Hybridization and correlation in a model calculation of a two-electron bond

The paper presents a quantitative examination of some aspects of the molecular two-electron problem, using a calculation for a two-electron homonuclear bond based on a restricted set of one 2s and one 2p orbital per nucleus. The single-determinant approximations with pure 2s STO's and with hybrid AO's are considered, as well as “partial” configuration mixing (CI) over MO's involving one hybrid per atom and “complete” CI over the whole four-orbital basis. The calculations simulate an exact calculation as regards hybridization and (left-right) correlation effects. These are studied, for the lowest state, at various distances, introducing the axial electron density as a means for interpreting quantitatively the various effects. The importance of orthogonalizing the 2s AO's to the corresponding 1s AO's and the MO's used to the MO formed by 1s AO's is reviewed, pending further numerical analysis.     

Some new aspects of bonding in cyclopropane

The peculiar properties of the three-membered ring in cyclopropane are partially due to characteristic relaxation effects of the carbon orbitals in the molecule. AO contraction in the two strongly C? C bonding MO's of A type is essential for the stability of the C₃ ring, whereas AO expansion in the E'-type HOMO contributes to the π character of the peripheral C? C bonds.     

The electronic structure of aryl thiol esters

A combination of experimental data and the CNDO/2-SCF-MO method are used to evaluate the importance of d-orbitals to the electronic structure of aryl thiol esters. The thioester group is calculated to withdraw electron density through σ and 2p_π-3d_π bonding and donate by p_π-p_π bonding. Electron donating substituents para to the thiol ester group cause the latter group to accept electron density regardless of d-orbital participation.     

Approximate Self-Consistent Molecular Orbital Theory I S-P Separation Model Modification of CNDO-MO

A newly developed approximate self-consistent molecular orbital formulation, so called: ‘s–p separation model CNDO-MO method’, is proposed. The Pariser Parr¹⁾ and Nishimoto Mataga²⁾ approximations are separately applied to the ns and np (n=l to 3) AO's. The MO's of both closed and open shell cases are formulated. It seems to be a good method for molecular structure interpretation for both polar and nonpolar compounds.     

Extended ab initio calculations on cyclopropane,cyclopropene and cyclopropenone

The three-membered ring systems, cyclopropane, cyclopropene and cyclopropenone, have been investigated using a (9,5,1 ) Gaussian basis set. A detailed study of the chemical binding in these systems has been of particular interest. Results for the molecular ground states have been compared with predictions made previously using smaller basis sets and also with pertinent experimental findings.     

Elektronenstruktur von strukturell offenen Derivaten des [Mo6X14]2−-Clusters: [Mo5Cl13]2− und [Mo4I11]2−

Electronic Structure of Structural Open Derivatives of the [Mo₆X₁₄]^2?-Cluster: [Mo₅Cl₁₃]^2? and [Mo₄I₁₁]^2? The electronic structure of structural open derivatives of the [Mo₆X₁₄]^2?-cluster [Mo₅Cl₁₃]^2? and [Mo₄I₁₁]^2? has been studied by the EHMO method. In [Mo₅Cl₁₃]^2? 9 occupied MO's with dominant Mo4d character are responsible for the formation of the 8 metal-metal bonds. In [Mo₄I₁₁]^2? the stronger covalent character of the Mo? I bonds affects the localization and the energy of molecular orbitals and also the charge distribution. The metal-metal bonds are formed by 8 MO's containing considerable participation of halogen AO's contrary to the chloride cluster. There is no bonding between the Mo atoms at the wing tips of the Mo₄ butterfly and the reason for decreasing the dihedral angle between the Mo₃ planes in [Mo₄I₁₁]^2? compared with the octahedral angle is apparently the stabilization of the whole system (Mo? Mo and Mo? I bonds). The unpaired electron occupies in both clusters a slightly antibonding (with regard to the Mo? Mo bonds) orbital.     

