mirror of https://gitlab.com/QEF/q-e.git
2503 lines
87 KiB
Fortran
2503 lines
87 KiB
Fortran
!
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! Copyright (C) 2004-2011 Quantum ESPRESSO group
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! This file is distributed under the terms of the
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! GNU General Public License. See the file `License'
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! in the root directory of the present distribution,
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! or http://www.gnu.org/copyleft/gpl.txt .
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!
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!-------------------------------------------------------------------
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module funct
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!-------------------------------------------------------------------
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! This module contains data defining the DFT functional in use
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! and a number of functions and subroutines to manage them.
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! Data are PRIVATE and are accessed and set only by function calls.
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! Basic drivers to compute XC quantities are also included.
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!
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! setting routines: set_dft_from_name (previously which_dft)
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! set_dft_from_indices
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! enforce_input_dft
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! start_exx
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! stop_exx
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! set_finite_size_volume
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! retrieve functions: get_dft_name
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! get_iexch
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! get_icorr
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! get_igcx
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! get_igcc
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! get_exx_fraction
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! dft_name
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! write_dft_name
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! logical functions: dft_is_gradient
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! dft_is_meta
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! dft_is_hybrid
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! dft_is_nonlocc
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! exx_is_active
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! dft_has_finite_size_correction
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!
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! XC computation drivers: xc, xc_spin, gcxc, gcx_spin, gcc_spin, gcc_spin_more
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! derivatives of XC computation drivers: dmxc, dmxc_spin, dmxc_nc, dgcxc,
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! dgcxc_spin
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!
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USE io_global, ONLY: stdout
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USE kinds, ONLY: DP
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USE control_flags, ONLY : lwfpbe0, lwfpbe0nscf ! Lingzhu Kong
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IMPLICIT NONE
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PRIVATE
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SAVE
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! subroutines/functions managing dft name and indices
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PUBLIC :: set_dft_from_indices, set_dft_from_name
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PUBLIC :: enforce_input_dft, write_dft_name, dft_name
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PUBLIC :: init_dft_exxrpa, enforce_dft_exxrpa
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PUBLIC :: get_dft_name, get_iexch, get_icorr, get_igcx, get_igcc, get_inlc
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PUBLIC :: dft_is_gradient, dft_is_meta, dft_is_hybrid, dft_is_nonlocc
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! additional subroutines/functions for hybrid functionals
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PUBLIC :: start_exx, stop_exx, get_exx_fraction, exx_is_active
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PUBLIC :: set_exx_fraction
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PUBLIC :: set_screening_parameter, get_screening_parameter
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! additional subroutines/functions for finite size corrections
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PUBLIC :: dft_has_finite_size_correction, set_finite_size_volume
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! driver subroutines computing XC
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PUBLIC :: xc, xc_spin, gcxc, gcx_spin, gcc_spin, gcc_spin_more
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PUBLIC :: dmxc, dmxc_spin, dmxc_nc
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PUBLIC :: dgcxc, dgcxc_spin
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PUBLIC :: nlc
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! general XC driver
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PUBLIC :: vxc_t, exc_t
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! vector XC driver
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PUBLIC :: evxc_t_vec, gcx_spin_vec
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!
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! PRIVATE variables defining the DFT functional
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!
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PRIVATE :: dft, dft_shortname, iexch, icorr, igcx, igcc, inlc
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PRIVATE :: discard_input_dft
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PRIVATE :: isgradient, ismeta, ishybrid
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PRIVATE :: exx_fraction, exx_started
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PRIVATE :: has_finite_size_correction, &
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finite_size_cell_volume, finite_size_cell_volume_set
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!
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character (len=25) :: dft = 'not set'
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character (len=6) :: dft_shortname = ' '
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!
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! dft is the exchange-correlation functional, described by
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! one of the following keywords ("dft_shortname"):
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! "pz" = "sla+pz" = Perdew-Zunger LDA
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! "bp" = "b88+p86" = Becke-Perdew grad.corr.
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! "pw91" = "sla+pw+ggx+ggc" = PW91 (aka GGA)
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! "blyp" = "sla+b88+lyp+blyp" = BLYP
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! "pbe" = "sla+pw+pbx+pbc" = PBE
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! "revpbe"= "sla+pw+rpb+pbc" = revPBE (Zhang-Yang)
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! "pbesol"= "sla+pw+psx+psc" = PBEsol
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! "hcth" = "nox+noc+hcth+hcth" = HCTH/120
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! "olyp" = "nox+lyp+optx+blyp" = OLYP
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! "wc" = "sla+pw+wcx+pbc" = Wu-Cohen
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! "tpss" = "sla+pw+tpss+tpss" = TPSS Meta-GGA
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! "pbe0" = "pb0x+pw+pb0x+pbc" = PBE0
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! "hse" = "sla+pw+hse+pbc" = Heyd-Scuseria-Ernzerhof HSE 06
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! "b3lyp" = "b3lp+vwn+b3lp+b3lp"= B3LYP
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! "vdw-df"= "sla+pw+rpb+vdw1" = vdW-DF
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! "vdw-df2"="sla+pw+rpb+vdw2" = vdW-DF2
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! "vdw-df-c09"
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! "vdw-df2-c09"
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! or by any nonconflicting combination of the following keywords
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! (case-insensitive):
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!
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! Exchange: "nox" none iexch=0
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! "sla" Slater (alpha=2/3) iexch=1 (default)
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! "sl1" Slater (alpha=1.0) iexch=2
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! "rxc" Relativistic Slater iexch=3
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! "oep" Optimized Effective Potential iexch=4
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! "hf" Hartree-Fock iexch=5
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! "pb0x" PBE0 (Slater*0.75+HF*0.25) iexch=6
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! "b3lp" B3LYP(Slater*0.80+HF*0.20) iexch=7
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! "kzk" Finite-size corrections iexch=8
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!
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! Correlation: "noc" none icorr=0
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! "pz" Perdew-Zunger icorr=1 (default)
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! "vwn" Vosko-Wilk-Nusair icorr=2
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! "lyp" Lee-Yang-Parr icorr=3
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! "pw" Perdew-Wang icorr=4
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! "wig" Wigner icorr=5
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! "hl" Hedin-Lunqvist icorr=6
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! "obz" Ortiz-Ballone form for PZ icorr=7
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! "obw" Ortiz-Ballone form for PW icorr=8
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! "gl" Gunnarson-Lunqvist icorr=9
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! "b3lp" B3LYP (same as "vwn") icorr=10
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! "kzk" Finite-size corrections icorr=11
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!
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! Gradient Correction on Exchange:
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! "nogx" none igcx =0 (default)
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! "b88" Becke88 (beta=0.0042) igcx =1
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! "ggx" Perdew-Wang 91 igcx =2
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! "pbx" Perdew-Burke-Ernzenhof exch igcx =3
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! "rpb" revised PBE by Zhang-Yang igcx =4
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! "hcth" Cambridge exch, Handy et al igcx =5
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! "optx" Handy's exchange functional igcx =6
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! "tpss" TPSS meta-gga igcx =7
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! "pb0x" PBE0 (PBE exchange*0.75) igcx =8
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! "b3lp" B3LYP (Becke88*0.72) igcx =9
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! "psx" PBEsol exchange igcx =10
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! "wcx" Wu-Cohen igcx =11
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! "hse" HSE screened exchange igcx =12
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! "rw86" revised PW86 igcx =13
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! "pbe" same as PBX, back-comp. igcx =14
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! "tpss" same as META, back-comp. igcx =15
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! "c09x" Cooper 09 igcx =16
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!
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! Gradient Correction on Correlation:
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! "nogc" none igcc =0 (default)
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! "p86" Perdew86 igcc =1
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! "ggc" Perdew-Wang 91 corr. igcc =2
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! "blyp" Lee-Yang-Parr igcc =3
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! "pbc" Perdew-Burke-Ernzenhof corr igcc =4
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! "hcth" Cambridge corr, Handy et al igcc =5
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! "tpss" TPSS meta-gga igcc =6
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! "b3lp" B3LYP (Lee-Yang-Parr*0.81) igcc =7
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! "psc" PBEsol corr igcc =8
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!
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! Van der Waals functionals (nonlocal term only)
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! "nonlc" none inlc =0 (default)
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! "vdw1" vdW-DF1 inlc =1
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! "vdw2" vdW-DF2 inlc =2
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!
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! References:
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! pz J.P.Perdew and A.Zunger, PRB 23, 5048 (1981)
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! vwn S.H.Vosko, L.Wilk, M.Nusair, Can.J.Phys. 58,1200(1980)
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! wig E.P.Wigner, Trans. Faraday Soc. 34, 67 (1938)
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! hl L.Hedin and B.I.Lundqvist, J. Phys. C4, 2064 (1971)
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! gl O.Gunnarsson and B.I.Lundqvist, PRB 13, 4274 (1976)
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! pw J.P.Perdew and Y.Wang, PRB 45, 13244 (1992)
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! obpz G.Ortiz and P.Ballone, PRB 50, 1391 (1994)
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! obpw as above
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! b88 A.D.Becke, PRA 38, 3098 (1988)
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! p86 J.P.Perdew, PRB 33, 8822 (1986)
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! pbe J.P.Perdew, K.Burke, M.Ernzerhof, PRL 77, 3865 (1996)
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! pw91 J.P.Perdew and Y. Wang, PRB 46, 6671 (1992)
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! blyp C.Lee, W.Yang, R.G.Parr, PRB 37, 785 (1988)
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! hcth Handy et al, JCP 109, 6264 (1998)
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! olyp Handy et al, JCP 116, 5411 (2002)
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! revPBE Zhang and Yang, PRL 80, 890 (1998)
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! rw86 E. Amonn D. Murray et al, J. Chem. Theory comp. 5, 2754 (2009)
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! wc Z. Wu and R. E. Cohen, PRB 73, 235116 (2006)
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! tpss J.Tao, J.P.Perdew, V.N.Staroverov, G.E. Scuseria,
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! PRL 91, 146401 (2003)
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! kzk H.Kwee, S. Zhang, H. Krakauer, PRL 100, 126404 (2008)
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! pbe0 J.P.Perdew, M. Ernzerhof, K.Burke, JCP 105, 9982 (1996)
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! hse Heyd, Scuseria, Ernzerhof, J. Chem. Phys. 118, 8207 (2003)
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! Heyd, Scuseria, Ernzerhof, J. Chem. Phys. 124, 219906 (2006).
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! b3lyp P.J. Stephens,F.J. Devlin,C.F. Chabalowski,M.J. Frisch
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! J.Phys.Chem 98, 11623 (1994)
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! pbesol J.P. Perdew et al., PRL 100, 136406 (2008)
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! vdW-DF M. Dion et al., PRL 92, 246401 (2004)
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! T. Thonhauser et al., PRB 76, 125112 (2007)
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! vdw-DF2 Lee et al., Phys. Rev. B 82, 081101 (2010)
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! c09x V. R. Cooper, Phys. Rev. B 81, 161104(R) (2010)
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!
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integer, parameter:: notset = -1
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!
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integer :: iexch = notset
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integer :: icorr = notset
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integer :: igcx = notset
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integer :: igcc = notset
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integer :: inlc = notset
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real(DP):: exx_fraction = 0.0_DP
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real(DP):: screening_parameter = 0.0_DP
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logical :: isgradient = .false.
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logical :: ismeta = .false.
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logical :: ishybrid = .false.
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logical :: exx_started = .false.
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logical :: has_finite_size_correction = .false.
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logical :: finite_size_cell_volume_set = .false.
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real(DP):: finite_size_cell_volume = notset
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logical :: isnonlocc = .false.
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logical :: discard_input_dft = .false.
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!
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! internal indices for exchange-correlation
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! iexch: type of exchange
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! icorr: type of correlation
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! igcx: type of gradient correction on exchange
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! igcc: type of gradient correction on correlation
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! inlc: type of non local correction on correlation
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!
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! ismeta: .TRUE. if gradient correction is of meta-gga type
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! ishybrid: .TRUE. if the xc functional is an HF+DFT hybrid like
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! PBE0, B3LYP, HSE or HF itself
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!
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! see comments above and routine "set_dft_from_name" below
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!
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! data
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integer :: nxc, ncc, ngcx, ngcc, ncnl
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parameter (nxc = 8, ncc =11, ngcx =16, ngcc = 10, ncnl=2)
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character (len=4) :: exc, corr
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character (len=4) :: gradx, gradc, nonlocc
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dimension exc (0:nxc), corr (0:ncc), gradx (0:ngcx), gradc (0: ngcc), nonlocc (0: ncnl)
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data exc / 'NOX', 'SLA', 'SL1', 'RXC', 'OEP', 'HF', 'PB0X', 'B3LP', 'KZK' /
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data corr / 'NOC', 'PZ', 'VWN', 'LYP', 'PW', 'WIG', 'HL', 'OBZ', &
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'OBW', 'GL' , 'B3LP', 'KZK' /
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data gradx / 'NOGX', 'B88', 'GGX', 'PBX', 'RPB', 'HCTH', 'OPTX',&
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'META', 'PB0X', 'B3LP','PSX', 'WCX', 'HSE', 'RW86', 'PBE', &
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'TPSS', 'C09X' /
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data gradc / 'NOGC', 'P86', 'GGC', 'BLYP', 'PBC', 'HCTH', 'META',&
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'B3LP', 'PSC', 'PBE', 'TPSS' /
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data nonlocc / ' ', 'VDW1', 'VDW2' /
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CONTAINS
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!-----------------------------------------------------------------------
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subroutine set_dft_from_name( dft_ )
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!-----------------------------------------------------------------------
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!
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! translates a string containing the exchange-correlation name
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! into internal indices iexch, icorr, igcx, igcc
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!
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implicit none
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! input
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character(len=*) :: dft_
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! local
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integer :: len, l, i
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character (len=50):: dftout
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logical :: dft_defined = .false.
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logical, external :: matches
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character (len=1), external :: capital
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integer :: save_iexch, save_icorr, save_igcx, save_igcc, save_inlc
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!
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!
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! Exit if discard_input_dft
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!
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if ( discard_input_dft ) return
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!
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! save current status of XC indices
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!
