Applying an electric field, for example, speeds up the electrons, giving them a little bit more energy, shifting their energy levels slightly higher. In that case, many other achievable states exist, with just a slightly higher energy. It may happen that the highest occupied orbital (HOMO, where the M stands for ‘molecular’, but that is the convention I adopt here) corresponds to an energy value within a band. See the below figure for a visual representation of the above:įinally, just like with the hydrogen atom, the electrons occupy the available bands from bottom up. There are so many atoms and electrons, the bunched up discrete values simply merge, forming literal bands in the energy spectrum. Now, increase the size of the molecule - to the point it becomes a solid. Instead of just a few far apart values, a molecular energy spectrum contains bunches of values stemming from the splitting and rearranging of the underlying atomic energy levels. The corresponding energy levels split and shift, forming so-called bonding and anti-bonding orbitals. One may imagine that all the atomic orbitals interact with those of other atoms. Something large, like an organic one, for example. For now, we just need to acknowledge that the energy spectrum of a hydrogen atom consists of discrete values, with the electron in the ground state occupying the lowest possible level. I will leave the detailed discussion of the hydrogen atom for a later time. The discrete nature of the energy spectrum is a feature of any bound quantum system, whether we talk about an electron bound to a nucleus, a photon confined between two mirrors, or even a quasiparticle trapped in a potential well. Solving the time independent Schrödinger equation for the single electron of the hydrogen atom yields a set of discrete eigenvalues (energy levels) and corresponding eigenvectors (in this case, orbitals). Let’s start with a simple atom, say, hydrogen. If you’ve got some time on your hands, or want to understand what is it we’re trying to do, enjoy the read! Short Introduction cube file and the band alignment procedure. If you are in a rush, feel free to skip to the end, where I present a short python script to perform the projection of a. Today, we will be talking about the alignment of the band gap edges of semiconductors with respect to vacuum - as calculated with density functional theory (DFT).
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