Subsystem density-functional theory (DFT) is a powerful and efficient alternative to Kohn-Sham DFT for large systems composed of several weakly interacting subunits. Here, we provide a systematic investigation of the spin-density distributions obtained in subsystem DFT calculations for radicals in explicit environments. This includes a small radical in a solvent shell, a π-stacked guanine-thymine radical cation, and a benchmark application to a model for the special pair radical cation, which is a dimer of bacteriochlorophyll pigments, from the photosynthetic reaction center of purple bacteria. We investigate the differences in the spin densities resulting from subsystem DFT and Kohn-Sham DFT calculations. In these comparisons, we focus on the problem of overdelocalization of spin densities due to the self-interaction error in DFT. It is demonstrated that subsystem DFT can reduce this problem, while it still allows to describe spin-polarization effects crossing the boundaries of the subsystems. In practical calculations of spin densities for radicals in a given environment, it may thus be a pragmatic alternative to Kohn-Sham DFT calculations. In our calculation on the special pair radical cation, we show that the coordinating histidine residues reduce the spin-density asymmetry between the two halves of this system, while inclusion of a larger binding pocket model increases this asymmetry. The unidirectional energy transfer in photosynthetic reaction centers is related to the asymmetry introduced by the protein environment.
Long-range charge-transfer processes in extended systems are difficult to describe with quantum chemical methods. In particular, cost-effective (non-hybrid) approximations within time-dependent density functional theory (DFT) are not applicable unless special precautions are taken. Here, we show that the efficient subsystem DFT can be employed as a constrained DFT variant to describe the energetics of long-range charge-separation processes. A formal analysis of the energy components in subsystem DFT for such excitation energies is presented, which demonstrates that both the distance dependence and the long-range limit are correctly described. In addition, electronic couplings for these processes as needed for rate constants in Marcus theory can be obtained from this method. It is shown that the electronic structure of charge-separated states constructed by a positively charged subsystem interacting with a negatively charged one is difficult to converge - charge leaking from the negative subsystem to the positive one can occur. This problem is related to the delocalization error in DFT and can be overcome with asymptotically correct exchange-correlation (XC) potentials or XC potentials including a sufficiently large amount of exact exchange. We also outline an approximate way to obtain charge-transfer couplings between locally excited and charge-separated states.
We introduce alchemical perturbations as a rapid and accurate tool to estimate fundamental structural and energetic properties in pure and mixed ionic crystals. We investigated formation energies, lattice constants, and bulk moduli for all sixteen iso-valence-electron combinations of pure pristine alkali halides involving elements Me ∈ {Na, K, Rb, Cs} and X ∈ {F, Cl, Br, I}. For rock salt, zinc-blende, and cesium chloride symmetry, alchemical Hellmann-Feynman derivatives, evaluated along lattice scans of sixteen reference crystals, have been obtained for coupling to all respective 16 × 15 target crystals. Mean absolute errors (MAEs) are on par with the density functional theory level of accuracy for energies and bulk moduli. The predicted lattice constants are less accurate but reproduce qualitative trends. The reference salt NaCl affords the most accurate alchemical estimates of relative energies (MAE < 40 meV per atom). The best predictions of lattice constants are based on NaF as a reference salt (MAE < 0.5 Å), accounting only for qualitative trends. The best reference salt for the prediction of bulk moduli is CsCl (MAE < 0.4 × 10 dynes cm). The alchemical predictions distinguish competing rock salt and cesium chloride phases in binary and ternary solid mixtures with CsCl. Using pure RbI as a reference salt, they reproduce the reversal of the rock salt/cesium chloride stability trend for binary MeXCsCl as well as for ternary MeX(Me'Y)CsCl mixtures.
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