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pCCD and ppRPA

This commit is contained in:
Pierre-Francois Loos 2020-03-24 12:28:56 +01:00
parent a8d26d6e36
commit 5ef788cbc9
22 changed files with 117 additions and 116 deletions
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2
examples/molecule.LiF
View File

@ -2,4 +2,4 @@
2 6 6 0 0
# Znuc x y z
Li 0. 0. 0.
F 0. 0. 3.5
F 0. 0. 2.954767548731

2
examples/molecule.LiH
View File

@ -2,4 +2,4 @@
2 2 2 0 0
# Znuc x y z
Li 0. 0. 0.
H 0. 0. 3.5
H 0. 0. 3.051018991463

46
input/basis
View File

@ -1,24 +1,30 @@
1 9
S 4
1 234.0000000 0.0025870
2 35.1600000 0.0195330
3 7.9890000 0.0909980
4 2.2120000 0.2720500
1 6
S 8
1 17880.0000000 0.0007380
2 2683.0000000 0.0056770
3 611.5000000 0.0288830
4 173.5000000 0.1085400
5 56.6400000 0.2909070
6 20.4200000 0.4483240
7 7.8100000 0.2580260
8 1.6530000 0.0150630
S 8
1 17880.0000000 -0.0001720
2 2683.0000000 -0.0013570
3 611.5000000 -0.0067370
4 173.5000000 -0.0276630
5 56.6400000 -0.0762080
6 20.4200000 -0.1752270
7 7.8100000 -0.1070380
8 1.6530000 0.5670500
S 1
1 0.6669000 1.0000000
S 1
1 0.2089000 1.0000000
S 1
1 0.0513800 1.0000000
1 0.4869000 1.0000000
P 3
1 28.3900000 0.0460870
2 6.2700000 0.2401810
3 1.6950000 0.5087440
P 1
1 3.0440000 1.0000000
P 1
1 0.7580000 1.0000000
P 1
1 0.1993000 1.0000000
1 0.4317000 1.0000000
D 1
1 1.9650000 1.0000000
D 1
1 0.4592000 1.0000000
1 2.2020000 1.0000000

4
input/methods
View File

@ -3,7 +3,7 @@
# MP2 MP3 MP2-F12
T F F
# CCD CCSD CCSD(T) drCCD rCCD lCCD pCCD
F F F F F F F
F F F F F F T
# CIS RPA RPAx ppRPA ADC
F F F F F
# G0F2 evGF2 G0F3 evGF3
@ -11,6 +11,6 @@
# G0W0 evGW qsGW
F F F
# G0T0 evGT qsGT
T F F
F F F
# MCMP2
F

4
input/molecule
View File

@ -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

2
input/molecule.xyz
View File

@ -1,3 +1,3 @@
1
He 0.0000000000 0.0000000000 0.0000000000
Ne 0.0000000000 0.0000000000 0.0000000000

2
input/options
View File

@ -9,7 +9,7 @@
# GF: maxSCF thresh DIIS n_diis lin renorm
256 0.00001 T 5 T 3
# GW: maxSCF thresh DIIS n_diis COHSEX SOSEX BSE TDA G0W GW0 lin eta
256 0.00001 T 5 F F T F F F T 0.000
256 0.00001 T 5 F F F F F F F 0.000
# ACFDT: AC Kx XBS
T F T
# MCMP2: nMC nEq nWalk dt nPrint iSeed doDrift

