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qp2/plugins/local/non_h_ints_mu/jast_deriv_utils.irp.f
eginer 1221d48395 failure attempts in mu(r)
2024-09-05 22:01:22 +02:00

947 lines
26 KiB
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subroutine get_deriv_r12_j12(x,mu,d_dx_j)
implicit none
include 'constants.include.F'
BEGIN_DOC
! d/dr12 j(mu,r12)
END_DOC
double precision, intent(in) :: x,mu
double precision, intent(out) :: d_dx_j
d_dx_j = 0.d0
if(x .lt. 1d-10) return
if(j2e_type .eq. "Mu" .or. j2e_type .eq. "Mur") then
d_dx_j = 0.5d0 * (1.d0 - derf(mu * x))
else if(j2e_type .eq. "Mugauss" .or. j2e_type .eq. "Murgauss" ) then
double precision :: x_tmp
x_tmp = mu * x
! gradient of j(mu,x)
d_dx_j = 0.5d0 * (1.d0 - derf(x_tmp))
! gradient of gaussian additional term
x_tmp *= alpha_mu_gauss
x_tmp *= x_tmp
d_dx_j += -0.5d0 * mu * c_mu_gauss * x * dexp(-x_tmp)
else
print *, ' Error in get_deriv_r12_j12: Unknown j2e_type = ', j2e_type
stop
endif
end
subroutine get_deriv_mu_j12(x,mu,d_d_mu)
implicit none
BEGIN_DOC
! d/dmu j(mu,r12)
END_DOC
include 'constants.include.F'
double precision, intent(in) :: x,mu
double precision, intent(out) :: d_d_mu
double precision :: x_tmp,inv_mu_2,inv_alpha_2
d_d_mu = 0.d0
if(x .lt. 1d-10) return
x_tmp = x*mu
if(mu.lt.1.d-10) return
inv_mu_2 = mu*mu
inv_mu_2 = 1.d0/inv_mu_2
if(j2e_type .eq. "Mu" .or. j2e_type .eq. "Mur") then
! e^{-(r12*mu)^2}/(2 sqrt(pi) * mu^2)
d_d_mu = dexp(-x_tmp*x_tmp) * inv_sq_pi_2 * inv_mu_2
else if(j2e_type .eq. "Mugauss" .or. j2e_type .eq. "Murgauss" ) then
d_d_mu = dexp(-x_tmp*x_tmp) * inv_sq_pi_2 * inv_mu_2
inv_alpha_2 = 1.d0/alpha_mu_gauss
inv_alpha_2 *= inv_alpha_2
x_tmp *= alpha_mu_gauss
x_tmp *= x_tmp
d_d_mu += -0.25d0 * c_mu_gauss*inv_alpha_2*dexp(-x_tmp) * (1.d0 + 2.d0 * x_tmp) * inv_mu_2
else
print *, ' Error in get_deriv_r12_j12: Unknown j2e_type = ', j2e_type
stop
endif
end
! ---
double precision function j12_mu(r1, r2)
BEGIN_DOC
! j(mu,r12) = 1/2 r12 (1 - erf(mu r12)) - 1/2 (sqrt(pi) * mu) e^{-(mu*r12)^2}
END_DOC
include 'constants.include.F'
implicit none
double precision, intent(in) :: r1(3), r2(3)
double precision :: mu_tmp, r12
if(j2e_type .eq. "Mu") 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 if(j2e_type .eq. "Mugauss") 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)) )
double precision :: r12_tmp
r12_tmp = mu_erf * r12
j12_mu = 0.5d0 * r12 * (1.d0 - derf(r12_tmp)) - inv_sq_pi_2 * dexp(-r12_tmp*r12_tmp) / mu_erf
r12_tmp *= alpha_mu_gauss
j12_mu += 0.25d0 * c_mu_gauss / (alpha_mu_gauss*alpha_mu_gauss*mu_erf) * dexp(-r12_tmp*r12_tmp)
else
print *, ' Error in j12_mu: Unknown j2e_type = ', j2e_type
stop
endif ! j2e_type
return
end
! ---
subroutine grad1_j12_mu(r1, r2, grad)
BEGIN_DOC
!
! gradient of j(mu(r1,r2),r12) form of jastrow.
!
! if mu(r1,r2) = cst --->
!
! d/dx1 j(mu,r12) = 0.5 * (1 - erf(mu *r12))/r12 * (x1 - x2)
!
! if mu(r1,r2) /= cst --->
!
