Assessment of a Middle-Range Hybrid Functional

Abstract

While hybrid functionals are largely responsible for the utility of modern Kohn-Sham density functional theory, they are not without their weaknesses. In the solid state, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally demanding and can introduce unphysical effects. Both problems can be remedied by a screened hybrid which uses exact exchange only at short-range. Many molecular properties, in contrast, benefit from the inclusion of long-range exact exchange. Recently, the authors reconciled these two seemingly contradictory requirements by introducing the HISS functional [J. Chem. Phys. 2007, 127, 221103], which uses exact exchange only in the middle range. In this paper, we expand upon our previous work, benchmarking the performance of the HISS functional for several simple properties and applying it to the dissociation of homonuclear diatomic cations and to the polarizability of linear H 2 chains to determine the importance of middle-range exact exchange for these systems, which are expected to be sensitive to the asymptotic exchange potential.

Self-consistent generalized Kohn-Sham local hybrid functionals of screened exchange: Combining local and range-separated hybridization

“…It is especially notable that the SC-Lh-LSDA screened local hybrid provides comparable thermochemistry and significantly improved reaction barriers relative to the HSE06 screened hybrid. Though the results are not quite comparable to recent middle-range hybrids, 45,50 we feel that they are encouraging.…”

“…This functional, like previous screened hybrids incorporating a constant fraction of SR 31,42 or middle-range 45,50 HF exchange, should be readily applicable in calculations on solids. 33,37 In contrast, we expect that local hybrids of FR HF exchange will inherit the computational difficulties of global hybrids in calculations on metals and narrow-bandgap semiconductors.…”

“…The observation that both screened and LC hybrids can accurately treat molecular thermochemistry 41 led to recent work on "middle-range" hybrids. 45,50 Most existing range-separated hybrid functionals use a universal range-separation parameter and a constant fraction of HF exchange in each range. Despite its successes, this approach has clear limitations.…”

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

“…[51][52][53] The HISS functional is a range-separated functional that has HF exchange only at the middle range of the electron-electron interaction (sometimes it is also referred as a three-range functional). 54 Finally, the HSEsol functional is a recent reparametrization of the original HSE functional specific for solid-state calculations. 25 Results for the four additional functionals mentioned in the previous paragraph are only available for comparison to the present results for the S(13) subset.…”

Time-dependent density functional theory calculations of near-edge X-ray absorption fine structure with short-range corrected functionals

“…35 This functional was called a screened hybrid functional and shows promise in the study of periodic systems. [36][37][38] Subsequently, a three range functional was introduced to combine the screened hybrid functional with a long-range corrected functional, 39,40 Recently, Hirao and coworkers optimized the LCgau-BOP method 31 for core excitations. 22 This functional introduces HF exchange at short range through the inclusion of a Gaussian function in the long-range corrected scheme.…”