exercises:2014_uzh_molsim:h2o_diff
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exercise:mm_uzh:h2o_diff [2014/05/08 21:20] – talirz | exercises:2014_uzh_molsim:h2o_diff [2020/08/21 10:15] (current) – external edit 127.0.0.1 | ||
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When simulating liquids or solids under periodic boundary conditions, we are making two fundamental approximations: | When simulating liquids or solids under periodic boundary conditions, we are making two fundamental approximations: | ||
- | - We simulate an infinite system, thus neglecting the fact that any real-world system | + | - We simulate an infinite system, thus neglecting the fact that any real-world system |
- We impose the condition that the properties of the system under study repeat //exactly// from one simulation cell to the next. The quality of this approximation depends on the system under study and the quantity of interest. | - We impose the condition that the properties of the system under study repeat //exactly// from one simulation cell to the next. The quality of this approximation depends on the system under study and the quantity of interest. | ||
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Calculating transport properties typically requires lots of sampling. | Calculating transport properties typically requires lots of sampling. | ||
- | Start the MD simulation for 32 water molecules and see how far you can get (aim at least for 200ps). | + | Start the MD simulation for 32 water molecules and see how far you can get (aim at least for 200 ps). |
+ | <note tip> | ||
+ | This simulation will take a considerable amount of time. | ||
+ | Tasks 1 and 2 can already be completed, while it is running. | ||
+ | </ | ||
< | < | ||
- | - While the job is running, check output of CP2K to verify that all is fine. What is the average temperature? | + | - While the job is running, check the output of CP2K to verify that all is fine. What is the average temperature? |
- | - We want to simulate diffusion at room temperature. Why aren't we using the NVT ensemble? //Hint:// Think about how thermostats work. | + | - We want to simulate diffusion at room temperature. Why aren't we using the $NVT$ ensemble? //Hint:// Think about how thermostats work. |
- | - Use the provided script '' | + | - Use the provided script '' |
- | - How are temperature fluctuations expected to depend on system size? Use gnuplot' | + | - How are temperature fluctuations expected to depend on system size? Use gnuplot' |
</ | </ | ||
- | The mean squared displacement (msd) | + | The mean squared displacement (msd) is defined as |
- | $$\text{msd}(t) = \langle |r(t)-r(0)|^2 \rangle$$ | + | $$\text{msd}(t) = \langle |r(t+t_0)-r(t_0)|^2 \rangle$$ |
- | is related to the diffusion constant (see eq. 17 in the article). | + | where the average $\langle |
- | We have provided a Fortran program to calculate | + | Our simulations are not large enough to obtain reasonable statistics just from averaging over all water molecules. |
+ | We therefore perform an additional average over the time $t_0$: $\text{msd}(t)$ is calculated as an average over all non-overlapping time windows of width $t$ that fit into the total simulation time $T$. | ||
+ | We have provided a Fortran program | ||
<code bash> | <code bash> | ||
- | gfortran msd.f90 -o msd.x | + | gfortran msd.f90 -o msd.x # compile msd.x executable |
- | ./msd.x < msd.in | + | ./msd.x < msd.in |
</ | </ | ||
- | //Note:// By default, the msd is calculated | + | Per default, |
+ | |||
+ | Once you have calculated the msd, have a look into section III of the article on how to fit the diffusion constant. | ||
< | < | ||
- | - While your simulation is running, calculate the msd for the provided simulations of 64, 128 and 256 water molecules, modifying '' | + | - We have precalculated trajectories |
- | - Plot the msd as a function of time using a double logarithmic scale. Can you identify different regimes? | + | - Plot the msd as a function of time on a double logarithmic scale. Can you identify different regimes? |
- | - Obtain the diffusion constant $D_{pbc}$ by fitting a line through the mean square displacement data in the range $2-10$ ps. | + | - Obtain the diffusion constant $D_{pbc}$ by fitting a line through the mean square displacement data in the range $2-10$ ps. |
- | - Compare against the values in Table I. //Note:// We are using a slightly different force field, but the values should be similar. If not, check your units! | + | - Compare against the values in Table I of the article. //Note:// We are using a slightly different force field, but the values should be of a similar |
</ | </ | ||
- | On the next day, when your MD simulation | + | When your MD of the 32 water molecules |
- | < | + | < |
- | - Calculate | + | - Calculate $D_{PBC}(L)$ |
- Plot $D_{PBC}$ as a function of $1/L$, where $L$ is the length of the edge of the simulation box. | - Plot $D_{PBC}$ as a function of $1/L$, where $L$ is the length of the edge of the simulation box. | ||
- Perform a linear fit of this curve to obtain the diffusion constant $D=D_{pbc}(L=\infty)$ | - Perform a linear fit of this curve to obtain the diffusion constant $D=D_{pbc}(L=\infty)$ | ||
- | - Use Eq. 12 in the article to calculate the viscosity. | + | - Use equation (12) in the article to calculate the viscosity |
- | - Compare the result | + | - Compare the results |
</ | </ |
exercises/2014_uzh_molsim/h2o_diff.1399584056.txt.gz · Last modified: 2020/08/21 10:14 (external edit)