New procedure to evaluate aromaticity at the density functional theory, Hartree-Fock, and post-self-consistent field levels.

The spatial exchange interaction, arising from the exchange-type two-electron integrals (i(p)j(q)/i'(p)j'(q)) between two different groups P and Q, is another driving force for the delocalization of π-electrons besides orbital charge-transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange-type two-electron integrals, ensuring that the corresponding π-electrons are completely localized within their respective groups and the π-orbitals are fully localized. The extra stabilization energy (ESE) of benzene is -36.3 kcal/mol (B3LYP/6-31G*), and the level of density functional theory, Hartree-Fock, and post-self-consistent field (Møller-Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled-cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block-localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the CC single bond lengths in the ground state with its π-localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π-delocalization on single bonds is so small as to be negligible.

Bonding of seven carbonyl groups to a single metal atom: theoretical study of M(CO)n (M = Ti, Zr, Hf; n = 7, 6, 5, 4).

The equilibrium geometries, thermochemistry, and vibrational frequencies of the homoleptic metal-carbonyls of the group 4 elements, M(CO)n (M = Ti, Zr, Hf; n = 7, 6, 5, 4) were predicted using density functional theory. Analogous M(CO)n structures were found for all three metals. The global minima for the 18-electron M(CO)7 molecules are all singlet C(3v) capped octahedra. The global minima for the 16-electron M(CO)6 species are triplet M(CO)6 structures distorted from O(h) symmetry to D(3d) symmetry. However, the corresponding singlet M(CO)6 structures lie within 5 kcal/mol of the triplet global minima. The global minima for M(CO)n (n = 5, 4) are triplet structures derived from the D(3d) distorted octahedral structures of M(CO)6 by removal of one or two CO groups, respectively. Quintet D(3h) trigonal bipyramidal structures for M(CO)5 and singlet T(d) tetrahedral structures for M(CO)4 are also found, as well as higher energy structures for M(CO)6 and M(CO)7 containing a unique CO group bonded to the metal atom through both M-C and M-O bonds. The dissociation energies M(CO)7 --> M(CO)6 + CO are substantial, indicating no fundamental problem in bonding seven CO groups to a single metal atom.

Restricted geometry optimization: a different way to estimate stabilization energies for aromatic molecules of various types.

At RHF, MPn, and DFT levels, a procedure of geometry optimization under the restrictions of pi-orbital interactions (GOR) was developed, thus providing a conjugated molecule with the following two types of localized reference geometries: a "GL" geometry where all double bonds are localized, and n different "GE-n" geometries, in each of which only two double bonds were permitted to conjugate. Interestingly, the molecular energy differences between the corresponding pairs of GE-n and GL geometries were found to be additive in each of the acyclic polyenes, and these were not additive for benzene. As a result, an extra stabilization energy (ESE) value of -39.0 kcal/mol was found in benzene. Afterward, GOR was applied to benzene- and furan-like species, strained aromatic molecules, and substituted benzenes, and the calculated ESEs for these molecules were found to be in reasonable ranges. The GOR can isolate a specific group from other groups, and it has several special functions. First, with regard to the substituent effect, the ESE difference between substituted benzene and benzene can be partitioned into conjugative and inductive parts. Second, the behavior of strained aromatic molecules can be ascertained from the roles of their resonance interactions, strained-induced bond localization (SIBL), and inductive effects, indicating that it is resonance interactions, rather than SIBL, which are responsible for localizing double bonds. Emphatically, it is the GL and GE-n geometries of aromatic molecules, rather than nonaromatic compounds, which can be used as the reference structures for calculating ESE. Particularly, these localized geometries are no longer arbitrary.

Theoretical studies on novel main group metallocene-like complexes involving planar hexacoordinate carbon eta6-B6C2- ligand.

The geometric structures for a novel series of main group 1 and 2 metal atom complexes with planar hexacoordinate carbon dianion (eta6-B6C)2- ligand, involving metallocene-like, K[(eta6-B6C)Ca]n(eta6-B6C)K (n = 1-3) and [(eta6-B6C)Ca]n(eta6-B6C)2- (n = 1, 2), as well as relative pyramidal [(eta6-B6C)M]i- (M = Na, K, and CaCl, i = 1; M = Ca, i = 0) and bipyramidal (eta6-B6C)(CaCl)2, have been optimized to be the local minima on the corresponding potential hypersurfaces at the B3LYP/6-311+G(d) level of theory. Natural bond orbital analysis indicates that the electrostatic interaction between the metal ions and the planar hexacoordinate carbon B6C2- rings plays a crucial role in stabilizing these highly symmetrical complexes. The pi-d interaction in Ca-containing complexes also plays an important role in the stabilization of these molecules. It is found that the Ca2+ cation could be considered the best candidate for (eta6-B6C)2- to build ionic organometallic compounds. In these predicted multideck metallocene-like complexes there exist similarities in many structural properties, such as geometry parameters, Wiberg bond indices, natural atomic charges, atomic electronic configurations, and frontier orbital energies, as well as increments of the dissociation energy (to -[(eta6-B6C)Ca]- units and metal cations) for adding one -[(eta6-B6C)Ca]- unit and so on, which suggests that the -[(eta6-B6C)Ca]- unit could be used as a building block to construct more K[(eta6-B6C)Ca]n(eta6-B6C)K chain-type metallocene-like complexes along their sixfold molecular axis.

Theoretical studies on the role of pi-electron delocalization in determining the conformation of N-benzylideneaniline with three types of LMO basis sets.

To understand the role of pi-electron delocalization in determining the conformation of the NBA (Ph-N==CH-Ph) molecule, the following three LMO (localized molecular orbital) basis sets are constructed: a LFMO (highly localized fragment molecular orbital), an NBO (natural bond orbital), and a special NBO (NBO-II) basis sets, and their localization degrees are evaluated with our suggesting index D(L). Afterward, the vertical resonance energy DeltaE(V) is obtained from the Morokuma's energy partition over each of three LMO basis sets. DeltaE(V) = DeltaE(H) (one electron energy) + DeltaE(two) (two electron energy), and DeltaE(two) = DeltaE(Cou) (Coulomb) + DeltaE(ex) (exchange) + DeltaE(ec) (or SigmaDeltaE(n)) (electron correction). DeltaE(H) is always stabilizing, and DeltaE(Cou) is destabilizing for all time. In the case of the LFMO basis set, DeltaE(Cou) is so great that DeltaE(two) > |DeltaE(H)|. Therefore, DeltaE(V) is always destabilizing, and is least destabilizing at about the theta = 90 degrees geometry. Of the three calculation methods such as HF, DFT, and MPn (n = 2, 3, and 4), the MPn method provides DeltaE(V) with the greatest value. In the case of the NBO basis set, on the contrary, DeltaE(V) is stabilizing due to DeltaE(Cou) being less destabilizing, and it is most stabilizing at a planar geometry. The LFMO basis set has the highest localization degree, and it is most appropriate for the energy partition. In the NBA molecule, pi-electron delocalization is destabilization, and it has a tendency to distort the NBA molecular away from its planar geometry as far as possible.