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grid_module.f90
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subroutine grid_setup
call grid_setup_radial !The new radial efficient grid
! call grid_setup_old !The old rectangular awfully slow grid
end subroutine grid_setup
!=========================================================================================
subroutine grid_setup_radial
!..Sets up the radial grid with Becke construction for polyatomic systems
!..Writes basis functions on the grid points
!..Global
use global; use grid_params; use functional_m; use basis_set, only:expo_bas_min
implicit none
!..Local
integer :: Idims(32)
real(dp) :: rsb(105), rsb1, rsb3, rsbi, rsbj, x_be, u_be
real(dp), allocatable :: rrad(:), wrad(:), vrad(:), a_be(:,:)
real(dp), allocatable :: x_tr(:), y_tr(:), z_tr(:), w_tr(:), v_tr(:)
real(dp) :: rgd, xat, yat, zat, wrd3, vrd3, w_at, xx, yy, zz
real(dp), external :: at_weight, at_weight_old, f_bas, f_bas_pot
integer :: i, iat, jat, iele, jele, ilow, irad, iang, ig, igr, ngr, ibs
!..Dimensions for Lebedev angular grids
Idims = (/ 6, 14, 26, 38, 50, 74, 86, 110, 146, 170, 194, 230, 266, 302,&
350, 434, 590, 770, 974, 1202, 1454, 1730, 2030, 2354, 2702, 3074,&
3470, 3890, 4334, 4802, 5294, 5810 /)
!..Slater Bragg Radius for elements in Angstom
rsb = (/ 0.529177D+00,0.31D+00,1.45D+00,1.05D+00,0.85D+00, &
0.70D+00, 0.65D+00, 0.60D+00, 0.50D+00, 0.38D+00, &
1.80D+00, 1.50D+00, 1.25D+00, 1.10D+00, 1.00D+00, &
1.00D+00, 1.00D+00, 0.71D+00, 2.20D+00, 1.80D+00, &
1.60D+00, 1.40D+00, 1.35D+00, 1.40D+00, 1.40D+00, &
1.40D+00, 1.35D+00, 1.35D+00, 1.35D+00, 1.35D+00, &
1.30D+00, 1.25D+00, 1.15D+00, 1.15D+00, 1.15D+00, &
0.88D+00, 2.35D+00, 2.00D+00, 1.80D+00, 1.55D+00, &
1.45D+00, 1.45D+00, 1.35D+00, 1.30D+00, 1.35D+00, &
1.40D+00, 1.60D+00, 1.55D+00, 1.55D+00, 1.45D+00, &
1.45D+00, 1.40D+00, 1.40D+00, 1.08D+00, 2.60D+00, &
2.15D+00, 1.95D+00, 1.85D+00, 1.85D+00, 1.85D+00, &
1.85D+00, 1.85D+00, 1.85D+00, 1.80D+00, 1.75D+00, &
1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, &
1.75D+00, 1.55D+00, 1.45D+00, 1.35D+00, 1.35D+00, &
1.30D+00, 1.35D+00, 1.35D+00, 1.35D+00, 1.50D+00, &
1.90D+00, 1.80D+00, 1.60D+00, 1.90D+00, 1.27D+00, &
1.20D+00, 2.60D+00, 2.15D+00, 1.95D+00, 1.80D+00, &
1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, &
1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, &
1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00, 1.75D+00 /)
rsb = rsb/0.529177d0 ! convert to Bohr
!..Cutoff radius for grid around atoms based on how diffuse basis set is
!..Maybe this should be atom dependent later
