mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-09-01 13:43:40 +02:00
854 lines
24 KiB
Fortran
854 lines
24 KiB
Fortran
|
|
! ---
|
|
|
|
BEGIN_PROVIDER [ double precision, grad1_u12_num, (n_points_extra_final_grid, n_points_final_grid, 3)]
|
|
&BEGIN_PROVIDER [ double precision, grad1_u12_squared_num, (n_points_extra_final_grid, n_points_final_grid)]
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! grad_1 u(r1,r2)
|
|
!
|
|
! this will be integrated numerically over r2:
|
|
! we use grid for r1 and extra_grid for r2
|
|
!
|
|
! for 99 < j1b_type < 199
|
|
!
|
|
! u(r1,r2) = j12_mu(r12) x v(r1) x v(r2)
|
|
! grad1 u(r1, r2) = [(grad1 j12_mu) v(r1) + j12_mu grad1 v(r1)] v(r2)
|
|
!
|
|
END_DOC
|
|
|
|
implicit none
|
|
integer :: ipoint, jpoint
|
|
double precision :: r1(3), r2(3)
|
|
double precision :: v1b_r1, v1b_r2, u2b_r12
|
|
double precision :: grad1_v1b(3), grad1_u2b(3)
|
|
double precision :: dx, dy, dz
|
|
double precision, external :: j12_mu, j1b_nucl
|
|
|
|
PROVIDE j1b_type
|
|
PROVIDE final_grid_points_extra
|
|
|
|
grad1_u12_num = 0.d0
|
|
grad1_u12_squared_num = 0.d0
|
|
|
|
if(j1b_type .eq. 100) then
|
|
|
|
!$OMP PARALLEL &
|
|
!$OMP DEFAULT (NONE) &
|
|
!$OMP PRIVATE (ipoint, jpoint, r1, r2, v1b_r1, v1b_r2, u2b_r12, grad1_v1b, grad1_u2b, dx, dy, dz) &
|
|
!$OMP SHARED (n_points_final_grid, n_points_extra_final_grid, final_grid_points, &
|
|
!$OMP final_grid_points_extra, grad1_u12_num, grad1_u12_squared_num)
|
|
!$OMP DO SCHEDULE (static)
|
|
do ipoint = 1, n_points_final_grid ! r1
|
|
|
|
r1(1) = final_grid_points(1,ipoint)
|
|
r1(2) = final_grid_points(2,ipoint)
|
|
r1(3) = final_grid_points(3,ipoint)
|
|
|
|
do jpoint = 1, n_points_extra_final_grid ! r2
|
|
|
|
r2(1) = final_grid_points_extra(1,jpoint)
|
|
r2(2) = final_grid_points_extra(2,jpoint)
|
|
r2(3) = final_grid_points_extra(3,jpoint)
|
|
|
|
call grad1_j12_mu(r1, r2, grad1_u2b)
|
|
|
|
dx = grad1_u2b(1)
|
|
dy = grad1_u2b(2)
|
|
dz = grad1_u2b(3)
|
|
|
|
grad1_u12_num(jpoint,ipoint,1) = dx
|
|
grad1_u12_num(jpoint,ipoint,2) = dy
|
|
grad1_u12_num(jpoint,ipoint,3) = dz
|
|
|
|
grad1_u12_squared_num(jpoint,ipoint) = dx*dx + dy*dy + dz*dz
|
|
enddo
|
|
enddo
|
|
!$OMP END DO
|
|
!$OMP END PARALLEL
|
|
|
|
elseif((j1b_type .gt. 100) .and. (j1b_type .lt. 200)) then
|
|
|
|
PROVIDE final_grid_points
|
|
|
|
!$OMP PARALLEL &
|
|
!$OMP DEFAULT (NONE) &
|
|
!$OMP PRIVATE (ipoint, jpoint, r1, r2, v1b_r1, v1b_r2, u2b_r12, grad1_v1b, grad1_u2b, dx, dy, dz) &
|
|
!$OMP SHARED (n_points_final_grid, n_points_extra_final_grid, final_grid_points, &
|
|
!$OMP final_grid_points_extra, grad1_u12_num, grad1_u12_squared_num)
|
|
!$OMP DO SCHEDULE (static)
|
|
do ipoint = 1, n_points_final_grid ! r1
|
|
|
|
r1(1) = final_grid_points(1,ipoint)
|
|
r1(2) = final_grid_points(2,ipoint)
|
|
r1(3) = final_grid_points(3,ipoint)
|
|
|
|
v1b_r1 = j1b_nucl(r1)
|
|
call grad1_j1b_nucl(r1, grad1_v1b)
|
|
|
|
do jpoint = 1, n_points_extra_final_grid ! r2
|
|
|
|
r2(1) = final_grid_points_extra(1,jpoint)