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save_iexch = iexch
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save_icorr = icorr
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save_igcx = igcx
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save_igcc = igcc
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save_inlc = inlc
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!
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! convert to uppercase
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!
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len = len_trim(dft_)
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dftout = ' '
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do l = 1, len
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dftout (l:l) = capital (dft_(l:l) )
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enddo
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!
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! ----------------------------------------------
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! FIRST WE CHECK ALL THE SPECIAL NAMES
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! Note: comparison is now done via exact matching
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! not using function "matches"
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! ----------------------------------------------
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!
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if ( 'REVPBE' .EQ. TRIM(dftout) ) then
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! special case : revPBE
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call set_dft_value (iexch,1) !Default
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call set_dft_value (icorr,4)
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call set_dft_value (igcx, 4)
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call set_dft_value (igcc, 4)
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call set_dft_value (inlc, 0)
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dft_defined = .true.
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else if ('RPBE' .EQ. TRIM(dftout)) then
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! special case : RPBE
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call errore('set_dft_from_name', &
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& 'RPBE (Hammer-Hansen-Norskov) not implemented (revPBE is)',1)
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else if ('PBE0'.EQ. TRIM(dftout) ) then
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! special case : PBE0
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call set_dft_value (iexch,6)
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call set_dft_value (icorr,4)
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call set_dft_value (igcx, 8)
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call set_dft_value (igcc, 4)
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call set_dft_value (inlc,0) !Default
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dft_defined = .true.
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else if ('HSE' .EQ. TRIM( dftout) ) then
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! special case : HSE
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call set_dft_value (iexch,1) !Default
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call set_dft_value (icorr,4)
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call set_dft_value (igcx, 12)
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call set_dft_value (igcc, 4)
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call set_dft_value (inlc,0) !Default
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dft_defined = .true.
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else if ('PBESOL'.EQ. TRIM(dftout) ) then
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! special case : PBEsol
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call set_dft_value (iexch,1) !Default
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call set_dft_value (icorr,4)
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call set_dft_value (igcx,10)
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call set_dft_value (igcc, 8)
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call set_dft_value (inlc,0) !Default
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dft_defined = .true.
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else if ('VDW-DF2-C09' .EQ. TRIM(dftout) ) then
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! Special case vdW-DF2 with C09 exchange
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call set_dft_value (iexch, 1)
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call set_dft_value (icorr, 4)
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call set_dft_value (igcx, 16)
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call set_dft_value (igcc, 0)
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call set_dft_value (inlc, 2)
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dft_defined = .true.
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else if ('VDW-DF-C09' .EQ. TRIM(dftout) ) then
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! Special case vdW-DF with C09 exchange
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call set_dft_value (iexch, 1)
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call set_dft_value (icorr, 4)
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call set_dft_value (igcx, 16)
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call set_dft_value (igcc, 0)
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call set_dft_value (inlc, 1)
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dft_defined = .true.
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else if ('VDW-DF2' .EQ. TRIM(dftout) ) then
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! Special case vdW-DF2
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call set_dft_value (iexch, 0)
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call set_dft_value (icorr, 4)
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call set_dft_value (igcx, 13)
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call set_dft_value (igcc, 0)
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call set_dft_value (inlc, 2)
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dft_defined = .true.
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else if ('VDW-DF' .EQ. TRIM(dftout)) then
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! Special case vdW-DF
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call set_dft_value (iexch, 1)
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call set_dft_value (icorr, 4)
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call set_dft_value (igcx, 4)
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call set_dft_value (igcc, 0)
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call set_dft_value (inlc, 1)
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dft_defined = .true.
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else if ('PBE' .EQ. TRIM(dftout) ) then
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! special case : PBE
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call set_dft_value (iexch,1) !Default
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call set_dft_value (icorr,4)
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call set_dft_value (igcx, 3)
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call set_dft_value (igcc, 4)
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call set_dft_value (inlc,0) !Default
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dft_defined = .true.
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else if ('WC' .EQ. TRIM(dftout) ) then
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! special case : Wu-Cohen
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call set_dft_value (iexch,1) !Default
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call set_dft_value (icorr,4)
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call set_dft_value (igcx,11)
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call set_dft_value (igcc, 4)
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call set_dft_value (inlc,0) !Default
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dft_defined = .true.
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else if ('B3LYP'.EQ. TRIM(dftout) ) then
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|
! special case : B3LYP hybrid
|
|
call set_dft_value (iexch,7)
|
|
call set_dft_value (icorr,2)
|
|
call set_dft_value (igcx, 9)
|
|
call set_dft_value (igcc, 7)
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
else if ('PBC'.EQ. TRIM(dftout) ) then
|
|
! special case : PBC = PW + PBC
|
|
call set_dft_value (iexch,1) !Default
|
|
call set_dft_value (icorr,4)
|
|
call set_dft_value (igcx, 0) !Default
|
|
call set_dft_value (igcc, 4)
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special case : BP = B88 + P86
|
|
else if ('BP'.EQ. TRIM(dftout) ) then
|
|
call set_dft_value (iexch,1) !Default
|
|
call set_dft_value (icorr,1) !Default
|
|
call set_dft_value (igcx, 1)
|
|
call set_dft_value (igcc, 1)
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special case : PW91 = GGX + GGC
|
|
else if ('PW91'.EQ. TRIM(dftout) ) then
|
|
call set_dft_value (iexch,1) !Default
|
|
call set_dft_value (icorr,4)
|
|
call set_dft_value (igcx, 2)
|
|
call set_dft_value (igcc, 2)
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special case : HCTH
|
|
else if ('HCTH'.EQ. TRIM(dftout)) then
|
|
call set_dft_value(iexch,0) ! contained in hcth
|
|
call set_dft_value(icorr,0) ! contained in hcth
|
|
call set_dft_value (igcx,5)
|
|
call set_dft_value (igcc,5)
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special case : OLYP = OPTX + LYP
|
|
else if ('OLYP'.EQ. TRIM(dftout)) then
|
|
call set_dft_value(iexch,0) ! contained in optx
|
|
call set_dft_value(icorr,3)
|
|
call set_dft_value(igcx, 6)
|
|
call set_dft_value(igcc, 3)
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special case : TPSS meta-GGA Exc
|
|
else IF ('TPSS'.EQ. TRIM(dftout ) ) THEN
|
|
CALL set_dft_value( iexch, 1 )
|
|
CALL set_dft_value( icorr, 4 )
|
|
CALL set_dft_value( igcx, 7 )
|
|
CALL set_dft_value( igcc, 6 )
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special cases : OEP no GC part (nor LDA...) and no correlation by default
|
|
else IF ('OEP' .EQ. TRIM(dftout) ) THEN
|
|
call set_dft_value (iexch,4)
|
|
call set_dft_value (icorr, 0)
|
|
CALL set_dft_value( igcx, 0 )
|
|
call set_dft_value (igcc, 0) !Default
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special cases : HF no GC part (nor LDA...) and no correlation by default
|
|
else IF ('HF' .EQ. TRIM(dftout) ) THEN
|
|
call set_dft_value (iexch,5)
|
|
call set_dft_value (icorr, 0)
|
|
CALL set_dft_value( igcx, 0 )
|
|
call set_dft_value (igcc, 0) !Default
|
|
call set_dft_value (inlc,0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special cases : BLYP (note, BLYP=>B88)
|
|
else IF ('BLYP' .EQ. TRIM(dftout) ) THEN
|
|
call set_dft_value (iexch,1) !Default
|
|
call set_dft_value (icorr,3)
|
|
CALL set_dft_value( igcx, 1 )
|
|
call set_dft_value (igcc, 3)
|
|
call set_dft_value (inlc, 0) !Default
|
|
dft_defined = .true.
|
|
|
|
! special cases : PZ (LDA is equivalent to PZ)
|
|
else IF (('PZ' .EQ. TRIM(dftout) ).OR.('LDA' .EQ. TRIM(dftout) )) THEN
|
|
call set_dft_value (iexch,1)
|
|
call set_dft_value (icorr, 1)
|
|
CALL set_dft_value( igcx, 0)
|
|
call set_dft_value (igcc, 0)
|
|
call set_dft_value (inlc,0)
|
|
dft_defined = .true.
|
|
|
|
END IF
|
|
|
|
!
|
|
! ----------------------------------------------------------------
|
|
! If the DFT was not yet defined, check every part of the string
|
|
! ----------------------------------------------------------------
|
|
!
|
|
if (.not. dft_defined) then
|
|
|
|
! write(*,"(A,A)") "Setting by parts: ", TRIM(dftout)
|
|
|
|
! exchange
|
|
iexch = notset
|
|
do i = 0, nxc
|
|
if (matches (exc (i), dftout) ) call set_dft_value (iexch, i)
|
|
enddo
|
|
if (iexch .eq. notset) call set_dft_value (iexch,0)
|
|
|
|
! correlation
|
|
icorr = notset
|
|
do i = 0, ncc
|
|
if (matches (corr (i), dftout) ) call set_dft_value (icorr, i)
|
|
enddo
|
|
if (icorr .eq. notset) call set_dft_value (icorr,0)
|
|
|
|
! gradient correction, exchange
|
|
igcx = notset
|
|
do i = 0, ngcx
|
|
if (matches (gradx (i), dftout) ) call set_dft_value (igcx, i)
|
|
enddo
|
|
if (igcx .eq. notset) call set_dft_value (igcx,0)
|
|
|
|
! gradient correction, correlation
|
|
igcc = notset
|
|
do i = 0, ngcc
|
|
if (matches (gradc (i), dftout) ) call set_dft_value (igcc, i)
|
|
enddo
|
|
if (igcc .eq. notset) call set_dft_value (igcc,0)
|
|
|
|
! non-local correlation
|
|
! THE LOOP IS REVERSED TO HANDLE THE VDW2 CASE BEFORE THE VDW
|
|
inlc = notset
|
|
do i = ncnl ,1, -1
|
|
if (matches (nonlocc (i), dftout) ) call set_dft_value (inlc, i)
|
|
enddo
|
|
if (inlc .eq. notset) call set_dft_value (inlc,0)
|
|
|
|
endif
|
|
|
|
! ----------------------------------------------------------------
|
|
! Last check
|
|
! No more defaults, the code exit if the dft is not defined
|
|
! ----------------------------------------------------------------
|
|
|
|
if (igcx == 13 .and. iexch > 0 ) &
|
|
call errore('set_dft_from_name','revPW86 already contains LDA contribution',iexch)
|
|
|
|
! Back compatibility - TO BE REMOVED
|
|
|
|
if (igcx == 14) igcx = 3 ! PBE -> PBX
|
|
if (igcc == 9) igcc = 4 ! PBE -> PBC
|
|
|
|
if (igcx == 15) igcx = 7 ! TPSS -> META
|
|
if (igcc == 10) igcc = 6 ! TPSS -> META
|
|
|
|
if (igcx == 6) &
|
|
call errore('set_dft_from_name','OPTX untested! please test',-igcx)
|
|
|
|
if (iexch <=0 .and. &
|
|
icorr <=0 .and. &
|
|
igcx <= 0 .and. &
|
|
igcc <= 0 .and. &
|
|
inlc <= 0) &
|
|
call errore('set_dft_from_name','No dft definition was found',0)
|
|
|
|
!
|
|
! Fill variables and exit
|
|
!
|
|
dft = dftout
|
|
|
|
dftout = exc (iexch) //'-'//corr (icorr) //'-'//gradx (igcx) //'-' &
|
|
&//gradc (igcc) //'-'// nonlocc(inlc)
|
|
|
|
|
|
call set_auxiliary_flags
|
|
!
|
|
! check dft has not been previously set differently
|
|
!
|
|
if (save_iexch .ne. notset .and. save_iexch .ne. iexch) then
|
|
write (stdout,*) iexch, save_iexch
|
|
call errore('set_dft_from_name',' conflicting values for iexch',1)
|
|
end if
|
|
if (save_icorr .ne. notset .and. save_icorr .ne. icorr) then
|
|
write (stdout,*) icorr, save_icorr
|
|
call errore('set_dft_from_name',' conflicting values for icorr',1)
|
|
end if
|
|
if (save_igcx .ne. notset .and. save_igcx .ne. igcx) then
|
|
write (stdout,*) igcx, save_igcx
|
|
call errore('set_dft_from_name',' conflicting values for igcx',1)
|
|
end if
|
|
if (save_igcc .ne. notset .and. save_igcc .ne. igcc) then
|
|
write (stdout,*) igcc, save_igcc
|
|
call errore('set_dft_from_name',' conflicting values for igcc',1)
|
|
end if
|
|
if (save_inlc .ne. notset .and. save_inlc .ne. inlc) then
|
|
write (stdout,*) inlc, save_inlc
|
|
call errore('set_dft_from_name',' conflicting values for inlc',1)
|
|
end if
|
|
|
|
return
|
|
end subroutine set_dft_from_name
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine set_auxiliary_flags
|
|
!-----------------------------------------------------------------------
|
|
! set logical flags describing the complexity of the xc functional
|
|
! define the fraction of exact exchange used by hybrid fuctionals
|
|
!
|
|
logical, external :: matches
|
|
|
|
!! Reversed as before VDW
|
|
isgradient = ( (igcx > 0) .or. ( igcc > 0) )
|
|
|
|
isnonlocc = (inlc > 0)
|
|
|
|
ismeta = (igcx == 7)
|
|
|
|
! PBE0
|
|
IF ( iexch==6 .or. igcx ==8 ) exx_fraction = 0.25_DP
|
|
! HSE
|
|
IF ( igcx ==12 ) THEN
|
|
exx_fraction = 0.25_DP
|
|
screening_parameter = 0.106_DP
|
|
END IF
|
|
! HF or OEP
|
|
IF ( iexch==4 .or. iexch==5 ) exx_fraction = 1.0_DP
|
|
!B3LYP
|
|
IF ( matches( 'B3LP',dft ) .OR. matches( 'B3LYP',dft ) ) &
|
|
exx_fraction = 0.2_DP
|
|
ishybrid = ( exx_fraction /= 0.0_DP )
|
|
|
|
has_finite_size_correction = ( iexch==8 .or. icorr==11)
|
|
|
|
return
|
|
end subroutine set_auxiliary_flags
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine set_dft_value (m, i)
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
implicit none
|
|
integer :: m, i
|
|
! local
|
|
|
|
if ( m /= notset .and. m /= i) then
|
|
write(*, '(A,2I4)') "parameters", m, i
|
|
call errore ('set_dft_value', 'two conflicting matching values', 1)
|
|
end if
|
|
m = i
|
|
return
|
|
|
|
end subroutine set_dft_value
|
|
|
|
!-----------------------------------------------------------------------
|
|
subroutine enforce_input_dft (dft_, nomsg)
|
|
!
