mirror of https://gitlab.com/QEF/q-e.git
183 lines
5.4 KiB
Fortran
183 lines
5.4 KiB
Fortran
!
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! Copyright (C) 2002 Vanderbilt 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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! This routine has been modified in order to be compatible with the
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! ld1 code. The numerical algorithm is unchanged.
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! ADC Nov 2003
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! ADC Sep 2007 Clean-up
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!
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!-------------------------------------------------------------------------
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!
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subroutine dir_outward(idim1,mesh,lcur,jcur,e0,dx,snl,r,rab,ruae)
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!
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! subroutine to compute solutions to the full dirac equation
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!
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! the dirac equation in rydberg units reads:
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!
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! df(r) k alpha
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! ----- = + - f(r) - ( e - v(r) ) ----- g(r)
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! dr r 2
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!
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! dg(r) k 4 alpha
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! ----- = - - g(r) + ( e - v(r) + -------- ) ----- f(r)
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! dr r alpha**2 2
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!
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! where
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! alpha is the fine structure constant
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! f(r) is r*minor component
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! g(r) is r*major component
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! k is quantum number
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! k = - (l+1) if j = l+0.5
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! k = + l if j = l-0.5
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! IMPORTANT: on output, snl(:,1) contains the MAJOR component
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! snl(:,2) contains the MINOR component
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!
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!----------------------------------------------------------------------------
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!
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use kinds, only : DP
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use ld1inc, only : cau_fact, zed
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implicit none
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integer :: idim1
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real(DP) :: r(idim1), & ! the radial mesh
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rab(idim1), & ! derivative of the radial mesh
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ruae(idim1), & ! the all electron potential
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snl(idim1,2) ! the wavefunction
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real(DP) :: e0, & ! the starting energy eigenvalue
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dx, & ! dx mesh value
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jcur ! the j of the state
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integer :: mesh, & ! the dimension of the mesh
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lcur ! the l of the state
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real(DP) :: tbya, abyt, &
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zz(idim1,2,2), &
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tolinf,alpha2,alpha, &
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yy(idim1,2), &
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gamma0, &
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vzero, &
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f0,f1,f2,g0,g1,g2, &
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ecur
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real(DP) :: r2(idim1), f(idim1), int_0_inf_dr
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integer :: ir, & ! counter
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kcur ! current k
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!
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! r o u t i n e i n i t i a l i s a t i o n
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! set ( 2 / fine structure constant )
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!tbya = 2.0_DP * 137.04_DP
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tbya = 2.0_DP * cau_fact
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! set ( fine structure constant / 2 )
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abyt = 1.0_DP / tbya
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r2=r**2
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if (jcur.eq.lcur+0.5_DP) then
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kcur = - ( lcur + 1 )
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else
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kcur = lcur
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endif
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!
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! set initial upper and lower bounds for the eigen value
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ecur=e0
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!
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yy = 0.0_DP
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!
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! define the zz array
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! ===================
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!
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do ir = 1,mesh
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zz(ir,1,1) = rab(ir) * DBLE(kcur) / r(ir)
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zz(ir,2,2) = - zz(ir,1,1)
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zz(ir,1,2) = - rab(ir) * ( ecur - ruae(ir) ) * abyt
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zz(ir,2,1) = - zz(ir,1,2) + rab(ir) * tbya
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enddo
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!
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! ===========================================================
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! analytic start up of minor and major components from origin
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! ===========================================================
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!
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! with finite nucleus so potential constant at origin we have
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!
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! f(r) = sum_n f_n r ** ( ig + n )
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! g(r) = sum_n g_n r ** ( ig + n )
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!
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! with
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!
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! f_n+1 = - (ecur-v(0)) * abyt * g_n / ( ig - kcur + n + 1 )
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! g_n+1 = (ecur-v(0)+tbya**2 ) * abyt * f_n / ( ig + kcur + n + 1)
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!
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! if kcur > 0 ig = + kcur , f_0 = 1 , g_0 = 0
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! if kcur < 0 ig = - kcur , f_0 = 0 , g_1 = 1
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!
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!vzero = ruae(1)
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!
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! set f0 and g0
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!if ( kcur .lt. 0 ) then
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! ig = - kcur
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! f0 = 0
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! g0 = 1
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!else
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! ig = kcur
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! f0 = 1
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! g0 = 0
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!endif
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!
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!f1 = - (ecur-vzero) * abyt * g0 / DBLE( ig - kcur + 1 )
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!g1 = (ecur-vzero+tbya**2) * abyt * f0 / DBLE( ig + kcur + 1 )
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!f2 = - (ecur-vzero) * abyt * g1 / DBLE( ig - kcur + 2 )
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!g2 = (ecur-vzero+tbya**2) * abyt * f1 / DBLE( ig + kcur + 2 )
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!
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!
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!do ir = 1,5
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! yy(ir,1) = r(ir)**ig * ( f0 + r(ir) * ( f1 + r(ir) * f2 ) )
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! yy(ir,2) = r(ir)**ig * ( g0 + r(ir) * ( g1 + r(ir) * g2 ) )
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!enddo
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!
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! The following boundary conditions are for the Coulomb nuclear potential
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! ADC 05/10/2007
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!
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vzero = ruae(1)+zed*2.0_DP/r(1)
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!
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gamma0=sqrt(kcur**2-4.0_DP*(abyt*zed)**2)
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if ( kcur .lt. 0 ) then
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f0 = (kcur+gamma0)/(2.0_DP*abyt*zed)
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g0 = 1.0_DP
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else
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f0 = 1.0_DP
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g0 = (kcur-gamma0)/(2.0_DP*abyt*zed)
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endif
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f1 = - (ecur-vzero) * abyt * g0 / ( gamma0 - kcur + 1 )
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g1 = (ecur-vzero+tbya**2) * abyt * f0 / ( gamma0 + kcur + 1 )
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f2 = - (ecur-vzero) * abyt * g1 / ( gamma0 - kcur + 2 )
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g2 = (ecur-vzero+tbya**2) * abyt * f1 / ( gamma0 + kcur + 2 )
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do ir = 1,5
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yy(ir,1) = r(ir)**gamma0 * ( f0 + r(ir) * ( f1 + r(ir) * f2 ) )
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yy(ir,2) = r(ir)**gamma0 * ( g0 + r(ir) * ( g1 + r(ir) * g2 ) )
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enddo
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! ===========================
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! outward integration to mesh
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! ===========================
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!
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! fifth order predictor corrector integration routine
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call cfdsol(zz,yy,6,mesh,idim1)
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!
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! =======================================================
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! copy the wavefunction
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! =======================================================
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!
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snl=0.0_DP
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do ir=1,mesh
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snl(ir,2)=yy(ir,1)
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snl(ir,1)=yy(ir,2)
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enddo
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return
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end subroutine dir_outward
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