New tensor draws together two approaches for determining ground state electronic properties
New tensor draws together two approaches for determining ground state electronic properties lead image
With the right assumptions and approximations, density functional theory can determine the ground state properties of molecules, including the very complicated interactions between electrons, from the electron density. Promising practical approaches for this include meta-Generalized Gradient Approximations (mGGAs), which employ kinetic energy density to estimate molecular energies, and current-density functional theory (CDFT), where magnetic field effects are modeled via the induced electrical currents in a molecule. To date, key features of both approaches have been considered separately, but new work looks to unify mGGAs and CDFT.
Authors Sen and Tellgren report the findings of an analysis of a kinetic energy tensor, demonstrating its ability to encode both kinetic energy density from mGGAs and vorticity from CDFT. The tensor allows a combination of the simplicity and accuracy found in mGGAs approaches while incorporating magnetic fields.
“Knowing the value of a quantity tends to restrict the quantum state of a system in some ways, but usually not a very useful way that’s easy to describe,” said Tellgren. “In this case, knowing this kinetic energy tensor restricts the quantum state in a specific way, and that’s how you can tell how many orbitals are in a specific location.”
The tensor contains chemical information beyond what is practically available from kinetic energy density or vorticity alone, allowing a discrimination between regions of a molecule that are dominated by one, two, three or four-or-more orbitals.
The authors’ work places renewed importance on the the local rotation of the current flow called vorticity. Tellgren said he hopes the work will lead to specific models that take advantage of the information in the tensor to accurately describe ground states.
Source: “A local tensor that unifies kinetic energy density and vorticity in density functional theory,” by Sangita Sen and Erik I. Tellgren, The Journal of Chemical Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5041931 .
