mirror of https://gitlab.com/QEF/q-e.git
175 lines
5.9 KiB
Plaintext
175 lines
5.9 KiB
Plaintext
This example shows how to perform electronic structure calculations
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using pw.x for a system undergoing the presence of a static homogeneous
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finite electric field. The method is explained in:
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P. Umari and A. Pasquarello, PRL 89,157602 (2002)
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I. Souza, J.Iniguez, and D.Vanderbilt, PRL 89, 117602 (2002)
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The related parameters are:
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In namelist &CONTROL
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lelfield LOGICAL ( default = .FALSE. )
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If .TRUE. a homogeneous finite electric field
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described through the modern theory of the polarization
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is applied.
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gdir INTEGER
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For Berry phase calculation: direction of the k-point
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strings in reciprocal space. Allowed values: 1, 2, 3
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1=first, 2=second, 3=third reciprocal lattice vector
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For calculations with finite electric fields
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(lelfield==.true.), gdir is the direction of the field
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This is NOT USED if K_POINTS {automatic} IS PRESENT
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nppstr INTEGER
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For Berry phase calculation: number of k-points to be
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calculated along each symmetry-reduced string
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The same for calculation with finite electric fields
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(lelfield==.true.)
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This is NOT USED if K_POINTS {automatic} IS PRESENT
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nberrycyc INTEGER ( default = 1 )
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In the case of a finite electric field (lelfield==.true.)
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it defines the number of iterations for converging the
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wavefunctions in the electric field Hamiltonian, for each
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external iteration on the charge density
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In namelist &ELECTRONS
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efield REAL ( default = 0.D0 )
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For finite electric field calculations (lelfield == .true.),
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it defines the intensity of the field in a.u.
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This is NOT USED if K_POINTS {automatic} IS PRESENT
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in the case of K_POINTS {automatic} the electric field is given in
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Cartesian coordinates through:
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efield_cart(1) 1st component of the electric field in (Rydberg-type) atomic units
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efield_cart(2) 2st component of the electric field in (Rydberg-type) atomic units
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efield_cart(3) 3rd component of the electric field in (Rydberg-type) atomic units
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To perform a calculations with an electric field, an estimate of
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the optimized wavefunctions is needed to build the electric field
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operator (See: I. Souza, J.Iniguez and D. Vanderbilt, PRB 69, 085106,
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2004). Therefore when lelfield ==.true. a copy of the wavefunctions
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is read from disk (i.e. startingwfc should be 'file').
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When K_POINTS {automatic} IS NOT present
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The parameters GDIR defines the direction of the electric field.
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The k_points must be given as a series of k-points-strings.
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A k-points-string is a series of NPPSTR uniform spaced k-points
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along the direction gdir. All the k-points in a string must have
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the same weight.
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PAY ATTENTION: in pw.x the default units for k-points coordinates
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is 2pi/alat and NOT crystalline units.
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Example of k-strings:
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nppstr=4
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gdir=1
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0.0 KY KZ 1.
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0.25 KY KZ 1.
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0.50 KY KZ 1.
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0.75 KY KZ 1.
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nppstr=4
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gdir=3
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KX KY 0.0 1.
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KX KY 0.25 1.
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KX KY 0.50 1.
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KX KY 0.75 1.
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When K_POINTS {automatic} IS present
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the string are calculated directly by pw.x and
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the electric field must be given in Cartesian coordinates,
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also the Polarization (electronic and ionic) is then
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reported in Cartesian coordinates
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For every usual iteration of pw.x when the Hartree and exchange-correlation
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potentials are kept fixed, when lelfield==.true. there are NBERRYCYC
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iterations. During each of these iterations, the electric field operator
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(which depends on the wave-functions) is kept fixed; then
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the new electric field operator is built from the eigen-wavefunctions,
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and a new iteration starts. This has been introduced because
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the electric field Hamiltonian depends self consistently on the
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wavefunctions.
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For every iteration on the charge (usual pw.x iterations), the code
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reports the Electronic and Ionic Dipole in a.u. per unit cell and
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the expectations values of the operator e^{+iGz}. The letter
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is given for the corresponding supercell containing N_kx*N_ky*N_kz
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unit cells (N_kx,N_ky,N_kz are the number of k-points along x,y,z)
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Example 1 - dielectric constant of Si
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The system is described by a 8-atom cubic unit cell.
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We use a regular mesh of 3X3X7 k-points, where we have 7 k-points
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along the directions of the electric field: gdir=3,nppstr=7
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The first calculation just calculates the electronic structure
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without electric field. The second calculation turns on the field
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but with 0 a.u. intensity. The third calculation applies a field
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of 0.001 a.u..
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The electronic dipole D[0.a.u.] at 0 field is a small number in the
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order of 1.0d-4. After the third calculation the electronic dipole
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D[0.001 a.u.] at 0.001 a.u. field is 0.9265.
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The high-frequency dielectric constant eps_inf is then given by
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eps_inf=4*pi*(D[0.001 a.u.]-D[0.0 a.u.])/(0.001 a.u. * Omega) + 1
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where Omega is the volume of the unit cell (1054.9778 (a.u.)^3).
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We obtain:
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eps_inf=12.04
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(Compare: other DFT calculations, 12.7-13.1 , exp. 11.4 )
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The result 12.14 is not fully converged with respect to the k-points grid
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P.Umari and A. Pasquarello, PRB 68, 085114 (2003).
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Example 2 - effective charges of AlAs
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The setup of the system is quite the same as in the previous case, with
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alat=10.60 a.u. and Omega=1191.0160 (a.u.)^3. The calculation follows the
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same logic. Moreover, forces on atoms are computed (tprnfor=.true.)
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The electronic dipole D[0.001 a.u.] at 0.001 a.u. field is 0.7400. This yields
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eps_inf=8.808.
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The forces F[0.001 a.u.] on atoms (z component) are 0.03054 a.u., almost equal
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for all atoms, while F[0.0 a.u.] is almost zero. The Born effective charges Z*
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are thus
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eZ* = (F[0.001 a.u.]-F[0.0 a.u.])/0.001 a.u. = 3.054 a.u., Z* = 2.16
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BEWARE the electron charge factor "e": e=sqrt(2) in Ry atomic units (e^=2) !
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