46
input/weight
View File

@ -1,24 +1,30 @@
1 9
S 4
1 234.0000000 0.0025870
2 35.1600000 0.0195330
3 7.9890000 0.0909980
4 2.2120000 0.2720500
1 6
S 8
1 17880.0000000 0.0007380
2 2683.0000000 0.0056770
3 611.5000000 0.0288830
4 173.5000000 0.1085400
5 56.6400000 0.2909070
6 20.4200000 0.4483240
7 7.8100000 0.2580260
8 1.6530000 0.0150630
S 8
1 17880.0000000 -0.0001720
2 2683.0000000 -0.0013570
3 611.5000000 -0.0067370
4 173.5000000 -0.0276630
5 56.6400000 -0.0762080
6 20.4200000 -0.1752270
7 7.8100000 -0.1070380
8 1.6530000 0.5670500
S 1
1 0.6669000 1.0000000
S 1
1 0.2089000 1.0000000
S 1
1 0.0513800 1.0000000
1 0.4869000 1.0000000
P 3
1 28.3900000 0.0460870
2 6.2700000 0.2401810
3 1.6950000 0.5087440
P 1
1 3.0440000 1.0000000
P 1
1 0.7580000 1.0000000
P 1
1 0.1993000 1.0000000
1 0.4317000 1.0000000
D 1
1 1.9650000 1.0000000
D 1
1 0.4592000 1.0000000
1 2.2020000 1.0000000

2
src/QuAcK/CCD.f90
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@ -48,7 +48,7 @@ subroutine CCD(maxSCF,thresh,max_diis,nBas,nEl,ERI,ENuc,ERHF,eHF)
double precision,allocatable :: r2(:,:,:,:)
double precision,allocatable :: t2(:,:,:,:)
integer :: n_diis
integer :: n_diis,i,j,a,b
double precision :: rcond
double precision,allocatable :: error_diis(:,:)
double precision,allocatable :: t_diis(:,:)

3
src/QuAcK/G0T0.f90
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@ -137,6 +137,9 @@ subroutine G0T0(doACFDT,exchange_kernel,doXBS,BSE,TDA,singlet_manifold,triplet_m
! Compute T-matrix version of the self-energy
!----------------------------------------------
rho1s = 0d0
rho1t = 0d0
call self_energy_Tmatrix_diag(eta,nBas,nC,nO,nV,nR,nOOs,nVVs,nOOt,nVVt,eHF(:), &
Omega1s(:),rho1s(:,:,:),Omega2s(:),rho2s(:,:,:), &
Omega1t(:),rho1t(:,:,:),Omega2t(:),rho2t(:,:,:), &

7
src/QuAcK/QuAcK.f90
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@ -367,6 +367,7 @@ program QuAcK
call cpu_time(start_CCD)
call CCD(maxSCF_CC,thresh_CC,n_diis_CC,nBas,nEl,ERI_MO_basis,ENuc,ERHF,eHF)
call cpu_time(end_CCD)
t_CCD = end_CCD - start_CCD
write(*,'(A65,1X,F9.3,A8)') 'Total CPU time for CCD = ',t_CCD,' seconds'
@ -669,10 +670,10 @@ program QuAcK
if(doG0T0) then
call cpu_time(start_G0T0)
! call G0T0(doACFDT,exchange_kernel,doXBS,BSE,TDA, &
! singlet_manifold,triplet_manifold,linGW,eta, &
! nBas,nC(1),nO(1),nV(1),nR(1),nS(1),ENuc,ERHF,ERI_MO_basis,eHF)
call soG0T0(eta,nBas,nC(1),nO(1),nV(1),nR(1),ENuc,ERHF,ERI_MO_basis,eHF)
! call G0T0(doACFDT,exchange_kernel,doXBS,BSE,TDA, &
! singlet_manifold,triplet_manifold,linGW,eta, &
! nBas,nC(1),nO(1),nV(1),nR(1),nS(1),ENuc,ERHF,ERI_MO_basis,eHF)
call cpu_time(end_G0T0)

