Delocalization error and "functional tuning" in Kohn-Sham calculations of molecular properties.

Abstract

Kohn-Sham theory (KST) is the "workhorse" of numerical quantum chemistry. This is particularly true for first-principles calculations of ground- and excited-state properties for larger systems, including electronic spectra, electronic dynamic and static linear and higher order response properties (including nonlinear optical (NLO) properties), conformational or dynamic averaging of spectra and response properties, or properties that are affected by the coupling of electron and nuclear motion. This Account explores the sometimes dramatic impact of the delocalization error (DE) and possible benefits from the use of long-range corrections (LC) and "tuning" of functionals in KST calculations of molecular ground-state and response properties. Tuning refers to a nonempirical molecule-specific determination of adjustable parameters in functionals to satisfy known exact conditions, for instance, that the energy of the highest occupied molecular orbital (HOMO) should be equal to the negative vertical ionization potential (IP) or that the energy as a function of fractional electron numbers should afford straight-line segments. The presentation is given from the viewpoint of a chemist interested in computations of a variety of molecular optical and spectroscopic properties and of a theoretician developing methods for computing such properties with KST. In recent years, the use of LC functionals, functional tuning, and quantifying the DE explicitly have provided valuable insight regarding the performance of KST for molecular properties. We discuss a number of different molecular properties, with examples from recent studies from our laboratory and related literature. The selected properties probe different aspects of molecular electronic structure. Electric field gradients and hyperfine coupling constants can be exquisitely sensitive to the DE because it affects the ground-state electron density and spin density distributions. For π-conjugated molecules, it is shown how the DE manifests itself either in too strong or too weak delocalization of localized molecular orbitals (LMOs). Optical rotation is an electric-magnetic linear response property that is calculated in a similar fashion as the electric polarizability, but it is more sensitive to approximations and can benefit greatly from tuning and small DE. Hyperpolarizabilities of π-conjugated "push-pull" systems are examples of NLO properties that can be greatly improved by tuning of range-separated exchange (RSE) functionals, in part due to improved charge-transfer excitation energies. On-going work on band gap predictions is also mentioned. The findings may provide clues for future improvements of KST because different molecular properties exhibit varying sensitivity to approximations in the electronic structure model. The utility of analyzing molecular properties and the impact of the DE in terms of LMOs, representing "chemist's orbitals" such as individual lone pairs and bonds, is highlighted.