! 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
double precision :: mu_val, mu_tmp, mu_der(3)
grad = 0.d0
if(j2e_type .eq. "Mu".or.j2e_type .eq. "Mugauss") 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
call get_deriv_r12_j12(r12,mu_erf,tmp)
! tmp = 0.5d0 * (1.d0 - derf(mu_erf * r12)) / r12
grad(1) = tmp * dx
grad(2) = tmp * dy
grad(3) = tmp * dz
grad *= 1.d0/r12
elseif(j2e_type .eq. "Mur" .or. j2e_type .eq. "Murgauss") then
double precision :: jast
call grad_j_sum_mu_of_r(r1,r2,jast,grad)
elseif(j2e_type .eq. "Bump") then
double precision ::grad_jast(3)
call get_grad_j_bump_mu_of_r(r1,r2,grad_jast)
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) then
grad(1) = 0.d0
grad(2) = 0.d0
grad(3) = 0.d0
return
endif
tmp = 0.5d0 * (1.d0 - derf(mu_erf * r12)) / r12
grad(1) = 0.5d0 * tmp * dx
grad(2) = 0.5d0 * tmp * dy
grad(3) = 0.5d0 * tmp * dz
grad(1) += 0.5d0 * grad_jast(1)
grad(2) += 0.5d0 * grad_jast(2)
grad(3) += 0.5d0 * grad_jast(3)
else
print *, ' Error in grad1_j12_mu: Unknown j2e_type = ', j2e_type
stop
endif ! j2e_type
grad = -grad
return
end
! ---
double precision function env_nucl(r)
implicit none
double precision, intent(in) :: r(3)
integer :: i
double precision :: a, d, e, x, y, z
if(env_type .eq. "Sum_Slat") then
env_nucl = 1.d0
do i = 1, nucl_num
a = env_expo(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)) )
env_nucl = env_nucl - env_coef(i) * dexp(-a*dsqrt(d))
enddo
elseif(env_type .eq. "Prod_Gauss") then
env_nucl = 1.d0
do i = 1, nucl_num
a = env_expo(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)
env_nucl = env_nucl * e
enddo
elseif(env_type .eq. "Sum_Gauss") then
env_nucl = 1.d0
do i = 1, nucl_num
a = env_expo(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)) )
env_nucl = env_nucl - env_coef(i) * dexp(-a*d)
enddo
elseif(env_type .eq. "Sum_Quartic") then
env_nucl = 1.d0
do i = 1, nucl_num
a = env_expo(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
env_nucl = env_nucl - env_coef(i) * dexp(-a*d*d)
enddo
else
print *, ' Error in env_nucl: Unknown env_type = ', env_type
stop
endif
return
end
! ---
double precision function env_nucl_square(r)
implicit none
double precision, intent(in) :: r(3)
integer :: i
double precision :: a, d, e, x, y, z
if(env_type .eq. "Sum_Slat") then
env_nucl_square = 1.d0
do i = 1, nucl_num
a = env_expo(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)) )
env_nucl_square = env_nucl_square - env_coef(i) * dexp(-a*dsqrt(d))
enddo
env_nucl_square = env_nucl_square * env_nucl_square
elseif(env_type .eq. "Prod_Gauss") then
env_nucl_square = 1.d0
do i = 1, nucl_num
a = env_expo(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)
env_nucl_square = env_nucl_square * e
enddo
env_nucl_square = env_nucl_square * env_nucl_square
elseif(env_type .eq. "Sum_Gauss") then
env_nucl_square = 1.d0
do i = 1, nucl_num
a = env_expo(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)) )
env_nucl_square = env_nucl_square - env_coef(i) * dexp(-a*d)
enddo
env_nucl_square = env_nucl_square * env_nucl_square
elseif(env_type .eq. "Sum_Quartic") then
env_nucl_square = 1.d0
do i = 1, nucl_num
a = env_expo(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
env_nucl_square = env_nucl_square - env_coef(i) * dexp(-a*d*d)
enddo
env_nucl_square = env_nucl_square * env_nucl_square
else
print *, ' Error in env_nucl_square: Unknown env_type = ', env_type
stop
endif
return
end
! ---
subroutine grad1_env_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(env_type .eq. "Sum_Slat") then
fact_x = 0.d0
fact_y = 0.d0
fact_z = 0.d0
do i = 1, nucl_num
a = env_expo(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 * env_coef(i) * 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(env_type .eq. "Prod_Gauss") 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_env1s_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_env1s(j,i)) * env_expo(j)
dx = x - nucl_coord(j,1)
dy = y - nucl_coord(j,2)
dz = z - nucl_coord(j,3)
phase += List_env1s(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(env_type .eq. "Sum_Gauss") then
fact_x = 0.d0
fact_y = 0.d0
fact_z = 0.d0
do i = 1, nucl_num
a = env_expo(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 * env_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(env_type .eq. "Sum_Quartic") then
fact_x = 0.d0
fact_y = 0.d0
fact_z = 0.d0
do i = 1, nucl_num
a = env_expo(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 * env_coef(i) * 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 *, ' Error in grad1_env_nucl: Unknown env_type = ', env_type
stop
endif
return
end
! ---
subroutine mu_r_val_and_grad(r1, r2, mu_val, mu_der)
BEGIN_DOC
! various flavours of mu(r1,r2)
! depends on essentially the density and other related quantities
!
