Simple quantum-mechanical model of covalent bonding using a tight-binding basis

We present a method which uses a tight-binding basis set to describe the energetics of covalent bonds. While having the same ability to model covalent bonding, the current method is significantly faster than the direct diagonalization of the tight-binding Hamiltonian, and has the merit of being linear in the size of the system, resulting in the ability to do molecular dynamics for thousands of atoms. At present, the method works only for systems with fixed bonding topologies.