|
|
r2(2) = final_grid_points_extra(2,jpoint)
|
|
r2(3) = final_grid_points_extra(3,jpoint)
|
|
|
|
v1b_r2 = j1b_nucl(r2)
|
|
u2b_r12 = j12_mu(r1, r2)
|
|
call grad1_j12_mu(r1, r2, grad1_u2b)
|
|
|
|
dx = (grad1_u2b(1) * v1b_r1 + u2b_r12 * grad1_v1b(1)) * v1b_r2
|
|
dy = (grad1_u2b(2) * v1b_r1 + u2b_r12 * grad1_v1b(2)) * v1b_r2
|
|
dz = (grad1_u2b(3) * v1b_r1 + u2b_r12 * grad1_v1b(3)) * v1b_r2
|
|
|
|
grad1_u12_num(jpoint,ipoint,1) = dx
|
|
grad1_u12_num(jpoint,ipoint,2) = dy
|
|
grad1_u12_num(jpoint,ipoint,3) = dz
|
|
|
|
grad1_u12_squared_num(jpoint,ipoint) = dx*dx + dy*dy + dz*dz
|
|
enddo
|
|
enddo
|
|
!$OMP END DO
|
|
!$OMP END PARALLEL
|
|
|
|
elseif((j1b_type .ge. 200) .and. (j1b_type .lt. 300)) then
|
|
|
|
!$OMP PARALLEL &
|
|
!$OMP DEFAULT (NONE) &
|
|
!$OMP PRIVATE (ipoint, jpoint, r1, r2, grad1_u2b, dx, dy, dz) &
|
|
!$OMP SHARED (n_points_final_grid, n_points_extra_final_grid, final_grid_points, &
|
|
!$OMP final_grid_points_extra, grad1_u12_num, grad1_u12_squared_num)
|
|
!$OMP DO SCHEDULE (static)
|
|
do ipoint = 1, n_points_final_grid ! r1
|
|
|
|
r1(1) = final_grid_points(1,ipoint)
|
|
r1(2) = final_grid_points(2,ipoint)
|
|
r1(3) = final_grid_points(3,ipoint)
|
|
|
|
do jpoint = 1, n_points_extra_final_grid ! r2
|
|
|
|
r2(1) = final_grid_points_extra(1,jpoint)
|
|
r2(2) = final_grid_points_extra(2,jpoint)
|
|
r2(3) = final_grid_points_extra(3,jpoint)
|
|
|
|
call grad1_j12_mu(r1, r2, grad1_u2b)
|
|
|
|
dx = grad1_u2b(1)
|
|
dy = grad1_u2b(2)
|
|
dz = grad1_u2b(3)
|
|
|
|
grad1_u12_num(jpoint,ipoint,1) = dx
|
|
grad1_u12_num(jpoint,ipoint,2) = dy
|
|
grad1_u12_num(jpoint,ipoint,3) = dz
|
|
|
|
grad1_u12_squared_num(jpoint,ipoint) = dx*dx + dy*dy + dz*dz
|
|
enddo
|
|
enddo
|
|
!$OMP END DO
|
|
!$OMP END PARALLEL
|
|
|
|
else
|
|
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented yet'
|
|
stop
|
|
|
|
endif
|
|
|
|
END_PROVIDER
|
|
|
|
! ---
|
|
|
|
double precision function j12_mu(r1, r2)
|
|
|
|
include 'constants.include.F'
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r1(3), r2(3)
|
|
double precision :: mu_tmp, r12
|
|
|
|
if((j1b_type .ge. 0) .and. (j1b_type .lt. 200)) then
|
|
|
|
r12 = dsqrt( (r1(1) - r2(1)) * (r1(1) - r2(1)) &
|
|
+ (r1(2) - r2(2)) * (r1(2) - r2(2)) &
|
|
+ (r1(3) - r2(3)) * (r1(3) - r2(3)) )
|
|
mu_tmp = mu_erf * r12
|
|
|
|
j12_mu = 0.5d0 * r12 * (1.d0 - derf(mu_tmp)) - inv_sq_pi_2 * dexp(-mu_tmp*mu_tmp) / mu_erf
|
|
|
|
else
|
|
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented for j12_mu'
|
|
stop
|
|
|
|
endif
|
|
|
|
return
|
|
end function j12_mu
|
|
|
|
! ---
|
|
|
|
subroutine grad1_j12_mu(r1, r2, grad)
|
|
|
|
BEGIN_DOC
|
|
! gradient of j(mu(r1,r2),r12) form of jastrow.
|
|
!
|
|
! if mu(r1,r2) = cst ---> j1b_type < 200 and
|
|
!
|
|
! d/dx1 j(mu,r12) = 0.5 * (1 - erf(mu *r12))/r12 * (x1 - x2)
|
|
!
|
|
! if mu(r1,r2) /= cst ---> 200 < j1b_type < 300 and
|
|
!
|
|
! d/dx1 j(mu(r1,r2),r12) = exp(-(mu(r1,r2)*r12)**2) /(2 *sqrt(pi) * mu(r1,r2)**2 ) d/dx1 mu(r1,r2)
|
|
!