! change the variable "murho_type" to change type
!
! murho_type == -1 :: mu(r1,r2) = (rho(r1) mu_mf(r1) + rho(r2) mu_mf(r2))/[rho(r1)+rho(r2)]
!
! == 0 :: mu(r1,r2) = (sqrt(rho(r1)) mu_mf(r1) + sqrt(rho(r2)) mu_mf(r2))/[sqrt(rho(r1))+sqrt(rho(r2))]
!
! == -2 :: mu(r1,r2) = 0.5(mu_mf(r1) + mu_mf(r2))
END_DOC
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
double precision :: mu_mf_r1, dm_r1, grad_mu_mf_r1(3), grad_dm_r1(3)
double precision :: mu_mf_r2, dm_r2, grad_mu_mf_r2(3), grad_dm_r2(3)
double precision :: num, denom, grad_denom(3), grad_num(3)
double precision :: dsqrt_dm_r1
PROVIDE murho_type
PROVIDE mu_r_ct mu_erf
if(murho_type .eq. 0) then
call grad_mu_of_r_mean_field(r1,mu_mf_r1, dm_r1, grad_mu_mf_r1, grad_dm_r1)
call grad_mu_of_r_mean_field(r2,mu_mf_r2, dm_r2, grad_mu_mf_r2, grad_dm_r2)
dsqrt_dm_r1 = dsqrt(dm_r1)
denom = (dsqrt_dm_r1 + dsqrt(dm_r2) )
if(denom.lt.1.d-7)then
mu_val = 1.d+10
mu_der = 0.d0
return
endif
num = (dsqrt(dm_r1) * mu_mf_r1 + dsqrt(dm_r2) * mu_mf_r2)
mu_val = num / denom
grad_denom = grad_dm_r1/dsqrt_dm_r1
grad_num = dsqrt(dm_r1) * grad_mu_mf_r1 + mu_mf_r1 * grad_dm_r1
mu_der = (grad_num * denom - num * grad_denom)/(denom*denom)
else if(murho_type .eq. -1) then
call grad_mu_of_r_mean_field(r1,mu_mf_r1, dm_r1, grad_mu_mf_r1, grad_dm_r1)
call grad_mu_of_r_mean_field(r2,mu_mf_r2, dm_r2, grad_mu_mf_r2, grad_dm_r2)
denom = (dm_r1 + dm_r2 )
if(denom.lt.1.d-7)then
mu_val = 1.d+10
mu_der = 0.d0
return
endif
num = (dm_r1 * mu_mf_r1 + dm_r2 * mu_mf_r2)
mu_val = num / denom
grad_denom = grad_dm_r1
grad_num = dm_r1 * grad_mu_mf_r1 + mu_mf_r1 * grad_dm_r1
mu_der = (grad_num * denom - num * grad_denom)/(denom*denom)
else if(murho_type .eq. -2) then
call grad_mu_of_r_mean_field(r1,mu_mf_r1, dm_r1, grad_mu_mf_r1, grad_dm_r1)
call grad_mu_of_r_mean_field(r2,mu_mf_r2, dm_r2, grad_mu_mf_r2, grad_dm_r2)
mu_val = 0.5d0 * (mu_mf_r1 + mu_mf_r2)
mu_der = 0.5d0 * grad_mu_mf_r1
else if(murho_type .eq. 1) 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)
!
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(murho_type .eq. 2) 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)
!