A chemoenzymatic total synthesis of the hirsutene-type sesquiterpene (+)-connatusin B from toluene

The first total synthesis of the hirsutene-type sesquiterpenoid natural product (+)-connatusin B (2) is reported. The cis-1,2-dihydrocatechol 3, which is obtained in enantiomerically pure form via the enzymatic dihydroxylation of toluene, served as the starting material. Diels-Alder cycloaddition and oxa-di-π-methane rearrangement reactions represent key chemical steps in the reaction sequence leading to the cyclopropane ring-fused linear triquinane 14. Reductive cleavage of the three-membered ring within this framework and various functional group interconversions then provide the title compound 2.     

The geometry of small rings—V : Geometric variations and hybridization in three-membered heretocycles C2X (X=N,O, Si,P, S) and CXY (X,Y=N,O)

Structural data relating to 369 organic derivatives of C₂X(X=N, O, Si, P, S) and CXY(X, Y=N, O) heterocycles have been retrieved from the Cambridge Crystallogrphic Database and analysed in conjuction with pertinent gas-phase results. Heterocycle geometries are compared with each other, and with those for the ‘parent’ carbocycles cyclopropane and cyclopropene. For saturated C₂X rings the previously observed (gas phase) decrease in CC bond length (d_cc) and bent-back angle (γ) with increasing heteroatom electronegativity (χ_x) are confirmed as linear relationships using mean solid state geometry for X=C, N, O, S. The CX bonds shows an effective increase in length with increasing χ_x, in line with their facile cleavage in ring opening reactions. A model for hybridization changes at C in saturated C₂X rings is derived empirically and is in broad agreement with theoretical studies. There is no evidence for geometric variations in the heterocyclic rings induced by π-acceptor substituents, but π-donor substituent effects are directly comparable to those occurring in cyclopropane and cyclopropene. Geometric variations in unsaturated heterocycles are analogous to those in cyclopropene derivatives; CC double bond lengths in available C₂X systems appear to indicate a π_x dependence. Heteroatom-heteroatom bonds in CYX systems are weak, with N weaker than NN, in agreement with thermochemical reasoning.     

A semiempirical method based on geminal functions

An attempt has been made to develop a semiempirical method which considers only the n- and π-electrons, with the eigenfunctions expressed as an antisymmetrized product of two-electron functions or geminals. These geminals are expressed as a linear combination of products of Hückel-type MO's and the matrix elements are evaluated assuming the strong orthogonality condition to hold among the geminals, with an average effective Hamiltonian where the interaction between paired electrons is explicitly included. A first application of the method to N₂, HCN, C₂H₂, and C₂H^? was carried out without the introduction of parameters adjustable to best fit. A parametric approximation was then used for studying the electronic structure of diazabarrelene, an unknown molecule containing three pairs of π-electrons and two pairs of n-electrons. It is concluded that the explicit introduction of (π,π) and (n-π)-electron interaction describes the ground state more realistically than the simplest Hückel method. The separation of the energy levels was also affected, but the calculated transitions compared rather poorly with the spectroscopic observations. Diazabarrelene is expected to be not less stable than barrelene and attempts to its synthesis should be considered worthy of being made.     

The geometry of small rings—IV: Molecular geometry of cyclopropene and its derivatives

Numeric structural data for 34 derivatives of cyclopropene and cyclopropenium ion have been retrieved from the Cambridge Crystallographic Database and analysed in conjunction with available gas-phase results. Geometric data indicate that the vinylic C atoms in cyclopropene use sp^1.19 hybrids in bond formation to substituents and contribute sp^2.68 hybridges to the ring σ-framework. The D_3h-symmetric cyclopropenium ion has a bond length of 1.373(3)Å, which can be related to distances in unstrained systems. Comparison of data for cyclopropenylidenes and 3,3-difluorocyclopropene with analogous cyclopropanes shows that π-donor effects (distal bond lengthening, vicinal bond shortening) are apparent in cyclopropene. Rehybridization and π-donation are largely responsible for cyclopropenylidene geometry, rather than significant contributions from dipolar and pseudo-aromatic resonance forms. Insufficient data exist to quantify the effect of π-acceptor substituents on cyclopropene, but some lengthening of vicinal bonds is apparent. Three major bonding patterns are exhibited by organomental derivatives of cyclopropenium and cyclopropene.     

