261 lines
8.2 KiB
Fortran
261 lines
8.2 KiB
Fortran
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!=======================================================================
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!
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MODULE CALCULATORS_P
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!
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USE ACCURACY_REAL
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!
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! This module contains the subroutines allowing to compute
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! various properties of the electron/plasma liquids:
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!
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!
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! * exact plasmon dispersion : CALC_EPD
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!
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! * fluctuation potential : CALC_FLP
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!
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CONTAINS
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!=======================================================================
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!
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SUBROUTINE CALC_EPD
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!
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! This subroutine computes the exact plasmon dispersion
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 16 Dec 2020
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!
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!
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USE FERMI_SI, ONLY : EF_SI
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!
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USE PLASMON_DISP_EXACT
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!
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USE PRINT_FILES, ONLY : IO_PD
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!
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IMPLICIT NONE
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!
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INTEGER, PARAMETER :: N_ZERO = 10000 ! max number of zeros
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!
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INTEGER :: IS,IC ! lower and upper indices
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INTEGER :: IP
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!
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REAL (WP) :: ENE_P_Q(N_ZERO)
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REAL (WP) :: YQ(N_ZERO)
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!
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CALL PLASMON_DISP_EX(IS,IC,YQ,ENE_P_Q)
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!
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DO IP = IS, IC !
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WRITE(IO_PD,*) YQ(IP),ENE_P_Q(IP) / EF_SI !
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END DO !
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!
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END SUBROUTINE CALC_EPD
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!
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!=======================================================================
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!
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SUBROUTINE CALC_FLP
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!
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! This subroutine computes the modulus of the fluctuation potential.
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! The fluctuation potential is given by
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!
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! V_q = A_q e^{i q . r}
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!
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! with
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!
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! | V_C(q) | ^{1/2}
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! A_q = | ______________________ |
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! | |
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! | d [ epsilon] / d omega | omega = omega(q) (1)
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!
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!
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!
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! where omega(q) is the plasmon dispersion
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!
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!
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!
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! References: (1) B. I. Lundqvist, Phys. kondens. Materie 9, 236-248 (1969)
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!
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!
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!
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!
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! Intermediate parameters:
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!
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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! * DMN : problem dimension
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!
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!
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! Output parameters:
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!
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! * FLPR : real part of the screened potential
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! * FLPI : imaginary part of the screened potential
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!
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!
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!
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! WARNING : only REAL a at present
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 11 Jun 2021
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE REAL_NUMBERS, ONLY : ZERO,TWO,THREE,TEN, &
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HALF
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USE COMPLEX_NUMBERS, ONLY : IC
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USE DF_VALUES, ONLY : ESTDY,EPS_T,D_FUNC
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USE MATERIAL_PROP, ONLY : RS,DMN
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USE CONSTANTS_P1, ONLY : H_BAR,M_E,E,EPS_0
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USE ENE_CHANGE, ONLY : EV
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USE FERMI_SI, ONLY : EF_SI,KF_SI
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USE EXT_FIELDS, ONLY : T
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USE SCREENING_TYPE
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USE SCREENING_VEC
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!
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USE E_GRID
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USE Q_GRID
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USE R_GRID
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USE UNITS, ONLY : UNIT
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USE OUT_VALUES_P
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USE PLASMON_DISPERSION
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!
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USE COULOMB_K, ONLY : COULOMB_FF
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USE INTERPOLATION
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USE DERIVATION
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USE PLASMON_ENE_SI
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USE PLASMON_DISP_EXACT
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USE PLASMON_DISP_REAL
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USE RE_EPS_0_TREATMENT
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!
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USE CALCULATORS_1
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USE CALCULATORS_3
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!
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USE OUT_VALUES_3, ONLY : I_ZE
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USE OUT_VALUES_P, ONLY : I_FP
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USE PRINT_FILES, ONLY : IO_ZE,IO_FP
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 4) :: D_FUNCL,D_FUNCT
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!
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INTEGER, PARAMETER :: N_ZERO = 10000 ! max number of zeros
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!
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INTEGER :: LOGF
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INTEGER :: IE,IQ,IR
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INTEGER :: NB
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INTEGER :: IQ_MIN,IQ_MAX
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!
