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ECMD

This commit is contained in:
Pierre-Francois Loos 2019-07-15 12:07:54 +02:00
parent ab7a4609b7
commit 4d6e969a54
8 changed files with 303 additions and 51 deletions
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34
input/basis
View File

@ -1,9 +1,29 @@
1 3
S 3 1.00
38.3600000 0.0238090
5.7700000 0.1548910
1.2400000 0.4699870
1 6
S 8 1.00
17880.0000000 0.0007380
2683.0000000 0.0056770
611.5000000 0.0288830
173.5000000 0.1085400
56.6400000 0.2909070
20.4200000 0.4483240
7.8100000 0.2580260
1.6530000 0.0150630
S 8 1.00
17880.0000000 -0.0001720
2683.0000000 -0.0013570
611.5000000 -0.0067370
173.5000000 -0.0276630
56.6400000 -0.0762080
20.4200000 -0.1752270
7.8100000 -0.1070380
1.6530000 0.5670500
S 1 1.00
0.2976000 1.0000000
0.4869000 1.0000000
P 3 1.00
28.3900000 0.0460870
6.2700000 0.2401810
1.6950000 0.5087440
P 1 1.00
1.2750000 1.0000000
0.4317000 1.0000000
D 1 1.00
2.2020000 1.0000000

4
input/molecule
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@ -1,4 +1,4 @@
# nAt nEla nElb nCore nRyd
1 1 1 0 0
1 5 5 0 0
# Znuc x y z
He 0.0 0.0 0.0
Ne 0.0 0.0 0.0

34
input/weight
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@ -1,9 +1,29 @@
1 3
S 3 1.00
38.3600000 0.0238090
5.7700000 0.1548910
1.2400000 0.4699870
1 6
S 8 1.00
17880.0000000 0.0007380
2683.0000000 0.0056770
611.5000000 0.0288830
173.5000000 0.1085400
56.6400000 0.2909070
20.4200000 0.4483240
7.8100000 0.2580260
1.6530000 0.0150630
S 8 1.00
17880.0000000 -0.0001720
2683.0000000 -0.0013570
611.5000000 -0.0067370
173.5000000 -0.0276630
56.6400000 -0.0762080
20.4200000 -0.1752270
7.8100000 -0.1070380
1.6530000 0.5670500
S 1 1.00
0.2976000 1.0000000
0.4869000 1.0000000
P 3 1.00
28.3900000 0.0460870
6.2700000 0.2401810
1.6950000 0.5087440
P 1 1.00
1.2750000 1.0000000
0.4317000 1.0000000
D 1 1.00
2.2020000 1.0000000

23
src/QuAcK/LSD_SR.f
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@ -1,25 +1,3 @@
ccc example: use the subroutine lsdsr to compute the complementary
ccc short-range exchange-correlation energy 'excsr' and
ccc the corresponding up and down potentials 'vxcsrup','vxcsrdown'
ccc at polarization z=0.7, cutoff mu=0.5, and for 0.2 < rs < 20,
ccc and write them on a file
c program testex
c implicit none
c double precision z,rs,mu
c double precision excsr,vxcsrup,vxcsrdown
c integer i
c open(9,file='testex',status='unknown')
c z=0.7d0
c mu=0.5d0
c do i=1,100
c rs=0.2*i
c call lsdsr(rs,z,mu,excsr,vxcsrup,vxcsrdown)
c write(9,*) rs,excsr,vxcsrup,vxcsrdown
c enddo
c stop
c end
subroutine lsdsr(rs,z,mu,excsr,vxcsrup,vxcsrdown)
ccc Hartree atomic units used
ccc for given density parameter 'rs', spin polarization 'z'
@ -30,6 +8,7 @@ ccc interacting electron gas) => 'excsr'
ccc and the corresponding exchange-correlation potentials for
ccc spin-up and spin-down electrons => 'vxcsrup','vxcsrdown'
ccc from Paziani, Moroni, Gori-Giorgi, and Bachelet, cond-mat/0601353
implicit none
double precision rs,z,mu,excsr,vxcsrup,vxcsrdown
double precision eclr,exlr,ec,ecd,ecz,ex

2
src/QuAcK/basis_correction.f90
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@ -50,7 +50,7 @@ subroutine basis_correction(nBas,nO,nShell,CenterShell,TotAngMomShell,KShell,DSh
! Set quadrature grid
SGn = 0
SGn = 1
call read_grid(SGn,nRad,nAng,nGrid)

