用分子片轨道逐步剔除法研究电子离域

估计分子中不同类型的电子离域作用（如p-π → d-π和p-π → σ~*）的相 对强弱对理解分子中化学键的本质有关键的作用。剔除某一分子片轨道（d-π或σ ~*）后分子体系能量的改变可用来计算电子离域到该轨道的离域能。由于轨道之间 的相互作用,使离域能的计算与轨道剔除的次序有关。为克服这种不确定性,可以 逐步轮流增加某一对特定轨道（d-π和σ~*）的库仑积分,以使这对轨道在分子波 函数中的比重逐步减少,即将这对轨道轮流逐步剔除。这样可将轨道间的相互影响 减小以至消除,从而得到各轨道的精确的离域能。以H_3PO中P-O键为例说明了轨道 逐步剔除方法的应用。     

Borazine: to be or not to be aromatic

Aromaticity of borazine, which has been subject of controversial discussions, is addressed. Beside a short review on aromaticity of borazine we report a detailed analysis of two molecular fields, the induced magnetic field (B ^ind) and the electron localization function (ELF). The induced magnetic field of borazine shows a long-range shielding cone perpendicular to the molecular plane, as in benzene, but lower in magnitude. Contrary to benzene, borazine shows two weakly paratropic regions, one of them inside the ring, and the second one enveloping the boron atoms. It is necessary to separate σ and π contributions to identify whether borazine exhibits π-aromatic character comparable to benzene. Nucleus-independent chemical shift (NICS) isolines show that the σ electrons are much stronger localized than π electrons, their local paramagnetic contributions generate a short-range response and a paratropic (deshielding) region in the ring center (similar to an anti-aromatic response). Three regions can be identified as chemically meaningful domains exhibiting an internally strong electron delocalization (ELF = 0.823). Borazine may be described as a π aromatic compound, but it is not a globally aromatic species, as the electronic system is not as delocalized as in benzene. Dedicated to the 70th birthday of Prof. Tadeusz Marek Krygowski.     

Electronic nature of carbonium ions and their silicon analogues

Nonclassical ions or carbonium ions have multi-center bonding from delocalized sigma or pi electrons. The 2-norbornyl cation, its derivative 6,6-difluoro-2-norbornyl cation, tris-homocyclopropenyl cation, 7-norbornenyl cation, and 4-cyclopentenyl cation and their corresponding silicon analogues were studied in this work. All carbocations have topologically different 3c-2e systems. The magnitude of all delocalization indexes between each atomic pair of the 3c-2e bond can be used to predict homoaromaticity. The silicon analogues have a topologically different 3c-2e bond from their corresponding carbocation.     

Resolving the Unpaired‐Electron Orbital Distribution in a Stable Organic Radical by Kondo Resonance Mapping

The adsorption geometry and the electronic structure of a Blatter radical derivative on a gold surface were investigated by a combination of high‐resolution noncontact atomic force microscopy and scanning tunneling microscopy. While the hybridization with the substrate hinders direct access to the molecular states, we show that the unpaired‐electron orbital can be probed with Ångström resolution by mapping the spatial distribution of the Kondo resonance. The Blatter derivative features a peculiar delocalization of the unpaired‐electron orbital over some but not all moieties of the molecule, such that the Kondo signature can be related to the spatial fingerprint of the orbital. We observe a direct correspondence between these two quantities, including a pronounced nodal plane structure. Finally, we demonstrate that the spatial signature of the Kondo resonance also persists upon noncovalent dimerization of molecules.     

The nature of the delocalized cations in azulenic bacteriorhodopsin analogs.

Depending on the size and shape of their azulenic chromophores, azulenic bacteriorhodopsin (bR) pigment analogs can exist as either an initial pigment P1, a more red-shifted final pigment P2 or an equilibrium mixture of both. The absorption spectra of red-shifted bR analogs exhibit characteristic narrow-band shapes similar to charge fully delocalized cyanine-like dyes. Therefore, all such red-shifted pigments are believed to be highly delocalized, bond-equalized carbocations. We have determined structural requirements that facilitate their formation. To describe fully the red-shift potentials of these retinal analogs, we have introduced a new parameter-percent red-shift (PRS). A large PRS value not only reflects the extent of red-shift, but is also suggestive of extensive delocalization of the positive charge. Relevance of these findings in consideration of the possibility of forming stable O-intermediates is presented. The postulated resonance hybrid-like structures for different cations of the positively charged protonated Schiff base chromophores are in fact structurally distinct species, equilibrating in response to local perturbations within the supramolecular protein environment.     