|
|
! + 0.5 * (1 - erf(mu(r1,r2) *r12))/r12 * (x1 - x2)
|
|
END_DOC
|
|
include 'constants.include.F'
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r1(3), r2(3)
|
|
double precision, intent(out) :: grad(3)
|
|
double precision :: dx, dy, dz, r12, tmp
|
|
|
|
grad = 0.d0
|
|
|
|
if((j1b_type .ge. 0) .and. (j1b_type .lt. 200)) then
|
|
|
|
dx = r1(1) - r2(1)
|
|
dy = r1(2) - r2(2)
|
|
dz = r1(3) - r2(3)
|
|
|
|
r12 = dsqrt(dx * dx + dy * dy + dz * dz)
|
|
if(r12 .lt. 1d-10) return
|
|
|
|
tmp = 0.5d0 * (1.d0 - derf(mu_erf * r12)) / r12
|
|
|
|
grad(1) = tmp * dx
|
|
grad(2) = tmp * dy
|
|
grad(3) = tmp * dz
|
|
|
|
elseif((j1b_type .ge. 200) .and. (j1b_type .lt. 300)) then
|
|
|
|
double precision :: mu_val, mu_tmp, mu_der(3)
|
|
|
|
dx = r1(1) - r2(1)
|
|
dy = r1(2) - r2(2)
|
|
dz = r1(3) - r2(3)
|
|
r12 = dsqrt(dx * dx + dy * dy + dz * dz)
|
|
|
|
call mu_r_val_and_grad(r1, r2, mu_val, mu_der)
|
|
mu_tmp = mu_val * r12
|
|
tmp = inv_sq_pi_2 * dexp(-mu_tmp*mu_tmp) / (mu_val * mu_val)
|
|
grad(1) = tmp * mu_der(1)
|
|
grad(2) = tmp * mu_der(2)
|
|
grad(3) = tmp * mu_der(3)
|
|
|
|
if(r12 .lt. 1d-10) return
|
|
tmp = 0.5d0 * (1.d0 - derf(mu_tmp)) / r12
|
|
grad(1) = grad(1) + tmp * dx
|
|
grad(2) = grad(2) + tmp * dy
|
|
grad(3) = grad(3) + tmp * dz
|
|
|
|
else
|
|
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented yet'
|
|
stop
|
|
|
|
endif
|
|
|
|
return
|
|
end subroutine grad1_j12_mu
|
|
|
|
! ---
|
|
|
|
double precision function j1b_nucl(r)
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r(3)
|
|
integer :: i
|
|
double precision :: a, d, e, x, y, z
|
|
|
|
if((j1b_type .eq. 2) .or. (j1b_type .eq. 102)) then
|
|
|
|
j1b_nucl = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
d = ( (r(1) - nucl_coord(i,1)) * (r(1) - nucl_coord(i,1)) &
|
|
+ (r(2) - nucl_coord(i,2)) * (r(2) - nucl_coord(i,2)) &
|
|
+ (r(3) - nucl_coord(i,3)) * (r(3) - nucl_coord(i,3)) )
|
|
j1b_nucl = j1b_nucl - dexp(-a*dsqrt(d))
|
|
enddo
|
|
|
|
elseif((j1b_type .eq. 3) .or. (j1b_type .eq. 103)) then
|
|
|
|
j1b_nucl = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
d = ( (r(1) - nucl_coord(i,1)) * (r(1) - nucl_coord(i,1)) &
|
|
+ (r(2) - nucl_coord(i,2)) * (r(2) - nucl_coord(i,2)) &
|
|
+ (r(3) - nucl_coord(i,3)) * (r(3) - nucl_coord(i,3)) )
|
|
e = 1.d0 - dexp(-a*d)
|
|
j1b_nucl = j1b_nucl * e
|
|
enddo
|
|
|
|
elseif((j1b_type .eq. 4) .or. (j1b_type .eq. 104)) then
|
|
|
|
j1b_nucl = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
d = ( (r(1) - nucl_coord(i,1)) * (r(1) - nucl_coord(i,1)) &
|
|
+ (r(2) - nucl_coord(i,2)) * (r(2) - nucl_coord(i,2)) &
|
|
+ (r(3) - nucl_coord(i,3)) * (r(3) - nucl_coord(i,3)) )
|
|
j1b_nucl = j1b_nucl - j1b_pen_coef(i) * dexp(-a*d)
|
|
enddo
|
|
|
|
elseif((j1b_type .eq. 5) .or. (j1b_type .eq. 105)) then
|
|
|
|
j1b_nucl = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
x = r(1) - nucl_coord(i,1)
|
|
y = r(2) - nucl_coord(i,2)
|
|
z = r(3) - nucl_coord(i,3)
|
|
d = x*x + y*y + z*z
|
|
j1b_nucl = j1b_nucl - dexp(-a*d*d)
|
|
enddo
|
|
|
|
else
|
|
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented for j1b_nucl'
|
|
stop
|
|
|
|
endif
|
|
|
|
return
|
|
end function j1b_nucl
|
|
|
|
! ---
|
|
|
|
double precision function j1b_nucl_square(r)