rsb_cut_off= sqrt(abs(log(sqrt(tol_wg))/expo_bas_min))
if( .not. allocated(rrad) ) allocate(rrad(nrad), wrad(nrad), vrad(nrad))
!..nang might not be one of the predifined values (Idims). Choose closest largest Idims
ilow = 0
do i=1,32
if( Idims(i) < nang ) ilow = i
enddo
nang=Idims(ilow+1)
if(.not. allocated(xang)) allocate (xang(nang), yang(nang), zang(nang), wang(nang))
!..Create the a_ij matrix for the appropriate definition of Voronoi polyhedra
if(.not. allocated(a_be)) allocate( a_be(natom, natom) )
do iat=1, natom
iele=min( Int(charge(iat)+0.1d0), 105)
rsbi=rsb(iele)
do jat=1,iat-1
jele=min( Int(charge(jat)+0.1d0), 105)
rsbj=rsb(jele)
x_be=rsbi/rsbj
u_be=(x_be-1.d0)/(x_be+1.d0)
a_be(iat,jat) = u_be/(u_be*u_be-1.d0)
a_be(iat,jat) = max( min(a_be(iat,jat), 0.5d0), -0.5d0)
a_be(jat,iat) = -a_be(iat,jat)
enddo
enddo
!..Temporary grid allocation x_tr, y_tr, z_tr, w_tr
ngr = natom*nrad*nang
if(.not. allocated(x_tr)) allocate (x_tr(ngr), y_tr(ngr), z_tr(ngr), w_tr(ngr), v_tr(ngr))
!..Create generic radial grid (to be multiplied with rsb for each different atom)
call generic_radial_grid(nrad, rrad, wrad, vrad)
!..Create generic radial grid xang**2+yang**2+zang**2 = 1
call generic_angular_grid(nang, xang, yang, zang, wang)
wang=4.d0*pi*wang !To integrate to 4 pi solid angle for sphere
!..Set grids on the atoms
ig=1; ngrid=0
do iat = 1, natom
xat=xcoo(iat); yat=ycoo(iat); zat=zcoo(iat)
iele = min( Int(charge(iat)+0.1d0), 105)
rsb1=rsb(iele); rsb3=rsb1*rsb1*rsb1
do irad=1,nrad
rgd = rsb1*rrad(irad); wrd3= rsb3*wrad(irad); vrd3=rsb3*vrad(irad)
do iang=1,nang
x_tr(ig) = xat + rgd*xang(iang)
y_tr(ig) = yat + rgd*yang(iang)
z_tr(ig) = zat + rgd*zang(iang)
w_at = at_weight(iat, x_tr(ig), y_tr(ig), z_tr(ig), a_be)
! w_at = at_weight_old(iat, x_tr(ig), y_tr(ig), z_tr(ig))
w_tr(ig) = wang(iang)*wrd3*w_at
v_tr(ig) = wang(iang)*vrd3*w_at
if(w_tr(ig) > tol_wg) ngrid=ngrid+1 !Re-Define Grid dimension
ig=ig+1
enddo !iang=1,nang
enddo !irad=1,nrad
enddo !iat = 1, natom
deallocate(rrad, wrad )
!..Allocate grid with dimension ngrid
allocate( x_grid(ngrid), y_grid(ngrid), z_grid(ngrid), &
w_grid(ngrid), v_grid(ngrid), bas_f_grid(ngrid, lnbasis) )
!..Prunning ... removing grid points with small weight
igr=0
do ig=1,ngr
if(w_tr(ig) > tol_wg) then
igr=igr+1
xx=x_tr(ig); yy=y_tr(ig); zz=z_tr(ig)
x_grid(igr) = xx; y_grid(igr) = yy; z_grid(igr) = zz
w_grid(igr) = w_tr(ig); v_grid(igr) = v_tr(ig)
do ibs=1,nbasis
bas_f_grid(igr,ibs) = f_bas(ibs, xx, yy, zz)
enddo
endif
enddo
deallocate ( x_tr, y_tr, z_tr, w_tr, v_tr)
print*,' Grid has been generated! Size: ',ngrid, ' Points'
grid_stat=.true.