36
src/QuAcK/excitation_density_Tmatrix.f90
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@ -46,9 +46,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
do d=c,nBas-nR
cd = cd + 1
rho1(p,i,ab) = rho1(p,i,ab) &
! + ERI(p,i,c,d)*X1(cd,ab)
+ (ERI(p,i,c,d) + ERI(p,i,d,c))*X1(cd,ab) &
/sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(c,d)))
+ ERI(p,i,c,d)*X1(cd,ab)
! + (ERI(p,i,c,d) + ERI(p,i,d,c))*X1(cd,ab) &
! /sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(c,d)))
end do
end do
@ -58,9 +58,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
do l=k,nO
kl = kl + 1
rho1(p,i,ab) = rho1(p,i,ab) &
! + ERI(p,i,k,l)*Y1(kl,ab)
+ (ERI(p,i,k,l) + ERI(p,i,l,k))*Y1(kl,ab) &
/sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(k,l)))
+ ERI(p,i,k,l)*Y1(kl,ab)
! + (ERI(p,i,k,l) + ERI(p,i,l,k))*Y1(kl,ab) &
! /sqrt((1d0 + Kronecker_delta(p,i))*(1d0 + Kronecker_delta(k,l)))
end do
end do
@ -76,9 +76,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
do d=c,nBas-nR
cd = cd + 1
rho2(p,a,ij) = rho2(p,a,ij) &
! + ERI(p,nO+a,c,d)*X2(cd,ij)
+ (ERI(p,nO+a,c,d) + ERI(p,nO+a,d,c))*X2(cd,ij) &
/sqrt((1d0 + Kronecker_delta(p,nO+a))*(1d0 + Kronecker_delta(c,d)))
+ ERI(p,nO+a,c,d)*X2(cd,ij)
! + (ERI(p,nO+a,c,d) + ERI(p,nO+a,d,c))*X2(cd,ij) &
! /sqrt((1d0 + Kronecker_delta(p,nO+a))*(1d0 + Kronecker_delta(c,d)))
end do
end do
@ -88,9 +88,9 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
do l=k,nO
kl = kl + 1
rho2(p,a,ij) = rho2(p,a,ij) &
! + ERI(p,nO+a,k,l)*Y2(kl,ij)
+ (ERI(p,nO+a,k,l) + ERI(p,nO+a,l,k))*Y2(kl,ij) &
/sqrt((1d0 + Kronecker_delta(p,nO+a))*(1d0 + Kronecker_delta(k,l)))
+ ERI(p,nO+a,k,l)*Y2(kl,ij)
! + (ERI(p,nO+a,k,l) + ERI(p,nO+a,l,k))*Y2(kl,ij) &
! /sqrt((1d0 + Kronecker_delta(p,nO+a))*(1d0 + Kronecker_delta(k,l)))
end do
end do
@ -118,7 +118,6 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
cd = cd + 1
rho1(p,i,ab) = rho1(p,i,ab) &
+ (ERI(p,i,c,d) - ERI(p,i,d,c))*X1(cd,ab)
print*,rho1(p,i,ab),ERI(p,i,c,d),X1(cd,ab)
end do
end do
@ -129,7 +128,6 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
kl = kl + 1
rho1(p,i,ab) = rho1(p,i,ab) &
+ (ERI(p,i,k,l) - ERI(p,i,l,k))*Y1(kl,ab)
print*,rho1(p,i,ab),ERI(p,i,k,l),Y1(kl,ab)
end do
end do
@ -222,16 +220,6 @@ subroutine excitation_density_Tmatrix(ispin,nBas,nC,nO,nV,nR,nOO,nVV,ERI,X1,Y1,r
end do
! do p=nC+1,nBas-nR
! do i=nC+1,nO
! do ab=1,nVV
! print*,p,i,ab,rho1(p,i,ab)
! end do
! end do
! end do
! call matout(nVV,nOO,Y1)
end if
end subroutine excitation_density_Tmatrix

2
src/QuAcK/linear_response_C_pp.f90
View File

@ -25,7 +25,7 @@ subroutine linear_response_C_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,C_pp)
! Define the chemical potential
eF = e(nO) + e(nO+1)
! eF = 0d0
eF = 0d0
! Build C matrix for the singlet manifold

2
src/QuAcK/linear_response_D_pp.f90
View File

@ -25,7 +25,7 @@ subroutine linear_response_D_pp(ispin,nBas,nC,nO,nV,nR,nOO,nVV,e,ERI,D_pp)
! Define the chemical potential
eF = e(nO) + e(nO+1)
! eF = 0d0
eF = 0d0
! Build the D matrix for the singlet manifold