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r(3)
|
|
integer :: i
|
|
double precision :: a, d, e, x, y, z
|
|
|
|
if((j1b_type .eq. 2) .or. (j1b_type .eq. 102)) then
|
|
|
|
j1b_nucl_square = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
d = ( (r(1) - nucl_coord(i,1)) * (r(1) - nucl_coord(i,1)) &
|
|
+ (r(2) - nucl_coord(i,2)) * (r(2) - nucl_coord(i,2)) &
|
|
+ (r(3) - nucl_coord(i,3)) * (r(3) - nucl_coord(i,3)) )
|
|
j1b_nucl_square = j1b_nucl_square - dexp(-a*dsqrt(d))
|
|
enddo
|
|
j1b_nucl_square = j1b_nucl_square * j1b_nucl_square
|
|
|
|
elseif((j1b_type .eq. 3) .or. (j1b_type .eq. 103)) then
|
|
|
|
j1b_nucl_square = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
d = ( (r(1) - nucl_coord(i,1)) * (r(1) - nucl_coord(i,1)) &
|
|
+ (r(2) - nucl_coord(i,2)) * (r(2) - nucl_coord(i,2)) &
|
|
+ (r(3) - nucl_coord(i,3)) * (r(3) - nucl_coord(i,3)) )
|
|
e = 1.d0 - dexp(-a*d)
|
|
j1b_nucl_square = j1b_nucl_square * e
|
|
enddo
|
|
j1b_nucl_square = j1b_nucl_square * j1b_nucl_square
|
|
|
|
elseif((j1b_type .eq. 4) .or. (j1b_type .eq. 104)) then
|
|
|
|
j1b_nucl_square = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
d = ( (r(1) - nucl_coord(i,1)) * (r(1) - nucl_coord(i,1)) &
|
|
+ (r(2) - nucl_coord(i,2)) * (r(2) - nucl_coord(i,2)) &
|
|
+ (r(3) - nucl_coord(i,3)) * (r(3) - nucl_coord(i,3)) )
|
|
j1b_nucl_square = j1b_nucl_square - j1b_pen_coef(i) * dexp(-a*d)
|
|
enddo
|
|
j1b_nucl_square = j1b_nucl_square * j1b_nucl_square
|
|
|
|
elseif((j1b_type .eq. 5) .or. (j1b_type .eq. 105)) then
|
|
|
|
j1b_nucl_square = 1.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
x = r(1) - nucl_coord(i,1)
|
|
y = r(2) - nucl_coord(i,2)
|
|
z = r(3) - nucl_coord(i,3)
|
|
d = x*x + y*y + z*z
|
|
j1b_nucl_square = j1b_nucl_square - dexp(-a*d*d)
|
|
enddo
|
|
j1b_nucl_square = j1b_nucl_square * j1b_nucl_square
|
|
|
|
else
|
|
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented for j1b_nucl_square'
|
|
stop
|
|
|
|
endif
|
|
|
|
return
|
|
end function j1b_nucl_square
|
|
|
|
! ---
|
|
|
|
subroutine grad1_j1b_nucl(r, grad)
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r(3)
|
|
double precision, intent(out) :: grad(3)
|
|
integer :: ipoint, i, j, phase
|
|
double precision :: x, y, z, dx, dy, dz
|
|
double precision :: a, d, e
|
|
double precision :: fact_x, fact_y, fact_z
|
|
double precision :: ax_der, ay_der, az_der, a_expo
|
|
|
|
if((j1b_type .eq. 2) .or. (j1b_type .eq. 102)) then
|
|
|
|
fact_x = 0.d0
|
|
fact_y = 0.d0
|
|
fact_z = 0.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
x = r(1) - nucl_coord(i,1)
|
|
y = r(2) - nucl_coord(i,2)
|
|
z = r(3) - nucl_coord(i,3)
|
|
d = dsqrt(x*x + y*y + z*z)
|
|
e = a * dexp(-a*d) / d
|
|
|
|
fact_x += e * x
|
|
fact_y += e * y
|
|
fact_z += e * z
|
|
enddo
|
|
|
|
grad(1) = fact_x
|
|
grad(2) = fact_y
|
|
grad(3) = fact_z
|
|
|
|
elseif((j1b_type .eq. 3) .or. (j1b_type .eq. 103)) then
|
|
|
|
x = r(1)
|
|
y = r(2)
|
|
z = r(3)
|
|
|
|
fact_x = 0.d0
|
|
fact_y = 0.d0
|
|
fact_z = 0.d0
|
|
do i = 1, List_all_comb_b2_size
|
|
|
|
phase = 0
|
|
a_expo = 0.d0
|
|
ax_der = 0.d0
|
|
ay_der = 0.d0
|
|
az_der = 0.d0
|
|
do j = 1, nucl_num
|
|
a = dble(List_all_comb_b2(j,i)) * j1b_pen(j)
|
|
dx = x - nucl_coord(j,1)
|