end subroutine grid_setup_radial
!===============================================================================
function at_weight(iat, x, y, z, a_be)
!..For polyatomic systems Becke recipe
!..Global
use global; implicit none
!..The function
real(dp) :: at_weight
!..Arguments
integer :: iat
real(dp), intent(IN) :: x, y, z, a_be(natom,natom)
!..Local
real(dp) :: P(natom), x_A, y_A, z_A, x_B, y_B, z_B
real(dp) :: r_A, r_B, ss, xmu_ab
integer :: i,j, ifu, int_fuz=4
P = 1.d0
do i=1, natom-1
x_A=x-xcoo(i); y_A=y-ycoo(i); z_A=z-zcoo(i)
r_A=sqrt(x_A*x_A + y_A*y_A + z_A*z_A)
do j=i+1, natom
x_B=x-xcoo(j); y_B=y-ycoo(j); z_B=z-zcoo(j)
r_B=sqrt(x_B*x_B + y_B*y_B + z_B*z_B)
xmu_ab=(r_A-r_B) / R_AB(i,j)
xmu_ab=xmu_ab+a_be(i,j)*(1.d0-xmu_ab*xmu_ab)
do ifu=1,int_fuz
xmu_ab=(1.5d0-0.5d0*xmu_ab*xmu_ab)*xmu_ab
enddo
xmu_ab=0.5d0*xmu_ab
P(i) = P(i) * (0.5 - xmu_ab)
P(j) = P(j) * (0.5 + xmu_ab)
enddo
enddo
ss=0.d0
do i=1,natom
ss=ss+P(i)
enddo
at_weight = P(iat) / ss
end function at_weight
!===============================================================================
function at_weight_old(iat, x, y, z)
!..Global
use global; use grid_params, only:Del_fuz; implicit none
!..The function
real(dp) :: at_weight_old
!..Arguments
integer :: iat
real(dp), intent(IN) :: x, y, z
!..Local
real(dp) :: P, Pat, x_A, y_A, z_A, QAB, ss
integer :: i,j
ss=0.d0
do i=1, natom
P = 1.d0
x_A=x-xcoo(i); y_A=y-ycoo(i); z_A=z-zcoo(i)
do j=1, natom
if(j /= i) then
QAB = 0.5d0*R_AB(i,j) - (x_A*x_AB(i,j)+y_A*y_AB(i,j)+z_A*z_AB(i,j))
P = P*0.5d0*(1.d0+tanh (QAB/(Del_fuz*R_AB(i,j))))
endif
enddo
if(i == iat) Pat=P
ss=ss+P
enddo
at_weight_old= Pat / ss
end function at_weight_old
!=================================================================================
subroutine generic_radial_grid(nrad, rradg, wradg, vradg)
!..Global
use global; implicit none
integer :: irad, nrad, nrad_max
real(dp) :: rradg(nrad), wradg(nrad), vradg(nrad)
real(dp) :: xirad, xdd, xd2, rrr, rr5, xnradmx
real(dp) :: rrplus(nrad), rrminus(nrad)
!..Radial Grid from PMW Gill at al CPL 197, 499 (1992)
!..using Euler Mac Laurin quadrature defined in
!..N.C. Handy, SF Boys, Theoret. Chim. Acta 31, 195 (1973)
!..C. W. Murray, N. C. Handy, G. J. Laming, Mol. Phys. 78, 997 (1993).
! nrad: number of radial points
! rradg(nrad): array with radial points
! wradg(nrad): array with radial weights
nrad_max=nrad+1
rrminus(1) = 0.d0
do irad=1,nrad
xdd=nrad_max - irad; xirad=irad; xnradmx=nrad_max
rrr=xirad/xdd
rradg(irad) = rrr*rrr; xd2=xdd*xdd
if(irad > 1) then
rrminus(irad) = 0.5d0*(rradg(irad)+rradg(irad-1))
rrplus(irad-1) = rrminus(irad)
endif
! if (rradg(irad) > rsb_cut_off) exit
rr5=rrr*rrr*rrr*rrr*rrr
wradg(irad) = 2.d0*xnradmx*rr5/xd2
! if (rradg(irad) > rsb_cut_off) wradg(irad) =0.d0
enddo
rrplus(nrad) = 2.d0*rradg(nrad)-rrminus(nrad)
do irad=1,nrad
vradg(irad) = (rrplus(irad)**3-rrminus(irad)**3)/3.d0
enddo
Print*,'Number of radial points (per atom): ', nrad
end subroutine generic_radial_grid
!=================================================================================
subroutine generic_angular_grid(nang, x, y, z, w)
use global; implicit none
integer :: nang,n
real(dp) :: x(nang), y(nang), z(nang), w(nang)
select case (nang)
case (6)
call LD0006(X,Y,Z,W,N)
case (14)
call LD0014(X,Y,Z,W,N)
case (26)
call LD0026(X,Y,Z,W,N)
case (38)
call LD0038(X,Y,Z,W,N)
case (50)
call LD0050(X,Y,Z,W,N)
case (74)