27
src/QuAcK/linear_response_pp.f90
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@ -1,5 +1,5 @@
subroutine linear_response_pp(ispin,ortho_eigvec,BSE,nBas,nC,nO,nV,nR,nOO,nVV, &
e,ERI,Omega1,X1,Y1,Omega2,X2,Y2,EcppRPA)
e,ERI,Omega1,X1,Y1,Omega2,X2,Y2,EcRPA)
! Compute the p-p channel of the linear response: see Scuseria et al. JCP 139, 104113 (2013)
@ -22,6 +22,8 @@ subroutine linear_response_pp(ispin,ortho_eigvec,BSE,nBas,nC,nO,nV,nR,nOO,nVV, &
integer :: ab,cd,ij,kl
integer :: p,q,r,s
double precision :: trace_matrix
double precision :: EcRPA1
double precision :: EcRPA2
double precision,allocatable :: B(:,:)
double precision,allocatable :: C(:,:)
double precision,allocatable :: D(:,:)
@ -37,7 +39,7 @@ subroutine linear_response_pp(ispin,ortho_eigvec,BSE,nBas,nC,nO,nV,nR,nOO,nVV, &
double precision,intent(out) :: Omega2(nOO)
double precision,intent(out) :: X2(nVV,nOO)
double precision,intent(out) :: Y2(nOO,nOO)
double precision,intent(out) :: EcppRPA
double precision,intent(out) :: EcRPA
! Memory allocation
@ -117,10 +119,11 @@ subroutine linear_response_pp(ispin,ortho_eigvec,BSE,nBas,nC,nO,nV,nR,nOO,nVV, &
! print*, 'pp-RPA matrix'
! call matout(nOO+nVV,nOO+nVV,M(:,:))
! write(*,*)
! Diagonalize the p-h matrix
call diagonalize_general_matrix(nOO+nVV,M,Omega,Z)
if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV,M,Omega,Z)
! write(*,*) 'pp-RPA excitation energies'
! call matout(nOO+nVV,1,Omega(:))
@ -132,11 +135,11 @@ subroutine linear_response_pp(ispin,ortho_eigvec,BSE,nBas,nC,nO,nV,nR,nOO,nVV, &
! Compute the RPA correlation energy
! EcppRPA = 0.5d0*( sum(Omega1(:)) - sum(Omega2(:)) - trace_matrix(nVV,C(:,:)) - trace_matrix(nOO,D(:,:)) )
! print*,+sum(Omega1(:)),- trace_matrix(nVV,C(:,:))
! print*,-sum(Omega2(:)),- trace_matrix(nOO,D(:,:))
EcppRPA = +sum(Omega1(:)) - trace_matrix(nVV,C(:,:))
! EcppRPA = -sum(Omega2(:)) - trace_matrix(nOO,D(:,:))
EcRPA = 0.5d0*( sum(Omega1(:)) - sum(Omega2(:)) - trace_matrix(nVV,C(:,:)) - trace_matrix(nOO,D(:,:)) )
EcRPA1 = +sum(Omega1(:)) - trace_matrix(nVV,C(:,:))
EcRPA2 = -sum(Omega2(:)) - trace_matrix(nOO,D(:,:))
if(abs(EcRPA - EcRPA1) > 1d-10 .or. abs(EcRPA - EcRPA2) > 1d-10) &
print*,'!!! Issue in pp-RPA linear reponse calculation RPA1 != RPA2 !!!'
! write(*,*)'X1'
! call matout(nVV,nVV,X1)
@ -147,12 +150,4 @@ subroutine linear_response_pp(ispin,ortho_eigvec,BSE,nBas,nC,nO,nV,nR,nOO,nVV, &
! write(*,*)'Y2'
! call matout(nOO,nOO,Y2)
! print*,'Ec(pp-RPA) = ',EcppRPA
! print*,'Eigenvalues'
! call matout(nOO+nVV,1,Omega)
! print*,'Eigenvectors'
! call matout(nOO+nVV,nOO+nVV,matmul(transpose(Z),Z))
end subroutine linear_response_pp

