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exercises:2015_uzh_molsim:nacl_free_energy

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exercises:2015_uzh_molsim:nacl_free_energy [2015/05/26 16:19] yakutovich |
exercises:2015_uzh_molsim:nacl_free_energy [2020/08/21 10:15] |
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- | ====== Profiles of potential energy and free energy ====== | ||

- | We are going to start with the simplified example of isolated $\text{Na}^+$ and $\text{Cl}^-$ in the //gas phase//, where we can directly compare the results of our computer simulation against the analytical formula used to describe the interaction potential. | ||

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- | We have provided an input file '' | ||

- | < | ||

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- | - Look into '' | ||

- | - Use '' | ||

- | - 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 [[nacl_md|previous exercise]]? (2P) | ||

- | </ | ||

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- | For the next task, we remain with our simple system, but now perform molecular dynamics at $T=1\, | ||

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- | We have prepared a script '' | ||

- | It then integrates the average value of the Shake Lagrange multiplier to calculate the (low-temperature) free energy profile. | ||

- | < | ||

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- | - 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 '' | ||

- | - What effects would you expect at higher temperature? | ||

- | </ | ||

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- | Now, we are ready to move to a more realistic system -- NaCl in water. | ||

- | We have performed constrained MD of NaCl in water and saved the trajectory of the corresponding Lagrange multipliers (ask your teaching assistant). | ||

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- | The script '' | ||

- | < | ||

- | - Perform the free energy integration and plot the free energy profile. | ||

- | - In the [[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) | ||

- | </ | ||

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- | Another way to gain access to the free energy is through the radial distribution function (rdf) of the // | ||

- | 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 & | ||

- | P(r) & | ||

- | F(r) &=& -k_BT \ln\,P(r) | ||

- | \end{eqnarray}$$ | ||

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- | We have performed a trajectory spanning 50 ns of unconstrained molecular dynamics of NaCl in water (ask your teaching assistant). The individual frames are spaced by 1 ps in order to reduce correlation between subsequent frames. | ||

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- | < | ||

- | - In the [[h2o_md|previous exercise]], we computed the O-O radial distribution function for water with acceptable statistics using just 20 ps of simulated time. Give two reasons, why collecting enough statistics for the Na-Cl radial distribution function requires much longer simulation times (with our setup). | ||

- | - Compute the radial distribution function for the provided trajectory and plot it as a function of Na-Cl distance. | ||

- | - Use the equations above to compute the free energy profile. Does it agree with the one constructed from the Shake Lagrange multipliers? | ||

- | </ |

exercises/2015_uzh_molsim/nacl_free_energy.txt ยท Last modified: 2020/08/21 10:15 (external edit)

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