Diffusion: diffus.f

This procedure computes time dependence of the mean square displacement (MSD) and evaluates the self-diffusion coefficient.

Compilation:

f77 -O3 -o diffus diffus.f tranal_base.f

Input parameters for this utility follow after the trajectory parameters in the NAMELIST block DIFF:

 $DIFF
 parameter=value(s),
 ...
 $END

The following parameters are used:

• FILDIF = <filename>

  Defines the name of the output file

• IDF = <int.num>

  Defined the type of molecules for which diffusion is calculated

• DTT = <value>

  Defines the time interval (in $s$) for MSD calculations. It is very recommended that this parameter is equal to the time step of the trajectory multiplied by ISTEP parameter defined in the trajectory (TRAJ) section of the input file. If the above requirement is not fulfilled, the program may still work but less accurately.

• NTT = <int.value>

  Defines the number of steps for MSD calculation. The total time of tracking the MSD will be thus DTT*NTT.

• IAT = <int.value>

  If IAT=0, MSD is calculated for the centers of masses of the selected molecules. Otherwise MSD is calculated for IAT-th atom of each molecule.

• LCOM = <logical>

  Specifies whether to correct for the total center-of-mass motion of the selected molecules (that is, of type IDF). If .true., the COM for each molecule is computed relative to center of mass motion of the molecules of this type. The default is .false.. Note also, that correction for the center of mass motion of the whole system is not carried out (except the case of only one molecule type and LCOM=.t.).

• FBEG=<value>

  Defines the beginning of linear fitting of the MSD curve to evaluate the self-diffusion coefficient as: FBEG*DTT*NTT . The default value is 0.2 , that is initial 20% of the MSD vs time dependense is not included. It is always recommended to look at the computed MSD vs time dependence to evaluate acceptable value for this parameter.

Futher comments

For each time $t$ the MSD is computed as:

$$\langle \Delta r^2(t)\rangle = \langle (\vec{r}(t_0+t)-\vec{r}(t_0))^2\rangle$$ (14)

where averaging is taken over all molecules of type IDF and all acceptable initial times $t_0$: $t_{beg} \le t_0 \le t_{end}-t$, where $t_{beg}$ and $t_{end}$ are the initial and final time of a continuous part of the whole trajectory respectively. A trajectory is regarded as continuous if each next configuration differ from the previous no more than parameter BREAKM defined in the trajectory part (TRAJ) of the input file.

The output file consists of the following columns:

The first column- time $t$.

The second: for each $t$, evaluation of the diffusion coefficient as:

$$D_{av} = \frac{\langle \Delta r^2(t)\rangle}{6t}$$

The third column: for each $t$, evaluation of the diffusion coefficient as:

$$D_{dif} = \frac{1}{6}\frac{\partial\langle \Delta r^2(t)\rangle}{\partial t}$$

The 4-th column: root square of the MSD (average particle displacement)

5-th - 7-th columns: Evaluation of diffusion coefficient in X-, Y-, and Z-directions as:

$$D_{X} = \frac{\langle \Delta x^2(t)\rangle}{2t}$$

In all cases, diffusion is given in $10^{-5}cm^2/s$.