21
src/QuAcK/ec_srlda.f90
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@ -15,31 +15,38 @@ subroutine ec_srlda(nGrid,weight,rho,mu)
! Local variables
integer :: iG
double precision :: r
double precision :: r,ra,rb
double precision :: rs
double precision :: ecsr
double precision :: ec,vcup,vcdw
double precision :: ec_lda,ecmd_lda
double precision :: ec,ecmd,vcup,vcdw
! Initialization
ecsr = 0d0
ec_lda = 0d0
ecmd_lda = 0d0
do iG=1,ngrid
r = max(0d0,rho(iG))
ra = 0.5d0*r
rb = 0.5d0*r
if(r > threshold) then
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
ecsr = ecsr + weight(iG)*ec*r
call ESRC_MD_LDAERF(mu(iG),ra,rb,.true.,ecmd)
ec_lda = ec_lda + weight(iG)*ec*r
ecmd_lda = ecmd_lda + weight(iG)*ecmd*r
end if
end do
write(*,'(A32,1X,F16.10)') 'ecsr = ',ecsr
write(*,*)
write(*,'(A32,1X,F16.10)') 'Ec(sr-LDA) = ',ec_lda
write(*,'(A32,1X,F16.10)') 'Ecmd(sr-LDA) = ',ec_lda + ecmd_lda
write(*,*)
end subroutine ec_srlda

200
src/QuAcK/ecmd_lda.f90 Normal file
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@ -0,0 +1,200 @@
!****************************************************************************
subroutine ESRC_MD_LDAERF (mu,rho_a,rho_b,dospin,e)
!*****************************************************************************
! Short-range spin-dependent LDA correlation functional with multideterminant reference
! for OEP calculations from Section V of
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
!
! Input: rhot : total density
! rhos : spin density
! mu : Interation parameter
! dospin : use spin density
!
! Ouput: e : energy
!
! Created: 26-08-11, J. Toulouse
!*****************************************************************************
implicit none
double precision, intent(in) :: rho_a,rho_b,mu
logical, intent(in) :: dospin
double precision, intent(out):: e
double precision :: e1
double precision :: rhoa,rhob
double precision :: rhot, rhos
rhoa=max(rho_a,1.0d-15)
rhob=max(rho_b,1.0d-15)
rhot = rhoa + rhob
rhos = rhoa - rhob
call ec_only_lda_sr(mu,rho_a,rho_b,e1)
if(isnan(e1))then
print*,'e1 is NaN'
print*,mu,rho_a,rho_b
stop
endif
e1 = 0d0
call DELTA_LRSR_LDAERF (rhot,rhos,mu,dospin,e)
if(isnan(e))then
print*,'e is NaN'
print*,mu,rhot,rhos
stop
endif
e = e1 + e
end
!****************************************************************************
subroutine DELTA_LRSR_LDAERF (rhot,rhos,mu,dospin,e)
!*****************************************************************************
! LDA approximation to term Delta_(LR-SR) from Eq. 42 of
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
!
! Input: rhot : total density
! rhos : spin density
! mu : Interation parameter
! dospin : use spin density
!
! Ouput: e : energy
!
! Warning: not tested for z != 0
!
! Created: 26-08-11, J. Toulouse
!*****************************************************************************
implicit none
double precision rhot, rhos, mu
logical dospin
double precision e
double precision f13, f83, pi, rsfac, alpha2
double precision rs, rs2, rs3
double precision rhoa, rhob, z, z2, onepz, onemz, zp, zm, phi8
double precision g0s,g0f
double precision bd2, bd3
double precision c45, c4, c5
double precision bc2, bc4, bc3t, bc5t, d0
double precision delta2,delta3,delta4,delta5,delta6
double precision delta
parameter(f13 = 0.333333333333333d0)
parameter(f83 = 2.6666666666666665d0)
parameter(pi = 3.141592653589793d0)
parameter(rsfac = 0.620350490899400d0)
parameter(alpha2 = 0.2715053589826032d0)
rs = rsfac/(rhot**f13)
rs2 = rs*rs
rs3 = rs2*rs
! Spin-unpolarized case
if (.not.dospin) then
z = 0.d0
! Spin-polarized case
else
rhoa=max((rhot+rhos)*.5d0,1.0d-15)
rhob=max((rhot-rhos)*.5d0,1.0d-15)
z=min((rhoa-rhob)/(rhoa+rhob),0.9999999999d0)
endif
z2=z*z
bd2=dexp(-0.547d0*rs)*(-0.388d0*rs+0.676*rs2)/rs2
bd3=dexp(-0.31d0*rs)*(-4.95d0*rs+rs2)/rs3
onepz=1.d0+z
onemz=1.d0-z
phi8=0.5d0*(onepz**f83+onemz**f83)
zp=onepz/2.d0
zm=onemz/2.d0
c45=(zp**2)*g0s(rs*zp**(-f13))+(zm**2)*g0s(rs*zm**(-f13))
c4=c45+(1.d0-z2)*bd2-phi8/(5.d0*alpha2*rs2)
c5=c45+(1.d0-z2)*bd3
bc2=-3.d0*(1-z2)*(g0f(rs)-0.5d0)/(8.d0*rs3)
bc4=-9.d0*c4/(64.d0*rs3)
bc3t=-(1-z2)*g0f(rs)*(2.d0*dsqrt(2.d0)-1)/(2.d0*dsqrt(pi)*rs3)
bc5t = -3.d0*c5*(3.d0-dsqrt(2.d0))/(20.d0*dsqrt(2.d0*pi)*rs3)
d0=(0.70605d0+0.12927d0*z2)*rs
delta2=0.073867d0*(rs**(1.5d0))
delta3=4*(d0**6)*bc3t+(d0**8)*bc5t;
delta4=4*(d0**6)*bc2+(d0**8)*bc4;
delta5=(d0**8)*bc3t;
delta6=(d0**8)*bc2;
delta=(delta2*(mu**2)+delta3*(mu**3)+delta4*(mu**4)+delta5*(mu**5)+delta6*(mu**6))/((1+(d0**2)*(mu**2))**4)
! multiply by rhot to get energy density
! e=delta*rhot
e=delta
end
!*****************************************************************************
double precision function g0s(rs)
!*****************************************************************************
! g"(0,rs,z=1) from Eq. 32 of
! Paziani, Moroni, Gori-Giorgi and Bachelet, PRB 73, 155111 (2006)
!
! Created: 26-08-11, J. Toulouse
!*****************************************************************************
implicit none
double precision rs
double precision rs2, f53, alpha2
parameter(f53 = 1.6666666666666667d0)
parameter(alpha2 = 0.2715053589826032d0)
rs2=rs*rs
g0s=(2.d0**f53)*(1.d0-0.02267d0*rs)/((5.d0*alpha2*rs2)*(1.d0+0.4319d0*rs+0.04d0*rs2))
end
double precision function g0f(x)
!cc on-top pair-distribution function
!cc Gori-Giorgi and Perdew, PRB 64, 155102 (2001)
!cc x -> rs
implicit none
double precision C0f,D0f,E0f,F0f,x
C0f = 0.0819306d0
D0f = 0.752411d0
E0f = -0.0127713d0
F0f = 0.00185898d0
g0f=(1.d0-(0.7317d0-D0f)*x+C0f*x**2+E0f*x**3+ &
F0f*x**4)*exp(-abs(D0f)*x)/2.d0
return
end
subroutine ec_only_lda_sr(mu,rho_a,rho_b,ec)
implicit none
include 'parameters.h'
double precision, intent(out) :: ec
double precision, intent(in) :: mu,rho_a,rho_b
! Double precision numbers
double precision :: rsfac,rho,rs,rhoa,rhob,z
double precision :: eccoul, ecd, ecz, ecdd, eczd
double precision :: eclr
rsfac = (3.0d0/(4.0d0*pi))**(1d0/3d0)
ec = 0.d0
! Test on density
rho = rho_a + rho_b
if (dabs(rho).ge.1.d-12) then
rs=rsfac/(rho**(1d0/3d0))
rhoa=max(rho_a,1.0d-15)
rhob=max(rho_b,1.0d-15)
z=(rhoa-rhob)/(rhoa+rhob)
call ecPW(rs,z,eccoul,ecd,ecz,ecdd,eczd)
call ecorrlr(rs,z,mu,eclr)
ec=(eccoul-eclr)*rho
endif
end