N-acylaminophenylcyclopropanes in reaction with nitrous acid generated in situ

The reaction of N-acylaminophenylcyclopropanes with HNO₂ proceeds regioselectively with introduction of an N = O fragment into the three-membered ring and formation of the corresponding Δ²-isoxazolines. For ortho-substituted N-acylaminophenylcyclopropanes side processes were observed, caused by the intramolecular participation of the N-acyl group in conversions of the carbenium ions formed on opening the cyclopropane ring under the action of the nitrosating reagent, and by direct insertion of the modified ortho substituent into the three-membered ring.     

The interaction of alkali metal cations with oxygen-containing ligands

Ab initio SCF calculations on the interaction of Li⁺ cation with H₂O and H₂CO using two basis sets are presented. Partitioning of SCF energies of interaction into Coulomb-, exchange- and delocalization energies has been performed. Coulomb- and delocalization energies are compared with classical electrostatic and polarization energies. A detailed analysis of the calculated wave functions demonstrates that in the complexes investigated here, charge transfer is of minor importance only. Polarization of the molecules in the strong inhomogeneous field of the cation leads to complicated electron density rearrangements which can be interpreted most easily in terms of polarization of individual localized MO's.     

Bonding Properties of Cyclopropane and Their Chemical Consequences

Among the cyclic compounds of carbon, cyclopropane and its derivatives are outstanding by virtue of their unusual structural, spectroscopic, and chemical properties. The cyclopropane ring more closely resembles the C?C double bond than the cyclobutane ring: it is a small ring with “double bond character”. Cyclopropyl and vinyl groups interact with neighbouring π-electron systems and p-electron centers; both cyclopropane derivatives and olefins form metal complexes, and add strong acids, halogens, and ozone; they both undergo catalytic hydrogenation and cycloadditions. While distinct differences in reactivity do exist–the double bond usually being more reactive than the three-membered ring–there are no fundamental differences in behavior.–Although cyclopropane derivatives have been known for more than 90 years, intensive studies have been limited to the past 25 years. The development of carbene chemistry has rendered cyclopropane derivatives far more readily accessible. In recent years, the synthetic potential of the small-ring function has been increasingly exploited. A considerable number of newly developed methods utilizing this approach clearly demonstrates that the reactivity of the cyclopropene ring, like that of the C?C double bond, qualify it as a “functional carbon group”. This development is in full swing; we may therefore justifiably devote considerable effort to the study of cyclopropane chemistry.     

The potential energy surface of singlet cyclobutadiene and substituted analogs: a coupled-cluster study

Coupled-cluster investigations (CCSD/cc-pVDZ and CCSD/cc-pVQZ//CCSD/cc-pVDZ) of singlet cyclobutadiene and fifteen-substituted analogs were conducted. A local minimum with a square frame does not exist on their potential surfaces. The well-known rectangular D_2h minimum, the square D_4h transition state, and two additional stationary points were found on cyclobutadiene’s potential surface. This included a transition state with a rhombic carbon ring and C_2h symmetry, separating two equivalent puckered C_2v local minima. The predicted barriers were 19.7 and 19.8 kcal/mol at the CCSD/cc-pVDZ and CCSD/cc-pVQZ//CCSD/cc-pVDZ levels, respectively. The relative strain energies of rectangular D_2h cyclobutadiene and all fifteen-substituted analogs were obtained from isodesmic reactions. Progressive substitution with methyl or BH₂ groups continuously lowers ring strain while increasing substitution with fluorines or trifluoromethyl groups steadily increases ring strain. C₄(BH₂)₄ is 16.6 and 13.3 kcal/mol less strained than cyclobutadiene while C₄F₄ is 17.7 and 21.5 kcal/mol more strained at the levels above. Cyclobutadiene is more strained than both cyclopropene and cyclobutene by 12.2 and 37.0 kcal/mol, respectively. Electron density contours indicate that fluorine substitution raised the electron density especially in the short C=C ring bonds above/below the ring plane (π-electrons) but not in the ring plane (σ-electrons). BH₂-substitutions lower the ring π-electron density with little effect in the ring plane. Methyl substituents have little effect on electron densities. All rings retain a strong bond alternation tendency (rectangular) whether substituted with electron-donating or -attracting groups. One-bond coupling constants and the percent p-character in ring C-to-C and C-to-substituent bonds are described.     