Some answers to frequently asked questions about the distortive tendencies of π-electronic system

The paper reviews briefly the various computational strategies, which have been devised by different groups to probe the symmetrizing vs distortive propensities of the π-bonding species of polyenes. All methods point to the same conclusion that the π-bonding components of benzene, allyl, aromatic annulenes and related species have intrinsic distortive tendencies; these species maintain bond-equalized geometries due to the symmetrizing driving force of the corresponding σ frames. Some frequently asked questions, that deal with the compatibility of the π-distortivity scenario with the greater body of experimental data regarding aromatic stability and π-delocalization, are addressed. Many of these questions are immediately answered, once the notion is accepted that delocalized π-systems possess a duality: their π-component is distortive and at the same time resonance stabilized relative to the localized structure with the same geometry. The notion of distortive π-electronic components of polyenes is shown to find a natural place in the wider context of a unified model of electronic delocalization that is valid for both conjugated π- and σ-electronic systems.     

Higher Coordination Numbers of the Typical Elements

The bonding in electron-deficient molecules, e.g. the boron hydrides and certain metal alkyls, and in molecules which appear to violate the rare gas rule, e.g. hydrogen bonded complexes, interhalogen compounds and compounds of the typical elements with high coordination numbers such as PCI₅ and SF₆ can be described by a simple molecular orbital treatment involving delocalized α-bonds. The contribution of d-orbitals to the bonding in the interhalogen compounds and rare gas fluorides is very small. The stereochemistry and physical properties of the PX₅ system are explained readily by the delocalization treatment and it is likely that here also the importance of spd hybridization has been overemphasized in the past.     

Structure/reactivity relationships in the benzo[c]phenanthrene skeleton: stable ion and electrophilic substitution (nitration, bromination) study of substituted analogues, novel carbocations and substituted derivatives

A series of novel carbocations were generated by low-temperature protonation of substituted benzo[c]phenanthrenes, B[c]Phs, and their charge delocalization pathways were elucidated by NMR on the basis of the magnitude of Deltadelta13C values. It has been shown that the protonation regioselectivity is strongly controlled by methoxy and hydroxyl substituents, whose directive effects override methyl substitution effects. Regiocontrol by -OMe and -OH substituents, and its stronger influence relative to methyl groups, was also observed in the nitration and bromination reactions. Charge distribution modes in the regioisomeric protonated carbocations formed via parent B[c]Ph as well as in the benzylic carbocation formed via fjord-region epoxide ring opening were deduced by gauge-invariant atomic orbital density functional theory (GIAO-DFT) and from the natural population analysis (NPA)-derived changes in charges over CHs. These patterns were compared with those derived from NMR experiments in the substituted derivatives. NMR-based charge delocalization mapping provided insight into structure/activity relationships in the methylated and fluorinated B[c]Phs. Regioselectivities observed in the nitration and bromination reactions in representative cases are the same as those via protonations. Among a group of novel nitro and bromo derivatives synthesized in this study are examples, where the nitro group is introduced into the fjord region, for which the X-ray structure could be obtained in one case.     

A new method for empirical force field calculations on localized and delocalized carbocations

A new empirical force field method for localized and delocalized carbocations is described. Additional geometry parameters for carbocations were added to Allinger's MMP2 molecular mechanics program, which can treat delocalized π-systems. The effect of hyperconjugation in carbocations is introduced via a quantum chemical term into force field calculations for the first time. The calculated heats of formation are in excellent agreement with a wide range of experimental data; the largest deviations are about 3.5 kcal/mol. The calculated structures agree very well with those computed at correlated ab initio levels (MP2(full)/6-31G*). The relative energies and geometries of different conformations of representative carbocations also were in good agreement with MP4/6-31G*//MP2(full)/6-31G* results. © 1996 by John Wiley & Sons, Inc.     