36
src/QuAcK/fc_srlda.f90
View File

@ -18,9 +18,10 @@ subroutine fc_srlda(nBas,nGrid,weight,MO,rho,mu,eG0W0)
! Local variables
integer :: iG,p
double precision :: r
double precision :: rs
double precision :: ec,vcup,vcdw
double precision :: r,ra,rb,rap,ram
double precision :: rs,rsp,rsm
double precision :: ec,ecp,ecm,vcup,vcdw
double precision,parameter :: delta = 1d-6
double precision,allocatable :: de(:)
! Memory allocation
@ -33,13 +34,38 @@ subroutine fc_srlda(nBas,nGrid,weight,MO,rho,mu,eG0W0)
do iG=1,ngrid
r = max(0d0,rho(iG))
r = max(0d0,rho(iG))
ra = 0.5d0*r
rb = 0.5d0*r
if(r > threshold) then
rs = (4d0*pi*r/3d0)**(-1d0/3d0)
call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
! call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
if(abs(ra) > delta) then
rap = ra + delta
ram = ra - delta
rsp = (4d0*pi*rap/3d0)**(-1d0/3d0)
rsm = (4d0*pi*ram/3d0)**(-1d0/3d0)
! call lsdsr(rsp,0d0,mu(iG),ecp,vcup,vcdw)
! call lsdsr(rsm,0d0,mu(iG),ecm,vcup,vcdw)
call lsdsr(rs,0d0,mu(iG),ec,vcup,vcdw)
! call ESRC_MD_LDAERF(mu(iG),rap,rb,.true.,ecp)
! call ESRC_MD_LDAERF(mu(iG),ram,rb,.true.,ecm)
! vcup = (ecp - ecm)/(2d0*delta)
else
vcup = 0d0
end if
do p=1,nBas