|
|
! translates a string containing the exchange-correlation name
|
|
! into internal indices and force any subsequent call to set_dft_from_name
|
|
! to return without changing them
|
|
!
|
|
implicit none
|
|
character(len=*), intent(in) :: dft_
|
|
logical, intent(in), optional :: nomsg
|
|
|
|
call set_dft_from_name (dft_)
|
|
if (dft == 'not set') call errore('enforce_input_dft','cannot fix unset dft',1)
|
|
discard_input_dft = .true.
|
|
|
|
if ( present (nomsg) ) return
|
|
|
|
write (stdout,'(/,5x,a)') "IMPORTANT: XC functional enforced from input :"
|
|
call write_dft_name
|
|
write (stdout,'(5x,a)') "Any further DFT definition will be discarded"
|
|
write (stdout,'(5x,a/)') "Please, verify this is what you really want"
|
|
|
|
return
|
|
end subroutine enforce_input_dft
|
|
|
|
!-----------------------------------------------------------------------
|
|
subroutine enforce_dft_exxrpa ( )
|
|
!
|
|
implicit none
|
|
!
|
|
!character(len=*), intent(in) :: dft_
|
|
!logical, intent(in), optional :: nomsg
|
|
|
|
iexch = 0; icorr = 0; igcx = 0; igcc = 0
|
|
exx_fraction = 1.0_DP
|
|
ishybrid = ( exx_fraction /= 0.0_DP )
|
|
|
|
write (stdout,'(/,5x,a)') "XC functional enforced to be EXXRPA"
|
|
call write_dft_name
|
|
write (stdout,'(5x,a)') "!!! Any further DFT definition will be discarded"
|
|
write (stdout,'(5x,a/)') "!!! Please, verify this is what you really want !"
|
|
|
|
return
|
|
end subroutine enforce_dft_exxrpa
|
|
|
|
!-----------------------------------------------------------------------
|
|
subroutine init_dft_exxrpa ( )
|
|
!
|
|
implicit none
|
|
!
|
|
exx_fraction = 1.0_DP
|
|
ishybrid = ( exx_fraction /= 0.0_DP )
|
|
|
|
write (stdout,'(/,5x,a)') "Only exx_fraction is set to 1.d0"
|
|
write (stdout,'(5x,a)') "XC functional still not changed"
|
|
call write_dft_name
|
|
|
|
return
|
|
end subroutine init_dft_exxrpa
|
|
|
|
!-----------------------------------------------------------------------
|
|
subroutine start_exx
|
|
if (.not. ishybrid) &
|
|
call errore('start_exx','dft is not hybrid, wrong call',1)
|
|
exx_started = .true.
|
|
end subroutine start_exx
|
|
!-----------------------------------------------------------------------
|
|
subroutine stop_exx
|
|
if (.not. ishybrid) &
|
|
call errore('stop_exx','dft is not hybrid, wrong call',1)
|
|
exx_started = .false.
|
|
end subroutine stop_exx
|
|
!-----------------------------------------------------------------------
|
|
function exx_is_active ()
|
|
logical exx_is_active
|
|
exx_is_active = exx_started
|
|
end function exx_is_active
|
|
!-----------------------------------------------------------------------
|
|
subroutine set_exx_fraction (exxf_)
|
|
implicit none
|
|
real(DP):: exxf_
|
|
exx_fraction = exxf_
|
|
write (stdout,'(5x,a,f6.2)') 'EXX fraction changed: ',exx_fraction
|
|
end subroutine set_exx_fraction
|
|
!---------------------------------------------------------------------
|
|
subroutine set_screening_parameter (scrparm_)
|
|
implicit none
|
|
real(DP):: scrparm_
|
|
screening_parameter = scrparm_
|
|
write (stdout,'(5x,a,f12.7)') 'EXX Screening parameter changed: ', &
|
|
& screening_parameter
|
|
end subroutine set_screening_parameter
|
|
!----------------------------------------------------------------------
|
|
function get_screening_parameter ()
|
|
real(DP):: get_screening_parameter
|
|
get_screening_parameter = screening_parameter
|
|
return
|
|
end function get_screening_parameter
|
|
!-----------------------------------------------------------------------
|
|
function get_iexch ()
|
|
integer get_iexch
|
|
get_iexch = iexch
|
|
return
|
|
end function get_iexch
|
|
!-----------------------------------------------------------------------
|
|
function get_icorr ()
|
|
integer get_icorr
|
|
get_icorr = icorr
|
|
return
|
|
end function get_icorr
|
|
!-----------------------------------------------------------------------
|
|
function get_igcx ()
|
|
integer get_igcx
|
|
get_igcx = igcx
|
|
return
|
|
end function get_igcx
|
|
!-----------------------------------------------------------------------
|
|
function get_igcc ()
|
|
integer get_igcc
|
|
get_igcc = igcc
|
|
return
|
|
end function get_igcc
|
|
!-----------------------------------------------------------------------
|
|
function get_inlc ()
|
|
integer get_inlc
|
|
get_inlc = inlc
|
|
return
|
|
end function get_inlc
|
|
!-----------------------------------------------------------------------
|
|
function dft_is_nonlocc ()
|
|
logical :: dft_is_nonlocc
|
|
dft_is_nonlocc = isnonlocc
|
|
return
|
|
end function dft_is_nonlocc
|
|
!-----------------------------------------------------------------------
|
|
function get_exx_fraction ()
|
|
real(DP):: get_exx_fraction
|
|
get_exx_fraction = exx_fraction
|
|
return
|
|
end function get_exx_fraction
|
|
!-----------------------------------------------------------------------
|
|
function get_dft_name ()
|
|
character (len=25) :: get_dft_name
|
|
get_dft_name = dft
|
|
return
|
|
end function get_dft_name
|
|
!-----------------------------------------------------------------------
|
|
function dft_is_gradient ()
|
|
logical :: dft_is_gradient
|
|
dft_is_gradient = isgradient
|
|
return
|
|
end function dft_is_gradient
|
|
!-----------------------------------------------------------------------
|
|
function dft_is_meta ()
|
|
logical :: dft_is_meta
|
|
dft_is_meta = ismeta
|
|
return
|
|
end function dft_is_meta
|
|
!-----------------------------------------------------------------------
|
|
function dft_is_hybrid ()
|
|
logical :: dft_is_hybrid
|
|
dft_is_hybrid = ishybrid
|
|
return
|
|
end function dft_is_hybrid
|
|
!-----------------------------------------------------------------------
|
|
function dft_has_finite_size_correction ()
|
|
logical :: dft_has_finite_size_correction
|
|
dft_has_finite_size_correction = has_finite_size_correction
|
|
return
|
|
end function dft_has_finite_size_correction
|
|
!-----------------------------------------------------------------------
|
|
subroutine set_finite_size_volume(volume)
|
|
real, intent (IN) :: volume
|
|
if (.not. has_finite_size_correction) &
|
|
call errore('set_finite_size_volume', &
|
|
'dft w/o finite_size_correction, wrong call',1)
|
|
if (volume <= 0.d0) &
|
|
call errore('set_finite_size_volume', &
|
|
'volume is not positive, check omega and/or nk1,nk2,nk3',1)
|
|
finite_size_cell_volume = volume
|
|
finite_size_cell_volume_set = .TRUE.
|
|
end subroutine set_finite_size_volume
|
|
!-----------------------------------------------------------------------
|
|
|
|
!-----------------------------------------------------------------------
|
|
subroutine set_dft_from_indices(iexch_,icorr_,igcx_,igcc_, inlc_)
|
|
integer :: iexch_, icorr_, igcx_, igcc_, inlc_
|
|
if ( discard_input_dft ) return
|
|
if (iexch == notset) iexch = iexch_
|
|
if (iexch /= iexch_) then
|
|
write (stdout,*) iexch, iexch_
|
|
call errore('set_dft',' conflicting values for iexch',1)
|
|
end if
|
|
if (icorr == notset) icorr = icorr_
|
|
if (icorr /= icorr_) then
|
|
write (stdout,*) icorr, icorr_
|
|
call errore('set_dft',' conflicting values for icorr',1)
|
|
end if
|
|
if (igcx == notset) igcx = igcx_
|
|
if (igcx /= igcx_) then
|
|
write (stdout,*) igcx, igcx_
|
|
call errore('set_dft',' conflicting values for igcx',1)
|
|
end if
|
|
if (igcc == notset) igcc = igcc_
|
|
if (igcc /= igcc_) then
|
|
write (stdout,*) igcc, igcc_
|
|
call errore('set_dft',' conflicting values for igcc',1)
|
|
end if
|
|
if (inlc == notset) inlc = inlc_
|
|
if (inlc /= inlc_) then
|
|
write (stdout,*) inlc, inlc_
|
|
call errore('set_dft',' conflicting values for inlc',1)
|
|
end if
|
|
dft = exc (iexch) //'-'//corr (icorr) //'-'//gradx (igcx) //'-' &
|
|
&//gradc (igcc)//'-'//nonlocc (inlc)
|
|
! WRITE( stdout,'(a)') dft
|
|
call set_auxiliary_flags
|
|
return
|
|
end subroutine set_dft_from_indices
|
|
!---------------------------------------------------------------------
|
|
subroutine dft_name(iexch_, icorr_, igcx_, igcc_, inlc_, longname_, shortname_)
|
|
!---------------------------------------------------------------------
|
|
! convert the four indices iexch, icorr, igcx, igcc
|
|
! into user-readable strings
|
|
!
|
|
implicit none
|
|
integer iexch_, icorr_, igcx_, igcc_, inlc_
|
|
character (len=6) :: shortname_
|
|
character (len=25):: longname_
|
|
!
|
|
if (iexch_==1.and.igcx_==0.and.igcc_==0) then
|
|
shortname_ = corr(icorr_)
|
|
else if (iexch_==1.and.icorr_==3.and.igcx_==1.and.igcc_==3) then
|
|
shortname_ = 'BLYP'
|
|
else if (iexch_==1.and.icorr_==1.and.igcx_==1.and.igcc_==0) then
|
|
shortname_ = 'B88'
|
|
else if (iexch_==1.and.icorr_==1.and.igcx_==1.and.igcc_==1) then
|
|
shortname_ = 'BP'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==2.and.igcc_==2) then
|
|
shortname_ = 'PW91'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==3.and.igcc_==4) then
|
|
shortname_ = 'PBE'
|
|
else if (iexch_==6.and.icorr_==4.and.igcx_==8.and.igcc_==4) then
|
|
shortname_ = 'PBE0'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==4.and.igcc_==4) then
|
|
shortname_ = 'revPBE'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==10.and.igcc_==8) then
|
|
shortname_ = 'PBESOL'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==12.and.igcc_==4) then
|
|
shortname_ = 'HSE'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==11.and.igcc_==4) then
|
|
shortname_ = 'WC'
|
|
else if (iexch_==7.and.(icorr_==10.or.icorr_==2).and.igcx_==9.and. &
|
|
igcc_==7) then
|
|
shortname_ = 'B3LYP'
|
|
else if (iexch_==0.and.icorr_==3.and.igcx_==6.and.igcc_==3) then
|
|
shortname_ = 'OLYP'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==4.and.igcc_==0.and.inlc_==1) then
|
|
shortname_ = 'VDW-DF'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==12.and.igcc_==0.and.inlc_==2) then
|
|
shortname_ = 'VDW-DF2'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==16.and.igcc_==0.and.inlc_==1) then
|
|
shortname_ = 'VDW-DF-C09'
|
|
else if (iexch_==1.and.icorr_==4.and.igcx_==16.and.igcc_==0.and.inlc_==2) then
|
|
shortname_ = 'VDW-DF2-C09'
|
|
else
|
|
shortname_ = ' '
|
|
end if
|
|
write(longname_,'(5a5)') exc(iexch_),corr(icorr_),gradx(igcx_),gradc(igcc_),nonlocc(inlc_)
|
|
|
|
return
|
|
end subroutine dft_name
|
|
|
|
subroutine write_dft_name
|
|
!-----------------------------------------------------------------------
|
|
WRITE( stdout, '(5X,"Exchange-correlation = ",A, &
|
|
& " (",5I2,")")') TRIM( dft ), iexch, icorr, igcx, igcc, inlc
|
|
WRITE( stdout, '(5X,"EXX-fraction =",F12.2)') &
|
|
get_exx_fraction()
|
|
return
|
|
end subroutine write_dft_name
|
|
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
!------- LDA DRIVERS --------------------------------------------------
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine xc (rho, ex, ec, vx, vc)
|
|
!-----------------------------------------------------------------------
|
|
! lda exchange and correlation functionals - Hartree a.u.
|
|
!
|
|
! exchange : Slater, relativistic Slater
|
|
! correlation: Ceperley-Alder (Perdew-Zunger parameters)
|
|
! Vosko-Wilk-Nusair
|
|
! Lee-Yang-Parr
|
|
! Perdew-Wang
|
|
! Wigner
|
|
! Hedin-Lundqvist
|
|
! Ortiz-Ballone (Perdew-Zunger formula)
|
|
! Ortiz-Ballone (Perdew-Wang formula)
|
|
! Gunnarsson-Lundqvist
|
|
!
|
|
! input : rho=rho(r)
|
|
! definitions: E_x = \int E_x(rho) dr, E_x(rho) = rho\epsilon_c(rho)
|
|
! same for correlation
|
|
! output: ex = \epsilon_x(rho) ( NOT E_x(rho) )
|
|
! vx = dE_x(rho)/drho ( NOT d\epsilon_x(rho)/drho )
|
|
! ec, vc as above for correlation
|
|
!
|
|
implicit none
|
|
|
|
real(DP) :: rho, ec, vc, ex, vx
|
|
!
