C2H2 and C2H4 bond energy

TO USE THE FUNCTION LIBRARY (VERSION UP TO DATE) IN THE INTERACTIVE SHELL:

you@eulerX ~$ module load courses mmm vmd

you@eulerX ~$ mmm-init

REMEMBER: this is the command to load the module for the cp2k program:

you@eulerX ~$ module load cp2k

and to submit the job:

you@eulerX ~$ bsub < jobname

Download the 2.1 exercise into your $HOME folder and unzip it.

you@eulerX ~$ wget http://www.cp2k.org/_media/exercises:2015_ethz_mmm:exercise_2.1.zip
you@eulerX ~$ unzip exercises:2015_ethz_mmm:exercise_2.1.zip

All files of this exercise (input and scripts are all commented) can be downloaded from the wiki: exercise_2.1.zip

In this exercise you will test the general AMBER force field, which is suitable for a large class of molecules. In this example you will compute the classical energy of a simple acetylene molecule and apply small variations to the C-C bond lengths.

Then go to the directory “exercise_2.1/c2h2/”.

you@eulerX ~$ cd exercise_2.1/c2h2/

The input file structure of the template is the following:

c2h2.inp.templ

&FORCE_EVAL ! This section defines method for calculating energy and forces
METHOD FIST ! Using Molecular Mechanics
&MM
&FORCEFIELD ! This section specifies forcefield parameters
parm_file_name c2h2.top
! This file contains force field parameters (topology file)
parmtype AMBER
&SPLINE ! This section specifies parameters to set up the splines used in the nonboned interactions (both pair body potential and many body potential)
EMAX_SPLINE 15.0 ! Specify the maximum value of the potential up to which splines will be constructed
&END
&END FORCEFIELD
&POISSON ! This section specifies parameters for the Poisson solver
&EWALD ! This section specifies parameters for the EWALD summation method (for the electrostatics)
EWALD_TYPE SPME ! Smooth particle mesh using beta-Euler splines
ALPHA .36
GMAX 128 ! Number of grid points
&END EWALD
&END POISSON
&PRINT ! This section controls printing options
&FF_INFO
&END
&FF_PARAMETER_FILE
&END
&END
&END MM
&SUBSYS ! This section defines the system
&CELL ! Unit cell set up
ABC 50 50 50 ! Lengths of the cell vectors A, B, and C
&END CELL
&COORD ! This section specify all the atoms and their coordinates
H 0 0 0
C _C1_ 0 0
C _C2_ 0 0
H _H2_ 0 0
&END COORD
&TOPOLOGY
CHARGE_BETA ! Read MM charges from the BETA field of PDB file
CONNECTIVITY AMBER ! Use AMBER topology file for reading connectivity
CONN_FILE_NAME c2h2.top
! This file contains connectivity data
&END TOPOLOGY
&PRINT
&TOPOLOGY_INFO
AMBER_INFO
&END
&END
&END SUBSYS
&END FORCE_EVAL

&GLOBAL ! Section with general information regarding which kind of simulation to perform an parameters for the whole PROGRAM
PRINT_LEVEL LOW ! Global print level
PROJECT c2h2 ! Name of the project. This word will appear as part of a name of all ouput files (except main ouput file, specified with -o option)
RUN_TYPE ENERGY ! Calculating of energy for the fixed position of atoms
&END GLOBAL

The script to modify the C-C distance in the input and generate the curve is the following:

c2h2.chain

#
# task 2.1 C2H2 bond strength
#
# the distances of equilibrium
# and increment delta
#
dist_cc0=1.181
dist_hc=1.066
delta=0.0002
 
#
# loads the functions
# this script uses the functions: m_change m_replace m_getcolumn m_sum m_list
#
module load cp2k
. /cluster/apps/courses/mmm/m_functions.bash
 
 
#
# deletes old output file
#
rm curve.amber.c2h2
 
#
# loop over all values of n
#
 
for n in `m_list -5 5`
do
  dist_cc=`m_change $dist_cc0 $n $delta`
  c2=`m_sum $dist_hc $dist_cc`
  h2=`m_sum $c2 $dist_hc `
  #
  # replaces coordinates in the input
  #
  m_replace _C1_ $dist_hc < c2h2.inp.templ | m_replace _C2_ $c2  | m_replace _H2_ $h2 > c2h2.$dist_cc.inp
  #
  # Runs cp2k
  #
  echo RUNNING cp2k with the input c2h2.$dist_cc.inp
  # bsub -n 1 mpirun cp2k.popt -i c2h2.$dist_cc.inp > c2h2.$dist_cc.out
  cp2k.popt -i c2h2.$dist_cc.inp > c2h2.$dist_cc.out
  #
  # gets the energy from the output (in a.u.)
  #
  energy=` m_getcolumn 'ENERGY|' 9 < c2h2.$dist_cc.out ` 
  echo $dist_cc $energy  >> curve.amber.c2h2
#
# loop over n
#
done
 
