Study of N-Butane Conformations: Electronic Structure and Simulations

This report investigates the conformations of n-butane, a crucial concept in chemistry, by employing both electronic structure calculations and classical molecular dynamics (MD) simulations. The study begins with an analysis of n-butane's various conformations, including total eclipsed, gauche, eclipsed, and anti forms, highlighting their relative stabilities and energy levels. The methodology involves determining the electronic structure by calculating the energies of different butane structures at various dihedral angles. The Boltzmann distribution is then applied to calculate conformer populations at different temperatures (298 K and 498 K). The results are presented graphically, illustrating the relationship between energy, dihedral angle, and conformer populations. In addition, the report incorporates MD simulations using the OPLS force-field to model the dynamic behavior of n-butane at different temperatures. The discussion compares the findings from electronic structure calculations and MD simulations, emphasizing the impact of temperature on conformer populations and the influence of interatomic forces. The report concludes by summarizing the methods' feasibility in determining static structures and modeling dynamic behaviors.

Molecular conformations: study of
n-
butane
Abstract
The calculation of electronic structure is based on its feasibility to compute timescale, which
makes it to be considered as appropriate method of determining static structures.
It is always noted that the presence of molecules at room temperature may either undergo
rotation and vibration, but further change at different conformations. The crucial properties of
chemical system exhibited between the different in lowest energy structure and the structure that
are explored at room temperature, especially in biological systems.
Classical method that involves an example of classical molecular dynamic (MD) simulation will
facilitate modeling of certain behaviors since they require less power of computation.
Introduction
Conformation of n-Butane
In order to determine various conformation of n-butane, fixing is done on one carbon atom (C )
followed by rotation of the other, just like in ethane there are several conformation that are
resulted on the rotation of carbon – carbon single bonds, like for example rotation that involves
C2 – C3 to produce four types of conformation of n- butane, which include;
i. Total or fully eclipsed
ii. Gauche or skew
iii. Eclipsed
iv. Anti
The total or fully eclipsed (i ) is likely to have the conformation of highest energy meaning that it
is least stable, while the other eclipse (iii) that contains methyl-hydrogen eclipsing has a lower
energy compared to (i ), similarly the staggered conformations in which the two methyl groups
are anti each other and are called anti- conformers (iv) involves a conformation of least energy
meaning that its most stable, while the other that is known as gauche conformation (ii) has a
higher energy compared to (iv).
Hence the general ranking of the stability order will be anti- conformer (iv) > Gauche or skew
conformer (ii) > eclipse conformer (iii) > total or fully eclipse (i).

It should be noted that rotation of C2 – C3 bond, total eclipsed will be converted to gauche or
skew, which will inturn get converted to eclipsed and then anti, but anti will be converted to
eclipsed and not total eclipse, hence the rotation will lead to (I ) => (ii ) => (iii ) => (iv ) => (iii )
= > (ii ) => (i ) => (ii ) => (iii ).
Figure 1: energy diagram of n- butane showing correlation with C2 – C3 rotation
From the figure a higher energy is approximated be approximately 20 kJ/mol that corresponds to
eclipsing of two bulky methyl groups. The fully eclipse of methyl – methyl conformation a
rotation of 1800 will give out staggered conformation, having methyl far apart giving it most
stability but happens at lower energy as shown on the diagram. A rotation of the angle of 600 and
3000 will also give out another staggered conformation though at lesser stability as compared to
the first.
At an angle of 00 and 3600 will correspond to a full eclipse and occurs at highest energy points
and have a methyl – methyl eclipsing, while at 1200 and 2400 will correspond to eclipse form
which have methyl – hydrogen eclipsing, in between the staggered minimum an eclipse
maximum gauche conformation will exist along the curves differing slightly at angles and
energies.
Since the energy barrier that exist between fully eclipse and anti- form are small the rotation that
takes place between carbon – carbon bond increases with increase in the temperature hence
increasing the contribution of skew conformations.
The chemical and physical properties of the n- butane as a bulk is determined by the stable anti-
form, since most molecules prefer to be at this form, hence n – butane will have zero dipole
moment because addition vector for the dipole of the two methyl groups will cancel each other.

Methodology
Electronic structure
a) Determine the cylindrically symmetrical of the electron distribution of carbon – carbon –
carbon – carbon dihedral angle that is about on the line that is joining the four carbon
nuclei, the possibility of rotation is about the single bond, where the molecules can
experience numerous shape though the arrangement of atoms stay at the original position.
b) Determine the energies of 12 different structures of butane, while remembering to set
the dihedral angle to values of 0°, 30°, 60°, 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°
and 330°, respectively each time by Bond Torsion.
It will be noted that molecule will adopts a minimum energy geometry that is available to
it through rotation about single bonds and the numerous geometries a given molecule can
attain by bond rotation.
c) Record the energy of each structure and it should be noted that molecules will minimize
energetic consequences by structural adjustment and it will display its favored
orientations.
d) Then plot a graph of the calculated relative energies against the Carbon – Carbon –
Carbon – Carbon dihedral angle.
e) Calculate the populations of each conformer, using the formula for the Boltzmann distribution,
which is given by Equation below.
pI = e
Ei
KBT
Where;pi is the population of conformer
i
Ei is the energy of conformer
i
kB is the Botzmann constant
Note that when energies are measured in units per mole (such as kJ mol-1 used here),
kB is replaced with
the gas constant,
R, which is equal to 0.0008314 kJ mol-1 K -1..T is the temperature in Kelvin.
f) Calculate all the populations sum
g) Calculate the normalized population by dividing each of the original populations by the sum.
h) Repeat the population calculations at a temperature ranging from 298 to 498 K, and
i) Plot another graph showing the new (normalised) populations.