|
|
real(DP), parameter :: small = 1.E-10_DP, third = 1.0_DP / 3.0_DP, &
|
|
pi34 = 0.6203504908994_DP ! pi34=(3/4pi)^(1/3)
|
|
real(DP) :: rs
|
|
!
|
|
if (rho <= small) then
|
|
ec = 0.0_DP
|
|
vc = 0.0_DP
|
|
ex = 0.0_DP
|
|
vx = 0.0_DP
|
|
return
|
|
else
|
|
rs = pi34 / rho**third
|
|
! rs as in the theory of metals: rs=(3/(4pi rho))^(1/3)
|
|
endif
|
|
!..exchange
|
|
if (iexch == 1) THEN ! 'sla'
|
|
call slater (rs, ex, vx)
|
|
!==================================================================
|
|
!Lingzhu Kong
|
|
IF(lwfpbe0 .or. lwfpbe0nscf)THEN
|
|
ex = 0.75d0 * ex
|
|
vx = 0.75d0 * vx
|
|
END IF
|
|
!==================================================================
|
|
ELSEIF (iexch == 2) THEN ! 'sl1'
|
|
call slater1(rs, ex, vx)
|
|
ELSEIF (iexch == 3) THEN ! 'rxc'
|
|
CALL slater_rxc(rs, ex, vx)
|
|
ELSEIF ((iexch == 4).or.(iexch==5)) THEN ! 'oep','hf'
|
|
IF (exx_started) then
|
|
ex = 0.0_DP
|
|
vx = 0.0_DP
|
|
else
|
|
call slater (rs, ex, vx)
|
|
endif
|
|
ELSEIF (iexch == 6) THEN ! 'pb0x'
|
|
CALL slater(rs, ex, vx)
|
|
if (exx_started) then
|
|
ex = (1.0_DP - exx_fraction) * ex
|
|
vx = (1.0_DP - exx_fraction) * vx
|
|
end if
|
|
ELSEIF (iexch == 7) THEN ! 'b3lyp'
|
|
CALL slater(rs, ex, vx)
|
|
if (exx_started) then
|
|
ex = 0.8_DP * ex
|
|
vx = 0.8_DP * vx
|
|
end if
|
|
ELSEIF (iexch == 8) THEN ! 'sla+kzk'
|
|
if (.NOT. finite_size_cell_volume_set) call errore ('XC',&
|
|
'finite size corrected exchange used w/o initialization',1)
|
|
call slaterKZK (rs, ex, vx, finite_size_cell_volume)
|
|
else
|
|
ex = 0.0_DP
|
|
vx = 0.0_DP
|
|
endif
|
|
!..correlation
|
|
if (icorr == 1) then
|
|
call pz (rs, 1, ec, vc)
|
|
elseif (icorr == 2) then
|
|
call vwn (rs, ec, vc)
|
|
elseif (icorr == 3) then
|
|
call lyp (rs, ec, vc)
|
|
elseif (icorr == 4) then
|
|
call pw (rs, 1, ec, vc)
|
|
elseif (icorr == 5) then
|
|
call wigner (rs, ec, vc)
|
|
elseif (icorr == 6) then
|
|
call hl (rs, ec, vc)
|
|
elseif (icorr == 7) then
|
|
call pz (rs, 2, ec, vc)
|
|
elseif (icorr == 8) then
|
|
call pw (rs, 2, ec, vc)
|
|
elseif (icorr == 9) then
|
|
call gl (rs, ec, vc)
|
|
elseif (icorr ==10) then ! b3lyp
|
|
call vwn (rs, ec, vc)
|
|
elseif (icorr ==11) then
|
|
if (.NOT. finite_size_cell_volume_set) call errore ('XC',&
|
|
'finite size corrected correlation used w/o initialization',1)
|
|
call pzKZK (rs, ec, vc, finite_size_cell_volume)
|
|
else
|
|
ec = 0.0_DP
|
|
vc = 0.0_DP
|
|
endif
|
|
!
|
|
return
|
|
end subroutine xc
|
|
!!!!!!!!!!!!!!SPIN
|
|
!-----------------------------------------------------------------------
|
|
subroutine xc_spin (rho, zeta, ex, ec, vxup, vxdw, vcup, vcdw)
|
|
!-----------------------------------------------------------------------
|
|
! lsd exchange and correlation functionals - Hartree a.u.
|
|
!
|
|
! exchange : Slater (alpha=2/3)
|
|
! correlation: Ceperley & Alder (Perdew-Zunger parameters)
|
|
! Perdew & Wang
|
|
!
|
|
! input : rho = rhoup(r)+rhodw(r)
|
|
! zeta=(rhoup(r)-rhodw(r))/rho
|
|
!
|
|
implicit none
|
|
|
|
real(DP) :: rho, zeta, ex, ec, vxup, vxdw, vcup, vcdw
|
|
!
|
|
real(DP), parameter :: small= 1.E-10_DP, third = 1.0_DP/3.0_DP, &
|
|
pi34= 0.6203504908994_DP ! pi34=(3/4pi)^(1/3)
|
|
real(DP) :: rs
|
|
!
|
|
if (rho <= small) then
|
|
ec = 0.0_DP
|
|
vcup = 0.0_DP
|
|
vcdw = 0.0_DP
|
|
ex = 0.0_DP
|
|
vxup = 0.0_DP
|
|
vxdw = 0.0_DP
|
|
return
|
|
else
|
|
rs = pi34 / rho**third
|
|
endif
|
|
!..exchange
|
|
IF (iexch == 1) THEN ! 'sla'
|
|
call slater_spin (rho, zeta, ex, vxup, vxdw)
|
|
!==============================================================
|
|
!Lingzhu Kong
|
|
IF( lwfpbe0 .or. lwfpbe0nscf )THEN
|
|
ex = 0.75d0 * ex
|
|
vxup = 0.75d0 * vxup
|
|
vxdw = 0.75d0 * vxdw
|
|
END IF
|
|
!==============================================================
|
|
ELSEIF (iexch == 2) THEN ! 'sl1'
|
|
call slater1_spin (rho, zeta, ex, vxup, vxdw)
|
|
ELSEIF (iexch == 3) THEN ! 'rxc'
|
|
call slater_rxc_spin ( rho, zeta, ex, vxup, vxdw )
|
|
ELSEIF ((iexch == 4).or.(iexch==5)) THEN ! 'oep','hf'
|
|
IF (exx_started) then
|
|
ex = 0.0_DP
|
|
vxup = 0.0_DP
|
|
vxdw = 0.0_DP
|
|
else
|
|
call slater_spin (rho, zeta, ex, vxup, vxdw)
|
|
endif
|
|
ELSEIF (iexch == 6) THEN ! 'pb0x'
|
|
call slater_spin (rho, zeta, ex, vxup, vxdw)
|
|
if (exx_started) then
|
|
ex = (1.0_DP - exx_fraction) * ex
|
|
vxup = (1.0_DP - exx_fraction) * vxup
|
|
vxdw = (1.0_DP - exx_fraction) * vxdw
|
|
end if
|
|
ELSEIF (iexch == 7) THEN ! 'b3lyp'
|
|
call slater_spin (rho, zeta, ex, vxup, vxdw)
|
|
if (exx_started) then
|
|
ex = 0.8_DP * ex
|
|
vxup = 0.8_DP * vxup
|
|
vxdw = 0.8_DP * vxdw
|
|
end if
|
|
ELSE
|
|
ex = 0.0_DP
|
|
vxup = 0.0_DP
|
|
vxdw = 0.0_DP
|
|
ENDIF
|
|
!..correlation
|
|
if (icorr == 0) then
|
|
ec = 0.0_DP
|
|
vcup = 0.0_DP
|
|
vcdw = 0.0_DP
|
|
elseif (icorr == 1) then
|
|
call pz_spin (rs, zeta, ec, vcup, vcdw)
|
|
elseif (icorr == 2) then
|
|
call vwn_spin (rs, zeta, ec, vcup, vcdw)
|
|
elseif (icorr == 3) then
|
|
call lsd_lyp (rho, zeta, ec, vcup, vcdw) ! from CP/FPMD (more_functionals)
|
|
elseif (icorr == 4) then
|
|
call pw_spin (rs, zeta, ec, vcup, vcdw)
|
|
else
|
|
call errore ('lsda_functional (xc_spin)', 'not implemented', icorr)
|
|
endif
|
|
!
|
|
return
|
|
end subroutine xc_spin
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine xc_spin_vec (rho, zeta, length, evx, evc)
|
|
!-----------------------------------------------------------------------
|
|
! lsd exchange and correlation functionals - Hartree a.u.
|
|
!
|
|
! exchange : Slater (alpha=2/3)
|
|
! correlation: Ceperley & Alder (Perdew-Zunger parameters)
|
|
! Perdew & Wang
|
|
!
|
|
! input : rho = rhoup(r)+rhodw(r)
|
|
! zeta=(rhoup(r)-rhodw(r))/rho
|
|
!
|
|
implicit none
|
|
|
|
integer, intent(in) :: length
|
|
real(DP), intent(in) :: rho(length), zeta(length)
|
|
real(DP), intent(out) :: evx(length,3), evc(length,3)
|
|
!
|
|
real(DP), parameter :: small= 1.E-10_DP, third = 1.0_DP/3.0_DP, &
|
|
pi34= 0.6203504908994_DP ! pi34=(3/4pi)^(1/3)
|
|
!
|
|
integer :: i
|
|
logical :: comp_energy_loc
|
|
real(DP) :: rs(length)
|
|
!
|
|
!..exchange
|
|
select case (iexch)
|
|
case(1) ! 'sla'
|
|
call slater_spin_vec (rho, zeta, evx, length)
|
|
!=========================================================
|
|
!Lingzhu Kong
|
|
if (lwfpbe0 .or. lwfpbe0nscf) then
|
|
evx = 0.75_DP * evx
|
|
end if
|
|
!=========================================================
|
|
case(2) ! 'sl1'
|
|
do i=1,length
|
|
call slater1_spin (rho(i), zeta(i), evx(i,3), evx(i,1), evx(i,2))
|
|
end do
|
|
case(3) ! 'rxc'
|
|
do i=1,length
|
|
call slater_rxc_spin (rho(i), zeta(i), evx(i,3), evx(i,1), evx(i,2))
|
|
end do
|
|
case(4,5) ! 'oep','hf'
|
|
if (exx_started) then
|
|
evx = 0.0_DP
|
|
else
|
|
call slater_spin_vec (rho, zeta, evx, length)
|
|
endif
|
|
case(6) ! 'pb0x'
|
|
call slater_spin_vec (rho, zeta, evx, length)
|
|
if (exx_started) then
|
|
evx = (1.0_DP - exx_fraction) * evx
|
|
end if
|
|
case(7) ! 'b3lyp'
|
|
call slater_spin_vec (rho, zeta, evx, length)
|
|
if (exx_started) then
|
|
evx = 0.8_DP * evx
|
|
end if
|
|
case default
|
|
evx = 0.0_DP
|
|
end select
|
|
|
|
!..correlation
|
|
where (rho.gt.small)
|
|
rs = pi34 / rho**third
|
|
elsewhere
|
|
rs = 1.0_DP ! just a sane default, results are discarded anyway
|
|
end where
|
|
|
|
select case(icorr)
|
|
case (0)
|
|
evc = 0.0_DP
|
|
case (1)
|
|
do i=1,length
|
|
call pz_spin (rs(i), zeta(i), evc(i,3), evc(i,1), evc(i,2))
|
|
end do
|
|
case (2)
|
|
do i=1,length
|
|
call vwn_spin (rs(i), zeta(i), evc(i,3), evc(i,1), evc(i,2))
|
|
end do
|
|
case(3)
|
|
do i=1,length
|
|
call lsd_lyp (rho(i), zeta(i), evc(i,3), evc(i,1), evc(i,2)) ! from CP/FPMD (more_functionals)
|
|
end do
|
|
case(4)
|
|
call pw_spin_vec (rs, zeta, evc, length)
|
|
case default
|
|
call errore ('lsda_functional (xc_spin_vec)', 'not implemented', icorr)
|
|
end select
|
|
!
|
|
where (rho.le.small)
|
|
evx(:,1) = 0.0_DP
|
|
evc(:,1) = 0.0_DP
|
|
|
|
evx(:,2) = 0.0_DP
|
|
evc(:,2) = 0.0_DP
|
|
|
|
evx(:,3) = 0.0_DP
|
|
evc(:,3) = 0.0_DP
|
|
end where
|
|
!
|
|
end subroutine xc_spin_vec
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
!------- GRADIENT CORRECTIONS DRIVERS ----------------------------------
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine gcxc (rho, grho, sx, sc, v1x, v2x, v1c, v2c)
|
|
!-----------------------------------------------------------------------
|
|
! gradient corrections for exchange and correlation - Hartree a.u.
|
|
! See comments at the beginning of module for implemented cases
|
|
!
|
|
! input: rho, grho=|\nabla rho|^2
|
|
! definition: E_x = \int E_x(rho,grho) dr
|
|
! output: sx = E_x(rho,grho)
|
|
! v1x= D(E_x)/D(rho)
|
|
! v2x= D(E_x)/D( D rho/D r_alpha ) / |\nabla rho|
|
|
! sc, v1c, v2c as above for correlation
|
|
!
