diff --git a/plugins/local/basis_correction/weak_corr_func.irp.f b/plugins/local/basis_correction/weak_corr_func.irp.f
index a31ff3af..99ea504b 100644
--- a/plugins/local/basis_correction/weak_corr_func.irp.f
+++ b/plugins/local/basis_correction/weak_corr_func.irp.f
@@ -10,21 +10,28 @@
  double precision :: rho_a, rho_b, ec, rho, p2
  double precision :: wall0,wall1,weight,mu
  logical :: dospin
+ double precision, external :: g0_UEG_mu_inf
  dospin = .true. ! JT dospin have to be set to true for open shell
  print*,'Providing ecmd_lda_mu_of_r ...'
 
  ecmd_lda_mu_of_r = 0.d0
  call wall_time(wall0)
- if (mu_of_r_potential.EQ."proj")then
+ if (mu_of_r_potential.EQ."proj_DUMMY")then
   do istate = 1, N_states
     do ipoint = 1, n_points_final_grid
     ! mu(r) defined by Eq. (37) of J. Chem. Phys. 149, 194301 (2018)
     mu     = mu_of_r_prov(ipoint,istate)
     weight = final_weight_at_r_vector(ipoint)
-    rho = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate) + one_e_dm_and_grad_beta_in_r(4,ipoint,istate)
-    p2 = !TODO
-    rho_a = 0.5d0*(rho - dsqrt(-p2 + rho*rho))
-    rho_b = 0.5d0*(rho + dsqrt(-p2 + rho*rho))
+    rho_a = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate)
+    rho_b =  one_e_dm_and_grad_beta_in_r(4,ipoint,istate)
+    rho = rho_a + rho_b
+!    p2 = rho_a*rho_b
+!  We take the on-top pair density of the UEG which is (1-zeta^2) rhoc^2 g0 = 4 rhoa * rhob * g0
+    p2 = 4.d0 * rho_a * rho_b * g0_UEG_mu_inf(rho_a,rho_b)
+    rho_a = 0.5d0*(rho + dsqrt(rho*rho - 4.d0*p2))
+    rho_b = 0.5d0*(rho - dsqrt(rho*rho - 4.d0*p2))
+!    rho_a = 0.5d0*rho
+!    rho_b = 0.5d0*rho
     ! Ecmd within the LDA approximation of PRB 73, 155111 (2006)
     call ESRC_MD_LDAERF (mu,rho_a,rho_b,dospin,ec)
     if(isnan(ec))then
@@ -71,7 +78,7 @@ BEGIN_PROVIDER [double precision, ecmd_pbe_ueg_mu_of_r, (N_states)]
  double precision :: weight
  integer :: ipoint,istate
  double precision :: eps_c_md_PBE,mu,rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),on_top
- double precision :: g0_UEG_mu_inf
+ double precision, external :: g0_UEG_mu_inf
 
  ecmd_pbe_ueg_mu_of_r = 0.d0