|
dy = y - nucl_coord(j,2)
|
|
dz = z - nucl_coord(j,3)
|
|
|
|
phase += List_all_comb_b2(j,i)
|
|
a_expo += a * (dx*dx + dy*dy + dz*dz)
|
|
ax_der += a * dx
|
|
ay_der += a * dy
|
|
az_der += a * dz
|
|
enddo
|
|
e = -2.d0 * (-1.d0)**dble(phase) * dexp(-a_expo)
|
|
|
|
fact_x += e * ax_der
|
|
fact_y += e * ay_der
|
|
fact_z += e * az_der
|
|
enddo
|
|
|
|
grad(1) = fact_x
|
|
grad(2) = fact_y
|
|
grad(3) = fact_z
|
|
|
|
elseif((j1b_type .eq. 4) .or. (j1b_type .eq. 104)) then
|
|
|
|
fact_x = 0.d0
|
|
fact_y = 0.d0
|
|
fact_z = 0.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
x = r(1) - nucl_coord(i,1)
|
|
y = r(2) - nucl_coord(i,2)
|
|
z = r(3) - nucl_coord(i,3)
|
|
d = x*x + y*y + z*z
|
|
e = a * j1b_pen_coef(i) * dexp(-a*d)
|
|
|
|
fact_x += e * x
|
|
fact_y += e * y
|
|
fact_z += e * z
|
|
enddo
|
|
|
|
grad(1) = 2.d0 * fact_x
|
|
grad(2) = 2.d0 * fact_y
|
|
grad(3) = 2.d0 * fact_z
|
|
|
|
elseif((j1b_type .eq. 5) .or. (j1b_type .eq. 105)) then
|
|
|
|
fact_x = 0.d0
|
|
fact_y = 0.d0
|
|
fact_z = 0.d0
|
|
do i = 1, nucl_num
|
|
a = j1b_pen(i)
|
|
x = r(1) - nucl_coord(i,1)
|
|
y = r(2) - nucl_coord(i,2)
|
|
z = r(3) - nucl_coord(i,3)
|
|
d = x*x + y*y + z*z
|
|
e = a * d * dexp(-a*d*d)
|
|
|
|
fact_x += e * x
|
|
fact_y += e * y
|
|
fact_z += e * z
|
|
enddo
|
|
|
|
grad(1) = 4.d0 * fact_x
|
|
grad(2) = 4.d0 * fact_y
|
|
grad(3) = 4.d0 * fact_z
|
|
|
|
else
|
|
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented for grad1_j1b_nucl'
|
|
stop
|
|
|
|
endif
|
|
|
|
return
|
|
end subroutine grad1_j1b_nucl
|
|
|
|
! ---
|
|
|
|
subroutine mu_r_val_and_grad(r1, r2, mu_val, mu_der)
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r1(3), r2(3)
|
|
double precision, intent(out) :: mu_val, mu_der(3)
|
|
double precision :: r(3)
|
|
double precision :: dm_a(1), dm_b(1), grad_dm_a(3,1), grad_dm_b(3,1)
|
|
double precision :: dm_tot, tmp1, tmp2, tmp3
|
|
double precision :: rho1, grad_rho1(3),rho2,rho_tot,inv_rho_tot
|
|
double precision :: f_rho1, f_rho2, d_drho_f_rho1
|
|
double precision :: d_dx1_f_rho1(3),d_dx_rho_f_rho(3),nume
|
|
|
|
if(j1b_type .eq. 200) then
|
|
|
|
!
|
|
! r = 0.5 (r1 + r2)
|
|
!
|
|
! mu[rho(r)] = alpha sqrt(rho) + mu0 exp(-rho)
|
|
!
|
|
! d mu[rho(r)] / dx1 = 0.5 d mu[rho(r)] / dx
|
|
! d mu[rho(r)] / dx = [0.5 alpha / sqrt(rho) - mu0 exp(-rho)] (d rho(r) / dx)
|
|
!
|
|
|
|
PROVIDE mu_r_ct mu_erf
|
|
|
|
r(1) = 0.5d0 * (r1(1) + r2(1))
|
|
r(2) = 0.5d0 * (r1(2) + r2(2))
|
|
r(3) = 0.5d0 * (r1(3) + r2(3))
|
|
|
|
call density_and_grad_alpha_beta(r, dm_a, dm_b, grad_dm_a, grad_dm_b)
|
|
|
|
dm_tot = dm_a(1) + dm_b(1)
|
|
tmp1 = dsqrt(dm_tot)
|
|
tmp2 = mu_erf * dexp(-dm_tot)
|
|
|
|
mu_val = mu_r_ct * tmp1 + tmp2
|
|
|
|
mu_der = 0.d0
|
|
if(dm_tot .lt. 1d-7) return
|
|
|
|
tmp3 = 0.25d0 * mu_r_ct / tmp1 - 0.5d0 * tmp2
|
|
mu_der(1) = tmp3 * (grad_dm_a(1,1) + grad_dm_b(1,1))
|
|
mu_der(2) = tmp3 * (grad_dm_a(2,1) + grad_dm_b(2,1))
|
|
mu_der(3) = tmp3 * (grad_dm_a(3,1) + grad_dm_b(3,1))
|
|
|
|
elseif(j1b_type .eq. 201) then
|
|
|
|
!
|
|
! r = 0.5 (r1 + r2)
|
|
!
|
|
! mu[rho(r)] = alpha rho + mu0 exp(-rho)
|
|
!
|
|
! d mu[rho(r)] / dx1 = 0.5 d mu[rho(r)] / dx
|
|
! d mu[rho(r)] / dx = [0.5 alpha / sqrt(rho) - mu0 exp(-rho)] (d rho(r) / dx)
|
|
!