9
src/QuAcK/pCCD.f90
View File

@ -53,6 +53,8 @@ subroutine pCCD(maxSCF,thresh,max_diis,nBas,nC,nO,nV,nR,ERI,ENuc,ERHF,eHF)
allocate(delta_OOVV(nO,nV))
delta_OOVV(:,:) = 0d0
do i=nC+1,nO
do a=1,nV-nR
delta_OOVV(i,a) = 2d0*(eHF(nO+a) - eHF(i))
@ -63,6 +65,11 @@ subroutine pCCD(maxSCF,thresh,max_diis,nBas,nC,nO,nV,nR,ERI,ENuc,ERHF,eHF)
allocate(OOOO(nO,nO),OOVV(nO,nV),OVOV(nO,nV),OVVO(nO,nV),VVVV(nV,nV))
OOOO(:,:) = 0d0
OOVV(:,:) = 0d0
OVVO(:,:) = 0d0
VVVV(:,:) = 0d0
do i=nC+1,nO
do j=nC+1,nO
OOOO(i,j) = ERI(i,i,j,j)
@ -141,7 +148,7 @@ subroutine pCCD(maxSCF,thresh,max_diis,nBas,nC,nO,nV,nR,ERI,ENuc,ERHF,eHF)
- 2d0*(2d0*OVOV(i,a) - OVVO(i,a) - OOVV(i,a)*t(i,a))*t(i,a)
do j=nC+1,nO
r(i,a) = r(i,a) - 2d0*OOVV(j,a)*t(j,a)*t(i,a) + OOOO(j,i)*t(j,a) + y(i,j)*t(j,a)
r(i,a) = r(i,a) - 2d0*OOVV(j,a)*t(j,a)*t(i,a) + OOOO(j,i)*t(j,a) + y(i,j)*t(j,a)
end do
do b=1,nV-nR

2
src/QuAcK/print_excitation.f90
View File

@ -7,7 +7,7 @@ subroutine print_excitation(method,ispin,nS,Omega)
! Input variables
character*6,intent(in) :: method
character*12,intent(in) :: method
integer,intent(in) :: ispin,nS
double precision,intent(in) :: Omega(nS)

4
src/QuAcK/self_energy_Tmatrix_diag.f90
View File

@ -72,7 +72,7 @@ subroutine self_energy_Tmatrix_diag(eta,nBas,nC,nO,nV,nR,nOOs,nVVs,nOOt,nVVt,e,
do i=nC+1,nO
do cd=1,nVVt
eps = e(p) + e(i) - Omega1t(cd)
SigT(p) = SigT(p) + rho1t(p,i,cd)*rho1t(p,i,cd)/eps
! SigT(p) = SigT(p) + rho1t(p,i,cd)*rho1t(p,i,cd)/eps
enddo
enddo
enddo
@ -83,7 +83,7 @@ subroutine self_energy_Tmatrix_diag(eta,nBas,nC,nO,nV,nR,nOOs,nVVs,nOOt,nVVt,e,
do a=1,nV-nR
do kl=1,nOOt
eps = e(p) + e(nO+a) - Omega2t(kl)
SigT(p) = SigT(p) + rho2t(p,a,kl)*rho2t(p,a,kl)/eps
! SigT(p) = SigT(p) + rho2t(p,a,kl)*rho2t(p,a,kl)/eps
enddo
enddo
enddo

