[Q-e-developers] Fwd: Makov-Payne correction

[Nicola Marzari]

Ciao Paolo,


I spoke today with Oliviero Andreussi (that wrote the email
below) and he was also going to do some tests to try out.

Fig. 5 in the 2008 PRB Dabo at al was showing the discrepancy between 
the original M-P formula and our corrected one.


			nic



On 12/3/10 7:04 PM, Paolo Giannozzi wrote:
> It would be useful if anybody with previous Makov-Payne
> experience could make some tests
>
> P.
>
>> Dear all,
>>
>> I checked the equations in the subroutine PW/makov-payne.f90 and it
>> seems to me that the equation implemented is a modified version of
>> the original Makov-Payne correction of 1995. The modification is
>> due to the fact that in the original derivation the second
>> correction was computed assuming that pointlike charge that
>> compensate the molecular density was placed such as to give a zero
>> net dipole moment, while the implemented version is more general
>> and thus include a dipolar term. Moreover the correction has the
>> correct sign (the opposite of the one in the original equation).
>> This to say that the equation does not contain the factor one half
>> suggested in the paper by Ismaila and Nicola.
>> I would suggest the following changes to some of the lines of the
>> subroutine:
>>
>> from
>>
>>
>>    !
>>    ! ... Makov-Payne correction, PRB 51, 4014 (1995)
>>    ! ... Note that Eq. 15 has the wrong sign for the quadrupole term
>>    !
>>    corr1 = - madelung(ibrav) / alat * qq**2
>>    !
>>    aa = quadrupole
>>    bb = dipole(1)**2 + dipole(2)**2 + dipole(3)**2
>>    !
>>    corr2 = ( 4.D0 / 3.D0 * pi )*( qq*aa - bb ) / alat**3
>>
>>
>> to (I also made explicit the factor e2/2.0 to convert from Hartree
>> to Rydberg, that was implicitly in the original implementation, so
>> e2 should also be included in the declaration of the constants)
>>
>>    !
>>    ! ... Makov-Payne correction, PRB 51, 4014 (1995)
>>    ! ... Note that Eq. 15 has the wrong sign for the quadrupole term
>>    ! ... The prefactor of the quadrupole term is half the one in Eq. 15
>>    ! ... according to the results derived by Dabo et al., PRB 77,
>> 115139 (2008)
>>    !
>>    corr1 = - madelung(ibrav) / alat * qq**2 / 2.0D0 * e2
>>    !
>>    aa = quadrupole
>>    bb = dipole(1)**2 + dipole(2)**2 + dipole(3)**2
>>    !
>>    corr2 = ( 1.D0 / 3.D0 * pi )*( qq*aa - bb ) / alat**3 * e2
>>
>> Similarly, for the routine CPV/makov_payne.f90
>>
>>     !
>>     ! ... Makov-Payne correction, PRB 51, 43014 (1995)
>>     ! ... Note that Eq. 15 has the wrong sign for the quadrupole term
>>     !
>>     ! 1 / 2 Ry ->  a.u.
>>     corr1 = - 2.8373D0 / alat * charge**2 / 2.0D0
>>     !
>>     aa = quadrupole
>>     bb = dipole(1)**2 + dipole(2)**2 + dipole(3)**2
>>     !
>>     ! 4 / 3 ->  2 / 3 Ry ->  a.u.
>>     corr2 = ( 2.D0 / 3.D0 * pi )*( charge*aa - bb ) / alat**3
>>
>> to (in this case I assumed that e2 is defined in CP and with a
>> value equal to 1.0,
>> otherwise, probably is just better to forget about it)
>>
>>     !
>>     ! ... Makov-Payne correction, PRB 51, 43014 (1995)
>>     ! ... Note that Eq. 15 has the wrong sign for the quadrupole term
>>    ! ... The prefactor of the quadrupole term is half the one in Eq. 15
>>    ! ... according to the results derived by Dabo et al., PRB 77,
>> 115139 (2008)
>>     !
>>     ! 1 / 2 Ry ->  a.u.
>>     corr1 = - 2.8373D0 / alat * charge**2 / 2.0D0 * e2
>>     !
>>     aa = quadrupole
>>     bb = dipole(1)**2 + dipole(2)**2 + dipole(3)**2
>>     !
>>     ! 2/ 3 ->  1 / 3 Ry ->  a.u.
>>     corr2 = ( 1.D0 / 3.D0 * pi )*( charge*aa - bb ) / alat**3 * e2
>>
>> Please, if someone else can also check these corrections before
>> implementing them it would be better.
>
> ---
> Paolo Giannozzi, Democritos and University of Udine, Italy
>
>
> _______________________________________________
> Q-e-developers mailing list
> Q-e-developers at qe-forge.org
> http://qe-forge.org/mailman/listinfo/q-e-developers


-- 
----------------------------------------------------------------------
Prof Nicola Marzari    Department of Materials    University of Oxford
Chair of Materials Modelling  Director, Materials Modelling Laboratory
nicola.marzari at materials.ox.ac.uk     http://mml.materials.ox.ac.uk/NM