Equations are proposed for computing from ab initio wave functions quantities like 〈SA⋅SB〉, which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators derived from Löwdin orthogonalization. They result in local spin operators SA which obey the definition of angular momentum operators and commute with each other. These equations are evaluated for several typical closed and open shell molecules. For closed shells in the single Slater determinant approximation, 〈SA⋅SB〉 is −38 of the bond-order and 〈SA2〉 is +38 of the total number of bonds to center A. For open shells there are additional contributions from the unpaired electrons. In favorable cases, these additional terms have the value assumed as the whole answer in the usual applications of the Heisenberg Hamiltonian.

(18)O-isotope-labeling studies have led to the conclusion that there exist two major pathways for water oxidation catalyzed by dimeric ruthenium ions of the general type cis, cis-[L2Ru(III)(OH2)]2O(4+). We have proposed that both pathways involve concerted addition of H and OH fragments derived from H 2O to the complexes in their four-electron-oxidized states, i.e., [L2Ru(V)(O)]2O(4+), ultimately generating bound peroxy intermediates that decay with the evolution of O2. The pathways differ primarily in the site of addition of the OH fragment, which is either a ruthenyl O atom or a bipyridine ligand. In the former case, water addition is thought to give rise to a critical intermediate whose structure is L2Ru(IV)(OH)ORu(IV)(OOH)L2(4+); the structures of intermediates involved in the other pathway are less well defined but may involve bipyridine OH adducts of the type L2Ru(V)(O)ORu(IV)(OH)(L(*)OH)L(4+), which could react further to generate unstable dioxetanes or similar endoperoxides. Published experimental and theoretical support for these pathways is reviewed within the broader context of water oxidation catalysis and related reactions reported for other diruthenium and group 8 monomeric diimine-based catalysts. New experiments that are designed to probe the issue of bipyridine ligand "noninnocence" in catalysis are described. Specifically, the relative contributions of the two pathways have been shown to correlate with substituent effects in 4,4'- and 5,5'-substituted bipyridine complexes in a manner consistent with the formation of a reactive OH-adduct intermediate in one of the pathways, and the formation of OH-bipyridine adducts during catalytic turnover has been directly confirmed by optical spectroscopy. Finally, a photosensitized system for catalyzed water oxidation has been developed that allows assessment of the catalytic efficiencies of the complex ions under neutral and alkaline conditions; these studies show that the ions are far better catalysts than had previously been assumed based upon reported catalytic parameters obtained with strong oxidants in acidic media.

The diimide perylene motif exhibits a dramatic intensity reversal between the 0 --> 0 and 0 --> 1 vibronic bands upon pi-pi stacking; this distinct spectral property has previously been used to measure folding dynamics in covalently bound oligomers and synthetic biological hybrid foldamers. It is also used as a tool to assess organization of the pi-stacking, indicating the presence of H- or J-aggregation. The zeroth-order exciton model, often used to describe the optical properties of chromophoric aggregates, is solely a transition dipole coupling scheme, which ignores the explicit electronic structure of the system as well as vibrational coupling to the electronic transition. We have therefore examined the optical properties of gas-phase perylene tetracarboxylic diimide (PTCDI) and its chromophoric dimer as a function of conformation to relate the excited-state distributions predicted by exciton theory with that of time-dependent density functional theory (TDDFT). Using ground- and excited-state geometries, the Franck-Condon (FC) factors for the lowest energy molecular nature electronic transition have been calculated and the origin of the intensity reversal of 0 --> 0 and 0 --> 1 vibronic bands has been proposed.

Many intermolecular chemical interactions persist across length and timescales and can be considered to form a "network" or "graph." Obvious examples include the hydrogen bond networks formed by polar solvents such as water or alcohols. In fact, there are many similarities between intermolecular chemical networks like those formed by hydrogen bonding and the complex and distributed networks found in computer science. Contemporary network analyses are able to dissect the complex local and global changes that occur within the network over multiple time and length scales. This work discusses the ChemNetworks software, whose purpose is to process Cartesian coordinates of chemical systems into a network/graph formalism and apply topological network analyses that include network neighborhood, the determination of geodesic paths, the degree census, direct structural searches, and the distribution of defect states of network. These properties can help to understand the network patterns and organization that may influence physical properties and chemical reactivity. The focus of ChemNetworks is to quantitatively describe intermolecular chemical networks of entire systems at both the local and global levels and as a function of time. The code is highly general, capable of converting a wide variety of systems into a chemical network formalism, including complex solutions, liquid interfaces, or even self-assemblies.

Several singlet and triplet potential energy surfaces (PES) for the Bergman cyclization of cis-1,5-hexadiyne-3-ene (1a) have been computed by UDFT, CI, CASCI, CASSCF, and CASMP2 methods. It is found that the first six excited states of 1a can be qualitatively described as linear combinations of the configurations of weakly interacting ethylene and acetylene units. Although the symmetry relaxation from C2nu to C2 makes cyclization of the 13B state Woodward-Hoffmann allowed, it also increases the probability of competing cis-trans isomerization. Hydrogen atom abstraction is another plausible pathway because the terminal alkyne carbons possess a large radical character. In view of the competing processes, we conclude that the Bergman cyclization along the 13B path is unlikely despite its exothermicity (Delta = -42 kcal/mol). Calculations on cyclic analogues of 1a lead to similar conclusions. A less exothermic, but more plausible pathway for photochemical cyclization lies on the 2(1)A PES (Delta = -18 kcal/mol). Compared to the 1(1)A(1) and 1(3)B states, the 2(1)A state has less in-plane electron repulsion which may facilitate cyclization. The resulting p-benzyne intermediate has an unusual electronic structure combining singlet carbene and open-shell diradical features. Deactivation of the 2(1)A state of 1a is a competing pathway.