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Electron-electron repulsion in a quantum system facilitates the correlated motion of electrons, or electron correlation. The extent to which the movement of an electron is influenced by surrounding electrons is proportional to the correlation energy. This project explores unique electron correlation characteristics manifested in the excited singlet states of alternant hydrocarbons --- specifically, ethylene, butadiene, and hexatriene. Data was generated using the semiempirical Pariser-Parr-Pople Method, which combines molecular orbital theory approximation techniques (the Huckel and Hartree-Fock self-consistent field methods) and configuration interaction calculations. Slater determinants are used to derive configurational wavefunctions that account for all possible single- and double-electron excitations. Each electronic state can then be expressed as a linear combination of the singly- or doubly-excited configurations, with coefficients and corresponding transition energies calculated using the single or double configuration interaction method, respectively. The results indicate that certain wavefunctions --- referred to as plus and minus states --- are solely comprised of paired configurations (in equal magnitude), and all other coefficients are zero. The identical wavefunctions of the paired configurations allow for exact electron correlation symmetries to be demonstrated, yielding uncorrelated plus states (which produce an alternancy heap) and correlated minus states (yielding an alternancy hole). Analysis of each electronic state transition energy as a function of the range of electron-electron repulsion shows that at short ranges, the plus state energy increases due to the presence of alternancy heaps, while the minus state decreases because of alternancy holes. These results are consistent with the exact symmetries derived for the excited singlet states of alternant hydrocarbons.

Density functional theory has been used to investigate the structure, bonding and spectroscopic properties of a variety of interesting and potentially useful inorganic complexes. The photoluminescent (CuN(SiX 3 ) 2 ) 4 complex has an unusual square geometry with no formal Cu-Cu bonding. TDDFT calculations were performed to investigate the origin of the photoluminescence. It was determined that the complex undergoes a significant change in geometry in the cluster-centered, weakly Cu-Cu bonding, excited state. Another unusual copper cluster, Cu 3 (O 2 C X ) 6 , was also examined. This complex is triangular, paramagnetic, and has no formal Cu-Cu bonding. The complex is spin-frustrated, resulting from the arrangement and interaction of the three unpaired electrons on the Cu centers. The EPR parameters were calculated and the possibility of Jahn-Teller stabilization of the doublet state was investigated. The majority of this work focuses on the structure, energetics and bonding of series of isomeric transition metal complexes. There are a surprising number of “missing” (as of yet unobserved) simple, linear, sandwich complexes that could be formulated with transition metals and C n H n rings from n=3 to n=8. The Group 6 MC 12 H 12 isomers [(η 6 -C 6 H 6 ) 2 M, (η 5 -C 5 H 5 )M(η 7 -C 7 H 7 ), (η 4 -C 4 H 4 )M(η 8 -C 8 H 8 )], Group 8 MC 10 H 10 isomers [(η 5 -C 5 H 5 ) 2 M, (η 4 -C 4 H 4 )M(η 6 -C 6 H 6 ), (η 3 -C 3 H 3 )M(η 7 -C 7 H 7 )] and NiC 8 H 8 isomers [(η 4 -C 4 H 4 ) 2 Ni, (η 3 -C 3 H 3 )Ni(η 5 -C 5 H 5 )] were studied. The NiC 8 H 8 study was extended to include (η 2 -C 2 H 2 )Ni(η 6 -C 6 H 6 ) and (η 8 -C 8 H 8 )Ni. The ground-state geometry was determined for all isomers, and bonding analysis was performed to determine the dominantly bound fragment in all the species. It was found that, in general, the distance between the metal and ring centroids was long for π-bound rings and significantly shorter in δ-bound rings. The out-of-plane bending of the C-H bonds in the ring ligands varied according to how mismatched the ring π orbitals were in relation to the M δ orbitals. The bonding analysis found that the dominantly bound rings were not necessarily those with π bonds, the most covalent character, or best size match. Each complex was analyzed individually to determine the dominantly bound ring, and to understand the interactions. Attention was paid to the changes seen as the metal was changed both moving across and down the transition metal block.

The atom superposition and electron delocalization molecular orbital (ASED-MO) theory is used to study methane C-H bond activation over MoS2, MoC, and O/Ag(110), C1 coupling mechanisms to form C2H6 and C2H5OH on MoS2, CH2 coupling on MoC, and the binding properties of C2 olefins to 2 S in the CpMoS4MoCp (Cp = C5H5) complex and on MoS2. For methane C-H bond activation by the Mo IV oxidative insertion mechanism, the theory predicts low barriers for both MoS2 and MoC catalysts. These results suggest the possibility of incorporating methane into the Fischer-Tropsch process over these catalysts. The activation barrier for H abstraction by O on Ag(110) is calculated to be lower than over most oxides. The calculations also suggest the possibility of direct O insertion into a methane C-H bond to make methanol on the O/Ag(110) surface. It has been demonstrated by Klier and coworkers that the Fischer-Tropsch reaction over MoS2 proceeds by the CO insertion mechanism. The calculations also favor this mechanism. High barriers are found for the other C1 coupling mechanisms (CH3 + CH3, CH2 + CH3, and CH2 + CH2). Two CH2 coupling on MoC is also studied. The calculations show that the coupling barrier on MoC is smaller than that on MoS2 and the desorption of C2H4 is calculated to be easier on MoC. Complexes which have a S4 structure chelated by ligands (e.g. C2H4 and C2H2) have been insolated by DuBois and coworkers. Acetylene hydrogenation in these complexes were also observed. These seem to suggest that S2- in MoS2 basal planes would possibly have the same reactivities. This would be in contrast to the general belief that MoS2 basal planes are inert toward catalytic reactions and that hydrogenation over MoS2 occurs on the edge unsaturated Mo IV sites. Theoretical calculations carried out to study the binding strengths of C2 olefins to the sulfur anions in the CpMoS4MoCp complex and on MoS2 demonstrate that the binding of C2 olefins to MoS2 basal plane S2- is much weaker than in the complex