call LD0074(X,Y,Z,W,N)
case (86)
call LD0086(X,Y,Z,W,N)
case (110)
call LD0110(X,Y,Z,W,N)
case (146)
call LD0146(X,Y,Z,W,N)
case (170)
call LD0170(X,Y,Z,W,N)
case (194)
call LD0194(X,Y,Z,W,N)
case (230)
call LD0230(X,Y,Z,W,N)
case (266)
call LD0266(X,Y,Z,W,N)
case (302)
call LD0302(X,Y,Z,W,N)
case (350)
call LD0350(X,Y,Z,W,N)
case (434)
call LD0434(X,Y,Z,W,N)
case (590)
call LD0590(X,Y,Z,W,N)
case (770)
call LD0770(X,Y,Z,W,N)
case (974)
call LD0974(X,Y,Z,W,N)
case (1202)
call LD1202(X,Y,Z,W,N)
case (1454)
call LD1454(X,Y,Z,W,N)
case (1730)
call LD1730(X,Y,Z,W,N)
case (2030)
call LD2030(X,Y,Z,W,N)
case (2354)
call LD2354(X,Y,Z,W,N)
case (2702)
call LD2702(X,Y,Z,W,N)
case (3074)
call LD3074(X,Y,Z,W,N)
case (3470)
call LD3470(X,Y,Z,W,N)
case (3890)
call LD3890(X,Y,Z,W,N)
case (4334)
call LD4334(X,Y,Z,W,N)
case (4802)
call LD4802(X,Y,Z,W,N)
case (5294)
call LD5294(X,Y,Z,W,N)
case (5810)
call LD5810(X,Y,Z,W,N)
case default
stop 'generic_angular_grid: No such case for nang'
end select
print*,'Number of Angular points (per radius): ', N
end subroutine generic_angular_grid
!==========================================================================================
!...The next Fortran 77 routines are taken from :
!... /* http://www.ccl.net/ */
subroutine gen_oh(code, num, x, y, z, w, a, b, v)
implicit logical(a-z)
double precision x(*),y(*),z(*),w(*)
double precision a,b,v
integer code
integer num
double precision c
!hvd
!hvd This subroutine is part of a set of subroutines that generate
!hvd Lebedev grids [1-6] for integration on a sphere. The original
!hvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
!hvd translated into fortran by Dr. Christoph van Wuellen.
!hvd This subroutine was translated from C to fortran77 by hand.
!hvd
!hvd Users of this code are asked to include reference [1] in their
!hvd publications, and in the user- and programmers-manuals
!hvd describing their codes.
!hvd
!hvd This code was distributed through CCL /* (http://www.ccl.net/). */
!hvd
!hvd [1] V.I. Lebedev, and D.N. Laikov
!hvd A quadrature formula for the sphere of the 131st
!hvd algebraic order of accuracy
!hvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
!hvd
!hvd [2] V.I. Lebedev
!hvd A quadrature formula for the sphere of 59th algebraic
!hvd order of accuracy
!hvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
!hvd
!hvd [3] V.I. Lebedev, and A.L. Skorokhodov
!hvd Quadrature formulas of orders 41, 47, and 53 for the sphere
!hvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
!hvd
!hvd [4] V.I. Lebedev
!hvd Spherical quadrature formulas exact to orders 25-29
!hvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
!hvd
!hvd [5] V.I. Lebedev
!hvd Quadratures on a sphere
!hvd Computational Mathematics and Mathematical Physics, Vol. 16,
!hvd 1976, pp. 10-24.
!hvd
!hvd [6] V.I. Lebedev
!hvd Values of the nodes and weights of ninth to seventeenth
!hvd order Gauss-Markov quadrature formulae invariant under the
!hvd octahedron group with inversion
!hvd Computational Mathematics and Mathematical Physics, Vol. 15,
!hvd 1975, pp. 44-51.
!hvd
!vw
!vw Given a point on a sphere (specified by a and b), generate all
!vw the equivalent points under Oh symmetry, making grid points with
!vw weight v.
!vw The variable num is increased by the number of different points
!vw generated.
!vw
!vw Depending on code, there are 6...48 different but equivalent
!vw points.