|
|
|
|
PROVIDE mu_r_ct mu_erf
|
|
|
|
r(1) = 0.5d0 * (r1(1) + r2(1))
|
|
r(2) = 0.5d0 * (r1(2) + r2(2))
|
|
r(3) = 0.5d0 * (r1(3) + r2(3))
|
|
|
|
call density_and_grad_alpha_beta(r, dm_a, dm_b, grad_dm_a, grad_dm_b)
|
|
|
|
dm_tot = dm_a(1) + dm_b(1)
|
|
tmp2 = mu_erf * dexp(-dm_tot)
|
|
|
|
mu_val = mu_r_ct * dm_tot + tmp2
|
|
|
|
tmp3 = 0.5d0 * (mu_r_ct - tmp2)
|
|
mu_der(1) = tmp3 * (grad_dm_a(1,1) + grad_dm_b(1,1))
|
|
mu_der(2) = tmp3 * (grad_dm_a(2,1) + grad_dm_b(2,1))
|
|
mu_der(3) = tmp3 * (grad_dm_a(3,1) + grad_dm_b(3,1))
|
|
|
|
elseif(j1b_type .eq. 202) then
|
|
|
|
! mu(r1,r2) = {rho(r1) f[rho(r1)] + rho(r2) f[rho(r2)]} / RHO
|
|
!
|
|
! RHO = rho(r1) + rho(r2)
|
|
!
|
|
! f[rho] = alpha rho^beta + mu0 exp(-rho)
|
|
!
|
|
! d/dx1 mu(r1,r2) = 1/RHO^2 * {RHO * d/dx1 (rho(r1) f[rho(r1)])
|
|
! - d/dx1 rho(r1) * [rho(r1) f[rho(r1)] + rho(r2) f[rho(r2)]] }
|
|
!
|
|
! d/dx1 f[rho(r1)] = [0.5 alpha / sqrt(rho(r1)) - mu0 exp(-rho(r1))] (d rho(r1) / dx1)
|
|
!
|
|
! d/dx1 (rho(r1) f[rho(r1)] = rho(r1) * d/dx1 f[rho(r1)] + f[rho(r1)] * d/dx1 rho(r1)
|
|
|
|
!!!!!!!!! rho1,rho2,rho1+rho2
|
|
call get_all_rho_grad_rho(r1,r2,rho1,rho2,grad_rho1)
|
|
rho_tot = rho1 + rho2
|
|
if(rho_tot.lt.1.d-10)rho_tot = 1.d-10
|
|
inv_rho_tot = 1.d0/rho_tot
|
|
! f(rho) = mu_r_ct * rho**beta_rho_power + mu_erf * exp(-rho)
|
|
call get_all_f_rho(rho1,rho2,mu_r_ct,mu_erf,beta_rho_power,f_rho1,d_drho_f_rho1,f_rho2)
|
|
d_dx1_f_rho1(1:3) = d_drho_f_rho1 * grad_rho1(1:3)
|
|
d_dx_rho_f_rho(1:3) = rho1 * d_dx1_f_rho1(1:3) + f_rho1 * grad_rho1(1:3)
|
|
nume = rho1 * f_rho1 + rho2 * f_rho2
|
|
mu_val = nume * inv_rho_tot
|
|
mu_der(1:3) = inv_rho_tot*inv_rho_tot * (rho_tot * d_dx_rho_f_rho(1:3) - grad_rho1(1:3) * nume)
|
|
elseif(j1b_type .eq. 203) then
|
|
|
|
! mu(r1,r2) = {rho(r1) f[rho(r1)] + rho(r2) f[rho(r2)]} / RHO
|
|
!
|
|
! RHO = rho(r1) + rho(r2)
|
|
!
|
|
! f[rho] = alpha rho^beta + mu0
|
|
!
|
|
! d/dx1 mu(r1,r2) = 1/RHO^2 * {RHO * d/dx1 (rho(r1) f[rho(r1)])
|
|
! - d/dx1 rho(r1) * [rho(r1) f[rho(r1)] + rho(r2) f[rho(r2)]] }
|
|
!
|
|
! d/dx1 f[rho(r1)] = [0.5 alpha / sqrt(rho(r1)) ] (d rho(r1) / dx1)
|
|
!
|
|
! d/dx1 (rho(r1) f[rho(r1)] = rho(r1) * d/dx1 f[rho(r1)] + f[rho(r1)] * d/dx1 rho(r1)
|
|
|
|
!!!!!!!!! rho1,rho2,rho1+rho2
|
|
call get_all_rho_grad_rho(r1,r2,rho1,rho2,grad_rho1)
|
|
rho_tot = rho1 + rho2
|
|
if(rho_tot.lt.1.d-10)rho_tot = 1.d-10
|
|
inv_rho_tot = 1.d0/rho_tot
|
|
! f(rho) = mu_r_ct * rho**beta_rho_power + mu_erf
|
|
call get_all_f_rho_simple(rho1,rho2,mu_r_ct,mu_erf,beta_rho_power,f_rho1,d_drho_f_rho1,f_rho2)
|
|
d_dx1_f_rho1(1:3) = d_drho_f_rho1 * grad_rho1(1:3)
|
|
d_dx_rho_f_rho(1:3) = rho1 * d_dx1_f_rho1(1:3) + f_rho1 * grad_rho1(1:3)
|
|
nume = rho1 * f_rho1 + rho2 * f_rho2
|
|
mu_val = nume * inv_rho_tot
|
|
mu_der(1:3) = inv_rho_tot*inv_rho_tot * (rho_tot * d_dx_rho_f_rho(1:3) - grad_rho1(1:3) * nume)
|
|
elseif(j1b_type .eq. 204) then
|
|
|
|
! mu(r1,r2) = 1/2 * (f[rho(r1)] + f[rho(r2)]}
|
|
!
