Michael G. Medvedev

Density functional theory is straying from the path toward the exact functional

Whither the density in DFT calculations? The continuing development of density functional theory (DFT) has greatly expanded the size and complexity of molecules amenable to computationally tractable simulation. The conventional metric of success for new functionals has been the accuracy of their calculated energies. Medvedev et al. examined how well these functionals calculate electron density across a series of neutral and cationic atoms (see the Perspective by Hammes-Schiffer). Although historically the accuracies of energy and density have improved in tandem, certain recent functionals have sacrificed fidelity to the true density. Science, this issue p. 49; see also p. 28 Certain recent approaches to density functional theory have sacrificed fidelity to the true electron density. The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

Response to Comment on “Density functional theory is straying from the path toward the exact functional”

Kepp argues in his Comment, among other concerns, that the atomic densities we have considered are not relevant to molecular bonding. However, this does not change the main conclusion of our study, that unconstrained fitting of flexible functional forms can make a density functional more interpolative but less widely predictive.

Synthesis of Branched Tryptamines via the Domino Cloke–Stevens/Grandberg Rearrangement

The rearrangement of cyclopropylketone arylhydrazones generated in situ from arylhydrazine hydrochlorides and ketones leads to formation of tryptamine derivatives. The use of (2-arylcyclopropyl)ethanones in the reactions with model 4-bromophenylhydrazine hydrochloride gives branched tryptamines with aryl groups in the α-position to the amino group, while (2-methylcyclopropyl)ethanone gives a mixture of α- and β-substituted products in a ratio of 1:3. The method was found effective in the synthesis of enantiomerically pure tryptamine. Thus, (R,R)-(2-phenylcyclopropyl)ethanone gives the (S)-α-phenyltryptamine derivative with an enantiomeric excess over 99%.

Vibrational smearing of the electron density as function of the strength and directionality of interatomic interactions: nonvalent interactions of a nitro group within an island-type crystal [Fe(NO)2(SC6H4NO2)]2

We consider the static and dynamic characteristics of interatomic bonding in the region of nonvalent interactions of a nitro group in the crystal of complex [Fe(NO)2(SC6H4NO2)]2. Based on results obtained by modeling vibrations within the framework of the density functional theory and those of multitemperature X-ray diffraction studies, a purely vibrational nature of the abnormally large atomic displacement ellipsoid of one of the O atoms of the nitro group was revealed and a model for the influence of peculiar features of intermolecular bonding on the observed dynamics was suggested. Using topological analysis of the experimental electron density function, we studied the nature of nonvalent intermolecular interactions of the nitro group and evaluated their strength and directionality in the equilibrium state. The dependence of the “pseudodegeneracy” region of atom—atom interaction on the nature of the interaction revealed and a method for determining the vibrational smearing of interactions was suggested, which allows one to analyze the stability of the connectivity graph of the crystal.

Crystal structures of di-μ-bromido-bis{di­bromido­[η5-2-(di­methyl­amino)­inden­yl]zirconium(IV)} and di­bromido­bis­[η5-2-(di­methyl­amino)­inden­yl]zirconium(IV)

Molecules of di[(μ-bromido)(η5-2-dimethylaminoindenyl)dibromidozirconium(IV)], (I), and bis(η5-2-dimethylaminoindenyl)dibromidozirconium(IV), (II), are dinuclear with one CP ligand and four Br ligands for each of the ZrIV atoms and mononuclear with two CP and two Br ligands for the ZrIV atom, respectively.

Structure and condensation reactions of acyl(hydroxy)pyrido[1,2-a]indole borodifluoride complexes

Acyl(hydroxy)pyrido[1,2-a]indole-derived borodifluoride complexes were synthesized. Their structure was studied by single-crystal X-ray diffraction. The structural specific features were established for the dioxaborine ring in the 7-acetyl-8-hydroxypyrido[1,2-a]indole borodifluoride complex. The use of the borodifluoride complexes synthesized secures a smooth proceeding of their condensation reactions as compared to those of free ligands.