|
|
implicit none
|
|
|
|
real(DP) :: rho, grho, sx, sc, v1x, v2x, v1c, v2c
|
|
real(DP) :: sxsr, v1xsr, v2xsr
|
|
real(DP), parameter:: small = 1.E-10_DP
|
|
|
|
! exchange
|
|
if (rho <= small) then
|
|
sx = 0.0_DP
|
|
v1x = 0.0_DP
|
|
v2x = 0.0_DP
|
|
elseif (igcx == 1) then
|
|
call becke88 (rho, grho, sx, v1x, v2x)
|
|
elseif (igcx == 2) then
|
|
call ggax (rho, grho, sx, v1x, v2x)
|
|
elseif (igcx == 3) then
|
|
call pbex (rho, grho, 1, sx, v1x, v2x)
|
|
!==============================================================
|
|
!Lingzhu Kong
|
|
IF( lwfpbe0 .or. lwfpbe0nscf )THEN
|
|
sx = 0.75d0 * sx
|
|
v1x = 0.75d0 * v1x
|
|
v2x = 0.75d0 * v2x
|
|
END IF
|
|
!==============================================================
|
|
elseif (igcx == 4) then
|
|
call pbex (rho, grho, 2, sx, v1x, v2x)
|
|
elseif (igcx == 5 .and. igcc == 5) then
|
|
call hcth(rho, grho, sx, v1x, v2x)
|
|
elseif (igcx == 6) then
|
|
call optx (rho, grho, sx, v1x, v2x)
|
|
! case igcx == 7 (meta-GGA) must be treated in a separate call to another
|
|
! routine: needs kinetic energy density in addition to rho and grad rho
|
|
elseif (igcx == 8) then ! 'pbe0'
|
|
call pbex (rho, grho, 1, sx, v1x, v2x)
|
|
if (exx_started) then
|
|
sx = (1.0_DP - exx_fraction) * sx
|
|
v1x = (1.0_DP - exx_fraction) * v1x
|
|
v2x = (1.0_DP - exx_fraction) * v2x
|
|
end if
|
|
elseif (igcx == 9) then ! 'b3lyp'
|
|
call becke88 (rho, grho, sx, v1x, v2x)
|
|
if (exx_started) then
|
|
sx = 0.72_DP * sx
|
|
v1x = 0.72_DP * v1x
|
|
v2x = 0.72_DP * v2x
|
|
end if
|
|
elseif (igcx ==10) then ! 'pbesol'
|
|
call pbex (rho, grho, 3, sx, v1x, v2x)
|
|
elseif (igcx ==11) then ! 'wc'
|
|
call wcx (rho, grho, sx, v1x, v2x)
|
|
elseif (igcx ==12) then ! 'pbexsr'
|
|
call pbex (rho, grho, 1, sx, v1x, v2x)
|
|
if(exx_started) then
|
|
call pbexsr (rho, grho, sxsr, v1xsr, v2xsr, screening_parameter)
|
|
sx = sx - exx_fraction * sxsr
|
|
v1x = v1x - exx_fraction * v1xsr
|
|
v2x = v2x - exx_fraction * v2xsr
|
|
endif
|
|
elseif (igcx ==13) then ! 'rPW86'
|
|
call rPW86 (rho, grho, sx, v1x, v2x)
|
|
elseif (igcx ==16) then ! 'C09x'
|
|
call c09x (rho, grho, sx, v1x, v2x)
|
|
else
|
|
sx = 0.0_DP
|
|
v1x = 0.0_DP
|
|
v2x = 0.0_DP
|
|
endif
|
|
! correlation
|
|
if (rho.le.small) then
|
|
sc = 0.0_DP
|
|
v1c = 0.0_DP
|
|
v2c = 0.0_DP
|
|
elseif (igcc == 1) then
|
|
call perdew86 (rho, grho, sc, v1c, v2c)
|
|
elseif (igcc == 2) then
|
|
call ggac (rho, grho, sc, v1c, v2c)
|
|
elseif (igcc == 3) then
|
|
call glyp (rho, grho, sc, v1c, v2c)
|
|
elseif (igcc == 4) then
|
|
call pbec (rho, grho, 1, sc, v1c, v2c)
|
|
! igcc == 5 (HCTH) is calculated together with case igcx=5
|
|
! igcc == 6 (meta-GGA) is treated in a different routine
|
|
elseif (igcc == 7) then !'B3LYP'
|
|
call glyp (rho, grho, sc, v1c, v2c)
|
|
if (exx_started) then
|
|
sc = 0.81_DP * sc
|
|
v1c = 0.81_DP * v1c
|
|
v2c = 0.81_DP * v2c
|
|
end if
|
|
elseif (igcc == 8) then ! 'PBEsol'
|
|
call pbec (rho, grho, 2, sc, v1c, v2c)
|
|
else
|
|
sc = 0.0_DP
|
|
v1c = 0.0_DP
|
|
v2c = 0.0_DP
|
|
endif
|
|
!
|
|
return
|
|
end subroutine gcxc
|
|
!
|
|
!!!!!!!!!!!!!!SPIN
|
|
!-----------------------------------------------------------------------
|
|
subroutine gcx_spin (rhoup, rhodw, grhoup2, grhodw2, &
|
|
sx, v1xup, v1xdw, v2xup, v2xdw)
|
|
!-----------------------------------------------------------------------
|
|
! gradient corrections for exchange - Hartree a.u.
|
|
!
|
|
implicit none
|
|
!
|
|
! dummy arguments
|
|
!
|
|
real(DP) :: rhoup, rhodw, grhoup2, grhodw2, sx, v1xup, v1xdw, &
|
|
v2xup, v2xdw
|
|
! up and down charge
|
|
! up and down gradient of the charge
|
|
! exchange and correlation energies
|
|
! derivatives of exchange wr. rho
|
|
! derivatives of exchange wr. grho
|
|
!
|
|
real(DP) :: sxsr, v1xupsr, v2xupsr, v1xdwsr, v2xdwsr
|
|
real(DP), parameter :: small = 1.E-10_DP
|
|
real(DP) :: rho, sxup, sxdw
|
|
integer :: iflag
|
|
!
|
|
!
|
|
! exchange
|
|
rho = rhoup + rhodw
|
|
if (rho <= small .or. igcx == 0) then
|
|
sx = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
elseif (igcx == 1) then
|
|
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
|
|
call becke88_spin (rhoup, grhoup2, sxup, v1xup, v2xup)
|
|
else
|
|
sxup = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
endif
|
|
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
|
|
call becke88_spin (rhodw, grhodw2, sxdw, v1xdw, v2xdw)
|
|
else
|
|
sxdw = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
endif
|
|
sx = sxup + sxdw
|
|
elseif (igcx == 2) then
|
|
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
|
|
call ggax (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
|
|
else
|
|
sxup = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
endif
|
|
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
|
|
call ggax (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
|
|
else
|
|
sxdw = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
endif
|
|
sx = 0.5_DP * (sxup + sxdw)
|
|
v2xup = 2.0_DP * v2xup
|
|
v2xdw = 2.0_DP * v2xdw
|
|
elseif (igcx == 3 .or. igcx == 4 .or. igcx == 8 .or. &
|
|
igcx == 10 .or. igcx == 12) then
|
|
! igcx=3: PBE, igcx=4: revised PBE, igcx=8 PBE0, igcx=10: PBEsol
|
|
! igcx=12: HSE
|
|
if (igcx == 4) then
|
|
iflag = 2
|
|
elseif (igcx == 10) then
|
|
iflag = 3
|
|
else
|
|
iflag = 1
|
|
endif
|
|
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
|
|
call pbex (2.0_DP * rhoup, 4.0_DP * grhoup2, iflag, sxup, v1xup, v2xup)
|
|
else
|
|
sxup = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
endif
|
|
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
|
|
call pbex (2.0_DP * rhodw, 4.0_DP * grhodw2, iflag, sxdw, v1xdw, v2xdw)
|
|
else
|
|
sxdw = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
endif
|
|
sx = 0.5_DP * (sxup + sxdw)
|
|
v2xup = 2.0_DP * v2xup
|
|
v2xdw = 2.0_DP * v2xdw
|
|
if (igcx == 8 .and. exx_started ) then
|
|
sx = (1.0_DP - exx_fraction) * sx
|
|
v1xup = (1.0_DP - exx_fraction) * v1xup
|
|
v1xdw = (1.0_DP - exx_fraction) * v1xdw
|
|
v2xup = (1.0_DP - exx_fraction) * v2xup
|
|
v2xdw = (1.0_DP - exx_fraction) * v2xdw
|
|
end if
|
|
!=============================================================
|
|
!Lingzhu Kong
|
|
if (igcx == 3 .and. (lwfpbe0 .or. lwfpbe0nscf) ) then
|
|
sx = 0.75D0 * sx
|
|
v1xup = 0.75D0 * v1xup
|
|
v1xdw = 0.75D0 * v1xdw
|
|
v2xup = 0.75D0 * v2xup
|
|
v2xdw = 0.75D0 * v2xdw
|
|
end if
|
|
!=============================================================
|
|
if (igcx == 12 .and. exx_started ) then
|
|
|
|
call pbexsr_lsd (rhoup, rhodw, grhoup2, grhodw2, sxsr, &
|
|
v1xupsr, v2xupsr, v1xdwsr, v2xdwsr, &
|
|
screening_parameter)
|
|
! write(*,*) sxsr,v1xsr,v2xsr
|
|
sx = sx - exx_fraction*sxsr
|
|
v1xup = v1xup - exx_fraction*v1xupsr
|
|
v2xup = v2xup - exx_fraction*v2xupsr
|
|
v1xdw = v1xdw - exx_fraction*v1xdwsr
|
|
v2xdw = v2xdw - exx_fraction*v2xdwsr
|
|
end if
|
|
elseif (igcx == 9) then
|
|
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
|
|
call becke88_spin (rhoup, grhoup2, sxup, v1xup, v2xup)
|
|
else
|
|
sxup = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
endif
|
|
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
|
|
call becke88_spin (rhodw, grhodw2, sxdw, v1xdw, v2xdw)
|
|
else
|
|
sxdw = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
endif
|
|
sx = sxup + sxdw
|
|
|
|
if (exx_started ) then
|
|
sx = 0.72_DP * sx
|
|
v1xup = 0.72_DP * v1xup
|
|
v1xdw = 0.72_DP * v1xdw
|
|
v2xup = 0.72_DP * v2xup
|
|
v2xdw = 0.72_DP * v2xdw
|
|
end if
|
|
|
|
elseif (igcx == 11) then ! 'Wu-Cohen'
|
|
if (rhoup > small .and. sqrt (abs (grhoup2) ) > small) then
|
|
call wcx (2.0_DP * rhoup, 4.0_DP * grhoup2, sxup, v1xup, v2xup)
|
|
else
|
|
sxup = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
endif
|
|
if (rhodw > small .and. sqrt (abs (grhodw2) ) > small) then
|
|
call wcx (2.0_DP * rhodw, 4.0_DP * grhodw2, sxdw, v1xdw, v2xdw)
|
|
else
|
|
sxdw = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
endif
|
|
sx = 0.5_DP * (sxup + sxdw)
|
|
v2xup = 2.0_DP * v2xup
|
|
v2xdw = 2.0_DP * v2xdw
|
|
|
|
! case igcx == 5 (HCTH) and 6 (OPTX) not implemented
|
|
! case igcx == 7 (meta-GGA) must be treated in a separate call to another
|
|
! routine: needs kinetic energy density in addition to rho and grad rho
|
|
|
|
else
|
|
call errore ('gcx_spin', 'not implemented', igcx)
|
|
endif
|
|
!
|
|
return
|
|
end subroutine gcx_spin
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine gcx_spin_vec(rhoup, rhodw, grhoup2, grhodw2, &
|
|
sx, v1xup, v1xdw, v2xup, v2xdw, length)
|
|
!-----------------------------------------------------------------------
|
|
! gradient corrections for exchange - Hartree a.u.
|
|
!
|
|
implicit none
|
|
!
|
|
! dummy arguments
|
|
!
|
|
integer, intent(in) :: length
|
|
real(DP),intent(in) :: rhoup(length), rhodw(length)
|
|
real(DP),intent(in) :: grhoup2(length), grhodw2(length)
|
|
real(DP),intent(out) :: sx(length)
|
|
real(DP),intent(out) :: v1xup(length), v1xdw(length)
|
|
real(DP),intent(out) :: v2xup(length), v2xdw(length)
|
|
! up and down charge
|
|
! up and down gradient of the charge
|
|
! exchange and correlation energies
|
|
! derivatives of exchange wr. rho
|
|
! derivatives of exchange wr. grho
|
|
!
|
|
real(DP), parameter :: small = 1.E-10_DP
|
|
real(DP) :: rho(length), sxup(length), sxdw(length)
|
|
integer :: iflag
|
|
integer :: i
|
|
!
|
|
!
