Constrained Pentane Molecule

In this example we will consider the following isomer of pentane (n-pentane).

Figure 4.5: Structure of n-pentane

Note that the five carbon atoms seem to lie in a plane. Here we shall determine how planar the molecule remains at finite temperature. To do this we will constrain four of the carbon atoms to lie in a plane, and observe the motion of the fifth carbon atom relative to the plane.

The DFT Calculation

We will use the following cell file for this simulation. The cell parameters used represent convergence of the total energy with respect to the cell size to with $<$ 0.01 eV.

%block lattice_abc
7.5 13.0 7.0
90  90   90
%endblock lattice_abc


%block positions_abs
ang
C  3.8907 5.2248 2.3681
C  3.3763 6.6756 2.3664
C  4.5722 7.6442 2.3695
C  4.0585 9.0947 2.3669
C  2.6949 4.2567 2.367
H  4.4474 5.0677 1.5524
H  4.4449 5.0688 3.1857
H  2.8231 6.8319 1.5481
H  2.8185 6.8323 3.1814
H  5.1251 7.4882 3.188
H  5.1303 7.4871 1.5548
H  4.8356 9.724  2.369
H  3.5002 9.2526 3.1815
H  3.5054 9.2515 1.5487
H  3.0285 3.3141 2.3681
H  2.1401 4.4125 1.5496
H  2.1376 4.4136 3.1824
%endblock positions_abs

%block species_pot
C C_00.usp
H H_00.usp
%endblock species_pot

kpoints_mp_grid 1 1 1

A similar convergence with respect to the basis set size is obtained at $E_{cut-off} =$ 370 eV.

To constrain all but one carbon atom to lie in its initial of constant z, and to fix the centre of mass, we add the following constraint information to the cell file.

%block ionic_constraints
1 C  1   0 0 1
2 C  2   0 0 1
3 C  3   0 0 1
4 C  5   0 0 1
%endblock ionic_constraints

fix_com=true

i.e. we are insisting that the z co-ordinate of each carbon atom is constant, other than the fourth which is located at the end of the chain.

Molecular Dynamics Parameters

We will use the following parameters. These will conduct an NVE ( the only ensemble appropriate for an isolated molecule ) simulation for 500 steps, of 1 fs each which was identified as appropriate in the usual way.

task      = moleculardynamics

cut_off_energy = 370 eV

md_temperature = 300 k
md_num_iter    = 500
md_delta_t     = 1 fs
md_ensemble    = NVE

rand_seed = 1

We have again fixed rand_seed to ensure the results presented here are reproducible by the reader. This simulation should run in less than 18 hours on a 2.8 GHz Pentium IV.

Results

Plots of the z co-ordinate of each of the five carbon atoms are shown below. It is clear that the four constrained atoms do not move from their initial z positions. The z co-ordinate of the final carbon atom fluctuates with r.m.s. deviation from the mean of just 0.022 Å.

Figure 4.6: Z co-ordinate of the five carbon atoms throughout the constrained MD run.