Reactive empirical bond order explained

The reactive empirical bond-order (REBO) model is a function for calculating the potential energy of covalent bonds and the interatomic force. In this model, the total potential energy of system is a sum of nearest-neighbour pair interactions which depend not only on the distance between atoms but also on their local atomic environment. A parametrized bond order function was used to describe chemical pair bonded interactions.

The early formulation and parametrization of REBO for carbon systems was done by Tersoff in 1988,^{[1] [2]} based on works of Abell.^[3] The Tersoff's model could describe single, double and triple bond energies in carbon structures such as in hydrocarbons and diamonds. A significant step was taken by Brenner in 1990.^{[4] [5]} He extended Tersoff's potential function to radical and conjugated hydrocarbon bonds by introducing two additional terms into the bond order function.

Compared to classical first-principle and semi-empirical approaches, the REBO model is less time-consuming, since only the 1st- and 2nd-nearest-neighbour interactions were considered. This advantage of computational efficiency is especially helpful for large-scale atomic simulations (from 1000 to 1000000 atoms).^[6] In recent years, the REBO model has been widely used in the studies concerning mechanical and thermal properties of carbon nanotubes.^{[7] [8]}

Despite numerous successful applications of the first-generation REBO potential function, its several drawbacks have been reported. e.g. its form is too restrictive to simultaneously fit equilibrium distances, energies, and force constants for all types of C-C bonds, the possibility of modeling processes involving energetic atomic collisions is limited because both Morse-type terms go to finite values when the atomic distance decreases, and the neglect of a separate pi bond contribution leads to problems with the overbinding of radicals and a poor treatment of conjugacy.^{[9] [10]}

To overcome these drawbacks, an extension of Brenner's potential was proposed by Stuart et al.^[10] It is called the adaptive intermolecular reactive bond order (AIREBO) potential, in which both the repulsive and attractive pair interaction functions in REBO function are modified to fit bond properties, and the long-range atomic interactions and single bond torsional interactions are included. The AIREBO model has been used in recent studies using numerical simulations.^{[11] [12]}

References

1. Tersoff . J. . New empirical approach for the structure and energy of covalent systems . Physical Review B . American Physical Society . 37 . 12 . 15 April 1988 . 0163-1829 . 10.1103/physrevb.37.6991 . 9943969 . 6991–7000. 1988PhRvB..37.6991T .
2. Tersoff . J. . Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon . Physical Review Letters . American Physical Society . 61 . 25 . 19 December 1988 . 0031-9007 . 10.1103/physrevlett.61.2879 . 10039251 . 2879–2882. 1988PhRvL..61.2879T .
3. Abell . G. C. . Empirical chemical pseudopotential theory of molecular and metallic bonding . Physical Review B . American Physical Society . 31 . 10 . 15 May 1985 . 0163-1829 . 10.1103/physrevb.31.6184 . 9935490 . 6184–6196. 1985PhRvB..31.6184A .
4. Brenner . Donald W. . Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films . Physical Review B . American Physical Society . 42 . 15 . 15 November 1990 . 0163-1829 . 10.1103/physrevb.42.9458 . 9995183 . 9458–9471. 1990PhRvB..42.9458B .
5. Brenner . Donald W. . Erratum: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films . Physical Review B . American Physical Society . 46 . 3 . 15 July 1992 . 0163-1829 . 10.1103/physrevb.46.1948.2 . 10021572 . 1948. free .
6. Brenner . D.W. . The Art and Science of an Analytic Potential . Physica Status Solidi B . Wiley . 217 . 1 . 2000 . 0370-1972 . 10.1002/(sici)1521-3951(200001)217:1<23::aid-pssb23>3.0.co;2-n . 23–40. 2000PSSBR.217...23B .
7. Ruoff . Rodney S. . Qian . Dong . Liu . Wing Kam . Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements . Comptes Rendus Physique . Elsevier BV . 4 . 9 . 2003 . 1631-0705 . 10.1016/j.crhy.2003.08.001 . 993–1008.
8. Rafii-Tabar . H. . Computational modelling of thermo-mechanical and transport properties of carbon nanotubes . Physics Reports . Elsevier BV . 390 . 4–5 . 2004 . 0370-1573 . 10.1016/j.physrep.2003.10.012 . 235–452. 2004PhR...390..235R .
9. Pettifor . D. G. . Oleinik . I. I. . Analytic bond-order potentials beyond Tersoff-Brenner. I. Theory . Physical Review B . American Physical Society . 59 . 13 . 1 March 1999 . 0163-1829 . 10.1103/physrevb.59.8487 . 8487–8499. 1999PhRvB..59.8487P .
10. Stuart . Steven J. . Tutein . Alan B. . Harrison . Judith A. . A reactive potential for hydrocarbons with intermolecular interactions . The Journal of Chemical Physics . AIP Publishing . 112 . 14 . 8 April 2000 . 0021-9606 . 10.1063/1.481208 . 6472–6486. 2000JChPh.112.6472S .
11. Ni . Boris . Sinnott . Susan B. . Susan Sinnott. Mikulski . Paul T. . Harrison . Judith A. . Compression of Carbon Nanotubes Filled with C₆₀,CH₄, or Ne: Predictions from Molecular Dynamics Simulations . Physical Review Letters . American Physical Society . 88 . 20 . 6 May 2002 . 0031-9007 . 10.1103/physrevlett.88.205505 . 12005578 . 205505. 2002PhRvL..88t5505N .
12. Nikitin . A. . Ogasawara . H. . Mann . D. . Denecke . R. . Zhang . Z. . Dai . H. . Cho . K. . Nilsson . A. . Hydrogenation of Single-Walled Carbon Nanotubes . Physical Review Letters . American Physical Society . 95 . 22 . 23 November 2005 . 0031-9007 . 10.1103/physrevlett.95.225507 . 16384236 . 225507. cond-mat/0510399 . 14520468 .