mirror of https://gitlab.com/QEF/q-e.git
114 lines
4.5 KiB
Plaintext
114 lines
4.5 KiB
Plaintext
WARNING: For speeding up the execution time for testing purposes,
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the plane waves cut-off has been reduced to 20 Ryd (from 23 Ryd),
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the charge cut-off has been reduced to 160 Ryd (from 200 Ryd)
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and the CP-MD damped dynamics uses a step of 10 a.u. (from 5 a.u.)
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and 20 steps (from 400 steps)
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USE the original parameters for obtaining converged results.
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This example shows how to perform calculations with cp.x for a system
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under the presence of an homogeneous static finite electric field.
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The coupling of the system with the electric field is described through
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the Modern Theory of the Polarization.
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We illustrate here the same example (bulk MgO) appearing in the paper:
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P.Umari and A.Pasquarello,
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Physical Review Letters, 89, p.157602 (2002).
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The concerned input parameters are:
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in namelist &CONTROL:
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tefield LOGICAL ( default = .FALSE.)
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If .TRUE. perform calculations with a finite electric field
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which is described through the modern theory of the polarization
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in namelist &ELECTRONS:
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epol INTEGER ( default = 3 )
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direction of the finite electric field (only if tefield == .TRUE.)
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In the case of a PARALLEL calculation ONLY the case epol==3
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is implemented
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efield REAL ( default = 0.d0 )
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intensity in a.u. of the finite electric field
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(only if tefield == .TRUE.)
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NOTE: the implementation has been tested ONLY for orthorhombic cells.
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****************
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The first two calculations use fast conjugate-gradient minimization for
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calculating the system's properties keeping the position of the atoms
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fixed in the experimental equilibrium positions,
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in the presence of an electric field E of 0. a.u. and 0.001 a.u.
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along the 3rd direction.
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The third calculation uses damped Car-Parrinello molecular dynamic
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for relaxing the atomic structure under the presence of a 0.001 a.u.
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electric field. This allows the calculation of the static dielectric
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constant.
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Calculation of high-frequency dielectric constant:
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For the converged wavefunctions the output file reports the electric
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dipole D. We obtain:
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For E = 0.001 a.u. , we have D=15.4128 a.u.
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For E = 0. a.u. , we have D=14.8516 a.u.
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The high-frequency dielectric constant eps_inf is given by
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eps_inf = 4*pi*(D[E=0.001 a.u.]-D[E=0. a.u.])/(0.001 a.u. * Omega) + 1
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= 2.75
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where Omega is the volume of the cell in a.u.
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(cfr. PU&AP with other pseudos: 2.79, exp. 2.96)
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Calculation of Born-effective charges:
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The effective charges can be found as finite difference of atomic forces F,
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with respect to the electric field:
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For Mg: F[E=0.001 a.u.] = 0.197318*10**-2 a.u.
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F[E=0. a.u. ] = 0.93162*10**-5 a.u.
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For O: F[E=0.001 a.u.] = -0.203209*10**-2 a.u.
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F[E=0. a.u. ] = -0.7028*10**-4 a.u.
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the effective charge Z* are found through:
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Z*= (F[E=0.001 a.u.]-F[E=0. a.u. ] )/(0.001 a.u.)
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we find:
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Mg: 1.96
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O: -1.96
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(cfr. PU&AP with other pseudos: 1.96, exp.1.96)
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Note: the atomic forces are not strictly null at no electric field,
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because of the (very-)small error caused by the introduction of a
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discretized mesh for describing wavefunctions in the cell.
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Calculation of the static dielectric constant:
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The third calculation relaxes the atomic coordinates under the presence
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of an electric field of 0.001 a.u. .The wavefunctions are taken from
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the previous calculation. It is a Car-Parrinello simulation, where
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only the electronic degrees of freedom are damped.
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At the beginning of the relaxation, the electronic D1_el, and ionic D1_ion
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dipoles read:
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D1_el=15.4128 a.u. and D1_ion=1.0608 a.u.
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At the end of the relaxation, the electronic D2_el, and ionic D2_ion,
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dipoles read:
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D2_el=-12.0495 a.u. and D2_ion=-1.141061 a.u.
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NOTE: the electronic dipole is defined modulo a factor (2*L=31.824i a.u.,
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during the MD simulation the term "ln det S" changes the Riemann
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plane, this must be taken into account when addressing the
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electronic dipole. Therefore, it reads:
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D2_el=19.7745 a.u. and D2_ion=-1.141061 a.u.
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The difference d_Eps between static and high-frequency dielectric constant,
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is given by:
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d_Eps=4*pi*(D2_el+D2_ion-D1_el-d1_ion)/(0.001 a.u. * Omega)
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= 6.74
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(cfr. PU&AP with other pseudos 5.15, exp. 6.67 )
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The difference with respect to PU&AP is due to the better
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estimation of the optical phonon frequency at Gamma.
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