assembly of Carbon Atoms Space Mechanism of Naphthalene ... · Mechanism of Naphthalene from Small...

Self‐assembly of Carbon Atoms in Interstellar Space and Formation Mechanism of Naphthalene from Small Precursors: A Molecular 

Dynamics Study 

Niladri PatraUIC

Advisor: Dr. H. R. SadeghpourITAMP

Large Scale ordered Carbon Structures in Universe

• Molecules found in inter stellar medium (ISM ) are predominantly organic (mostly composed of carbon)

• 1/3 of them are in gas phase• A large set of polycyclic aromatic hydrocarbons (PAHs) are present in gas phase

in galactic and extragalactic

Questions remain unsolved or poorly understood !

• What are their size distributions? What are the type and number of different structures?

• What are degree of ionizations?• What are the conditions for synthesis of such PAHs?• What is the kinetics? Time scale and rate constants of formation of PAHs.• Can we predict the mechanism of formation process of PAHs?

Objectives: Develop a theoretical understanding of how large molecules are synthesized

• Accurate Quantum Chemical calculations can be used to understand the carbon chain growth through the intermediate transition states, both laboratory and astrophysical conditions

• Need to understand the dynamical processes far from equilibrium !

Computational Methods

Bottom-up Approach:

• Density of carbon atom (4.1x10-6 Å-3 - 5.78x10-10 Å-3) and for carbon-hydrogen system (C = 2.1x10-6 Å-3 and H = 2.1x10-6 Å-3 ).

• NVE ensemble and Langevin thermostat are used.

• Simulate all the systems at different temperatures (300 K - 8000 K).

• Initially all atom were randomly placed in gas phase. After short minimization, the systems were equilibrated upto 1.5 µs.

• We have used adaptive intermolecular reactive empirical bond order potential (AIREBO).

• For molecular dynamics simulations LAMMPS and for visualization VMD softwareswere used.

Self-assembly of Carbon Atoms in Gas phase

Adaptive Intermolecular Reactive Empirical Bond Order potential(AIREBO)

The AIREBO potential can be written as:

The covalent bonding (REBO) interactions:

The repulsive interactions:

where Qij, Aij and αij depend on the atom types i and j.

The attractive interactions:

The “bond order” for the interaction:

where, Pij σπ is the covalent bond interactionπijrc is the contributions from radical and conjugationπijdh is the contribution due to rotation around multiple bonds

Adaptive Intermolecular Reactive Empirical Bond Order potential(AIREBO)

The Lennard-Jones Potential:

The dispersion and intermolecular interactions:

where S(t) is the switching function

The torsional potential:

where

Self-assembly of Carbon Atoms at 500 K

• Initially short chains were formed.

• Long chains emerged from short chain and eventually big rings formed.

• Several big rings formed cluster after several hundred ns.

50 ns 100 ns 200 ns

Temperature = 500 K and carbon atom density = 4.1x10-6 Å-3

• Long chains emerged from short chains and eventually formed big rings.

• Several big rings formed cage like clusters.

• Formation of five member and six member rings were observed after 200 ns.

50 ns 100 ns 200 ns

Temperature = 1000 K and carbon atom density = 4.1x10-6 Å-3

Self-assembly of Carbon Atoms at 1000 K

Self-assembly of Carbon Atoms at 2000 K

25 ns 50 ns 100 ns

Temperature = 2000 K and carbon atom density = 4.1x10-6 Å-3

• Cage like structures formed within 25 ns.

• Formation of five member and six member rings were observed after 50 ns.

• Cylindrical nanostructures were observed after 100 ns.

Self-assembly of Carbon Atoms at 3000 K

10 ns 25 ns 90 ns

Temperature = 3000 K and carbon atom density = 4.1x10-6 Å-3

• Cage like structures formed within 5 ns.

• Formation of five member and six member rings were observed after 25 ns.

• Fullerene type cluster (C70-C86) were observed after 25 ns.