Electron delocalization in acyclic and N-heterocyclic carbenes and their complexes: a combined experimental and theoretical charge-density study

Combined experimental and theoretical charge-density studies on free and metal-coordinated N-heterocyclic carbenes have been performed to investigate the extent of electron delocalization in these remarkable species. Tracing the orientation of the major axis of the bond ellipticity (the least negative curvature in the electron density distribution) along the complete bond paths distinguishes unambiguously between fully delocalized systems and those with interrupted cyclic electron delocalization. Evaluation of charge-density-based properties such as atomic quadrupole moments serves as a direct and quantitative measure of the extent of pi-electron delocalization and reveals consistency between theory and experiment. A detailed topological analysis of theoretical charge densities for two benchmark carbene systems, viz., 1,2-dimethylpyrazol-3-ylidene 1a and 1,3-dimethylimidazol-2-ylidene 2a, and their corresponding stable chromium pentacarbonyl complexes 1 and 2, highlights the advantages of charge-density-based criteria to analyze such complex electronic situations. Thus, 1a and 2a display a different extent of electron delocalization; yet nearly identical p(pi) occupations at the carbene center are computed for 1a and 2a. However, atomic quadrupoles Q(zz) - the charge-density analogues of p(pi) occupation - reveal faithfully the electronic differences in 1a and 2a and demonstrate the sensitivity of charge-density-based properties to the bonding situation. The acyclic aminocarbene (iPr(2)N)(2)CCr(CO)(4) has also been studied, and the high barrier to rotation about the C-N bond is shown not to arise solely from p(pi)-p(pi) bonding.     

Are atoms sic to molecular electronic wavefunctions? II. Analysis of fors orbitals

Electronic wavefunctions that describe molecules in the full optimized reaction space (FORS) are multiconfigurational wavefunctions which are invariant under non-singular linear transformations of the occupied molecular orbitals. They offer therefore a considerably wider scope for orbital interpretations than the single-configuration Hartree-Fock approximation. For example they can be analyzed in terms of natural MOs and in terms of localized MOs. The latter turn out to be remarkably atomic in character and a new localization procedure can be formulated which yields atom-adapted molecular orbitals. These have the character of minimal-basis-set AOs that are optimally adapted to the molecular environment and furnish an unambigious atomic population analysis. On the other hand, chemically adapted molecular orbitals can be defined by an appropriate compromise between natural orbitals and localized orbitals. The freedom to use, as configuration-generating molecular orbitals, atom-adapted FORS MOs as well as chemically adapted FORS MOs makes FORS wavefunctions particularly suitable for chemical interpretations. The ensuing analysis establishes the minimal basis set (in molecule-adapted form) as a theoretically sound concept for the understanding of accurate molecular wavefunctions. An illustrative example is discussed.     

Lewis acidity of gallium halides

The Lewis acidity of GaF(3), GaF(2)Cl, GaFCl(2), and GaCl(3) in acid-base interactions has been studied by taking ammonia as their electron-donating counterpart. We have derived an unoccupied reactive orbital that shows the maximum localization on the Ga atomic center for each species. The orbital is located lower in energy compared to those in the corresponding boron and aluminum halides. In contrast to boron halides, the unoccupied reactive orbital of the acid site tends to be delocalized considerably on the halogens as the fluorines are substituted by chlorines in gallium halides. The trend observed in the effects of fluorine and chlorine on the acidity of the gallium halides is opposite to those found in the boron halides. This cannot be interpreted solely in terms of the electron-accepting strength of the gallium center, but can be understood by including electrostatic interactions and closed-shell repulsion with ammonia in the adducts. The origin of the difference in Lewis acidity of BCl(3), AlCl(3), and GaCl(3) has been clarified.     