!vw
!vw code=1: (0,0,1) etc ( 6 points)
!vw code=2: (0,a,a) etc, a=1/sqrt(2) ( 12 points)
!vw code=3: (a,a,a) etc, a=1/sqrt(3) ( 8 points)
!vw code=4: (a,a,b) etc, b=sqrt(1-2 a^2) ( 24 points)
!vw code=5: (a,b,0) etc, b=sqrt(1-a^2), a input ( 24 points)
!vw code=6: (a,b,c) etc, c=sqrt(1-a^2-b^2), a/b input ( 48 points)
!vw
goto (1,2,3,4,5,6) code
write (6,*) 'Gen_Oh: Invalid Code'
stop
1 continue
a=1.0d0
x(1) = a
y(1) = 0.0d0
z(1) = 0.0d0
w(1) = v
x(2) = -a
y(2) = 0.0d0
z(2) = 0.0d0
w(2) = v
x(3) = 0.0d0
y(3) = a
z(3) = 0.0d0
w(3) = v
x(4) = 0.0d0
y(4) = -a
z(4) = 0.0d0
w(4) = v
x(5) = 0.0d0
y(5) = 0.0d0
z(5) = a
w(5) = v
x(6) = 0.0d0
y(6) = 0.0d0
z(6) = -a
w(6) = v
num=num+6
return
!vw
2 continue
a=sqrt(0.5d0)
x( 1) = 0d0
y( 1) = a
z( 1) = a
w( 1) = v
x( 2) = 0d0
y( 2) = -a
z( 2) = a
w( 2) = v
x( 3) = 0d0
y( 3) = a
z( 3) = -a
w( 3) = v
x( 4) = 0d0
y( 4) = -a
z( 4) = -a
w( 4) = v
x( 5) = a
y( 5) = 0d0
z( 5) = a
w( 5) = v
x( 6) = -a
y( 6) = 0d0
z( 6) = a
w( 6) = v
x( 7) = a
y( 7) = 0d0
z( 7) = -a
w( 7) = v
x( 8) = -a
y( 8) = 0d0
z( 8) = -a
w( 8) = v
x( 9) = a
y( 9) = a
z( 9) = 0d0
w( 9) = v
x(10) = -a
y(10) = a
z(10) = 0d0
w(10) = v
x(11) = a
y(11) = -a
z(11) = 0d0
w(11) = v
x(12) = -a
y(12) = -a
z(12) = 0d0
w(12) = v
num=num+12
return
!vw
3 continue
a = sqrt(1d0/3d0)
x(1) = a
y(1) = a
z(1) = a
w(1) = v
x(2) = -a
y(2) = a
z(2) = a
w(2) = v
x(3) = a
y(3) = -a
z(3) = a
w(3) = v
x(4) = -a
y(4) = -a
z(4) = a
w(4) = v
x(5) = a
y(5) = a
z(5) = -a
w(5) = v
x(6) = -a
y(6) = a
z(6) = -a
w(6) = v
x(7) = a
y(7) = -a
z(7) = -a
w(7) = v
x(8) = -a
y(8) = -a
z(8) = -a
w(8) = v
num=num+8
return
!vw
4 continue
b = sqrt(1d0 - 2d0*a*a)
x( 1) = a
y( 1) = a
z( 1) = b
w( 1) = v
x( 2) = -a
y( 2) = a
z( 2) = b
w( 2) = v
x( 3) = a
y( 3) = -a
z( 3) = b
w( 3) = v
x( 4) = -a
y( 4) = -a
z( 4) = b
w( 4) = v
x( 5) = a
y( 5) = a
z( 5) = -b
w( 5) = v
x( 6) = -a
y( 6) = a
z( 6) = -b
w( 6) = v
x( 7) = a
y( 7) = -a
z( 7) = -b
w( 7) = v
x( 8) = -a
y( 8) = -a
z( 8) = -b
w( 8) = v
x( 9) = a
y( 9) = b
z( 9) = a
w( 9) = v
x(10) = -a
y(10) = b
z(10) = a
w(10) = v
x(11) = a
y(11) = -b
z(11) = a
w(11) = v
x(12) = -a
y(12) = -b
z(12) = a
w(12) = v
x(13) = a
y(13) = b
z(13) = -a
w(13) = v
x(14) = -a
y(14) = b
z(14) = -a
w(14) = v
x(15) = a
y(15) = -b
z(15) = -a
w(15) = v
x(16) = -a
y(16) = -b
z(16) = -a
w(16) = v
x(17) = b
y(17) = a
z(17) = a
w(17) = v
x(18) = -b
y(18) = a
z(18) = a
w(18) = v
x(19) = b
y(19) = -a
z(19) = a
w(19) = v
x(20) = -b
y(20) = -a
z(20) = a