Ab Initio investigation of the structures and stabilities of CH2N2, CHFN2, and CF2N2 isomers: Important consequences of MP2 optimizations

Ab initio calculations of the potential energy surfaces of CH₂N₂, CHFN₂, and CF₂N₂ at MP4SDTQ/6-31G*//MP2(full)/6-31G* reveal several surprising features. While diazomethane is more stable than diazirine, only the three-membered ring forms of the fluorine-substituted isomers are known experimentally. We find fluorodiazomethane and difluorodiazomethane not to be viable species: They have no barriers toward exothermic dissociation into N₂ and CHF or CF₂, respectively. In contrast, the three-membered ring isomers, fluorodiazirine and difluorodiazirine, have high barriers toward dissociation despite being high in energy. Diazomethane bends easily; a nonplanar C_s minimum is found at MP2(full)/6-31G* but C_2v symmetry is preferred at QCISD/6-31G*. © 1992 by John Wiley & Sons, Inc.     

Indo-Mo Model with s·p Separation

A newly developed self-consistent-field molecular orbital theory is described and tested. The intermediate neglect of differential overlap (INDO) approximation is used, and all interaction integrals are differentiated according to their dependence upon 2s and 2p AO's. The bonding parameter β_l is reformulated so that the model is calibrated to only one specific molecular property, namely, the ionization energy of Hi. We expect that this model will not be biased toward any special families of molecules.     

Determination of the electron density in methyl (±)‐(1S,2S,3R)‐2‐methyl‐1,3‐diphenylcyclopropanecarboxylate using refinements with X‐ray scattering factors from wavefunction calculations of the whole molecule

The molecule of the title compound, C₁₈H₁₈O₂, is a substituted cyclopropane ring. The electron density in this molecule has been determined by refining single‐crystal X‐ray data using scattering factors derived from quantum mechanical calculations. Topological analysis of the electron densities in the three cyclopropane C—C bonds was carried out. The results show the effects of this substitution on these C—C bonds.     

G2 ab initio calculations on three-membered rings: Role of hydrogen atoms

G2 ab initio calculations on all ABX three-membered rings (TMRs) that can be derived from cyclopropane by systematic substitution of the (SINGLE BOND)CH₂ groups by (SINGLE BOND)NH or (SINGLE BOND)O groups have been performed. Our results show that the decrease in the A(SINGLE BOND)B bond length as the electronegativity of X increases is significantly larger than that found for the corresponding acyclic analogs. In general, a systematic substitution of the (SINGLE BOND)CH₂ groups of cyclopropane by (SINGLE BOND)NH or (SINGLE BOND)O groups implies significant geometric changes that are not reflected in a parallel change of the corresponding conventional ring strain energy (CRSE). When the electronegativity of the groups forming the TMR increases the effect on the CRSE of the system is small, although the charge delocalization inside the ring decreases. The near constancy of the CRSE along the series can be explained in terms of the charge redistribution of the system where the (SINGLE BOND)CH₂ groups play a crucial role. There are, however, significant changes in the hydrogenation energies of the TMR investigated; our results show that, when in an ABX three-membered ring, the electronegativity of X increases the hydrogenation energy of A(SINGLE BOND)B bond decreases and vice versa. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1072–1086, 1998     

A general quadratic force field for the diazirine molecule

A general quadratic force field has been calculated for the vibrations of the diazirine molecule by the refinement of a series of force constants obtained recently ab initio by Wiberg et al. for cyclopropene. The calculated force constants have been refined to fit the frequencies for the H₂CN₂ and D₂CN₂ species and the isotopic shifts of the H¹³CN₂ and H₂C¹⁵N₂ species.