|
|
! exchange
|
|
rho = rhoup + rhodw
|
|
select case(igcx)
|
|
case(0)
|
|
sx = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
case(1)
|
|
do i=1,length
|
|
if (rhoup(i) > small .and. sqrt (abs (grhoup2(i)) ) > small) then
|
|
call becke88_spin (rhoup(i), grhoup2(i), sxup(i), v1xup(i), v2xup(i))
|
|
else
|
|
sxup(i) = 0.0_DP
|
|
v1xup(i) = 0.0_DP
|
|
v2xup(i) = 0.0_DP
|
|
endif
|
|
if (rhodw(i) > small .and. sqrt (abs (grhodw2(i)) ) > small) then
|
|
call becke88_spin (rhodw(i), grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
|
|
else
|
|
sxdw(i) = 0.0_DP
|
|
v1xdw(i) = 0.0_DP
|
|
v2xdw(i) = 0.0_DP
|
|
endif
|
|
end do
|
|
sx = sxup + sxdw
|
|
case(2)
|
|
do i=1,length
|
|
if (rhoup(i) > small .and. sqrt (abs (grhoup2(i)) ) > small) then
|
|
call ggax (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
|
|
else
|
|
sxup(i) = 0.0_DP
|
|
v1xup(i) = 0.0_DP
|
|
v2xup(i) = 0.0_DP
|
|
endif
|
|
if (rhodw(i) > small .and. sqrt (abs (grhodw2(i)) ) > small) then
|
|
call ggax (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
|
|
else
|
|
sxdw(i) = 0.0_DP
|
|
v1xdw(i) = 0.0_DP
|
|
v2xdw(i) = 0.0_DP
|
|
endif
|
|
end do
|
|
sx = 0.5_DP * (sxup + sxdw)
|
|
v2xup = 2.0_DP * v2xup
|
|
v2xdw = 2.0_DP * v2xdw
|
|
case(3,4,8,10)
|
|
! igcx=3: PBE, igcx=4: revised PBE, igcx=8 PBE0, igcx=10: PBEsol
|
|
if (igcx == 4) then
|
|
iflag = 2
|
|
elseif (igcx == 10) then
|
|
iflag = 3
|
|
else
|
|
iflag = 1
|
|
endif
|
|
|
|
call pbex_vec (2.0_DP * rhoup, 4.0_DP * grhoup2, iflag, sxup, v1xup, v2xup, length, small)
|
|
call pbex_vec (2.0_DP * rhodw, 4.0_DP * grhodw2, iflag, sxdw, v1xdw, v2xdw, length, small)
|
|
sx = 0.5_DP * (sxup + sxdw)
|
|
v2xup = 2.0_DP * v2xup
|
|
v2xdw = 2.0_DP * v2xdw
|
|
if (igcx == 8 .and. exx_started ) then
|
|
sx = (1.0_DP - exx_fraction) * sx
|
|
v1xup = (1.0_DP - exx_fraction) * v1xup
|
|
v1xdw = (1.0_DP - exx_fraction) * v1xdw
|
|
v2xup = (1.0_DP - exx_fraction) * v2xup
|
|
v2xdw = (1.0_DP - exx_fraction) * v2xdw
|
|
end if
|
|
!=============================================================
|
|
!Lingzhu Kong
|
|
if (igcx == 3 .and. (lwfpbe0 .or. lwfpbe0nscf) ) then
|
|
sx = 0.75D0 * sx
|
|
v1xup = 0.75D0 * v1xup
|
|
v1xdw = 0.75D0 * v1xdw
|
|
v2xup = 0.75D0 * v2xup
|
|
v2xdw = 0.75D0 * v2xdw
|
|
end if
|
|
!=============================================================
|
|
case(9)
|
|
do i=1,length
|
|
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i)) ) > small) then
|
|
call becke88_spin (rhoup(i), grhoup2(i), sxup(i), v1xup(i), v2xup(i))
|
|
else
|
|
sxup(i) = 0.0_DP
|
|
v1xup(i) = 0.0_DP
|
|
v2xup(i) = 0.0_DP
|
|
endif
|
|
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
|
|
call becke88_spin (rhodw(i), grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
|
|
else
|
|
sxdw(i) = 0.0_DP
|
|
v1xdw(i) = 0.0_DP
|
|
v2xdw(i) = 0.0_DP
|
|
endif
|
|
end do
|
|
sx = sxup + sxdw
|
|
|
|
if (exx_started ) then
|
|
sx = 0.72_DP * sx
|
|
v1xup = 0.72_DP * v1xup
|
|
v1xdw = 0.72_DP * v1xdw
|
|
v2xup = 0.72_DP * v2xup
|
|
v2xdw = 0.72_DP * v2xdw
|
|
end if
|
|
|
|
case(11) ! 'Wu-Cohen'
|
|
do i=1,length
|
|
if (rhoup(i) > small .and. sqrt(abs(grhoup2(i))) > small) then
|
|
call wcx (2.0_DP * rhoup(i), 4.0_DP * grhoup2(i), sxup(i), v1xup(i), v2xup(i))
|
|
else
|
|
sxup(i) = 0.0_DP
|
|
v1xup(i) = 0.0_DP
|
|
v2xup(i) = 0.0_DP
|
|
endif
|
|
if (rhodw(i) > small .and. sqrt(abs(grhodw2(i))) > small) then
|
|
call wcx (2.0_DP * rhodw(i), 4.0_DP * grhodw2(i), sxdw(i), v1xdw(i), v2xdw(i))
|
|
else
|
|
sxdw(i) = 0.0_DP
|
|
v1xdw(i) = 0.0_DP
|
|
v2xdw(i) = 0.0_DP
|
|
endif
|
|
end do
|
|
sx = 0.5_DP * (sxup + sxdw)
|
|
v2xup = 2.0_DP * v2xup
|
|
v2xdw = 2.0_DP * v2xdw
|
|
|
|
case default
|
|
call errore ('gcx_spin_vec', 'not implemented', igcx)
|
|
end select
|
|
!
|
|
if (igcx.ne.0) then
|
|
where (rho.le.small)
|
|
sx = 0.0_DP
|
|
v1xup = 0.0_DP
|
|
v2xup = 0.0_DP
|
|
v1xdw = 0.0_DP
|
|
v2xdw = 0.0_DP
|
|
end where
|
|
end if
|
|
!
|
|
end subroutine gcx_spin_vec
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine gcc_spin (rho, zeta, grho, sc, v1cup, v1cdw, v2c)
|
|
!-----------------------------------------------------------------------
|
|
! gradient corrections for correlations - Hartree a.u.
|
|
! Implemented: Perdew86, GGA (PW91), PBE
|
|
!
|
|
implicit none
|
|
!
|
|
! dummy arguments
|
|
!
|
|
real(DP) :: rho, zeta, grho, sc, v1cup, v1cdw, v2c
|
|
! the total charge
|
|
! the magnetization
|
|
! the gradient of the charge squared
|
|
! exchange and correlation energies
|
|
! derivatives of correlation wr. rho
|
|
! derivatives of correlation wr. grho
|
|
|
|
real(DP), parameter :: small = 1.E-10_DP, epsr=1.E-6_DP
|
|
!
|
|
!
|
|
if ( abs(zeta) > 1.0_DP ) then
|
|
sc = 0.0_DP
|
|
v1cup = 0.0_DP
|
|
v1cdw = 0.0_DP
|
|
v2c = 0.0_DP
|
|
return
|
|
else
|
|
!
|
|
! ... ( - 1.0 + epsr ) < zeta < ( 1.0 - epsr )
|
|
zeta = SIGN( MIN( ABS( zeta ), ( 1.0_DP - epsr ) ) , zeta )
|
|
endif
|
|
|
|
if (igcc == 0 .or. rho <= small .or. sqrt(abs(grho)) <= small) then
|
|
sc = 0.0_DP
|
|
v1cup = 0.0_DP
|
|
v1cdw = 0.0_DP
|
|
v2c = 0.0_DP
|
|
elseif (igcc == 1) then
|
|
call perdew86_spin (rho, zeta, grho, sc, v1cup, v1cdw, v2c)
|
|
elseif (igcc == 2) then
|
|
call ggac_spin (rho, zeta, grho, sc, v1cup, v1cdw, v2c)
|
|
elseif (igcc == 4) then
|
|
call pbec_spin (rho, zeta, grho, 1, sc, v1cup, v1cdw, v2c)
|
|
elseif (igcc == 8) then
|
|
call pbec_spin (rho, zeta, grho, 2, sc, v1cup, v1cdw, v2c)
|
|
else
|
|
call errore ('lsda_functionals (gcc_spin)', 'not implemented', igcc)
|
|
endif
|
|
!
|
|
return
|
|
end subroutine gcc_spin
|
|
!
|
|
! ==================================================================
|
|
SUBROUTINE gcc_spin_more( RHOA, RHOB, GRHOAA, GRHOBB, GRHOAB, &
|
|
SC, V1CA, V1CB, V2CA, V2CB, V2CAB )
|
|
! ==--------------------------------------------------------------==
|
|
! == GRADIENT CORRECTIONS FOR EXCHANGE AND CORRELATION ==
|
|
! == ==
|
|
! == EXCHANGE : BECKE88 ==
|
|
! == GGAX ==
|
|
! == CORRELATION : PERDEW86 ==
|
|
! == LEE, YANG & PARR ==
|
|
! == GGAC ==
|
|
! ==--------------------------------------------------------------==
|
|
|
|
IMPLICIT NONE
|
|
REAL(DP) :: RHOA,RHOB,GRHOAA,GRHOBB,GRHOAB
|
|
REAL(DP) :: SC,V1CA,V2CA,V1CB,V2CB,V2CAB
|
|
|
|
! ... Gradient Correction for correlation
|
|
|
|
REAL(DP) :: SMALL, RHO
|
|
PARAMETER(SMALL=1.E-20_DP)
|
|
|
|
SC=0.0_DP
|
|
V1CA=0.0_DP
|
|
V2CA=0.0_DP
|
|
V1CB=0.0_DP
|
|
V2CB=0.0_DP
|
|
V2CAB=0.0_DP
|
|
IF( igcc == 3 .or. igcc == 7) THEN
|
|
RHO=RHOA+RHOB
|
|
IF(RHO.GT.SMALL) then
|
|
CALL LSD_GLYP(RHOA,RHOB,GRHOAA,GRHOAB,GRHOBB,SC,&
|
|
V1CA,V2CA,V1CB,V2CB,V2CAB)
|
|
if (igcc == 7 .and. exx_started) then
|
|
SC = 0.81d0*SC
|
|
V1CA = 0.81d0*V1CA
|
|
V2CA = 0.81d0*V2CA
|
|
V1CB = 0.81d0*V1CB
|
|
V2CB = 0.81d0*V2CB
|
|
V2CAB = 0.81d0*V2CAB
|
|
endif
|
|
endif
|
|
ELSE
|
|
CALL errore( " gcc_spin_more ", " gradiet correction not implemented ", 1 )
|
|
ENDIF
|
|
! ==--------------------------------------------------------------==
|
|
RETURN
|
|
END SUBROUTINE gcc_spin_more
|
|
!
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
!------- NONLOCAL CORRECTIONS DRIVERS ----------------------------------
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine nlc (rho_valence, rho_core, enl, vnl, v)
|
|
!-----------------------------------------------------------------------
|
|
! non local correction for the correlation
|
|
!
|
|
! input: rho_valence, rho_core
|
|
! definition: E_nl = \int E_nl(rho',grho',rho'',grho'',|r'-r''|) dr
|
|
! output: enl = E_nl
|
|
! vnl= D(E_x)/D(rho)
|
|
! v = Correction to the potential
|
|
!
|
|
|
|
USE vdW_DF, ONLY: xc_vdW_DF, vdw_type
|
|
|
|
implicit none
|
|
|
|
REAL(DP), INTENT(IN) :: rho_valence(:,:), rho_core(:)
|
|
REAL(DP), INTENT(INOUT) :: v(:,:)
|
|
REAL(DP), INTENT(INOUT) :: enl, vnl
|
|
|
|
if (inlc == 1 .or. inlc == 2) then
|
|
|
|
vdw_type = inlc
|
|
call xc_vdW_DF(rho_valence, rho_core, enl, vnl, v)
|
|
|
|
else
|
|
enl = 0.0_DP
|
|
vnl = 0.0_DP
|
|
v = 0.0_DP
|
|
endif
|
|
!
|
|
return
|
|
end subroutine nlc
|
|
|
|
!-----------------------------------------------------------------------
|
|
!------- DRIVERS FOR DERIVATIVES OF XC POTENTIAL -----------------------
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
function dmxc (rho)
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
! derivative of the xc potential with respect to the local density
|
|
!
|
|
!
|
|
implicit none
|
|
!
|
|
real(DP), intent(in) :: rho
|
|
! input: the charge density ( positive )
|
|
real(DP) :: dmxc
|
|
! output: the derivative of the xc potential
|
|
!
|
|
! local variables
|
|
!
|
|
real(DP) :: dr, vxp, vcp, vxm, vcm, vx, ex, ec, rs
|
|
real(DP), external :: dpz
|
|
integer :: iflg
|
|
!
|
|
real(DP), parameter :: small = 1.E-30_DP, e2 = 2.0_DP, &
|
|
pi34 = 0.75_DP / 3.141592653589793_DP, third = 1.0_DP /3.0_DP
|
|
!
|
|
dmxc = 0.0_DP
|
|
if (rho < small) then
|
|
return
|
|
endif
|
|
!
|
|
! first case: analytical derivatives available
|
|
!
|
|
if (get_iexch() == 1 .and. get_icorr() == 1) then
|
|
rs = (pi34 / rho) **third
|
|
!..exchange
|
|
call slater (rs, ex, vx)
|
|
dmxc = vx / (3.0_DP * rho)
|
|
!..correlation
|
|
iflg = 2
|
|
if (rs < 1.0_DP) iflg = 1
|
|
dmxc = dmxc + dpz (rs, iflg)
|
|
else
|
|
!
|
|
! second case: numerical derivatives
|
|
!
|
|
dr = min (1.E-6_DP, 1.E-4_DP * rho)
|
|
call xc (rho + dr, ex, ec, vxp, vcp)
|
|
call xc (rho - dr, ex, ec, vxm, vcm)
|
|
dmxc = (vxp + vcp - vxm - vcm) / (2.0_DP * dr)
|
|
endif
|
|
!
|
|
! bring to rydberg units
|
|
!
|
|
dmxc = e2 * dmxc
|
|
return
|
|
!
|
|
end function dmxc
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine dmxc_spin (rhoup, rhodw, dmuxc_uu, dmuxc_ud, dmuxc_du, &
|
|
dmuxc_dd)
|
|
!-----------------------------------------------------------------------
|
|
! derivative of the xc potential with respect to the local density
|
|
! spin-polarized case
|
|
!
|
|
implicit none
|
|
!
|
|
real(DP), intent(in) :: rhoup, rhodw
|
|
! input: spin-up and spin-down charge density
|
|
real(DP), intent(out) :: dmuxc_uu, dmuxc_ud, dmuxc_du, dmuxc_dd
|
|
! output: up-up, up-down, down-up, down-down derivatives of the
|
|
! XC functional
|
|
!
|
|
! local variables
|
|
!
|
|
real(DP) :: rhotot, rs, zeta, fz, fz1, fz2, ex, vx, ecu, ecp, vcu, &
|
|
vcp, dmcu, dmcp, aa, bb, cc, dr, dz, ec, vxupm, vxdwm, vcupm, &
|
|
vcdwm, rho, vxupp, vxdwp, vcupp, vcdwp, zeta_eff
|
|
real(DP), external :: dpz, dpz_polarized
|
|
integer :: iflg
|
|
!
|
|
real(DP), parameter :: small = 1.E-30_DP, e2 = 2.0_DP, &
|
|
pi34 = 0.75_DP / 3.141592653589793_DP, third = 1.0_DP/3.0_DP, &
|
|
p43 = 4.0_DP / 3.0_DP, p49 = 4.0_DP / 9.0_DP, m23 = -2.0_DP / 3.0_DP
|
|
!
|
|
dmuxc_uu = 0.0_DP
|
|
dmuxc_du = 0.0_DP
|
|
dmuxc_ud = 0.0_DP
|
|
dmuxc_dd = 0.0_DP
|
|
!
