MathemaTB: A Mathematica package for tight-binding calculations

Abstract

MathemaTB is a package developed to enable tight-binding calculations within Mathematica. The package presents 62 functions dedicated to facilitating these quantum mechanical computations. MathemaTB offers functionalities to carry out matrix manipulation, data analysis and visualizations on molecules, wave functions, Hamiltonians, coefficient matrices, and energy spectra, providing a unique insight into the interplay between geometric and electronic structure. Crystal orbitals, projected dispersions and densities of states can be obtained with only a few lines of code. The effect of different structures, heteroatoms and tight-binding parameters can easily be explored. Calculations can be carried out on molecules (Hückel-type calculations) or on systems with periodicities in one, two or three dimensions. Particularly powerful features are the possibility to plot band structures both along paths (one-dimensional) and over planes (two-dimensional) in reciprocal space, where in each case the localization of the wave function onto different sites, symmetries or basis functions can be visualized with color coding. Further features involve crystal orbital plotting with color coding of the complex phase, mean field Hubbard tight-binding and manipulation of the Hamiltonian matrix with numerical and symbolic elements. The conjunction of tight-binding functions, matrix algebra functions for symmetry, overlap and change of basis, wave function- and dispersion functions and a high degree of interactivity and flexibility makes MathemaTB a useful package for electronic structure calculations. Program summaryProgram Title: MathemaTBProgram Files doi:http://dx.doi.org/10.17632/52bykkbr9n.1Licensing provisions: LGPLProgramming language: Wolfram Mathematica v. 11.0Supplementary material: MathemaTB manualNature of problem: The tight-binding method is a useful method for determining the electronic structure in molecules and condensed matter systems. The MathemaTB package provides an implementation of the tight-binding machinery that allows such calculations to be performed in Mathematica.Solution method: A package containing functions to aid in setting up, performing and analyzing tight-binding calculations within Mathematica. The package allows insightful and interactive electronic structure calculations with a high degree of flexibility.Additional comments including restrictions and unusual features: MathemaTB supports molecular and crystal orbitals with color-coding of the complex phase. Supports projected dispersions and local density of states. Allows overlap and change of basis of the Hamiltonian. Supports Hubbard mean field tight-binding. Supports numerical and analytical diagonalization of the Hamiltonian and Hamiltonians with symbolic quantities. Allows plotting the (projected) dispersion in two dimensions. Facilitates simulating differential conductance maps.