Communication: Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.     

An efficient grid-based scheme to compute QTAIM atomic properties without explicit calculation of zero-flux surfaces

We introduce a method to compute atomic properties according to the "quantum theory of atoms in molecules." An integration grid in real space is partitioned into subsets, omega(i). The subset, omega(i), is composed of all grid points contained in the atomic basin, Omega(i), so that integration over Omega(i) is reduced to simple quadrature over the points in omega(i). The partition is constructed from deMon2k's atomic center grids by following the steepest ascent path of the density starting from each point in the grid. We also introduce a technique that exploits the cellular nature of the grid to make the algorithm faster. The performance of the method is tested by computing properties of atoms and nonnuclear attractors (energies, charges, dipole, and quadrupole moments) for a set of representative molecules.     

Can one oxidize an atom by reducing the molecule that contains it?

Negative values for the condensed Fukui function are identified as the key to designing molecules in which reduction of the molecule is associated with oxidation of one of the atomic centers, or vice versa. Sufficient conditions for negative condensed Fukui functions are derived, and metal complexes are identified as likely candidates for this exotic redox chemistry. Based on our theoretical understanding of where negative values of the Fukui function occur [P. W. Ayers, R. C. Morrison and R. K. Roy. J. Chem. Phys., 2002, 116, 8731], molecular-orbital diagrams for molecules where molecular oxidation is coupled to atomic reduction (or vice versa) are sketched. Whether one could design a metal complex with these properties is an open question but, if one could, then that compound would have fascinating redox chemistry and interesting magnetic properties. Candidate molecules for this property include metal complexes with small metal-to-ligand and/or ligand-to-metal charge transfer excitation energies.     

Stockholder projector analysis: a Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.     

Determination of ammonia in tobacco and smoke

A gas chromatographic method has been developed for the determination of ammonia in tobacco and smoke. Ammonia is liberated from tobacco by a microdiffusion technique using a Conway diffusion cell. Bubbler traps containing dilute sulphuric acid are used to collect the ammonia from smoke.     

Organometallic polymers. XVI. Copolymerization of styrenetricarbonylchromium and the reaction of polystyrene with chromium hexacarbonyl

Styrenetricarbonylchromium (IV) has been synthesized. Monomer IV did not homopolymerize with free-radical initiation but copolymerized with styrene, methyl acrylate, and vinylcymantrene. The copolymerizations were carried out in benzene solutions at 70°C with azobisisobutyronitrile as the initiator. The relative reactivity ratios were determined for the styrene and methyl acrylate copolymerizations. They were (defining M₁ as monomer IV) r₁ ? 0, r₂ ? 1.39 for styrene copolymerizations and r₁ ? 0, r₂ ? 0.75 for methyl acrylate copolymerization. Polystyrene reacted with chromium-hexacarbonyl in refluxing DME to produce a polymer in which about 32% of the benzene rings were complexed with ? Cr(CO)₃ units. The use of a polystyrene of narrow molecular weight distribution in this reaction demonstrated that no decomposition of the polystyrene chains occurred.     

Characterization of beta-amino ester enolates as hexamers via 6Li NMR spectroscopy

Low-temperature 6Li NMR spectroscopic studies on a chiral beta-amino ester enolate reveal a complex mixture of homo- and heterochiral aggregates. Subsequent warming of the samples led to rapid intra-aggregate exchange, resulting in four distinct resonances consistent with an ensemble of hexamers. An implicit fit of the aggregate populations to the Boltzmann distribution provided the free energy differences and equilibrium constants. An X-ray crystal structure obtained from the racemic enolate is consistent with the predominant aggregate in solution.     

Assessment of the March-Santamaria kinetic energy pair-density functional

The quality of the March-Santamaria kinetic energy function for the spin-resolved electron pair density is assessed. While the March-Santamaria functional is exact for all pair densities that arise from a single Slater determinant wavefunction, its value tends to decrease (instead of increase) with increase correlation.