keep working later - term3 of second derivative is wrong

doc/page/usage/excessmodels/uniquac.md

@@ -144,48 +144,30 @@ $$
 
 \(\qquad G^E\):
 
-$$
-\frac{\partial \frac{G^E}{RT}}{\partial n_i} = \ln \left(\frac{\phi_i}{x_i}
-\right) + \sum_k n_k \left(\frac{\frac{d \phi_k}{dn_i}}{\phi_k} -
-\frac{\frac{dx_k}{dn_i}}{x_k}\right) +
-\frac{z}{2}{q}_{i}\ln{\left(\frac{\theta_{i}}{\phi_{i}} \right)} + \frac{z}{2}
-\sum_k {n}_{k} {q}_{k} \left(\frac{\frac{d \theta_{k}}{d {n}_{i}}}{\theta_k} -
-\frac{\frac{d \phi_{k}}{d {n}_{i}}}{\phi_k} \right) - {q}_{i}
-\ln{\left(\sum_l \theta_{l} {\tau}_{li} \right)} - \sum_k {n}_{k} {q}_{k}
-\frac{\sum_l \frac{d \theta_{l}}{d {n}_{i}} {\tau}_{lk}}{\sum_l \theta_{l}
-{\tau}_{lk}}
-$$
-
-Nueva:
 $$
 \frac{\partial \frac{G^E}{RT}}{\partial n_i} = \ln 
 \left(\frac{n_T r_i}{\sum_l r_l n_l} \right) + \sum_k n_k 
-\left(\frac{r_k \sum_l r_l n_l - n_T r_k r_i}{(\sum_l r_l n_l)^2}\right) +
-\frac{z}{2} q_i n_i \ln \left(\frac{q_i \sum_l r_l n_l}{r_i \sum_l q_l n_l} 
-\right) - {q}_{i}
+\left(\frac{\sum_l r_l n_l - n_T r_i}{n_T \sum_l r_l n_l}\right) +
+\frac{z}{2} q_i \ln \left(\frac{q_i \sum_l r_l n_l}{r_i \sum_l q_l n_l} 
+\right) + \frac{z}{2} \sum_k n_k q_k \left(\frac{r_i \sum_l n_l q_l - q_i
+\sum_l n_l r_l}{(\sum_l n_l q_l) (\sum_l n_l r_l)} \right) - {q}_{i}
 \ln{\left(\sum_l \theta_{l} {\tau}_{li} \right)} - \sum_k {n}_{k} {q}_{k}
 \frac{\sum_l \frac{d \theta_{l}}{d {n}_{i}} {\tau}_{lk}}{\sum_l \theta_{l}
 {\tau}_{lk}}
 $$
 
-
-
 Differentiating each term of the first compositional derivative respect to
 \(n_j\) we get:
 
 \(\frac{\partial \frac{G^E}{RT}}{\partial n_i \partial n_j} =\)
 
 $$
-\frac{\frac{d \phi_i}{d n_j}}{\phi_i} - \frac{\frac{d x_i}{d n_j}}{x_i} 
+\frac{\sum_l n_l r_l - n_T r_j}{n_T \sum_l n_l r_l} 
 $$
 
 $$
-+\frac{\frac{d \phi_j}{dn_i}}{\phi_j} -
-\frac{\frac{dx_j}{dn_i}}{x_j}
-+ \sum_k n_k \left(\frac{\frac{d^2\phi_k}{dn_i dn_j} \phi_k -
-  \frac{d\phi_k}{dn_i} \frac{d\phi_k}{dn_j}}{\phi_k^2} \right)
-- \sum_k n_k \left(\frac{\frac{d^2x_k}{dn_i dn_j} x_k -
-  \frac{dx_k}{dn_i} \frac{dx_k}{dn_j}}{x_k^2} \right)
++ \frac{\sum_l n_l r_l - n_T r_i}{n_T \sum_l r_l n_l}
++ \sum_k n_k \left(\frac{r_i r_j}{(\sum_l n_l r_l)^2} - \frac{1}{n_T^2} \right)
 $$
 
 $$

src/models/excess_gibbs/uniquac.f90

@@ -361,8 +361,8 @@ subroutine excess_gibbs(self, n, T, Ge, GeT, GeT2, Gen, GeTn, Gen2)
             ! Combinatorial term
             Gen_comb(i) = (&
                log(n_tot * self%rs(i) / sum_nr) &
-               + sum(n * (self%rs * sum_nr - n_tot * self%rs(i)* self%rs) / sum_nr**2) &
-               + self%z / 2.0_pr * self%qs(i) * n(i) * log(self%qs(i) * sum_nr / self%rs(i) / sum_nq) &
+               + sum(n * (sum_nr - n_tot * self%rs(i)) / n_tot / sum_nr) &
+               + self%z / 2.0_pr * self%qs(i) * log(self%qs(i) * sum_nr / self%rs(i) / sum_nq) &
                + self%z / 2.0_pr * sum(n * self%qs * (self%rs(i) * sum_nq - self%qs(i) * sum_nr) / sum_nq / sum_nr) &
                )
 
@@ -379,15 +379,17 @@ subroutine excess_gibbs(self, n, T, Ge, GeT, GeT2, Gen, GeTn, Gen2)
       ! dn2
       if (dn2) then
          do concurrent(i=1:nc, j=1:nc)
-            trm1 = dphik_dn(i,j) / phik(i) - dxk_dni(i,j) / xk(i)
+            trm1 = (sum_nr - n_tot * self%rs(j)) / n_tot / sum_nr
 
             trm2 = (&
-               dphik_dn(j,i) / phik(j) - dxk_dni(j,i) / xk(j) &
-               + sum(n * (d2phik_dnidnj(:,i,j) * phik - dphik_dn(:,i) * dphik_dn(:,j)) / phik**2) &
-               - sum(n * (d2xk_dnidnj(:,i,j) * xk - dxk_dni(:,i) * dxk_dni(:,j)) / xk**2) &
+               (sum_nr - n_tot * self%rs(i)) / n_tot / sum_nr &
+               + sum(n * (self%rs(i) * self%rs(j) / sum_nr**2 - 1.0_pr / n_tot**2)) &
                )
 
-            trm3 = self%z / 2 * self%qs(i) * (dthetak_dni(i,j) / thetak(i) - dphik_dn(i,j) / phik(i))
+            trm3 = (&
+               self%z / 2 * self%qs(i) * (self%rs(i) * self%rs(j) * sum_nq - &
+               self%rs(i) * self%qs(j) * sum_nr) / sum_nq / sum_nr &
+               )
 
             trm4 = (&
                self%z / 2 * self%qs(j) * (dthetak_dni(j,i) / thetak(j) - dphik_dn(j,i) / phik(j)) &