w(20) = v
x(21) = b
y(21) = a
z(21) = -a
w(21) = v
x(22) = -b
y(22) = a
z(22) = -a
w(22) = v
x(23) = b
y(23) = -a
z(23) = -a
w(23) = v
x(24) = -b
y(24) = -a
z(24) = -a
w(24) = v
num=num+24
return
!vw
5 continue
b=sqrt(1d0-a*a)
x( 1) = a
y( 1) = b
z( 1) = 0d0
w( 1) = v
x( 2) = -a
y( 2) = b
z( 2) = 0d0
w( 2) = v
x( 3) = a
y( 3) = -b
z( 3) = 0d0
w( 3) = v
x( 4) = -a
y( 4) = -b
z( 4) = 0d0
w( 4) = v
x( 5) = b
y( 5) = a
z( 5) = 0d0
w( 5) = v
x( 6) = -b
y( 6) = a
z( 6) = 0d0
w( 6) = v
x( 7) = b
y( 7) = -a
z( 7) = 0d0
w( 7) = v
x( 8) = -b
y( 8) = -a
z( 8) = 0d0
w( 8) = v
x( 9) = a
y( 9) = 0d0
z( 9) = b
w( 9) = v
x(10) = -a
y(10) = 0d0
z(10) = b
w(10) = v
x(11) = a
y(11) = 0d0
z(11) = -b
w(11) = v
x(12) = -a
y(12) = 0d0
z(12) = -b
w(12) = v
x(13) = b
y(13) = 0d0
z(13) = a
w(13) = v
x(14) = -b
y(14) = 0d0
z(14) = a
w(14) = v
x(15) = b
y(15) = 0d0
z(15) = -a
w(15) = v
x(16) = -b
y(16) = 0d0
z(16) = -a
w(16) = v
x(17) = 0d0
y(17) = a
z(17) = b
w(17) = v
x(18) = 0d0
y(18) = -a
z(18) = b
w(18) = v
x(19) = 0d0
y(19) = a
z(19) = -b
w(19) = v
x(20) = 0d0
y(20) = -a
z(20) = -b
w(20) = v
x(21) = 0d0
y(21) = b
z(21) = a
w(21) = v
x(22) = 0d0
y(22) = -b
z(22) = a
w(22) = v
x(23) = 0d0
y(23) = b
z(23) = -a
w(23) = v
x(24) = 0d0
y(24) = -b
z(24) = -a
w(24) = v
num=num+24
return
!vw
6 continue
c=sqrt(1d0 - a*a - b*b)
x( 1) = a
y( 1) = b
z( 1) = c
w( 1) = v
x( 2) = -a
y( 2) = b
z( 2) = c
w( 2) = v
x( 3) = a
y( 3) = -b
z( 3) = c
w( 3) = v
x( 4) = -a
y( 4) = -b
z( 4) = c
w( 4) = v
x( 5) = a
y( 5) = b
z( 5) = -c
w( 5) = v
x( 6) = -a
y( 6) = b
z( 6) = -c
w( 6) = v
x( 7) = a
y( 7) = -b
z( 7) = -c
w( 7) = v
x( 8) = -a
y( 8) = -b
z( 8) = -c
w( 8) = v
x( 9) = a
y( 9) = c
z( 9) = b
w( 9) = v
x(10) = -a
y(10) = c
z(10) = b
w(10) = v
x(11) = a
y(11) = -c
z(11) = b
w(11) = v
x(12) = -a
y(12) = -c
z(12) = b
w(12) = v
x(13) = a
y(13) = c
z(13) = -b
w(13) = v
x(14) = -a
y(14) = c
z(14) = -b
w(14) = v
x(15) = a
y(15) = -c
z(15) = -b
w(15) = v
x(16) = -a
y(16) = -c
z(16) = -b
w(16) = v
x(17) = b
y(17) = a
z(17) = c
w(17) = v
x(18) = -b
y(18) = a
z(18) = c
w(18) = v
x(19) = b
y(19) = -a
z(19) = c
w(19) = v
x(20) = -b
y(20) = -a
z(20) = c
w(20) = v
x(21) = b
y(21) = a
z(21) = -c
w(21) = v
x(22) = -b
y(22) = a
z(22) = -c
w(22) = v
x(23) = b
y(23) = -a
z(23) = -c
w(23) = v
x(24) = -b
y(24) = -a
z(24) = -c
w(24) = v
x(25) = b
y(25) = c
z(25) = a
w(25) = v
x(26) = -b
y(26) = c
z(26) = a
w(26) = v
x(27) = b
y(27) = -c
z(27) = a
w(27) = v
x(28) = -b
y(28) = -c
z(28) = a
