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. Calculations can be carried out on molecules (Hückel-type calculations) or on systems with periodicities in one, two or three dimensions. The effect of different structures, heteroatoms and tight-binding parameters can easily be explored. Crystal orbitals, projected dispersions and densities of states can be obtained with only a few lines of code. 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. The package presents 62 functions dedicated to facilitating these quantum mechanical computations. MathemaTB is a package developed to enable tight-binding calculations within Mathematica.
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