13
src/QuAcK/soG0T0.f90
View File

@ -89,31 +89,28 @@ subroutine soG0T0(eta,nBas,nC,nO,nV,nR,ENuc,ERHF,ERI,eHF)
! Compute excitation densities for the T-matrix
call excitation_density_Tmatrix(ispin,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,sERI(:,:,:,:), &
X1(:,:),Y1(:,:),rho1(:,:,:), &
X2(:,:),Y2(:,:),rho2(:,:,:))
X1(:,:),Y1(:,:),rho1(:,:,:),X2(:,:),Y2(:,:),rho2(:,:,:))
!----------------------------------------------
! Compute T-matrix version of the self-energy
!----------------------------------------------
call self_energy_Tmatrix_diag_so(eta,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,seHF(:), &
Omega1(:),rho1(:,:,:), &
Omega2(:),rho2(:,:,:), &
Omega1(:),rho1(:,:,:),Omega2(:),rho2(:,:,:), &
SigT(:))
! Compute renormalization factor for T-matrix self-energy
call renormalization_factor_Tmatrix_so(eta,nBas2,nC2,nO2,nV2,nR2,nOO,nVV,seHF(:), &
Omega1(:),rho1(:,:,:), &
Omega2(:),rho2(:,:,:), &
Omega1(:),rho1(:,:,:),Omega2(:),rho2(:,:,:), &
Z(:))
!----------------------------------------------
! Solve the quasi-particle equation
!----------------------------------------------
eG0T0(:) = seHF(:) + SigT(:)
! eG0T0(:) = seHF(:) + Z(:)*SigT(:)
! eG0T0(:) = seHF(:) + SigT(:)
eG0T0(:) = seHF(:) + Z(:)*SigT(:)
!----------------------------------------------
! Dump results

14
src/QuAcK/sort_ppRPA.f90
View File

@ -74,16 +74,12 @@ subroutine sort_ppRPA(ortho_eigvec,nOO,nVV,Omega,Z,Omega1,X1,Y1,Omega2,X2,Y2)
ab = ab + 1
Omega1(ab) = Omega(pq)
Z1(1:nOO+nVV,ab) = Z(1:nOO+nVV,pq)
! X1(1:nVV,ab) = Z( 1: nVV,pq)
! Y1(1:nOO,ab) = Z(nVV+1:nOO+nVV,pq)
else
ij = ij + 1
Omega2(ij) = Omega(pq)
Z2(1:nOO+nVV,ij) = Z(1:nOO+nVV,pq)
! X2(1:nVV,ij) = Z( 1: nVV,pq)
! Y2(1:nOO,ij) = Z(nVV+1:nOO+nVV,pq)
end if
@ -115,11 +111,13 @@ subroutine sort_ppRPA(ortho_eigvec,nOO,nVV,Omega,Z,Omega1,X1,Y1,Omega2,X2,Y2)
end if
X1(1:nVV,1:nVV) = Z1( 1: nVV,1:nVV)
Y1(1:nOO,1:nVV) = Z1(nVV+1:nOO+nVV,1:nVV)
! Define submatrices X1, Y1, X2, & Y2
X2(1:nVV,1:nOO) = Z2( 1: nVV,1:nOO)
Y2(1:nOO,1:nOO) = Z2(nVV+1:nOO+nVV,1:nOO)
X1(1:nVV,1:nVV) = + Z1( 1: nVV,1:nVV)
Y1(1:nOO,1:nVV) = - Z1(nVV+1:nOO+nVV,1:nVV)
X2(1:nVV,1:nOO) = + Z2( 1: nVV,1:nOO)
Y2(1:nOO,1:nOO) = - Z2(nVV+1:nOO+nVV,1:nOO)
! write(*,*) 'Z1t.M.Z1'
! call matout(nVV,nVV,matmul(matmul(transpose(Z1),M),Z1))

2
src/eDFT/LIM_RKS.f90
View File

@ -73,7 +73,7 @@ subroutine LIM_RKS(x_rung,x_DFA,c_rung,c_DFA,nEns,wEns,nGrid,weight,maxSCF,thres
!------------------------------------------------------------------------
write(*,'(A40)') '*************************************************'
write(*,'(A40)') ' ZERO-WEIGHT CALCULATION '
write(*,'(A40)') ' EQUI-WEIGHT CALCULATION '
write(*,'(A40)') '*************************************************'
wLIM(1:nEns) = 1d0/dble(nEns)

2
src/eDFT/quadrature_grid.f90
View File

@ -66,7 +66,7 @@ subroutine quadrature_grid(nRad,nAng,nGrid,root,weight)
enddo
enddo
! Compute values of the basis functions (and the its gradient if required) at each grid point
! Print grids
20 format(T2,58('-'))
30 format(T20,'Radial Quadrature',/, &