Study of stretched H₂ reveals new class of error in density functional theory

The computational limitations for exactly solving the Schrödinger wave equation has led to widespread use of Kohn-Sham density functional theory (KS-DFT) for calculation of energies and properties of chemical systems. Existing approximate functionals used in KS-DFT, however, contain errors with delocalization and strong correlation, which can lead to systematic failures. A new investigation of the molecular properties of stretched H₂ molecules has uncovered a new type of error that can occur when using some functionals.

The paper reports a new class of density functional theory errors caused by the inadequate localization of spin density in elongated single bonds. This type of error, which can appear in both empirically fitted and non-empirically constrained functionals, can cause qualitative failure in predicting second derivative molecular properties such as static polarizability and force constants.

“This discovery was enabled by use of molecular properties as an effective magnifying glass, which revealed that many methods predict catastrophically or qualitatively incorrect behavior for highly stretched bonds,” said Diptarka Hait, an author on the paper.

While methods such as unrestricted Hartree-Fock and PBE0 provided reasonable behavior for the stretched H₂ system, other widely used approximations like B97-D and TPSS yielded physically impossible static polarizabilities and force constants. Several functionals also predicted an unphysical barrier for association of two hydrogen atoms to bond together.

Hait hopes the group’s work will encourage further discussion about balancing empirical data with non-empirical constraints for functional development, as well as stimulate work for mitigating this type of error.

Source: “Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H₂,” by Diptarka Hait, Adam Rettig, and Martin Head-Gordon, The Journal of Chemical Physics (2019). The article can be accessed at https://doi.org/10.1063/1.5080122 .