|
|
rhotot = rhoup + rhodw
|
|
if (rhotot <= small) return
|
|
zeta = (rhoup - rhodw) / rhotot
|
|
|
|
if (abs (zeta) > 1.0_DP) return
|
|
if (get_iexch() == 1 .and. get_icorr() == 1) then
|
|
!
|
|
! first case: analytical derivative available
|
|
!
|
|
!..exchange
|
|
rs = (pi34 / (2.0_DP * rhoup) ) **third
|
|
call slater (rs, ex, vx)
|
|
dmuxc_uu = vx / (3.0_DP * rhoup)
|
|
rs = (pi34 / (2.0_DP * rhodw) ) **third
|
|
call slater (rs, ex, vx)
|
|
dmuxc_dd = vx / (3.0_DP * rhodw)
|
|
!..correlation
|
|
rs = (pi34 / rhotot) **third
|
|
iflg = 2
|
|
if (rs < 1.0_DP) iflg = 1
|
|
dmcu = dpz (rs, iflg)
|
|
dmcp = dpz_polarized (rs, iflg)
|
|
call pz (rs, 1, ecu, vcu)
|
|
call pz_polarized (rs, ecp, vcp)
|
|
fz = ( (1.0_DP + zeta) **p43 + (1.0_DP - zeta) **p43 - 2.0_DP) &
|
|
/ (2.0_DP**p43 - 2.0_DP)
|
|
fz1 = p43 * ( (1.0_DP + zeta) **third- (1.0_DP - zeta) **third) &
|
|
/ (2.0_DP**p43 - 2.0_DP)
|
|
fz2 = p49 * ( (1.0_DP + zeta) **m23 + (1.0_DP - zeta) **m23) &
|
|
/ (2.0_DP**p43 - 2.0_DP)
|
|
aa = dmcu + fz * (dmcp - dmcu)
|
|
bb = 2.0_DP * fz1 * (vcp - vcu - (ecp - ecu) ) / rhotot
|
|
cc = fz2 * (ecp - ecu) / rhotot
|
|
dmuxc_uu = dmuxc_uu + aa + (1.0_DP - zeta) * bb + (1.0_DP - zeta)**2 * cc
|
|
dmuxc_du = dmuxc_du + aa + ( - zeta) * bb + (zeta**2 - 1.0_DP) * cc
|
|
dmuxc_ud = dmuxc_du
|
|
dmuxc_dd = dmuxc_dd+aa - (1.0_DP + zeta) * bb + (1.0_DP + zeta)**2 * cc
|
|
|
|
else
|
|
|
|
rho = rhoup + rhodw
|
|
dr = min (1.E-6_DP, 1.E-4_DP * rho)
|
|
call xc_spin (rho - dr, zeta, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
|
|
call xc_spin (rho + dr, zeta, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
|
|
dmuxc_uu = (vxupp + vcupp - vxupm - vcupm) / (2.0_DP * dr)
|
|
dmuxc_ud = dmuxc_uu
|
|
dmuxc_dd = (vxdwp + vcdwp - vxdwm - vcdwm) / (2.0_DP * dr)
|
|
dmuxc_du = dmuxc_dd
|
|
! dz = min (1.d-6, 1.d-4 * abs (zeta) )
|
|
dz = 1.E-6_DP
|
|
!
|
|
! If zeta is too close to +-1, the derivative is computed at a slightly
|
|
! smaller zeta
|
|
!
|
|
zeta_eff = SIGN( MIN( ABS( zeta ), ( 1.0_DP - 2.0_DP*dz ) ) , zeta )
|
|
|
|
call xc_spin (rho, zeta_eff - dz, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
|
|
call xc_spin (rho, zeta_eff + dz, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
|
|
dmuxc_uu = dmuxc_uu + (vxupp + vcupp - vxupm - vcupm) * &
|
|
(1.0_DP - zeta) / rho / (2.0_DP * dz)
|
|
dmuxc_ud = dmuxc_ud- (vxupp + vcupp - vxupm - vcupm) * &
|
|
(1.0_DP + zeta) / rho / (2.0_DP * dz)
|
|
dmuxc_du = dmuxc_du + (vxdwp + vcdwp - vxdwm - vcdwm) * &
|
|
(1.0_DP - zeta) / rho / (2.0_DP * dz)
|
|
dmuxc_dd = dmuxc_dd- (vxdwp + vcdwp - vxdwm - vcdwm) * &
|
|
(1.0_DP + zeta) / rho / (2.0_DP * dz)
|
|
endif
|
|
!
|
|
! bring to rydberg units
|
|
!
|
|
dmuxc_uu = e2 * dmuxc_uu
|
|
dmuxc_du = e2 * dmuxc_du
|
|
dmuxc_ud = e2 * dmuxc_ud
|
|
dmuxc_dd = e2 * dmuxc_dd
|
|
!
|
|
return
|
|
|
|
end subroutine dmxc_spin
|
|
|
|
!-----------------------------------------------------------------------
|
|
subroutine dmxc_nc (rho, mx, my, mz, dmuxc)
|
|
!-----------------------------------------------------------------------
|
|
! derivative of the xc potential with respect to the local density
|
|
! and magnetization
|
|
! non colinear case
|
|
!
|
|
implicit none
|
|
!
|
|
real(DP), intent(in) :: rho, mx, my, mz
|
|
! input: charge density and magnetization
|
|
real(DP), intent(out) :: dmuxc(4,4)
|
|
! output: derivative of XC functional
|
|
!
|
|
! local variables
|
|
!
|
|
REAL(DP) :: zeta, ex, ec, dr, dz, vxupm, vxdwm, vcupm, &
|
|
vcdwm, vxupp, vxdwp, vcupp, vcdwp, vxup, vxdw, vcup, vcdw
|
|
REAL(DP) :: amag, vs, dvxc_rho, dvxc_mx, dvxc_my, dvxc_mz, &
|
|
dbx_rho, dbx_mx, dbx_my, dbx_mz, dby_rho, dby_mx, &
|
|
dby_my, dby_mz, dbz_rho, dbz_mx, dbz_my, dbz_mz, zeta_eff
|
|
REAL(DP), PARAMETER :: small = 1.E-30_DP, e2 = 2.0_DP
|
|
!
|
|
!
|
|
dmuxc = 0.0_DP
|
|
!
|
|
IF (rho <= small) RETURN
|
|
amag = sqrt(mx**2+my**2+mz**2)
|
|
zeta = amag / rho
|
|
|
|
IF (abs (zeta) > 1.0_DP) RETURN
|
|
CALL xc_spin (rho, zeta, ex, ec, vxup, vxdw, vcup, vcdw)
|
|
vs=0.5_DP*(vxup+vcup-vxdw-vcdw)
|
|
|
|
dr = min (1.E-6_DP, 1.E-4_DP * rho)
|
|
CALL xc_spin (rho - dr, zeta, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
|
|
CALL xc_spin (rho + dr, zeta, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
|
|
dvxc_rho = ((vxupp + vcupp - vxupm - vcupm)+ &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm)) / (4.0_DP * dr)
|
|
IF (amag > 1.E-10_DP) THEN
|
|
dbx_rho = ((vxupp + vcupp - vxupm - vcupm)- &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))* mx / (4.0_DP*dr*amag)
|
|
dby_rho = ((vxupp + vcupp - vxupm - vcupm)- &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))* my / (4.0_DP*dr*amag)
|
|
dbz_rho = ((vxupp + vcupp - vxupm - vcupm)- &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))* mz / (4.0_DP*dr*amag)
|
|
! dz = min (1.d-6, 1.d-4 * abs (zeta) )
|
|
dz = 1.0E-6_DP
|
|
!
|
|
! If zeta is too close to +-1, the derivative is computed at a slightly
|
|
! smaller zeta
|
|
!
|
|
zeta_eff = SIGN( MIN( ABS( zeta ), ( 1.0_DP - 2.0_DP*dz ) ) , zeta )
|
|
|
|
CALL xc_spin (rho, zeta_eff - dz, ex, ec, vxupm, vxdwm, vcupm, vcdwm)
|
|
CALL xc_spin (rho, zeta_eff + dz, ex, ec, vxupp, vxdwp, vcupp, vcdwp)
|
|
|
|
! The variables are rho and m, so zeta depends on rho
|
|
!
|
|
dvxc_rho=dvxc_rho- ((vxupp + vcupp - vxupm - vcupm)+ &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*zeta/rho/(4.0_DP * dz)
|
|
dbx_rho = dbx_rho-((vxupp + vcupp - vxupm - vcupm)- &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mx*zeta/rho/(4.0_DP*dz*amag)
|
|
dby_rho = dby_rho-((vxupp + vcupp - vxupm - vcupm)- &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*my*zeta/rho/(4.0_DP*dz*amag)
|
|
dbz_rho = dbz_rho-((vxupp + vcupp - vxupm - vcupm)- &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mz*zeta/rho/(4.0_DP*dz*amag)
|
|
!
|
|
! here the derivatives with respect to m
|
|
!
|
|
dvxc_mx = ((vxupp + vcupp - vxupm - vcupm) + &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mx/rho/(4.0_DP*dz*amag)
|
|
dvxc_my = ((vxupp + vcupp - vxupm - vcupm) + &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*my/rho/(4.0_DP*dz*amag)
|
|
dvxc_mz = ((vxupp + vcupp - vxupm - vcupm) + &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mz/rho/(4.0_DP*dz*amag)
|
|
dbx_mx = (((vxupp + vcupp - vxupm - vcupm) - &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mx**2*amag/rho/ &
|
|
(4.0_DP*dz) + vs*(my**2+mz**2))/amag**3
|
|
dbx_my = (((vxupp + vcupp - vxupm - vcupm) - &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mx*my*amag/rho/ &
|
|
(4.0_DP*dz) - vs*(mx*my))/amag**3
|
|
dbx_mz = (((vxupp + vcupp - vxupm - vcupm) - &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mx*mz*amag/rho/ &
|
|
(4.0_DP*dz) - vs*(mx*mz))/amag**3
|
|
dby_mx = dbx_my
|
|
dby_my = (((vxupp + vcupp - vxupm - vcupm) - &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*my**2*amag/rho/ &
|
|
(4.0_DP*dz) + vs*(mx**2+mz**2))/amag**3
|
|
dby_mz = (((vxupp + vcupp - vxupm - vcupm) - &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*my*mz*amag/rho/ &
|
|
(4.0_DP*dz) - vs*(my*mz))/amag**3
|
|
dbz_mx = dbx_mz
|
|
dbz_my = dby_mz
|
|
dbz_mz = (((vxupp + vcupp - vxupm - vcupm) - &
|
|
(vxdwp + vcdwp - vxdwm - vcdwm))*mz**2*amag/rho/ &
|
|
(4.0_DP*dz) + vs*(mx**2+my**2))/amag**3
|
|
dmuxc(1,1)=dvxc_rho
|
|
dmuxc(1,2)=dvxc_mx
|
|
dmuxc(1,3)=dvxc_my
|
|
dmuxc(1,4)=dvxc_mz
|
|
dmuxc(2,1)=dbx_rho
|
|
dmuxc(2,2)=dbx_mx
|
|
dmuxc(2,3)=dbx_my
|
|
dmuxc(2,4)=dbx_mz
|
|
dmuxc(3,1)=dby_rho
|
|
dmuxc(3,2)=dby_mx
|
|
dmuxc(3,3)=dby_my
|
|
dmuxc(3,4)=dby_mz
|
|
dmuxc(4,1)=dbz_rho
|
|
dmuxc(4,2)=dbz_mx
|
|
dmuxc(4,3)=dbz_my
|
|
dmuxc(4,4)=dbz_mz
|
|
ELSE
|
|
dmuxc(1,1)=dvxc_rho
|
|
ENDIF
|
|
!
|
|
! bring to rydberg units
|
|
!
|
|
dmuxc = e2 * dmuxc
|
|
!
|
|
RETURN
|
|
|
|
end subroutine dmxc_nc
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine dgcxc (r, s2, vrrx, vsrx, vssx, vrrc, vsrc, vssc)
|
|
!-----------------------------------------------------------------------
|
|
USE kinds, only : DP
|
|
implicit none
|
|
real(DP) :: r, s2, vrrx, vsrx, vssx, vrrc, vsrc, vssc
|
|
real(DP) :: dr, s, ds
|
|
|
|
real(DP) :: sx, sc, v1xp, v2xp, v1cp, v2cp, v1xm, v2xm, v1cm, &
|
|
v2cm
|
|
s = sqrt (s2)
|
|
dr = min (1.d-4, 1.d-2 * r)
|
|
|
|
ds = min (1.d-4, 1.d-2 * s)
|
|
call gcxc (r + dr, s2, sx, sc, v1xp, v2xp, v1cp, v2cp)
|
|
|
|
call gcxc (r - dr, s2, sx, sc, v1xm, v2xm, v1cm, v2cm)
|
|
vrrx = 0.5d0 * (v1xp - v1xm) / dr
|
|
|
|
vrrc = 0.5d0 * (v1cp - v1cm) / dr
|
|
vsrx = 0.25d0 * (v2xp - v2xm) / dr
|
|
|
|
vsrc = 0.25d0 * (v2cp - v2cm) / dr
|
|
call gcxc (r, (s + ds) **2, sx, sc, v1xp, v2xp, v1cp, v2cp)
|
|
|
|
call gcxc (r, (s - ds) **2, sx, sc, v1xm, v2xm, v1cm, v2cm)
|
|
vsrx = vsrx + 0.25d0 * (v1xp - v1xm) / ds / s
|
|
|
|
vsrc = vsrc + 0.25d0 * (v1cp - v1cm) / ds / s
|
|
vssx = 0.5d0 * (v2xp - v2xm) / ds / s
|
|
|
|
vssc = 0.5d0 * (v2cp - v2cm) / ds / s
|
|
return
|
|
end subroutine dgcxc
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
subroutine dgcxc_spin (rup, rdw, gup, gdw, vrrxup, vrrxdw, vrsxup, &
|
|
vrsxdw, vssxup, vssxdw, vrrcup, vrrcdw, vrscup, vrscdw, vssc, &
|
|
vrzcup, vrzcdw)
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
! This routine computes the derivative of the exchange and correlatio
|
|
! potentials with respect to the density, the gradient and zeta
|
|
!