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REAL (WP) :: Y,X
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REAL (WP) :: ENE_P_Q(N_ZERO),ENE_P_Q1
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REAL (WP) :: YB(N_ZERO)
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REAL (WP) :: ENE_P
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REAL (WP) :: EPSR(NSIZE),EPSI(NSIZE),EN(NSIZE)
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REAL (WP) :: EPSR1(NSIZE),EPSI1(NSIZE)
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REAL (WP) :: REPS,IEPS,DEPSR_Q,DEPSI_Q
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REAL (WP) :: FLPR(NSIZE),FLPI(NSIZE),R(NSIZE)
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REAL (WP) :: RN,Q_SI,KS_SI,VC,A_Q
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REAL (WP) :: H
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!
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REAL (WP) :: SQRT,FLOAT,COS,SIN
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!
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COMPLEX (WP) :: DEPS
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!
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LOGF = 6 !
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!
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! Computing the exact plasmon dispersion in SI
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!
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IF(I_FP == 1) THEN !
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I_ZE = 1 !
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IO_ZE = 1 !
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CALL PLASMON_DISP_EX(IQ_MIN,IQ_MAX,YB,ENE_P_Q) !
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END IF !
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!
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! Computing the dielectric function from IQ_MIN to IQ_MAX
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! (plasmon dispersion bounds)
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!
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DO IQ = IQ_MIN,IQ_MAX ! start of q-loop
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!
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Y = Q_MIN + FLOAT(IQ - 1) * Q_STEP ! Y = q/k_F
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!
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X = HALF * Y ! X = q/(2k_F)
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!
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Q_SI = Y * KF_SI ! q in SI
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!
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! Computing an approximate plasmon dispersion
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!
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IF(I_FP == 3) THEN !
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CALL PLASMON_DISP_R(X,RS,T,PL_DISP,ENE_P_Q1) !
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END IF !
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!
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! Computing the dielectric function EPS(omega) for q
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!
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CALL CALC_EPS(X,EN,EPSR,EPSI) ! EN = E / E_F
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!
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! Plasmon energy at q in units of E / E_F
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!
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IF(I_FP == 1) THEN !
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ENE_P = ENE_P_Q(IQ) / EF_SI !
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ELSE IF(I_FP == 3) THEN !
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ENE_P = ENE_P_Q1 / EF_SI !
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END IF !
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!
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! Checking for screening vector
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!
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CALL SCREENING_VECTOR(SC_TYPE,DMN,X,RS,T,KS_SI) !
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!
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! Initialisation of derivative arrays
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!
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DO IE = 1, N_E !
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EPSR1(IE) = ZERO !
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EPSI1(IE) = ZERO !
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END DO !
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!
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H = EN(2) - EN(1) ! step for energy derivation (E / E_F)
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!
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! Computing the derivatives of EPSR and EPSI
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!
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CALL DERIV_1(EPSR,N_E,5,H,EPSR1) !
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CALL DERIV_1(EPSI,N_E,5,H,EPSI1) !
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!
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! Cubic spline interpolation of EPSR1(N) and EPSI1(N) at E = ENE_P
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!
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DEPSR_Q = CUBIC_SPLINE_INTERP(EPSR1,EN,N_E,ENE_P) !
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DEPSI_Q = CUBIC_SPLINE_INTERP(EPSI1,EN,N_E,ENE_P) !
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!
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DEPS = ABS(DEPSR_Q + IC * DEPSI_Q) !
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!
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! Calculation of Fourier transform of Coulomb potential in SI
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!
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CALL COULOMB_FF(DMN,UNIT,Q_SI,KS_SI,VC) !
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!
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! Computing the amplitude of the fluctuation potential (in eV)
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!
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A_Q = SQRT(ABS(VC / DEPS)) / EV ! ref. (1) eq. (17)
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!
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! Writing the results
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!
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IF(I_FP == 1) THEN ! writing to
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WRITE(IO_FP,*) Y,A_Q ! file
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ELSE IF(I_FP == 2) THEN !
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!
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! Loop in R
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!
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DO IR = 1, N_R !
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!
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RN = R_MIN + FLOAT(IR - 1) * R_STEP ! R = k_F * r
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!
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FLPR(IR) = A_Q * COS(TWO * X * RN) !
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FLPI(IR) = A_Q * SIN(TWO * X * RN) !
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R(IR) = RN !
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!
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WRITE(IO_FP,*) Y,RN,FLPR(IE),FLPI(IE) !
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!
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END DO !
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END IF !
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END DO ! end of q-loop
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!
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END SUBROUTINE CALC_FLP
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!
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END MODULE CALCULATORS_P
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