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README
This example shows how to perform electronic structure calculations using pw.x for a system undergoing the presence of a static homogeneous finite electric field. The method is explained in: P. Umari and A. Pasquarello, PRL 89,157602 (2002) I. Souza, J.Iniguez, and D.Vanderbilt, PRL 89, 117602 (2002) The concerned parameters are: In namelist &CONTROL lelfield LOGICAL ( default = .FALSE. ) If .TRUE. a homogeneous finite electric field described through the modern theory of the polarization is applied. gdir INTEGER For Berry phase calculation: direction of the k-point strings in reciprocal space. Allowed values: 1, 2, 3 1=first, 2=second, 3=third reciprocal lattice vector For calculations with finite electric fields (lelfield==.true.), gdir is the direction of the field nppstr INTEGER For Berry phase calculation: number of k-points to be calculated along each symmetry-reduced string The same for calculation with finite electric fields (lelfield==.true.) nberrycyc INTEGER ( default = 1 ) In the case of a finite electric field (lelfield==.true.) it defines the number of iterations for converging the wavefunctions in the electric field Hamiltonian, for each external iteration on the charge density In namelist &ELECTRONS efield REAL ( default = 0.D0 ) For finite electric field calculations (lelfield == .true.), it defines the intensity of the field in a.u. To perform a calculations with an electric field, an estimate of the optimized wavefunctions is needed to build the electric field operator (See: I. Souza, J.Iniguez and D. Vanderbilt, PRB 69, 085106, 2004). Therefore when lelfield ==.true. a copy of the wavefunctions is read from disk (i.e. restart_mode must be 'restart'). The parameters GDIR defines the direction of the electric field. The k_points must be given as a series of k-points-strings. A k-points-string is a series of NPPSTR uniform spaced k-points along the direction gdir. All the k-points in a string must have the same weight. PAY ATTENTION: in pw.x the default units for k-points coordinates is 2pi/alat and NOT crystalline units. Example of k-strings: nppstr=4 gdir=1 0.0 KY KZ 1. 0.25 KY KZ 1. 0.50 KY KZ 1. 0.75 KY KZ 1. nppstr=4 gdir=3 KX KY 0.0 1. KX KY 0.25 1. KX KY 0.50 1. KX KY 0.75 1. NOTE:It works fine in parallel with parallelization over the G points. However, for PARALLEL calculations gdir MUST BE 3. For every usual iteration of pw.x when the Hartree and exchange-correlation potentials are kept fixed, when lelfield==.true. there are NBERRYCYC iterations. During each of these iterations, the electric field operator (which depends on the wave-functions) is kept fixed; then the new electric field operator is built from the eigen-wavefunctions, and a new iteration starts. This has been introduced because the electric field Hamiltonian depends selfconsistently on the wavefunctions. NOTE:The option lelfield==.true. has been tested SO FAR only for orthorhombic unit cells For every iteration on the charge (usual pw.x iterations), the code reports the Electronic and Ionic Dipole in a.u. per unit cell and the expectation value of the operator e^{+iGz}. The letter is given for the corresponding supercell containing N_kx*N_ky*N_kz unit cells (N_kx,N_ky,N_kz are the number of k-points along x,y,z) Example: With this example, we show how to calculate the dielectric constant of bulk silicon. The system is described by a 8-atom cubic unit cell. We use a regular mesh of 3X3X7 k-points, where we have 7 k-points along the directions of the electric field: gdir=3,nppstr=7 The first calculation just calculates the electronic structure without electric field. The second calculation turns on the field but with 0 a.u. intensity. The third calculation applies a field of 0.001 a.u.. After the second calculation the electronic dipole D[0.a.u.] at 0 field reads: Electronic Dipole per cell (a.u.) -2.502553344652915E-004 After the third calculation the electronic dipole D[0.001 a.u.] at 0.001 a.u. field reads: Electronic Dipole per cell (a.u.) 0.934898995836340 The high-frequency dielectric constant eps_inf is then given by eps_inf=4*pi*(D[0.001 a.u.]-D[0.0 a.u.])/(0.001 a.u. * Omega) + 1 where Omega is the volume of the unit cell (1054.9778 (a.u.)^3). We obtain: eps_inf=12.14 (Compare: other DFT calculations, 12.7-13.1 , exp. 11.4 ) The result 12.14 is not fully converged on nppstr, for a discussion on convergence see: P.Umari and A. Pasquarello, PRB 68, 085114 (2003).