diff --git a/doc/Eqs/compute_fep_bar.jpg b/doc/Eqs/compute_fep_bar.jpg new file mode 100644 index 0000000000..772ec9c045 Binary files /dev/null and b/doc/Eqs/compute_fep_bar.jpg differ diff --git a/doc/Eqs/compute_fep_bar.tex b/doc/Eqs/compute_fep_bar.tex new file mode 100644 index 0000000000..a40aa1c297 --- /dev/null +++ b/doc/Eqs/compute_fep_bar.tex @@ -0,0 +1,7 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \left< \frac{1}{1 + \exp\left[\left(U_1 - U_0 - \Delta_0^1A \right) /kT \right]} \right>_0 = \left< \frac{1}{1 + \exp\left[\left(U_0 - U_1 + \Delta_0^1A \right) /kT \right]} \right>_1 \] + +\end{document} diff --git a/doc/Eqs/compute_fep_fdti.jpg b/doc/Eqs/compute_fep_fdti.jpg new file mode 100644 index 0000000000..ae8de241cc Binary files /dev/null and b/doc/Eqs/compute_fep_fdti.jpg differ diff --git a/doc/Eqs/compute_fep_fdti.tex b/doc/Eqs/compute_fep_fdti.tex new file mode 100644 index 0000000000..fdea6faa3d --- /dev/null +++ b/doc/Eqs/compute_fep_fdti.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left( \frac{\partial + A(\lambda)}{\partial\lambda} \right)_\lambda \mathrm{d}\lambda +\approx \sum_{i=0}^{n-1} w_i \frac{A(\lambda_{i} + \delta) - + A(\lambda_i)}{\delta} \] + +\end{document} diff --git a/doc/Eqs/compute_fep_fep.jpg b/doc/Eqs/compute_fep_fep.jpg new file mode 100644 index 0000000000..d84a76b0dd Binary files /dev/null and b/doc/Eqs/compute_fep_fep.jpg differ diff --git a/doc/Eqs/compute_fep_fep.tex b/doc/Eqs/compute_fep_fep.tex new file mode 100644 index 0000000000..718aad3c40 --- /dev/null +++ b/doc/Eqs/compute_fep_fep.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A = +- kT \sum_{i=0}^{n-1} \ln \left< \exp \left( - \frac{U(\lambda_{i+1}) - + U(\lambda_i)}{kT} \right) \right>_{\lambda_i} \] + +\end{document} diff --git a/doc/Eqs/compute_fep_lambda.jpg b/doc/Eqs/compute_fep_lambda.jpg new file mode 100644 index 0000000000..5ef9e8b9f2 Binary files /dev/null and b/doc/Eqs/compute_fep_lambda.jpg differ diff --git a/doc/Eqs/compute_fep_lambda.tex b/doc/Eqs/compute_fep_lambda.tex new file mode 100644 index 0000000000..08c8faaa3c --- /dev/null +++ b/doc/Eqs/compute_fep_lambda.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + \lambda = 0 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_0 \\ + \lambda = 1 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_1 +\end{eqnarray*} + +\end{document} diff --git a/doc/Eqs/compute_fep_ti.jpg b/doc/Eqs/compute_fep_ti.jpg new file mode 100644 index 0000000000..6b0c8fdc19 Binary files /dev/null and b/doc/Eqs/compute_fep_ti.jpg differ diff --git a/doc/Eqs/compute_fep_ti.tex b/doc/Eqs/compute_fep_ti.tex new file mode 100644 index 0000000000..6222dbd503 --- /dev/null +++ b/doc/Eqs/compute_fep_ti.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left< \frac{\partial + U(\lambda)}{\partial\lambda} \right>_\lambda \mathrm{d}\lambda +\approx \sum_{i=0}^{n-1} w_i \left< \frac{U(\lambda_{i} + \delta) - + U(\lambda_i)}{\delta} \right>_{\lambda_i} \] + +\end{document} diff --git a/doc/Eqs/compute_fep_u.jpg b/doc/Eqs/compute_fep_u.jpg new file mode 100644 index 0000000000..62df5dd0c0 Binary files /dev/null and b/doc/Eqs/compute_fep_u.jpg differ diff --git a/doc/Eqs/compute_fep_u.tex b/doc/Eqs/compute_fep_u.tex new file mode 100644 index 0000000000..e847a9ac44 --- /dev/null +++ b/doc/Eqs/compute_fep_u.tex @@ -0,0 +1,7 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ U(\lambda) = U_{\mathrm{bg}} + U_1(\lambda) + U_0(\lambda) \] + +\end{document} diff --git a/doc/Eqs/compute_fep_vol.jpg b/doc/Eqs/compute_fep_vol.jpg new file mode 100644 index 0000000000..a66facad39 Binary files /dev/null and b/doc/Eqs/compute_fep_vol.jpg differ diff --git a/doc/Eqs/compute_fep_vol.tex b/doc/Eqs/compute_fep_vol.tex new file mode 100644 index 0000000000..0301e39788 --- /dev/null +++ b/doc/Eqs/compute_fep_vol.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ \Delta_0^1 A = - kT \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( - + \frac{U(\lambda_{i+1}) - U(\lambda_i)}{kT} \right) +\right>_{\lambda_i}}{\left< V \right>_{\lambda_i}} \] + +\end{document} diff --git a/doc/Eqs/pair_coul_soft.jpg b/doc/Eqs/pair_coul_soft.jpg new file mode 100644 index 0000000000..dad9c745ba Binary files /dev/null and b/doc/Eqs/pair_coul_soft.jpg differ diff --git a/doc/Eqs/pair_coul_soft.tex b/doc/Eqs/pair_coul_soft.tex new file mode 100644 index 0000000000..2ff42a25b6 --- /dev/null +++ b/doc/Eqs/pair_coul_soft.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ +E = \lambda^n \frac{ C q_i q_j}{\epsilon +\left[ \alpha_{\mathrm{C}} (1-\lambda)^2 + r^2 \right]^{1/2}} \qquad r < r_c +\] + +\end{document} diff --git a/doc/Eqs/pair_lj_soft.jpg b/doc/Eqs/pair_lj_soft.jpg new file mode 100644 index 0000000000..856d6d5bbc Binary files /dev/null and b/doc/Eqs/pair_lj_soft.jpg differ diff --git a/doc/Eqs/pair_lj_soft.tex b/doc/Eqs/pair_lj_soft.tex new file mode 100644 index 0000000000..e32f11f0aa --- /dev/null +++ b/doc/Eqs/pair_lj_soft.tex @@ -0,0 +1,15 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ +E = \lambda^n 4 \epsilon +\left\{ + \frac{1}{ \left[ \alpha_{\mathrm{LJ}} (1-\lambda)^2 + + \left( \displaystyle\frac{r}{\sigma} \right)^6 \right]^2 } - + \frac{1}{ \alpha_{\mathrm{LJ}} (1-\lambda)^2 + + \left( \displaystyle\frac{r}{\sigma} \right)^6 } +\right\} \qquad r < r_c + \] + +\end{document}