Time correlation functions: trtcf.f

This utility computes some time correlation functions. For a molecular vector $\vec{n}(t)$, the time correlation function can be determined as:

$$c(t) = \frac{\langle\vec{n}(t_0)\cdot\vec{n}(t_0+t)\rangle} {\langle\vec{n}(t_0)^2\rangle}$$ (14)

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

The program can compute the following time correlation functions:

• Molecular translational velocity (velocity of the center of mass) and their X,Y,Z components in the laboratory or in the molecular coordinate systems
• Molecular angular velocity and their X,Y,Z components in the laboratory or in the molecular coordinate systems
• Dipole moment and its second Legendre polynomial
• Of a chosen molecular vector and its second Legendre polynomial

The second Legendre polynomial TCF is defined as:

$$c(t) = \frac{\langle L_2(\vec{n}(t_0)\cdot\vec{n}(t_0+t))\rangle} {\langle L_2(\vec{n}(t_0)^2)\rangle}$$ (15)

where $L_2(x) = 0.5(3\cos^2 x -1)$

Compilation:

f77 -O3 -o trtcf trtcf.f tranal_base.f

Note that compilation of trtcf.f requires, in addition to the common header file tranal.h, another header file trtcf.h, which may need to be edited in order to set array borders matching the studied system

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

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

The following parameters are used:

• FILTCF = <filename>

  Defines the name of the output file

• NSTEG = <int.num>

  Number of time steps in the time correlation functions

• DTCF = <value>

  TCF time step

  It is recommended that TCF time step be equal to the trajectory time step multiplied by parameter ISTEP defined in the trajectory part of the input. The total time of tracking TCF is NSTEG*DTCF

• ITCF = <i1>,<i2>,...,<i12>

  Flags (integers) specifying which TCF to compute (zero value - do not compute) Meanings of the flags are following:

  • <i1> - linear velocity of molecular center of mass

  • <i2> - angular molecular velocity

  • <i3> - dipole moment

  • <i4> - second Legendre polynomial of dipole moment

  • <i5> - a specific molecular vector (see below)

  • <i6> - second Legendre polynomial of a specific vector

  • <i7>,<i8>,<i9> - X, Y, and Z projections of the linear molecular velocity. The projections are calculated in the laboratory frame if the flags are equal to 1, and they are calculated in the principal molecular frame determined by the axis of the inertia tensor if the corresponding flags are equal to 2.

  • <i10>,<i11>,<i12> - X, Y, and Z projections of the angular molecular velocity. The projections are calculated in the laboratory frame if the flags are equal to 1, and they are calculated in the principal molecular frame determined by the axis of the inertia tensor if the corresponding flags are equal to 2.

• N1 = <n1-1>,<n2-2>,...
  N2 = <n2-1>,<n2-2>,...
  

  NTYPES values in each of the two lines, one per each molecular type. These values specify sites (two per each molecule) which define the molecular vector whose TCF is calculated