|
|
USE kinds, only : DP
|
|
implicit none
|
|
real(DP), intent(in) :: rup, rdw, gup (3), gdw (3)
|
|
! input: the charges and the gradient
|
|
real(DP), intent(out):: vrrxup, vrrxdw, vrsxup, vrsxdw, vssxup, &
|
|
vssxdw, vrrcup, vrrcdw, vrscup, vrscdw, vssc, vrzcup, vrzcdw
|
|
! output: derivatives of the exchange and of the correlation
|
|
!
|
|
! local variables
|
|
!
|
|
real(DP) :: r, zeta, sup2, sdw2, s2, s, sup, sdw, dr, dzeta, ds, &
|
|
drup, drdw, dsup, dsdw, sx, sc, v1xupp, v1xdwp, v2xupp, v2xdwp, &
|
|
v1xupm, v1xdwm, v2xupm, v2xdwm, v1cupp, v1cdwp, v2cp, v1cupm, &
|
|
v1cdwm, v2cm
|
|
! charge densities and square gradients
|
|
! delta charge densities and gra
|
|
! delta gradients
|
|
! energies
|
|
! exchange potentials
|
|
! exchange potentials
|
|
! coorelation potentials
|
|
! coorelation potentials
|
|
real(DP), parameter :: eps = 1.d-6
|
|
!
|
|
r = rup + rdw
|
|
if (r.gt.eps) then
|
|
zeta = (rup - rdw) / r
|
|
else
|
|
zeta = 2.d0
|
|
endif
|
|
sup2 = gup (1) **2 + gup (2) **2 + gup (3) **2
|
|
sdw2 = gdw (1) **2 + gdw (2) **2 + gdw (3) **2
|
|
|
|
s2 = (gup (1) + gdw (1) ) **2 + (gup (2) + gdw (2) ) **2 + &
|
|
(gup (3) + gdw (3) ) **2
|
|
sup = sqrt (sup2)
|
|
sdw = sqrt (sdw2)
|
|
s = sqrt (s2)
|
|
!
|
|
! up part of exchange
|
|
!
|
|
|
|
if (rup.gt.eps.and.sup.gt.eps) then
|
|
drup = min (1.d-4, 1.d-2 * rup)
|
|
dsup = min (1.d-4, 1.d-2 * sdw)
|
|
!
|
|
! derivatives of exchange: up part
|
|
!
|
|
call gcx_spin (rup + drup, rdw, sup2, sdw2, sx, v1xupp, v1xdwp, &
|
|
v2xupp, v2xdwp)
|
|
|
|
call gcx_spin (rup - drup, rdw, sup2, sdw2, sx, v1xupm, v1xdwm, &
|
|
v2xupm, v2xdwm)
|
|
vrrxup = 0.5d0 * (v1xupp - v1xupm) / drup
|
|
vrsxup = 0.25d0 * (v2xupp - v2xupm) / drup
|
|
|
|
call gcx_spin (rup, rdw, (sup + dsup) **2, sdw2, sx, v1xupp, &
|
|
v1xdwp, v2xupp, v2xdwp)
|
|
|
|
call gcx_spin (rup, rdw, (sup - dsup) **2, sdw2, sx, v1xupm, &
|
|
v1xdwm, v2xupm, v2xdwm)
|
|
vrsxup = vrsxup + 0.25d0 * (v1xupp - v1xupm) / dsup / sup
|
|
vssxup = 0.5d0 * (v2xupp - v2xupm) / dsup / sup
|
|
else
|
|
vrrxup = 0.d0
|
|
vrsxup = 0.d0
|
|
vssxup = 0.d0
|
|
endif
|
|
|
|
if (rdw.gt.eps.and.sdw.gt.eps) then
|
|
drdw = min (1.d-4, 1.d-2 * rdw)
|
|
dsdw = min (1.d-4, 1.d-2 * sdw)
|
|
!
|
|
! derivatives of exchange: down part
|
|
!
|
|
call gcx_spin (rup, rdw + drdw, sup2, sdw2, sx, v1xupp, v1xdwp, &
|
|
v2xupp, v2xdwp)
|
|
|
|
call gcx_spin (rup, rdw - drdw, sup2, sdw2, sx, v1xupm, v1xdwm, &
|
|
v2xupm, v2xdwm)
|
|
vrrxdw = 0.5d0 * (v1xdwp - v1xdwm) / drdw
|
|
|
|
vrsxdw = 0.25d0 * (v2xdwp - v2xdwm) / drdw
|
|
call gcx_spin (rup, rdw, sup2, (sdw + dsdw) **2, sx, v1xupp, &
|
|
v1xdwp, v2xupp, v2xdwp)
|
|
|
|
call gcx_spin (rup, rdw, sup2, (sdw - dsdw) **2, sx, v1xupm, &
|
|
v1xdwm, v2xupm, v2xdwm)
|
|
vrsxdw = vrsxdw + 0.25d0 * (v1xdwp - v1xdwm) / dsdw / sdw
|
|
vssxdw = 0.5d0 * (v2xdwp - v2xdwm) / dsdw / sdw
|
|
else
|
|
vrrxdw = 0.d0
|
|
vrsxdw = 0.d0
|
|
vssxdw = 0.d0
|
|
endif
|
|
!
|
|
! derivatives of correlation
|
|
!
|
|
|
|
if (r.gt.eps.and.abs (zeta) .le.1.d0.and.s.gt.eps) then
|
|
|
|
dr = min (1.d-4, 1.d-2 * r)
|
|
call gcc_spin (r + dr, zeta, s2, sc, v1cupp, v1cdwp, v2cp)
|
|
|
|
call gcc_spin (r - dr, zeta, s2, sc, v1cupm, v1cdwm, v2cm)
|
|
vrrcup = 0.5d0 * (v1cupp - v1cupm) / dr
|
|
|
|
vrrcdw = 0.5d0 * (v1cdwp - v1cdwm) / dr
|
|
|
|
ds = min (1.d-4, 1.d-2 * s)
|
|
call gcc_spin (r, zeta, (s + ds) **2, sc, v1cupp, v1cdwp, v2cp)
|
|
|
|
call gcc_spin (r, zeta, (s - ds) **2, sc, v1cupm, v1cdwm, v2cm)
|
|
vrscup = 0.5d0 * (v1cupp - v1cupm) / ds / s
|
|
vrscdw = 0.5d0 * (v1cdwp - v1cdwm) / ds / s
|
|
|
|
vssc = 0.5d0 * (v2cp - v2cm) / ds / s
|
|
! dzeta = min (1.d-4, 1.d-2 * abs (zeta) )
|
|
|
|
dzeta = 1.d-6
|
|
!
|
|
! If zeta is too close to +-1 the derivative is evaluated at a slightly
|
|
! smaller value
|
|
!
|
|
zeta = SIGN( MIN( ABS( zeta ), ( 1.0_DP - 2.0_DP*dzeta ) ) , zeta )
|
|
|
|
call gcc_spin (r, zeta + dzeta, s2, sc, v1cupp, v1cdwp, v2cp)
|
|
|
|
call gcc_spin (r, zeta - dzeta, s2, sc, v1cupm, v1cdwm, v2cm)
|
|
vrzcup = 0.5d0 * (v1cupp - v1cupm) / dzeta
|
|
vrzcdw = 0.5d0 * (v1cdwp - v1cdwm) / dzeta
|
|
else
|
|
vrrcup = 0.d0
|
|
vrrcdw = 0.d0
|
|
vrscup = 0.d0
|
|
vrscdw = 0.d0
|
|
vssc = 0.d0
|
|
vrzcup = 0.d0
|
|
vrzcdw = 0.d0
|
|
|
|
endif
|
|
return
|
|
end subroutine dgcxc_spin
|
|
|
|
!
|
|
!-----------------------------------------------------------------------
|
|
!------- VECTOR AND GENERAL XC DRIVERS -------------------------------
|
|
!-----------------------------------------------------------------------
|
|
!
|
|
!---------------------------------------------------------------
|
|
subroutine vxc_t(rho,rhoc,lsd,vxc)
|
|
!---------------------------------------------------------------
|
|
!
|
|
! this function returns the XC potential in LDA or LSDA approximation
|
|
!
|
|
use io_global, only : stdout
|
|
use kinds, only : DP
|
|
implicit none
|
|
integer:: lsd
|
|
real(DP):: vxc(2), rho(2),rhoc,arho,zeta
|
|
real(DP):: vx(2), vc(2), ex, ec
|
|
!
|
|
real(DP), parameter :: e2=2.0_dp, eps=1.e-30_dp
|
|
|
|
vxc(1)=0.0_dp
|
|
if (lsd.eq.1) vxc(2)=0.0_dp
|
|
|
|
if (lsd.eq.0) then
|
|
!
|
|
! LDA case
|
|
!
|
|
arho=abs(rho(1)+rhoc)
|
|
if (arho.gt.eps) then
|
|
call xc(arho,ex,ec,vx(1),vc(1))
|
|
vxc(1)=e2*(vx(1)+vc(1))
|
|
endif
|
|
else
|
|
!
|
|
! LSDA case
|
|
!
|
|
arho = abs(rho(1)+rho(2)+rhoc)
|
|
if (arho.gt.eps) then
|
|
zeta = (rho(1)-rho(2)) / arho
|
|
! zeta has to stay between -1 and 1, but can get a little
|
|
! out the bound during the first iterations.
|
|
if (abs(zeta).gt.1.0_dp) zeta = sign(1._dp, zeta)
|
|
call xc_spin(arho,zeta,ex,ec,vx(1),vx(2),vc(1),vc(2))
|
|
vxc(1) = e2*(vx(1)+vc(1))
|
|
vxc(2) = e2*(vx(2)+vc(2))
|
|
endif
|
|
endif
|
|
|
|
return
|
|
end subroutine vxc_t
|
|
|
|
|
|
!---------------------------------------------------------------
|
|
function exc_t(rho,rhoc,lsd)
|
|
!---------------------------------------------------------------
|
|
!
|
|
use kinds, only : DP
|
|
implicit none
|
|
integer:: lsd
|
|
real(DP) :: exc_t, rho(2),arho,rhot, zeta,rhoc
|
|
real(DP) :: ex, ec, vx(2), vc(2)
|
|
|
|
real(DP),parameter:: e2 =2.0_DP
|
|
|
|
exc_t=0.0_DP
|
|
|
|
if(lsd == 0) then
|
|
!
|
|
! LDA case
|
|
!
|
|
rhot = rho(1) + rhoc
|
|
arho = abs(rhot)
|
|
if (arho.gt.1.e-30_DP) then
|
|
call xc(arho,ex,ec,vx(1),vc(1))
|
|
exc_t=e2*(ex+ec)
|
|
endif
|
|
else
|
|
!
|
|
! LSDA case
|
|
!
|
|
rhot = rho(1)+rho(2)+rhoc
|
|
arho = abs(rhot)
|
|
if (arho.gt.1.e-30_DP) then
|
|
zeta = (rho(1)-rho(2)) / arho
|
|
! In atomic this cannot happen, but in PAW zeta can become
|
|
! a little larger than 1, or smaller than -1:
|
|
if( abs(zeta) > 1._dp) zeta = sign(1._dp, zeta)
|
|
call xc_spin(arho,zeta,ex,ec,vx(1),vx(2),vc(1),vc(2))
|
|
exc_t=e2*(ex+ec)
|
|
endif
|
|
endif
|
|
|
|
return
|
|
end function exc_t
|
|
|
|
subroutine evxc_t_vec(rho,rhoc,lsd,length,vxc,exc)
|
|
!---------------------------------------------------------------
|
|
!
|
|
! this function returns the XC potential in LDA or LSDA approximation
|
|
!
|
|
integer, intent(in) :: lsd, length
|
|
real(DP), intent(in) :: rho(length,2), rhoc(length)
|
|
real(DP), intent(out), optional :: vxc(length,2)
|
|
real(DP), intent(out), optional :: exc(length)
|
|
!
|
|
real(DP) :: arho
|
|
real(DP) :: arhoV(length), zetaV(length)
|
|
real(DP) :: evx(length,3), evc(length,3)
|
|
real(DP) :: ex, ec, vx, vc
|
|
!
|
|
integer :: i
|
|
real(DP), parameter :: e2 = 2.0_dp, eps = 1.e-30_dp
|
|
|
|
if (lsd.eq.0) then
|
|
!
|
|
! LDA case
|
|
!
|
|
do i=1,length
|
|
arho = abs(rho(i,1)+rhoc(i))
|
|
if (arho.gt.eps) then
|
|
call xc(arho,ex,ec,vx,vc)
|
|
else
|
|
ex = 0.0_dp
|
|
ec = 0.0_dp
|
|
vx = 0.0_dp
|
|
vc = 0.0_dp
|
|
end if
|
|
if (present(vxc)) vxc(i,1) = e2*(vx+vc)
|
|
if (present(exc)) exc(i) = e2*(ex+ec)
|
|
end do
|
|
else
|
|
!
|
|
! LSDA case
|
|
!
|
|
arhoV = abs(rho(:,1)+rho(:,2)+rhoc(:))
|
|
where (arhoV.gt.eps)
|
|
zetaV = (rho(:,1)-rho(:,2)) / arhoV
|
|
elsewhere
|
|
zetaV = 0.0_DP ! just a sane default, results are discarded anyway
|
|
end where
|
|
! zeta has to stay between -1 and 1, but can get a little
|
|
! out of bound during the first iterations.
|
|
zetaV = min( 1.0_DP, zetaV)
|
|
zetaV = max(-1.0_DP, zetaV)
|
|
call xc_spin_vec(arhoV, zetaV, length, evx, evc)
|
|
if (present(vxc)) then
|
|
vxc(:,1) = e2*(evx(:,1) + evc(:,1))
|
|
vxc(:,2) = e2*(evx(:,2) + evc(:,2))
|
|
end if
|
|
if (present(exc)) exc = e2*(evx(:,3)+evc(:,3))
|
|
end if
|
|
|
|
end subroutine evxc_t_vec
|
|
|
|
|
|
end module funct
|