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(murho_type .eq. 3) 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(murho_type .eq. 4) 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
if(rho_tot.lt.1.d-10)then
mu_val = mu_erf
mu_der = 0.d0
return
endif
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(murho_type .eq. 5) 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
if(rho_tot.lt.1.d-10)then
mu_val = mu_erf
mu_der = 0.d0
return
endif
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 * erf(zeta_erf_mu_of_r * rho) + mu_eff * (1 - erf(zeta_erf_mu_of_r*rho))
call get_all_f_rho_erf(rho1,rho2,mu_r_ct,beta_rho_power,mu_erf,zeta_erf_mu_of_r,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)
else
print *, ' Error in mu_r_val_and_grad: Unknown env_type = ', env_type
stop
endif
return
end
! ---
subroutine grad1_env_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 :: env_nucl_square
eps = 1d-5
tmp_eps = 0.5d0 / eps
r(1:3) = r1(1:3)
r(1) = r(1) + eps
vp = env_nucl_square(r)
r(1) = r(1) - 2.d0 * eps
vm = env_nucl_square(r)
r(1) = r(1) + eps
grad(1) = tmp_eps * (vp - vm)
r(2) = r(2) + eps
vp = env_nucl_square(r)
r(2) = r(2) - 2.d0 * eps
vm = env_nucl_square(r)
r(2) = r(2) + eps
grad(2) = tmp_eps * (vp - vm)
r(3) = r(3) + eps
vp = env_nucl_square(r)
r(3) = r(3) - 2.d0 * eps
vm = env_nucl_square(r)
r(3) = r(3) + eps
grad(3) = tmp_eps * (vp - vm)
return
end
! ---
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
! ---
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
! ---
subroutine f_mu_and_deriv_mu(rho, alpha, mu0, beta, f_mu, d_drho_f_mu)
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
implicit none
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)
BEGIN_DOC
! returns the density in r1,r2 and grad_rho at r1
END_DOC
implicit none
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)
BEGIN_DOC
! returns the values f(mu(r1)), f(mu(r2)) and d/drho(1) f(mu(r1))
END_DOC
implicit none
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)
BEGIN_DOC
! returns the values f(mu(r1)), f(mu(r2)) and d/drho(1) f(mu(r1))
END_DOC
implicit none
double precision, intent(in) :: rho1, rho2, alpha, mu0, beta
double precision, intent(out) :: f_rho1, d_drho_f_rho1, f_rho2
double precision :: tmp
if(rho1.lt.1.d-10) then
f_rho1 = 0.d0
d_drho_f_rho1 = 0.d0
else
call f_mu_and_deriv_mu_simple(rho1, alpha, mu0, beta, f_rho1, d_drho_f_rho1)
endif
if(rho2.lt.1.d-10)then
f_rho2 = 0.d0
else
call f_mu_and_deriv_mu_simple(rho2, alpha, mu0, beta, f_rho2, tmp)
endif
end
! ---
subroutine f_mu_and_deriv_mu_simple(rho, alpha, mu0, beta, f_mu, d_drho_f_mu)
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
implicit none
double precision, intent(in) :: rho, alpha, mu0, beta
double precision, intent(out) :: f_mu, d_drho_f_mu
f_mu = alpha**beta * (rho)**beta + mu0
d_drho_f_mu = alpha**beta * beta * rho**(beta-1.d0)
end
! ---
subroutine f_mu_and_deriv_mu_erf(rho,alpha,zeta,mu0,beta,f_mu,d_drho_f_mu)
include 'constants.include.F'
BEGIN_DOC
! function giving mu as a function of rho
!
! f_mu = (alpha * rho)**zeta * erf(beta * rho) + mu0 * (1 - erf(beta*rho))
!
! and its derivative with respect to rho d_drho_f_mu
!
! d_drho_f_mu = 2 beta/sqrt(pi) * exp(-(beta*rho)**2) * ( (alpha*rho)**zeta - mu0)
! + alpha * zeta * (alpha *rho)**(zeta-1) * erf(beta*rho)
END_DOC
implicit none
double precision, intent(in) :: rho, alpha, mu0, beta, zeta
double precision, intent(out) :: f_mu, d_drho_f_mu
f_mu = (alpha * rho)**zeta * derf(beta * rho) + mu0 * (1.d0 - derf(beta*rho))
d_drho_f_mu = 2.d0 * beta * inv_sq_pi * dexp(-(beta*rho)**2) * ( (alpha*rho)**zeta - mu0) &
+ alpha * zeta * (alpha *rho)**(zeta-1) * derf(beta*rho)
end
! ---
subroutine get_all_f_rho_erf(rho1, rho2, alpha, zeta, mu0, beta, f_rho1, d_drho_f_rho1, f_rho2)
BEGIN_DOC
! returns the values f(mu(r1)), f(mu(r2)) and d/drho(1) f(mu(r1))
! with f_mu = (alpha * rho)**zeta * erf(beta * rho) + mu0 * (1 - erf(beta*rho))
END_DOC
implicit none
double precision, intent(in) :: rho1, rho2, alpha, mu0, beta, zeta
double precision, intent(out) :: f_rho1, d_drho_f_rho1, f_rho2
double precision :: tmp
if(rho1 .lt. 1.d-10) then
f_rho1 = mu_erf
d_drho_f_rho1 = 0.d0
else
call f_mu_and_deriv_mu_erf(rho1, alpha, zeta, mu0, beta, f_rho1, d_drho_f_rho1)
endif
if(rho2 .lt. 1.d-10)then
f_rho2 = mu_erf
else
call f_mu_and_deriv_mu_erf(rho2, alpha, zeta, mu0, beta, f_rho2, tmp)
endif
end
! ---
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