w(28) = v
x(29) = b
y(29) = c
z(29) = -a
w(29) = v
x(30) = -b
y(30) = c
z(30) = -a
w(30) = v
x(31) = b
y(31) = -c
z(31) = -a
w(31) = v
x(32) = -b
y(32) = -c
z(32) = -a
w(32) = v
x(33) = c
y(33) = a
z(33) = b
w(33) = v
x(34) = -c
y(34) = a
z(34) = b
w(34) = v
x(35) = c
y(35) = -a
z(35) = b
w(35) = v
x(36) = -c
y(36) = -a
z(36) = b
w(36) = v
x(37) = c
y(37) = a
z(37) = -b
w(37) = v
x(38) = -c
y(38) = a
z(38) = -b
w(38) = v
x(39) = c
y(39) = -a
z(39) = -b
w(39) = v
x(40) = -c
y(40) = -a
z(40) = -b
w(40) = v
x(41) = c
y(41) = b
z(41) = a
w(41) = v
x(42) = -c
y(42) = b
z(42) = a
w(42) = v
x(43) = c
y(43) = -b
z(43) = a
w(43) = v
x(44) = -c
y(44) = -b
z(44) = a
w(44) = v
x(45) = c
y(45) = b
z(45) = -a
w(45) = v
x(46) = -c
y(46) = b
z(46) = -a
w(46) = v
x(47) = c
y(47) = -b
z(47) = -a
w(47) = v
x(48) = -c
y(48) = -b
z(48) = -a
w(48) = v
num=num+48
return
end
!-----------------------------------------------------------------------
SUBROUTINE LD0006(X,Y,Z,W,N)
DOUBLE PRECISION X( 6)
DOUBLE PRECISION Y( 6)
DOUBLE PRECISION Z( 6)
DOUBLE PRECISION W( 6)
INTEGER N
DOUBLE PRECISION A,B,V
!VW
!VW LEBEDEV 6-POINT ANGULAR GRID
!VW
N=1
V=0.1666666666666667D+0
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
N=N-1
RETURN
END
SUBROUTINE LD0014(X,Y,Z,W,N)
DOUBLE PRECISION X( 14)
DOUBLE PRECISION Y( 14)
DOUBLE PRECISION Z( 14)
DOUBLE PRECISION W( 14)
INTEGER N
DOUBLE PRECISION A,B,V
!VW
!VW LEBEDEV 14-POINT ANGULAR GRID
!VW
N=1
V=0.6666666666666667D-1
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
V=0.7500000000000000D-1
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
N=N-1
RETURN
END
SUBROUTINE LD0026(X,Y,Z,W,N)
DOUBLE PRECISION X( 26)
DOUBLE PRECISION Y( 26)
DOUBLE PRECISION Z( 26)
DOUBLE PRECISION W( 26)
INTEGER N
DOUBLE PRECISION A,B,V
!VW
!VW LEBEDEV 26-POINT ANGULAR GRID
!VW
N=1
V=0.4761904761904762D-1
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
V=0.3809523809523810D-1
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
V=0.3214285714285714D-1
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
N=N-1
RETURN
END
SUBROUTINE LD0038(X,Y,Z,W,N)
DOUBLE PRECISION X( 38)
DOUBLE PRECISION Y( 38)
DOUBLE PRECISION Z( 38)
DOUBLE PRECISION W( 38)
INTEGER N
DOUBLE PRECISION A,B,V
!VW
!VW LEBEDEV 38-POINT ANGULAR GRID
!VW
N=1
V=0.9523809523809524D-2
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
V=0.3214285714285714D-1
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
A=0.4597008433809831D+0
V=0.2857142857142857D-1