500 K 1000 K 2000 K

Time = 200 ns and carbon and hydrogen atom density =2.1x10-6 Å-3

• Unsaturated short chains, long chains, and branched chains were observed at 500 K

• Formation of H-terminated graphene type (PAHs) with five member and six member rings were observed at 1000 K

• Cages with absorbed H atoms were observed at 2000 K

Self-assembly of Carbon and Hydrogen Atoms

Part II: Investigation of Reaction Mechanisms and Determination Rate Constants

Naphthalene Formation from Benzene and o-benzyne

radical/π-bond 1,4 - cycloaddition

C6H6 + o-C6H4 C10H8 + C2H2Benzene o-benzyne naphthalene acetylene

Computational Methods:

• All single point and molecular dynamics calculations are performed at B3LYP/6-311g level.

• Conjugate Gradient method is used for structures minimization. • DFT-D3 method is used for dispersion correction.• Langevin damping is used in molecular dynamics simulation.• Time step is 1 fs and damping constant is 1 ps-1

.• Spherical periodic boundary conditions is used.

• One benzene and one singlet o-benzyne were placed perpendicularly at a height 6 to each other in gas phase at 300 K.

• Formation of benzobicyclo[2,2,2]octatriene (b) was observed within 0.5 ps.

• Temperature was increased to 4000 K to cross the energy barrier. After 15 ps, naphthalene and acetylene were formed.

• Naphthalene formation was also observed at 3000 K( 23 ps ) and 2000 K (35 ps).

Naphthalene formation from Benzene and o-benzyne

Naphthalene formation from Benzene and o-benzyne

• Transition Sate Theory (TST) rate constant can be written as

/ ∆ ,

where ∆ is the free energy difference between reactant and product.

• BLYP and Pseudopotential plane-wave are used for QMMD calculations (software - QUANTUM ESPRESSO ).

• Metadynamics method is used to evaluate the free energy of the reaction (software - PLUMED).

• Metadynamics performs two basic tasks:

1. Keep track of the visited configurations in the collective variables (CVs) spaces, or equivalently, of the shape of the potential

- done by maintaining a list of the Gaussians which have been added to the bias

Collective Variables: Atom position; Distance between two atoms; Angle; Torsion;Hydrogen bond; etc.

2. Add proper forces to the microscopic dynamics - evaluation of the bias force, i.e. the derivative of the bias potential with

respect to microscopic coordinates.

Determination of Rate Constant

• Two bond distance were chosen as CVs (b to c)

• Transition Sate Theory (TST) rate constant can be written as

Free Energy Surface and Rate Constant

Temperature (K)

Rate constant (s-1)

Reference Rate constant (s-1)JPC A 2011, 115, 5547-5559

3000 4.48x1013 9.47x1012

(fitting)2000 7.26x1010 1.58x109

300 1.63x10-8 2.01x10-7

(fitting)

• One benzene and one singlet o-C10H6 were placed perpendicularly at a height 6 to each other in gas phase at 300 K.

• Formation of benzobicyclo[2,2,2]octatetraene was observed within 0.7 ps.

• Temperature was increased to 4000 K to cross the energy barrier. After 18 ps, anthracene and acetylene were formed.

• Anthracene formation was also observed at 3000 K (26 ps) and 2000 K (39 ps).

Formation of Anthracene from Benzene and o-C10H6

Formation of Anthracene from Benzene and o-C10H6

Conclusion

• At low temperature carbon atoms form planar clusters

• At high temperature carbon atoms form cage like cluster; high temperature helps to overcome the energy barrier

• Small clusters can merge and form big cylindrical clusters over the time

• Hydrogen atoms terminate the growth of carbon clusters

• At room temperature, metadynamics method can be used to construct free energy surface for chemical reactions

• Rate constant can be calculated using transition state theory and free energy difference of the reactants and product

Acknowledgement: Dr. H. R. Sadeghpour(ITAMP), Prof. Petr Král (UIC), Dr. John Parkhill(Harvard University)

Funding: SAO predoc fellowshipComputer time: NCSA, NERSC, ODDYSEY (Harvard), and UIC (Král’s group clusters)