#
# Cleaning...
#
mkdir Logs
mv c2h2.*.inp c2h2.*.out Logs
rm RUN* *restart*

At this point submit the job grid, first loading the module for cp2k entering

you@eulerX c2h2$ module load cp2k
you@eulerX c2h2$ bsub < c2h2.chain

Finally, the gnuplot code to fit the curve to a parabolic function - and to extract the parameters of the bond interaction is the following

you@eulerX c2h2$ gnuplot fit.gnu

fit.gnu

#!/usr/bin/gnuplot
f(x)=k*(x-x0)*(x-x0)+e0         # definition of the function to be fitted
delta = 0.002                   #
e0=0.007720330647107            # initial value of e0
k = 500                         # initial value of k
x0=1                            # initial value of x0
#a0 = 1.3327436840              # 
set xlabel 'd (Angstrom)'       # label of the x-axis
set ylabel 'E (kcal/mol)'       # label of the y-axis
set title "c2h2 triple bond"    # main title

fit f(x) 'curve.a.c2h2' u ($1):(($2)*627) via k,x0,e0
# fitting procedure
#    ^ function to be fitted
#             ^ take data from the file curve.a.c2h2
#               and use the first column as X and the second one
#               ax Y (all values of the second column are multiplied by 627. 1 Hartree = 627 kcal/mol)
#                                               ^ k, x0, e0 - are parameters to be adjusted

plot 'curve.amber.c2h2' u ($1):(($2)*627)-e0 t 'computed AMBER' w lp lw 2 ps 2 pt 7, f(x)-e0 t 'k*(x-x0)^2' w l lw 2
#         ^ take data for the first plot from the file curve.a.c2h2
#                               ^ use the firts column as X and the second as Y
#                                               ^ title of the first plot: computed AMBER
#                                                              ^ draw points and lines
#                                                                ^ line width = 2 
#                                                                      ^ point size = 2
#                                                                           ^ point type = 7 
#                                                                                  ^ plot function f(x)-e0
#                                                                                               ^ title of the second plot: k*(x-x0)^2
#                                                                                                        ^ draw only line
#                                                                                                             ^ line width = 2


pause mouse                     # exit by right-clicking on the plot window
#    EOF

Compare the values that you obtain with the ones listed in the “human readable” potential file c2h2-force_field.pot that was generated by cp2k.

Now, perform the same exercise in another directory for the molecule C2H4.

you@eulerX c2h2$ cd ../c2h4

The new input c2h4.inp.templ is similar to the previous one, only with different project name (C2H4) and coordinates:

H   0 3.06 0 
H   0 4.94 0 
C   _C1_ 4.0 0
C   _C2_ 4.0 0
H   _H3_ 3.06 0
H   _H3_ 4.94 0

The script to modify the bond lengths changes slightly as well

c2h4.chain

#
# task 2.2 C2H4 bond strength
#
# the initial deltax of  C, C, H, H
# and increment delta
#
dist_hcx=0.560
dist_cc0=1.324
delta=0.002
 
#
# loads the functions
# this script uses the functions: m_change m_replace m_getcolumn m_sum m_list
#
module load cp2k
#. ~/Scripts/myfunctions.bash
. /cluster/apps/courses/mmm/m_functions.bash
 
 
#
# deletes old output file
#
rm curve.amber.c2h4
 
#
# loop over all values of n
#
 
for n in `m_list -5 5`
do
  dist_cc=`m_change $dist_cc0 $n $delta`
  c2=`m_sum $dist_hcx $dist_cc`
  h3=`m_sum $c2 $dist_hcx `
  #
  # replaces coordinates in the input
  #
  m_replace _C1_ $dist_hcx < c2h4.inp.templ | m_replace _C2_ $c2  | m_replace _H3_ $h3 > c2h4.$dist_cc.inp
  #
  # Runs cp2k
  #
  echo RUNNING cp2k with the input c2h4.$dist_cc.inp
  cp2k.popt -i c2h4.$dist_cc.inp > c2h4.$dist_cc.out
  #
  # gets the energy from the output (in a.u.)
  #
  energy=` m_getcolumn 'ENERGY|' 9 < c2h4.$dist_cc.out `
  echo $dist_cc $energy  >> curve.amber.c2h4
#
# loop over n
#
done
 
#
# Cleaning...
#
mkdir Logs
mv c2h4.*.inp c2h4.*.out Logs
rm RUN* *restart*

Use a fitting gnuplot script to verify the value of the parameters. What has changed with respect to the C2H2 case? Why?

Assignment:

Report the values of the bond length and force constants in all cases.
Discuss these values in view of the kind of molecules we are simulating.