assembly of Carbon Atoms Space Mechanism of Naphthalene ... Mechanism of Naphthalene from Small Precursors:

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

    Dynamics Study 

    Niladri Patra UIC

    Advisor: Dr. H. R. Sadeghpour ITAMP

  • 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 softwares were 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 interaction πijrc is the contributions from radical and conjugation πijdh 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 + C2H2 Benzene 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 fellowship Computer time: NCSA, NERSC, ODDYSEY (Harvard), and UIC (Král’s group clusters)