ReaxFF

ReaxFF (for English reactive force-field , reaction force field) is a force field for simulating chemical reactions, which is based on the bond order . It was published by Adri van Duin, William A. Goddard, III et al. developed at the California Institute of Technology . Force fields of conventional molecular dynamics simulations (e.g. with AMBER , CHARMM ) are not able to model chemical reactions, since the harmonic potentials or fixed bond lists used cannot describe the breakage and formation of chemical bonds. ReaxFF has no fixed binding lists. Instead, potentials are used that depend on the bond order. This ensures that the potential contributions for vanishing bond order (large interatomic distances) converge to zero.

In the original variant of ReaxFF, a parameterization for hydrocarbons was developed. In the meantime, there are a number of variants that differ in terms of additional or modified potentials and parameter sets.

Version 2001

The version published in 2001 was specially developed for simulating hydrocarbons. The system energy is made up of the following terms:

${\displaystyle E_{\mathrm {System} }=E_{\mathrm {Bond} }+E_{\mathrm {over} }+E_{\mathrm {under} }+E_{\mathrm {Val} }+E_{\mathrm {Pen} }+E_{\mathrm {Tors} }+E_{\mathrm {Conj} }+E_{\mathrm {vdWaals} }+E_{\mathrm {Coulomb} }}$.

Except for the and terms , all terms depend on one or more bond orders. The uncorrected bond order between atoms i and j is defined by: ${\displaystyle E_{\mathrm {vdWaals} }}$ ${\displaystyle E_{\mathrm {Coulomb} }}$

${\displaystyle {\begin{aligned}{\mathit {BO}}_{ij}^{'}&={\mathit {BO}}_{ij}^{'\sigma }+{\mathit {BO}}_{ij}^{'\pi }+{\mathit {BO}}_{ij}^{'\pi \pi }\\&=\exp \left(\rho _{\mathrm {bo} ,1}\left({\frac {r_{ij}^{\sigma }}{r_{0}}}\right)^{\rho _{\mathrm {bo} ,2}}\right)+\exp \left(\rho _{\mathrm {bo} ,3}\left({\frac {r_{ij}^{\pi }}{r_{0}}}\right)^{\rho _{\mathrm {bo} ,4}}\right)+\exp \left(\rho _{\mathrm {bo} ,5}\left({\frac {r_{ij}^{\pi \pi }}{r_{0}}}\right)^{\rho _{\mathrm {bo} ,6}}\right)\end{aligned}}}$

with the parameters and . The uncorrected bond order is thus the sum of the bond orders of the sigma ( ), pi- ( ), and double- pi bond orders ( ). According to this definition, the bond order can have a maximum value of 3, which means that double and triple bonds can also be described. ${\displaystyle \rho _{\mathrm {bo} ,1},\ldots \rho _{\mathrm {bo} ,6},r_{ij}^{\sigma },r_{ij}^{\pi }}$ ${\displaystyle r_{ij}^{\pi \pi }}$ ${\displaystyle {\mathit {BO}}_{ij}^{'}}$ ${\displaystyle \textstyle BO_{ij}^{'\sigma }}$ ${\displaystyle {\mathit {BO}}_{ij}^{'\pi }}$ ${\displaystyle {\mathit {BO}}_{ij}^{'\pi \pi }}$

In order to avoid overcoordination of atoms in a molecule, the bond orders are subjected to a correction. This correction has the effect that long-range bonds with a low bond order, whose atoms involved already have total bond orders close to their valence, get a bond order of zero.

The term corresponds to the binding energies and is through ${\displaystyle E_{\mathrm {Bond} }}$

${\displaystyle E_{\mathrm {Bond} }=-D_{\mathrm {e} }{\mathit {BO}}_{ij}\exp \left(\rho _{\mathrm {be} ,1}(1-{\mathit {BO}}_{ij}^{\rho _{\mathrm {be} ,1}})\right)}$,

with the parameters and given. Despite the correction of the bond order, molecules can become over- or under-coordinated. In the case of overcoordination, the term yields ${\displaystyle D_{\mathrm {e} }}$ ${\displaystyle \rho _{\mathrm {be} ,1}}$

${\displaystyle E_{\mathrm {over} }=\rho _{\mathrm {over} }\Delta _{i}\left({\frac {1}{1+e^{\lambda _{6}\Delta _{i}}}}\right)}$

a positive energy contribution. In it are and parameters. The overcoordination of the atom i results from ${\displaystyle \rho _{\mathrm {over} }}$ ${\displaystyle \lambda _{6}}$

${\displaystyle \Delta _{i}=\sum _{j}{\mathit {BO}}_{ij}^{'}-{\mathit {Val}}_{i}}$.

${\displaystyle {\mathit {Val}}_{i}}$is the valence of atom i (e.g. 4 for carbon).

The term gives an additional energy contribution through the resonance of the electrons between neighboring undercoordinated atoms. In a molecule or solid, atomic triples ijk have an optimal bond angle (equilibrium angle ), which depends on the elements and the chemical environment (e.g. the HCH angle in CH _{4 is} 109.7 °). A deviation from this equilibrium angle leads to a deterioration in the total energy. In ReaxFF this is realized by the term . In contrast to classical force fields, this depends on the chemical environment (sum of the bond orders). ${\displaystyle E_{\mathrm {under} }}$ ${\displaystyle \pi }$ ${\displaystyle E_{\mathrm {Val} }}$ ${\displaystyle \pi }$

literature

1. ^ ACT van Duin, S. Dasgupta, F. Lorant, WA Goddard III, "ReaxFF: A Reactive Force Field for Hydrocarbons", The Journal of Physical Chemistry A , 105 , 9396-9409 (2001); doi : 10.1021 / jp004368u .

Web links

• Adri van Duin's website