Density functional with full exact exchange, balanced nonlocality of correlation,and constraint satisfaction

摘要

We construct a nonlocal density functional approximation with full exact exchange, while preserving theconstraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This isachieved by interpolating between different approximations suitable for two extreme regions of the electrondensity. In a "normal" region, the exact exchange-correlation hole density around an electron is semilocalbecause its spatial range is reduced by correlation and because it integrates over a narrow range to —1. Theseregions are well described by popular semilocal approximations (many of which have been constructed non-empirically), because of proper accuracy for a slowly varying density or because of error cancellation betweenexchange and correlation. "Abnormal" regions, where nonlocality is unveiled, include those in which exchangecan dominate correlation (one-electron, nonuniform high density, and rapidly varying limits), and those opensubsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a valuegreater than -1. Regions between these extremes are described by a hybrid functional mixing exact andsemilocal exchange energy densities locally, i.e., with a mixing fraction that is a function of position r and afunctional of the density. Because our mixing fraction tends to 1 in the high-density limit, we employ full exactexchange according to the rigorous definition of the exchange component of any exchange-correlation energyfunctional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality ofexchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at leastfive empirical parameters, corresponding roughly to the four kinds of abnormal regions. Our local hybridfunctional is perhaps the first accurate fourth-rung density functional or hyper-generalized gradient approxi-mation, with full exact exchange, that is size-consistent in the way that simpler functionals are. It satisfies otherknown exact constraints, including exactness for all one-electron densities, and provides an excellent fit to the223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set,improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact con-straints, physical insights, and paradigm examples hopefully suppress "overfitting."