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--- exercise:mm_uzh:nacl_free_energy [2014/05/16 17:11] – talirz
+++ exercise:mm_uzh:nacl_free_energy [2014/05/19 21:45] – talirz
@@ Line 6: / Line 6: @@
 <note>**TASK 1**
-  - Look into ''NaCl_pot.in'' and write down the formula used for the potential energy of the interaction between $\text{Na}^+$ and $\text{Cl}^-$ in Hartree atomic units.
+  - Look into ''NaCl_pot.in'' and write down the formula used for the potential energy of the interaction between $\text{Na}^+$ and $\text{Cl}^-$ in Hartree atomic units. (2P)
   - Use ''./potential_energy.sh'' to calculate the potential energy as a function of Na-Cl distance. Create a plot of the resulting potential energy profile in ''pot_profile'' and the mathematical formula.
-  - What do you observe, when the distance approaches 1/2 of the simulation box? How might the finite size of the simulation box have impacted the MD simulation in the [[http://cp2k.org/exercise:mm_uzh:nacl_md|previous exercise]]?
+  - What do you observe, when the distance approaches 1/2 of the simulation box? How might the finite size of the simulation box have impacted the MD simulation in the [[http://cp2k.org/exercise:mm_uzh:nacl_md|previous exercise]]? (2P)
 </note>
@@ Line 17: / Line 17: @@
 <notes>**TASK 2**
-  - What is a Lagrange multiplier? How can we obtain the free energy profile as a function of the Na-Cl distance using the associated Lagrange multiplier?
+  - What is a Lagrange multiplier? How can we obtain the free energy profile as a function of the Na-Cl distance using the associated Lagrange multiplier? (2P)
   - Run the simulation. What kind of motion does the NaCl dimer perform?
-  - Compare the low-temperature free energy profile in ''fe_profile'' with the potential energy profile. Do the two profiles agree? //Note:// The profiles are shifted with respect to each other. What would be a reasonable reference point for both profiles?
+  - Compare the low-temperature free energy profile in ''fe_profile'' with the potential energy profile. Do the two profiles agree? //Note:// The profiles are shifted with respect to each other. What would be a reasonable reference point for both profiles? (2P)
   - What effects would you expect at higher temperature? //Hint:// If you like, you can adapt the temperature in the input file and give it a go.
 </note>
@@ Line 29: / Line 29: @@
 <note>**TASK 3**
   - Perform the free energy integration and plot the free energy profile.
-  - In the [[http://cp2k.org/exercise:mm_uzh:nacl_md|previous exercise]], you determined the average time required for dissociation of Na-Cl. Is the free energy barrier consistent with the time scale determined before? //Hint:// Use the Arrhenius equation. You can obtain an estimate for the attempt frequency from the high-frequency oscillations in the Na-Cl distance in the previous exercise.
+  - In the [[http://cp2k.org/exercise:mm_uzh:nacl_md|previous exercise]], you determined the average time required for dissociation of Na-Cl. Is the free energy barrier consistent with the time scale determined before? //Hint:// Use the Arrhenius equation. You can obtain an estimate for the attempt frequency from the high-frequency oscillations in the Na-Cl distance in the previous exercise. (2P)
 </note>
-Another way to gain access to the free energy is through the radial distribution function (rdf). The rdf $g(r)$ is related to the free energy $F(r)$ through the following set of equations
+Another way to gain access to the free energy is through the radial distribution function (rdf) of the //unconstrained// system.
+The rdf $g(r)$ is related to the free energy $F(r)$ through the following set of equations
 $$\begin{eqnarray}
 g(r)4\pi r^2 &\propto& \int \delta(r-r') \exp(-\beta H(r'))\,dr  \\