (because first of all a factor of 2*pi is always omitted for the reciprocal coordinates and all has to be scaled by (2*pi)^2 then) and by the length (square) of the reciprocal vectors (or 1/SCALE^2 with SCALE being the scaling factor appearing in the second line of POSCAR -- this is the proper scaling if using cartesian coordinates; but really care about that you plot/fit E versus |k-k_0| in the corresponding k direction). In addition you also have to re-scale all by 1/Rydberg/bohr^2 (1/13.605826/0.529177249^2) in order to transform from eV/Angstroem units to atomic units (with a free electron reference mass m_e=1). Just then you arrive with some 1/m_eff in 1/m_e units which can be inverted (and maybe gives a value more or less close to 0.6 after inversion). If you need a full tensor in the case of low-symmetry systems you have to take derivatives in different directions (most conveniently in x-, y-, z-direction and for monoclinic/triclinic also xy, yz, zx). So, re-think carefully the proper scaling and units (because the "plain" derivatives are anything else but the final answer ...).

Of course, effective masses in DFT (but also with hybrids etc.) are never exact (you may always have deviations of 10-20% or even more and usually also hole masses have larger errors than electron masses). But at least the correct order of magnitude (in you case maybe something in the range 0.5-0.7 should be reproduced correctly (unless DFT fails completely, e.g., due to to wrong band ordering or whatever other reason ...).

I hope these comments help a bit ...

Juergen

Jürgen Furthmüller Sir, I have a little confusion about the very useful reply of yours.

In my system the valence band maxima is at gamma point (0,0,0) and the conduction band minima is at B (0.5,0,0) in the reciprocal lattice coordinate. Now I want to calculate the effective mass at this two points only. My question is should I multiply the plain derivative value of d2E/dK2 (for VB it is -2*92.899, obtained from the quadratic fit by taking 5 points near the gamma point) by (2*pi)^2 and by square of the length of reciprocal lattice vectors (or by the 1/SCALE^2)? For a particular point (as here gamma or B) what should be value of the length reciprocal lattice vectors and how to obtain the value?