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exercise:mm_uzh:h2o_diff [2014/05/08 21:22] – talirzexercises: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 has surfaces. This approximation becomes problematic, when the real-world system to be studied consists only of a few simulation cells.+  - We simulate an infinite system, thus neglecting the fact that any real-world system is finite. This approximation becomes problematic, when the real-world system to be studied consists only of a few simulation cells.
   - 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. 
 +</note>
 <note>**TASK 1** <note>**TASK 1**
-  - 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 ''./get_t_sigma abc.ener'' to calculate the standard deviation of the temperature for your simulation as well as for the provided simulations of larger cells containing 64, 128 and 256 water molecules. +  - Use the provided script ''./get_t_sigma file.ener'' to calculate the standard deviation of the temperature for your simulation as well as for the provided simulations of larger cells containing 64, 128 and 256 water molecules. 
-  - How are temperature fluctuations expected to depend on system size? Use gnuplot's fitting functionality to check whether they follow the corresponding law.+  - How are temperature fluctuations expected to depend on system size? Use gnuplot's fitting functionality to check whether they follow the corresponding law. //Hint:// See e.g. [[http://books.google.ch/books?id=5qTzldS9ROIC|"Understanding Molecular Simulations"]] by Frenkel and Smit, sections 4.1 and 6.2. (2P)
 </note> </note>
  
-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 $\langle ... \rangle$ runs over all particles in the system.
  
-We have provided a Fortran program that calculates the msd from a trajectory in a ''.xyz'' file in units of $\unicode{x212B}^2$ as a function of time in fs.+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 that uses this algorithm to extract the msd from a trajectory in a ''.xyz'' file. 
 <code bash> <code bash>
-gfortran msd.f90 -o msd.x     # compile msd.x executable +gfortran msd.f90 -o msd.x  # compile msd.x executable 
-./msd.x < msd.in > msd-64.out # run it with msd.in input file+./msd.x < msd.in           # check input file 'msd.in' before you run!
 </code> </code>
 +Per default, ''msd.x'' writes the msd in units of $\unicode{x212B}^2$ as a function of time in fs.
 +
 +Once you have calculated the msd, have a look into section III of the article on how to fit the diffusion constant.
  
 <note>**TASK 2** <note>**TASK 2**
  
-  - While your simulation is running, calculate the msd for the provided simulations of 64, 128 and 256 water molecules, modifying ''msd.in'' as needed. //Note:// ''msd.x'' may run up to 30min for the largest cell. FIXME do we have a progress indicator? +  - We have precalculated trajectories for 64, 128 and 256 water molecules (ask your teaching assistant). Use ''msd.x'' to calculate the msd, modifying ''msd.in'' as needed. //Note:// ''msd.x'' may run up to 30 minutes for the largest cell. 
-  - Plot the msd as a function of time using a double logarithmic scale. Can you identify different regimes? //Note:// With our method, the number of samples collected for $\text{msd}(t_0)$ decreases like $1/t_0$. +  - Plot the msd as a function of time on a double logarithmic scale. Can you identify different regimes? Why does the signal become noisy towards long times? (2P) 
-  -  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 magnitude. If not, check your units!
 </note> </note>
  
-On the next day, when your MD simulation has finished. +When your MD of the 32 water molecules has finished (for example on the next day), you can start fitting the diffusion constant. 
-<note>**TASK 2**+<note>**TASK 3**
  
-  - Calculate also $D_{PBC}(L)$ for the 32 water molecules.+  - Calculate $D_{PBC}(L)$ also for the 32 water molecules.
   - 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 $\eta$ from the slope of $D_{PBC}(1/L)$. 
-  - Compare the result to data in the paper.+  - Compare the results to the data in the paper.
 </note> </note>
exercises/2014_uzh_molsim/h2o_diff.1399584120.txt.gz · Last modified: 2020/08/21 10:14 (external edit)