From aromaticity to self-organized criticality in graphene

The unique properties of graphene are rooted in its peculiar electronic structure where effects of electron delocalization are pivotal. We show that the traditional view of delocalization as formation of a local or global aromatic bonding framework has to be expanded in this case. A modification of the π-electron system of a finite-size graphene substrate results in a scale-invariant response in the relaxation of interatomic distances and reveals self-organized criticality as a mode of delocalized bonding. Graphene is shown to belong to a diverse class of finite-size extended systems with simple local interactions where complexity emerges spontaneously under very general conditions that can be a critical factor controlling observable properties such as chemical activity, electron transport, and spin-polarization.     

Direct-space analysis of the Si–Si bonding pattern in the π-bonded chain reconstructed Si(111)(2 × 1) surface

Atomic and bond properties of silicon atoms in the buckled π-bonded chain reconstructed Si(111)(2 × 1) system were investigated by applying the quantum theory of atoms in molecules to a number of wavefunctions from periodic ab initio calculations using a slab model for the surface and geometries from experiment. Reconstruction involves much larger surface-cell charge distortions than in the unrelaxed surface and drastic changes in the atomic polarizations of the surface layer atoms. The effect of buckling is to largely differentiate the properties (charge, energy, volume, atomic polarizations) of the two unique atoms of each surface layer. The direction of electronic charge transfer in the topmost chain (from the “up” to the “down” atom) was found to be opposite to what was claimed previously. The π conjugation is not strictly localized along the topmost layer chains (where it is also largely incomplete), but rather it extends over a 2D array of bonds between the topmost and the lower surface layers. Received: 19 July 2000 / Accepted: 2 October 2000 / Published online: 23 January 2001     

Ab initio calculation of the band structure of some boron-nitrogen polymers

Ab initio calculations using a Gaussian orbital basis set were performed on the two boron-nitrogen polymer systems polyaminoborane and polyboronimide. For the polyaminoborane system an alternating B-N bond model appears to be more stable than a symmetric B-N bond model. An electron drift from the NH₂ group to the BH₂ moiety was calculated for both models although the nitrogen atom was found to possess a negative charge stemming from polarization of the N-H bonds. The energy band diagrams derived from both models show rather featureless bands indicative of weakly interactive systems although that of polyboronimide indicates that it is a more delocalized system than its saturated counterpart. The conduction and valence bands at the X-point are composed of orbitals and the lowest electronic transition is predicted to be —* in nature. The electron distribution of polyboronimide indicates a movement of -electrons from the boron to the nitrogen coupled with a smaller -electron drift from the nitrogen to the boron.     

Electronic delocalization contribution to the anomeric effect evaluated by computational methods

This study proposes the determination of the electronic delocalization contribution to the Anomeric Effect (EDCAE, Delta Delta E(deloc), eq 3) as a computational alternative in the evaluation of the excess of the axial preference shown by an electronegative substituent located at alpha position to the annular heteroatom of a heterocyclic compound (anomeric position) in both the presence and the absence of electronic delocalization retaining the same molecular geometry. The determination of the EDCAE is computationally accessible through the application of the natural bond orbital analysis (NBO). This type of analysis allows the comparison of hypothetical molecules lacking electronic delocalization (Lewis molecules, in which the electrons are strictly located in bonds and lone pairs) with the fully delocalized molecules retaining the same geometry and the evaluation of the anomeric effect in terms of eq 3. The role of the Lewis molecules is the same as the cyclohexane used experimentally to evaluate the anomeric effect. The advantage of doing this is that Lewis molecules are stereoelectronically inert. Applying this methology to cyclic and acyclic molecules at B3LYP/6-31G(d,p) and HF/6-31G(d,p)//B3LYP/6-31G(d,p) levels of theory, we found that the anomeric effect shown by Cl in 1,3-dioxane; F, Cl, SMe, PH(3), and CO(2)Me groups in 1,3-dithiane is of stereoelectronic nature while the preference of F, OMe, and NH(2) in 1,3-dioxane and the P(O)Me(2) group in 1,3-dithiane is not. Furthermore, this methodology shows that anomeric effects without stereoelectronic origin can modify the molecular geometry in agreement with the geometric pattern required by the double-bond no-bond model, as recently proposed by Perrin.