Split electrons in partition density functional theory

Abstract

Partition Density Functional Theory (P-DFT) is a density embedding method that partitions a molecule into fragments by minimizing the sum of fragment energies subject to a local density constraint and a global electron-number constraint. To perform this minimization, we study a two-stage procedure in which the sum of fragment energies is lowered when electrons flow from fragments of lower electronegativity to fragments of higher electronegativity. The global minimum is reached when all electronegativities are equal. The non-integer fragment populations are dealt with in two different ways: (1) An ensemble approach (ENS) that involves averaging over calculations with different numbers of electrons (always integers); and (2) A simpler approach that involves fractionally occupying orbitals (FOO). We compare and contrast these two approaches and examine their performance in some of the simplest systems where one can transparently apply both, including simple models of heteronuclear diatomic molecules and actual diatomic molecules with 2 and 4 electrons. We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts, and they tend to retain integer numbers of electrons. We establish the conditions under which the ENS populations can become fractional and observe that, even in those cases, the total charge transferred is always lower in ENS than in FOO. Similarly, the FOO fragment dipole moments provide an upper bound to the ENS dipoles. We explain why, and discuss implications.

Yellow and Orange–Red Room‐Temperature Phosphorescence from Amorphous Nonaromatic Polymers

“…All conformational scans were performed by ABCluster, a code proposed by Zhang and Dolg. [ 28–30 ] The conformation (structure) optimizations were performed with the density functional theory (DFT) and time‐dependent density functional theory (TD‐DFT) on the basis of Gaussian 16 software (version A.03). [ 31 ] The spin‐orbit coupling (SOC) matrix elements between singlet and triplet states were evaluated through ORCA (version 5.0.0) with M062X functional and 6–31g(d,p) basic set.…”

Room‐Temperature Phosphorescent Tough Hydrogels Based on Ionically Crosslinked Nonaromatic Polymers

“…Theoretical Calculations: All conformational scans are performed by ABCluster, a code proposed by Zhang and Dolg. [53][54][55] Conformation (structure) optimizations were performed with density functional theory (DFT) and time-dependent density functional theory (TD-DFT) on the basis of Gaussian 16 software (version A.03). [56] The SOC matrix elements between singlet and triplet states were evaluated through ORCA (version 5.0.0).…”

Subsystem density‐functional theory (update)

“…For recent developments in partition DFT, which shares several features with sDFT but allows for fractional numbers of electrons per subsystem and enforces a common embedding potential for all subsystems, we refer to the work of Wasserman and coworkers. [26][27][28][29][30][31][32][33][34] Finally, the use of sDFT/FDE for accessing specific spin states and broken-symmetry sDFT approaches are presented in Section 4.4. A related review of developments and applications of sDFT/FDE for spin densities and spin-related properties is given in Ref.…”