|
|
! f[rho] = alpha rho^beta + mu0
|
|
!
|
|
! d/dx1 mu(r1,r2) = 1/2 * d/dx1 (rho(r1) f[rho(r1)])
|
|
!
|
|
! d/dx1 f[rho(r1)] = [0.5 alpha / sqrt(rho(r1)) ] (d rho(r1) / dx1)
|
|
!
|
|
! d/dx1 (rho(r1) f[rho(r1)] = rho(r1) * d/dx1 f[rho(r1)] + f[rho(r1)] * d/dx1 rho(r1)
|
|
|
|
!!!!!!!!! rho1,rho2,rho1+rho2
|
|
call get_all_rho_grad_rho(r1,r2,rho1,rho2,grad_rho1)
|
|
rho_tot = rho1 + rho2
|
|
if(rho_tot.lt.1.d-10)rho_tot = 1.d-10
|
|
inv_rho_tot = 1.d0/rho_tot
|
|
! f(rho) = mu_r_ct * rho**beta_rho_power + mu_erf
|
|
call get_all_f_rho_simple(rho1,rho2,mu_r_ct,mu_erf,beta_rho_power,f_rho1,d_drho_f_rho1,f_rho2)
|
|
d_dx1_f_rho1(1:3) = d_drho_f_rho1 * grad_rho1(1:3)
|
|
d_dx_rho_f_rho(1:3) = rho1 * d_dx1_f_rho1(1:3) + f_rho1 * grad_rho1(1:3)
|
|
mu_val = 0.5d0 * ( f_rho1 + f_rho2)
|
|
mu_der(1:3) = d_dx_rho_f_rho(1:3)
|
|
else
|
|
print *, ' j1b_type = ', j1b_type, 'not implemented yet'
|
|
stop
|
|
|
|
endif
|
|
|
|
return
|
|
end subroutine mu_r_val_and_grad
|
|
|
|
! ---
|
|
|
|
subroutine grad1_j1b_nucl_square_num(r1, grad)
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r1(3)
|
|
double precision, intent(out) :: grad(3)
|
|
double precision :: r(3), eps, tmp_eps, vp, vm
|
|
double precision, external :: j1b_nucl_square
|
|
|
|
eps = 1d-5
|
|
tmp_eps = 0.5d0 / eps
|
|
|
|
r(1:3) = r1(1:3)
|
|
|
|
r(1) = r(1) + eps
|
|
vp = j1b_nucl_square(r)
|
|
r(1) = r(1) - 2.d0 * eps
|
|
vm = j1b_nucl_square(r)
|
|
r(1) = r(1) + eps
|
|
grad(1) = tmp_eps * (vp - vm)
|
|
|
|
r(2) = r(2) + eps
|
|
vp = j1b_nucl_square(r)
|
|
r(2) = r(2) - 2.d0 * eps
|
|
vm = j1b_nucl_square(r)
|
|
r(2) = r(2) + eps
|
|
grad(2) = tmp_eps * (vp - vm)
|
|
|
|
r(3) = r(3) + eps
|
|
vp = j1b_nucl_square(r)
|
|
r(3) = r(3) - 2.d0 * eps
|
|
vm = j1b_nucl_square(r)
|
|
r(3) = r(3) + eps
|
|
grad(3) = tmp_eps * (vp - vm)
|
|
|
|
return
|
|
end subroutine grad1_j1b_nucl_square_num
|
|
|
|
! ---
|
|
|
|
subroutine grad1_j12_mu_square_num(r1, r2, grad)
|
|
|
|
include 'constants.include.F'
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r1(3), r2(3)
|
|
double precision, intent(out) :: grad(3)
|
|
double precision :: r(3)
|
|
double precision :: eps, tmp_eps, vp, vm
|
|
double precision, external :: j12_mu_square
|
|
|
|
eps = 1d-5
|
|
tmp_eps = 0.5d0 / eps
|
|
|
|
r(1:3) = r1(1:3)
|
|
|
|
r(1) = r(1) + eps
|
|
vp = j12_mu_square(r, r2)
|
|
r(1) = r(1) - 2.d0 * eps
|
|
vm = j12_mu_square(r, r2)
|
|
r(1) = r(1) + eps
|
|
grad(1) = tmp_eps * (vp - vm)
|
|
|
|
r(2) = r(2) + eps
|
|
vp = j12_mu_square(r, r2)
|
|
r(2) = r(2) - 2.d0 * eps
|
|
vm = j12_mu_square(r, r2)
|
|
r(2) = r(2) + eps
|
|
grad(2) = tmp_eps * (vp - vm)
|
|
|
|
r(3) = r(3) + eps
|
|
vp = j12_mu_square(r, r2)
|
|
r(3) = r(3) - 2.d0 * eps
|
|
vm = j12_mu_square(r, r2)
|
|
r(3) = r(3) + eps
|
|
grad(3) = tmp_eps * (vp - vm)
|
|
|
|
return
|
|
end subroutine grad1_j12_mu_square_num
|
|
|
|
! ---
|
|
|
|
double precision function j12_mu_square(r1, r2)
|
|
|
|
implicit none
|
|
double precision, intent(in) :: r1(3), r2(3)
|
|
double precision, external :: j12_mu
|
|
|
|
j12_mu_square = j12_mu(r1, r2) * j12_mu(r1, r2)
|
|
|
|
return
|
|
end function j12_mu_square
|
|
|
|
! ---
|
|
|
|
subroutine f_mu_and_deriv_mu(rho,alpha,mu0,beta,f_mu,d_drho_f_mu)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! function giving mu as a function of rho
|
|
!