Tables of results
Table1: calculated the energies of 12 different structures of butane
Angle Structure
energy E/kcal
mol-1
Structure
energy E/kJ
mol-1
Difference
E/kJ mol-1
Dihedral
angle
(◦)
0° -98700.06 -412961.06 25.9 0
30° -98702.16 -412969.85 17.11 30
60° -98705.22 -412982.67 4.29 60
90° -98703.95 -412977.34 9.62 90
120° -98702.24 -412970.18 16.78 120
150° -98704.16 -412978.21 8.75 150
180° -98706.01 -412985.98 0.98 180
210° -98704.18 -412978.29 8.67 -150
240° -98702.28 -412970.37 16.59 -120
270° -98703.91 -412977.17 9.79 -90
300° -98704.75 -412980.68 6.28 -60
330° -98701.75 -412968.14 25.9 -30
Graphical presentation of energy vs dihedral for n- butane
0 2 4 6 8 10 12 14
-98707
-98706
-98705
-98704
-98703
-98702
-98701
-98700
-98699
-98698
-98697
Energy Vs Dihedral for n-butane
Dihedral angleº
Energey (kcal/mol-1)
Figure 1: Graph of energy in E/kcal mol-1 Vs Dihedral angle in

0 2 4 6 8 10 12 14
-412990
-412985
-412980
-412975
-412970
-412965
-412960
-412955
-412950
-412945
Energy kJ Vs Dihedral for n-butane
Dihedral angleº
Energey (kcal/mol-1)
Figure 2: Graph of energy in kJ mol-1 Vs Dihedral angle in

Graph of the calculated populations vs. dihedral angle.
Figure3:Graph of normalised population at 289K in electronic structure
0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330°
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Normalised populati on at 498K
angle º
Normalised Energy (KJ mol-1)
Figure4: Graph of normalised population at 498K in electronic calculation
0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330°
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalised populati on at 298K
angle º
Normalised eNERGY (kJ mol-1)

Discussion
From the formula of Boltzmann distribution there is different in calculated formula because of
the different energies of conformers and temperature different, with higher calculated population
at lower temperature and lower calculated population at higher temperature since thy are
inversely proportionate as per the formula of Boltzmann distribution.
It is also observed that from the graph of normalized population at 298 K in electronic
calculation at an angle of 1800 the normalized energy is higher as compared to same angle of
angle of 1800 at 498 K since
The fully eclipse of methyl – methyl conformation a rotation of 1800 will give out staggered
conformation but happens at lower normalized energy as shown on the graph.

Classical simulations
Procedure
i. Reload your optimised structure of butane and set up a molecular dynamics simulation
using the OPLS force-field (Setup -> Molecular Mechanics).
ii. Select Compute -> Langevin Dynamics and run the simulation for 5000 ps using 0.002 ps
steps at 298 K, reading data every 125 steps and refreshing the screen every 8 data steps,
and select a bath relaxation time of 0.1 ps and a Friction coefficient of 5 ps-1. Save the
trajectory file by selecting Snapshots, and include the temperature in the filename.
iii. Next run another simulation in the same way, but this time 200 K higher, at 498 K.
Again, save the trajectory with temperature in the filename and, once analyzed, load the
data from the .csv file into your spreadsheet.

Graphical presentation
Figure5:Graph of normalised population at 289K in MD simulations
Figure 6:Gragh of normalised population at 498K in MD simulations

Discussion
The graph of population against dihedral classical at 498 K the energy is less as compared to that
at 298 K, since the interatomic forces at 489 K can be easily be broken down at higher
temperature as compared at 298 K which is at lower temperature hence the force holding the
particles are still stonger.
The determination of population at 298 K and 498 K in classical simulation is determined using
Langevin dynamics simulations that is identical to molecular dynamics simulations, while
populations at 298 K and 498 K calculated from the electronic structure is done using formula of
Boltzmann distribution.

Conclusion
In conclusion the calculation of electronic structure is based on its feasibility to compute
timescale, which helps in determining static structures, while the classical method which
involves an example of classical molecular dynamic (MD) simulation facilitates the modeling of
certain behaviors since they require less power of computation.

References
Segel, L. A. (2001).
modelling dynamic phenomena in molecular and biology . Cambridge : Cambridge
univ. press.
Cottrell, T. L. (1965). Dynamic aspects of molecular energy state. Edinb: oliver and Boyd.