Analytic bond-order potentials for atomistic simulations of materials

At the heart of atomistic simulations of materials are the interatomic potentials. Their ability to quantitatively describe the fundamental physics and chemistry at the atomic scale is the key to achieving reliable and meaningful results. We develop and apply the theory of analytic bond order potentials (BOPs) to devise robust and transferable interatomic potentials to be used for large scale atomistic modeling of covalently bonded materials. Bond-order potential theory provides the necessary methodology for the construction of BOPs via a systematic coarse-graining of electronic degrees of freedom to provide a reliable description of the interatomic interactions via explicit analytic functions of atomic coordinates. Our research includes the following steps:

1. First-principles density functional calculations of specific materials in order to devise a database of fundamental materials characteristics.
2. Development of the reduced two-center orthogonal tight-binding model using the DFT database of band structure and binding energy curves. The environment-dependent reduced TB parameters, including hopping integrals and repulsive terms, will be constructed using analytic dispersion curves along high-symmetry directions in the Brillouin zone.
3. Construction of analytic BOPs by using reduced TB parameters utilizing the direct link between reduced TB and analytic BOPs via the bond orders. Additional efforts will be undertaken to include environment dependence of analytic BOP parameters.
4. Careful validation of analytic BOPs by investigating their transferability. i.e. by calculating materials properties not included in fitting by analytic BOPs.

The functional forms of the classical interatomic bond-order potentials (BOPs) for covalently bonded materials have been recently derived by coarse-graining the quantum mechanical electronic structure using the chemically intuitive tight-binding (TB) framework. The main result of our work is the expression of the bond orders as explicit analytic functions of matrix-elements of the tight-binding Hamiltonian and the angular functions. Importantly, these BOPs explicitly include a separate π-bond contribution which is critical for a proper description of saturated π rupture both on radical formation and under torsion. We have demonstrated that these analytic BOPs allow the concept of single, double, triple and conjugate bonds in carbon systems to be quantified. Using tight-binding parameters of an already developed TB model for hydrocarbons as input, we were able to predict σ and π bond orders on average to an accuracy of 1% and 10% correspondingly, see Fig.10, without any fitting of BOP parameters.