|
|
! f_mu = alpha * rho**beta + mu0 * exp(-rho)
|
|
!
|
|
! and its derivative with respect to rho d_drho_f_mu
|
|
END_DOC
|
|
double precision, intent(in) :: rho,alpha,mu0,beta
|
|
double precision, intent(out) :: f_mu,d_drho_f_mu
|
|
f_mu = alpha * (rho)**beta + mu0 * dexp(-rho)
|
|
d_drho_f_mu = alpha * beta * rho**(beta-1.d0) - mu0 * dexp(-rho)
|
|
|
|
end
|
|
|
|
|
|
subroutine get_all_rho_grad_rho(r1,r2,rho1,rho2,grad_rho1)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! returns the density in r1,r2 and grad_rho at r1
|
|
END_DOC
|
|
double precision, intent(in) :: r1(3),r2(3)
|
|
double precision, intent(out):: grad_rho1(3),rho1,rho2
|
|
double precision :: dm_a(1), dm_b(1), grad_dm_a(3,1), grad_dm_b(3,1)
|
|
call density_and_grad_alpha_beta(r1, dm_a, dm_b, grad_dm_a, grad_dm_b)
|
|
rho1 = dm_a(1) + dm_b(1)
|
|
grad_rho1(1:3) = grad_dm_a(1:3,1) + grad_dm_b(1:3,1)
|
|
call density_and_grad_alpha_beta(r2, dm_a, dm_b, grad_dm_a, grad_dm_b)
|
|
rho2 = dm_a(1) + dm_b(1)
|
|
end
|
|
|
|
subroutine get_all_f_rho(rho1,rho2,alpha,mu0,beta,f_rho1,d_drho_f_rho1,f_rho2)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! returns the values f(mu(r1)), f(mu(r2)) and d/drho(1) f(mu(r1))
|
|
END_DOC
|
|
double precision, intent(in) :: rho1,rho2,alpha,mu0,beta
|
|
double precision, intent(out):: f_rho1,d_drho_f_rho1,f_rho2
|
|
double precision :: tmp
|
|
call f_mu_and_deriv_mu(rho1,alpha,mu0,beta,f_rho1,d_drho_f_rho1)
|
|
call f_mu_and_deriv_mu(rho2,alpha,mu0,beta,f_rho2,tmp)
|
|
end
|
|
|
|
|
|
subroutine get_all_f_rho_simple(rho1,rho2,alpha,mu0,beta,f_rho1,d_drho_f_rho1,f_rho2)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! returns the values f(mu(r1)), f(mu(r2)) and d/drho(1) f(mu(r1))
|
|
END_DOC
|
|
double precision, intent(in) :: rho1,rho2,alpha,mu0,beta
|
|
double precision, intent(out):: f_rho1,d_drho_f_rho1,f_rho2
|
|
double precision :: tmp
|
|
call f_mu_and_deriv_mu_simple(rho1,alpha,mu0,beta,f_rho1,d_drho_f_rho1)
|
|
call f_mu_and_deriv_mu_simple(rho2,alpha,mu0,beta,f_rho2,tmp)
|
|
end
|
|
|
|
subroutine f_mu_and_deriv_mu_simple(rho,alpha,mu0,beta,f_mu,d_drho_f_mu)
|
|
implicit none
|
|
BEGIN_DOC
|
|
! function giving mu as a function of rho
|
|
!
|
|
! f_mu = alpha * rho**beta + mu0
|
|
!
|
|
! and its derivative with respect to rho d_drho_f_mu
|
|
END_DOC
|
|
double precision, intent(in) :: rho,alpha,mu0,beta
|
|
double precision, intent(out) :: f_mu,d_drho_f_mu
|
|
f_mu = alpha * (rho)**beta + mu0
|
|
d_drho_f_mu = alpha * beta * rho**(beta-1.d0)
|
|
|
|
end
|
|
|